ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2" quasiNote that equilibriumwhilst the local longermaxima of the field are likely to dictate the stability, the energy componentseventually present in the toroidal-field system'scomponent"," Note that whilst the local maxima of the field components are likely to dictate the system's stability, the energy eventually present in the toroidal-field component"3in 0.7-300 keV simultaneously to model the nuclear hard component.,in 0.7–300 keV simultaneously to model the nuclear hard component.4" For each detector, the energy range of 0.7-10 keV, 15-70 keV, and 55-300 keV for the XIS, PIN, and GSO, respectively, are used in the fitting."," For each detector, the energy range of 0.7–10 keV, 15–70 keV, and 55–300 keV for the XIS, PIN, and GSO, respectively, are used in the fitting."5" A relative normalization between the XIS-F and XIS-B is left to be free, while that between the XIS and PIN, or between the PIN and GSO, is fixed to 1.18 (Maeda et al."," A relative normalization between the XIS-F and XIS-B is left to be free, while that between the XIS and PIN, or between the PIN and GSO, is fixed to 1.18 (Maeda et al."6" 2008) or 1.0?,, respectively."," 2008) or 1.0, respectively."7" The spectral models for the soft X-ray emission were included, but the model parameters of two models and model are fixed, and normalizations of the higher-temperature model and the model are left free."," The spectral models for the soft X-ray emission were included, but the model parameters of two models and model are fixed, and normalizations of the higher-temperature model and the model are left free."8" For the hard nuclear component, we at first tried the basic model; an absorbed"," For the hard nuclear component, we at first tried the basic model; an absorbed"9and high-n (ecarlv-tvpe) galaxies the mean size at given mass ab 2792.5 is —2 times smaller than today.,and $n$ (early-type) galaxies the mean size at given mass at $z \sim 2.5$ is $\sim 2 $ times smaller than today.10 Specifically they find that at given stellar mass the sizes of late-tvpe galaxies evolve as (1|D)USUmUU5 gaehereas the sizes of earlv-types evolve as (1|z)U.l15cU.lU," Specifically they find that at given stellar mass the sizes of late-type galaxies evolve as $(1+z)^{-0.40 \pm 0.06}$, whereas the sizes of early-types evolve as $(1+z)^{-0.45 \pm 0.10}$."11 We now apply our merger model to from the SOS anc Millennium SAAIs., We now apply our merger model to from the S08 and Millennium SAMs.12 These SAMs produce statistical samples of galaxies with properties that are closely matched to those observed in the universe., These SAMs produce statistical samples of galaxies with properties that are closely matched to those observed in the universe.13 Thus they provide an elfective means for testing the merger model in a cosmological framework., Thus they provide an effective means for testing the merger model in a cosmological framework.14 Since the modeled merger remnants are a function of the progenitor properties. we begin by examining the distributions of galaxy properties in the SAMs and making. comparisons to the observed distributions.," Since the modeled merger remnants are a function of the progenitor properties, we begin by examining the distributions of galaxy properties in the SAMs and making comparisons to the observed distributions."15 In the model. the most important properties of the progenitors are initial size. mass. and gas fraction.," In the model, the most important properties of the progenitors are initial size, mass, and gas fraction."16 Thus we begin by looking at the size-mass clistributions of progenitors in cach SAM., Thus we begin by looking at the size-mass distributions of progenitors in each SAM.17 The relations are plotted for SOS in Figure 5(a) and for Millennium in Figure 5(b).., The relations are plotted for S08 in Figure \ref{fig:spfsizemass} and for Millennium in Figure \ref{fig:millsizemass}.18 For each figure the progenitors are separated intoof six redshift binsmerger., For each figure the progenitors are separated into six redshift bins.19 Within cach bin. the progenitors are divided into mass bins with a width of 0.2 in log(M. ).," Within each bin, the progenitors are divided into mass bins with a width of 0.2 in $\log (\msun)$ ."20 Ehe local relations for low-n (solid blue) and high-n (dotted red) galaxies are shown for comparison., The local relations for $n$ (solid blue) and $n$ (dotted red) galaxies are shown for comparison.21 Additionally. the observed. redshift evolution of the size of the low-sn galaxies (2). is depicted with the blue-cashecl line.," Additionally, the observed redshift evolution of the size of the $n$ galaxies \citep{Trujillo06} is depicted with the blue-dashed line."22 This is calculated: using the median progenitor redshift’ in each redshift bin., This is calculated using the median progenitor redshift in each redshift bin.23 The size-mass relation produced by the progenitors in SOS reproduces the observed relation quite nicely. including evolution with redshift.," The size-mass relation produced by the progenitors in S08 reproduces the observed relation quite nicely, including evolution with redshift."24 The Millennium progenitors are also fairly close to the observed relation. but in the lowest redshilt bin they are 50% too laree on average.," The Millennium progenitors are also fairly close to the observed relation, but in the lowest redshift bin they are $\sim50\% $ too large on average."25 ‘This eap lessens with increasing redshift., This gap lessens with increasing redshift.26 Also of note is that the highest mass bin is twpically systematically high., Also of note is that the highest mass bin is typically systematically high.27 Lt is also interesting to note the dillerence in slope between the observed size-mass relations lor earlv- and late-tvpe galaxies., It is also interesting to note the difference in slope between the observed size-mass relations for early- and late-type galaxies.28 As noted before. if à merger explanation of the elliptical size-mass relation is to be successful. it must explain the rotation between the two observed. relations.," As noted before, if a merger explanation of the elliptical size-mass relation is to be successful, it must explain the rotation between the two observed relations."29 We discuss this with respect to our model in the next section., We discuss this with respect to our model in the next section.30 Observing cold. eas within galaxies ids. extremely challenging., Observing cold gas within galaxies is extremely challenging.31 Llowever a study by 2? used. à. photonietric estimate of gas fraction in order to calculate the changing ratio of gas to stellar mass (61/8) with galaxies from SDSS., However a study by \citet{Kannappan04} used a photometric estimate of gas fraction in order to calculate the changing ratio of gas to stellar mass (G/S) with galaxies from SDSS.32 ? use star formation rates from à large SDSS sample combined with theoretical modeling to estimate (6/8) as a function of both stellar mass and redshift., \citet{Calura07} use star formation rates from a large SDSS sample combined with theoretical modeling to estimate (G/S) as a function of both stellar mass and redshift.33 Neither study. provides fits to the observed relation. but it can be seen from Figure 5 of 7 that. for z«0.1. where for blue galaxies €!—4.6 and for red. galaxies C'—41.," Neither study provides fits to the observed relation, but it can be seen from Figure 5 of \citet{Calura07} that, for $z<0.1$, where for blue galaxies $C\sim 4.6$ and for red galaxies $C\sim344.1$."35 The values of log(Gys) falls approximately in a range between -4 and. 1.5., The values of $\log(G/S)$ falls approximately in a range between -4 and 1.5.36 The relation between G/S and stellar mass in the SAMs is shown in Figures 6(a) anc 6(b).., The relation between G/S and stellar mass in the SAMs is shown in Figures \ref{fig:spfgas} and \ref{fig:millgas}.37 The observational relation (Equation 14)) is also depicted to show that the progenitors from the SAMs have gas fraction to stellar mass relations with slopes similar to those observed., The observational relation (Equation \ref{eq:gas}) ) is also depicted to show that the progenitors from the SAMs have gas fraction to stellar mass relations with slopes similar to those observed.38 However. the distribution of progenitor gas fractions from the SAMs is not expected to exactly align with the depicted: observed relations for two reasons: 1) even the lowest redshift. bin (0«2<0.3) [rom the SAAIs includes redshifts significantly ügher than those from the observations (2<0.1). and 2) 16 progenitors are a small subset of all galaxies.," However, the distribution of progenitor gas fractions from the SAMs is not expected to exactly align with the depicted observed relations for two reasons: 1) even the lowest redshift bin $0<z<0.3$ ) from the SAMs includes redshifts significantly higher than those from the observations $z<0.1$ ), and 2) the progenitors are a small subset of all galaxies."39 Specifically. 1¢ galaxies shown from the SAAIs are those that undergo major mergers during the specified: redshift and are disk-ominated.," Specifically, the galaxies shown from the SAMs are those that undergo major mergers during the specified redshift and are disk-dominated."40 The properties of this subset may dilfer from xh the red. ancl blue populations in the observations., The properties of this subset may differ from both the red and blue populations in the observations.41 In act. the models of SOS have been tuned to reproduce the gas fraction vs. stellar mass observations of 2. for spirals.," In fact, the models of S08 have been tuned to reproduce the gas fraction vs. stellar mass observations of \citet{Kannappan04} for spirals."42 ]t can be seen that the distributions of CG/S in both SAAIs are bimodal with a gas-rich. (blue) and gas-poor (red) sequence., It can be seen that the distributions of G/S in both SAMs are bimodal with a gas-rich (blue) and gas-poor (red) sequence.43 While both SAMs capture the slope of the observed relation. they have gas to barvonic mass power law slopes which are significantly less than the 5=0.7 value sugeested in ? and the idealized mergers presented above.," While both SAMs capture the slope of the observed relation, they have gas to baryonic mass power law slopes which are significantly less than the $\gamma=0.7$ value suggested in \citet{Dekel06} and the idealized mergers presented above."44 A majority of the mergers are eas-rich: and of all mergers. for SOS. and Millennium. respectively. have total progenitor gas fractions greater than 0.1.," A majority of the mergers are gas-rich; and of all mergers, for S08 and Millennium respectively, have total progenitor gas fractions greater than 0.1."45 The relation from the SAAIs only evolves very mocestly over time. but for both SAAIs the fraction of mergers that are coming from high gas fraction progenitors increases with increasing redshift.," The relation from the SAMs only evolves very modestly over time, but for both SAMs the fraction of mergers that are coming from high gas fraction progenitors increases with increasing redshift."46 This is seen both as a disappearance of the red sequence (in SOS) and a decrease in the typical mass of progenitors as redshift increases (both S.Ms)., This is seen both as a disappearance of the red sequence (in S08) and a decrease in the typical mass of progenitors as redshift increases (both SAMs).47 There are also interesting correlations between gas paction and size., There are also interesting correlations between gas fraction and size.48 “Lo demonstrate this. we replot the size-mass relation with points drawn for progenitors colored. by CS (see Figures Tia) and Y(b))).," To demonstrate this, we replot the size-mass relation with points drawn for progenitors colored by G/S (see Figures \ref{fig:spfgfsizemass} and \ref{fig:millgfsizemass}) )."49 Reck points are gas-xor with —(2.0«log(6/7s)κ1.0., Red points are gas-poor with $-2.0<\log(G/S)<-1.0$.50 (νους. points have intermediate gas fractions with 1.0«log(C//S)0.0., Green points have intermediate gas fractions with $-1.0<\log(G/S)<0.0$.51 Bluc points are eas rich with 0.0«οσο)1.0., Blue points are gas rich with $0.0<\log(G/S)<1.0$.52 For roth SAMs. at given mass there is a significant trend of gas raction with size:fractions.," For both SAMs, at given mass there is a significant trend of gas fraction with size:."53 “Vhis is because these galaxies have lower densities and therefore have lowerstar formation rates and ive consumed less of their gas. since both SA assume a Ixennicutt-Schmidt-tvpe relationship for star. Ms.formation (star formation rate density. is proportional to a power of the gas densitv).," This is because these galaxies have lower densities and therefore have lowerstar formation rates and have consumed less of their gas, since both SAMs assume a Kennicutt-Schmidt-type relationship for star formation (star formation rate density is proportional to a power of the gas density)."54where again the overbar denotes a combined horizontal and temporal average.,where again the overbar denotes a combined horizontal and temporal average.55 Fie., Fig.56 6 is à plot of Ras a function of depth for Procyon and (he Sun., \ref{pturb} is a plot of $R$ as a function of depth for Procyon and the Sun.57 Unlike the case of the Sun. in Procyon the turbulent pressure varies ‘quasi-periodically with the position of the SAL and al Gimes (he instantaneous horizontal average of the turbulent. pressure divided by the eas pressure can have a peak value of as much as 50%.," Unlike the case of the Sun, in Procyon the turbulent pressure varies `quasi-periodically' with the position of the SAL and at times the instantaneous horizontal average of the turbulent pressure divided by the gas pressure can have a peak value of as much as 50."58. The instantaneous horizontally averaged turbulent kinetic energy divided by the local gas pressure can also reach 50 near the top of the box (not shown)., The instantaneous horizontally averaged turbulent kinetic energy divided by the local gas pressure can also reach 50 near the top of the box (not shown).59 In the simulation the masxinnun Mach number (defined as (he maxinmunm ο divided by the local sound speed) is about 2 near the top (in the vicinity ol the SAL peak)., In the simulation the maximum Mach number (defined as the maximum $v_z''$ divided by the local sound speed) is about 2 near the top (in the vicinity of the SAL peak).60 So motions will be supersonic ad small optical depth suggesting short characteristic (ime scales., So motions will be supersonic at small optical depth suggesting short characteristic time scales.61 By comparing the horizontal cross-section of the temperature [luctuation (left. panel οἱ Fie.7)) at shallow optical depth (7 = 0.001) with the vertical velocity αἱ optical depth unitv just inside the photosphere (rieht panel of Fig. 7)).," By comparing the horizontal cross-section of the temperature fluctuation (left panel of \ref{vzcontour}) ) at shallow optical depth $\tau$ = 0.001) with the vertical velocity at optical depth unity just inside the photosphere (right panel of Fig. \ref{vzcontour}) ),"62 one can identify regions in which hotter (colder) than average (hid moves down (up)., one can identify regions in which hotter (colder) than average fluid moves down (up).63 Alt small optical depth. the downflows appear brighter (hotter) (instead of darker below the photosphere) because the fluid is being aciabatically compressed.," At small optical depth, the downflows appear brighter (hotter) (instead of darker below the photosphere) because the fluid is being adiabatically compressed."64 This is a signature of convective overshool above the photosphere., This is a signature of convective $\it{overshoot}$ above the photosphere.65 Note the dark (cold) spot in the upper left hand corner of the left panel., Note the dark (cold) spot in the upper left hand corner of the left panel.66 This indicates upward moving (hue that is colder (han the horizontal mean temperature., This indicates upward moving fluid that is colder than the horizontal mean temperature.67 Generally only a few such updralts are sulliciently energetic to be able to continue travelling up even though ihey are negatively buovant., Generally only a few such updrafts are sufficiently energetic to be able to continue travelling up even though they are negatively buoyant.68" This reversal of (he granulation pattern (bright downllows and darker granular upllows) ""ab large height™ was also noted noted by Nordlund Dravins (1990) in their study of the Procvon atmospheric eranulation.", This reversal of the granulation pattern (bright downflows and darker granular upflows) “at large height” was also noted noted by Nordlund Dravins (1990) in their study of the Procyon atmospheric granulation.69 Our main conclusions regarding the time dependence of granulation and of the SAL in Procvon also appear robust., Our main conclusions regarding the time dependence of granulation and of the SAL in Procyon also appear robust.70 It is interesting (o compare the results of our simulation to an earlier less detailed hvedrodyvnamic study of Procvon’s atmospheric structure. and eranulation (Nordlund Dravins 1990: Dravins Nordlind 1990)., It is interesting to compare the results of our simulation to an earlier less detailed hydrodynamic study of Procyon's atmospheric structure and granulation (Nordlund Dravins 1990; Dravins Nordlund 1990).71 These authors included lime dependent bydroclvnamics in their non-grey atmosphere calculations., These authors included time dependent hydrodynamics in their non-grey atmosphere calculations.72 Even though, Even though73 , 74"following, all spectral uncertainties and upper-limits are given at 90 confidence level for one interesting parameter.","following, all spectral uncertainties and upper–limits are given at 90 confidence level for one interesting parameter."75" After checking that separate fits of the three cameras gave consistent results, we fitted them simultaneously, in order to increase the statistics; to this aim, we introduced relative normalization factors among the spectra of the three cameras."," After checking that separate fits of the three cameras gave consistent results, we fitted them simultaneously, in order to increase the statistics; to this aim, we introduced relative normalization factors among the spectra of the three cameras."76" Using an absorbed power-law (PL)) model, we obtained a hydrogen column density Nj=(6.2+0.5)x10?! cm~? and a photon-index I' = 0.94+0.03, with X2Id.o.f."," Using an absorbed power–law ) model, we obtained a hydrogen column density $N_{\rm H} = (6.2\pm0.5)\times 10^{21}$ $^{-2}$ and a photon–index $\Gamma$ = $\pm$ 0.03, with $\chi^{2}_{\nu}$ /d.o.f."77 = 1.30/277., = 1.30/277.78" On the other hand, using an absorbed blackbody (BB)) model, we obtained a hydrogen column density Ny=(0.9+0.2)x10?! cm""? and a temperature kTpp=1.52+0.03 keV, with X2/d.o.f."," On the other hand, using an absorbed blackbody ) model, we obtained a hydrogen column density $N_{\rm H} = (0.9\pm0.2)\times 10^{21}$ $^{-2}$ and a temperature $kT_{\rm BB} = 1.52 \pm 0.03$ keV, with $\chi^{2}_{\nu}$ /d.o.f."79" = 1.20/277; assuming a source distance of 5 kpc we obtained a radius ΠΡΗ=1314 m. In both cases the fit of the spectrum with a single—component model shows large residuals, therefore we repeated the fit with a model."," = 1.20/277; assuming a source distance of 5 kpc we obtained a radius $R_{\rm BB} = 131 \pm 4$ m. In both cases the fit of the spectrum with a single--component model shows large residuals, therefore we repeated the fit with a model."80" In this way we obtained a significant improvement of the fit quality (Fig. 4)),"," In this way we obtained a significant improvement of the fit quality (Fig. \ref{all_spetrum_powbb}) ),"81" since we obtained x2/d.o.f = 0.88/275; the corresponding best-fit parameters are Ny=(2.8+0.9)x10?! επι, T=0.517012 and kTppg=1961006 keV. In comparison with the single and model, the F-test analysis provided a probability, respectively, = 1.26 x 10-74 and P= 9.95 x 10-?? that the improvement of the fit occurs by chance."," since we obtained $\chi^{2}_{\nu}$ /d.o.f = 0.88/275; the corresponding best–fit parameters are $N_{\rm H} = (2.8\pm0.9) \times 10^{21}$ $^{-2}$, $\Gamma = 0.51^{+0.17}_{-0.29}$ and $kT_{\rm BB} = 1.26^{+0.16}_{-0.09}$ keV. In comparison with the single and model, the F–test analysis provided a probability, respectively, = 1.26 $\times$ $^{-24}$ and = 9.95 $\times$ $^{-20}$ that the improvement of the fit occurs by chance."82" Both components are significant at 99 confidence level: the normalization is Ip,=7.1448x1075 ph cm? s! keV-! at 1 keV and, assuming a source distance of 5 kpc, we obtained a radius Rep=12813? m for the component."," Both components are significant at 99 confidence level: the normalization is $I_{\rm PL} = 7.1^{+4.5}_{-4.6}\times10^{-5}$ ph $^{-2}$ $^{-1}$ $^{-1}$ at 1 keV and, assuming a source distance of 5 kpc, we obtained a radius $R_{\rm BB} = 128^{+13}_{-21}$ m for the component."83" The unabsorbed flux in the energy range 0.2-10 keV is fx~4x1077? erg cm? s1, about 42 of which is due to the component; this translates into a source luminosity Lx~1.2x1034 erg s1."," The unabsorbed flux in the energy range 0.2–10 keV is $f_{\rm X}\sim 4\times10^{-12}$ erg $^{-2}$ $^{-1}$, about 42 of which is due to the component; this translates into a source luminosity $L_{\rm X}\simeq 1.2\times10^{34}$ erg $^{-1}$."84" We looked also for narrow iron Κα emission lines between 6 and 7 keV, with different widths between 0 and 0.5 keV. We found no evidence for such a component, with an upper limit on its equivalent width of 0.2 keV (at 90 c.l.)"," We looked also for narrow iron $_{\alpha}$ emission lines between 6 and 7 keV, with different widths between 0 and 0.5 keV. We found no evidence for such a component, with an upper limit on its equivalent width of 0.2 keV (at 90 c.l.)"85 at most., at most.86 In the source folded light curve (Fig. 1)), In the source folded light curve (Fig. \ref{flc}) )87 we observed that the source spectrum becomes slightly harder at the end of the pulse maximum., we observed that the source spectrum becomes slightly harder at the end of the pulse maximum.88" In order to study the source behavior in more detail, we analyzed the background subtracted spectra in two"," In order to study the source behavior in more detail, we analyzed the background subtracted spectra in two"89most of the wavlength range. but. rises to Εθν in the UV (A«4200A)) and. near-lLR (ASOOOA)).,"most of the wavlength range, but rises to $\pm$ in the UV $\lambda < 4200$ ) and near-IR $\lambda > 8000$ )."90 ὃν using a relatively wide slit. making the observations as close as possible to we zenith. ane in some cases. making observations with the slit aligned along the parallactic angle. the etfeets of cüllerential refraction were minimised.," By using a relatively wide slit, making the observations as close as possible to the zenith, and, in some cases, making observations with the slit aligned along the parallactic angle, the effects of differential refraction were minimised."91 Only in two cases dooes cdillerential refraction significantly allect the accuracy of the Dux calibration: PINS1547-79 (airmass >1.5) and to a much lesser extent. PIS2314|03 (airmass 1.2)., Only in two cases does differential refraction significantly affect the accuracy of the flux calibration: PKS1547-79 (airmass $> 1.5$ ) and to a much lesser extent PKS2314+03 (airmass $\sim 1.2$ ).92 1 dimensional spectra of the near-nuclear regions were extracted from the 2 dimensional frames using extraction apertures that contained the bulk of the visible continuum emission (twpically 2.0 4 areseconds along the slit)., 1 dimensional spectra of the near-nuclear regions were extracted from the 2 dimensional frames using extraction apertures that contained the bulk of the visible continuum emission (typically 2 – 4 arcseconds along the slit).93 Following bias subtraction. cosmic ray removal. and correction for non-uniformities using Lat-Lielcls. the mean background. level was determined. for the “oA and e-ray images separately. using several apertures placed evenly around the source.," Following bias subtraction, cosmic ray removal, and correction for non-uniformities using flat-fields, the mean background level was determined for the `o'­ and `e'-ray images separately, using several apertures placed evenly around the source."94" The 0À and ""e-rav intensities for the radio galaxies were measured through circular apertures hat included the bulk of the lisht in the. near-nuclear regions (typically 3 6 arcseconds diameter) for each elescope rotator position or half-wave plate position. with he aperture size fixed through cach evele of rotator of our half-wave plate positions."," The `o'­ and `e'-ray intensities for the radio galaxies were measured through circular apertures that included the bulk of the light in the near-nuclear regions (typically 3 – 6 arcseconds diameter) for each telescope rotator position or half-wave plate position, with the aperture size fixed through each cycle of rotator of four half-wave plate positions."95 The intensities for all the rotator positions were then combined according to the escription of Tinbergen ancl Rutten (1992) to. produce he final polarization degrees ancl position angles shown in ‘Table 4., The intensities for all the rotator positions were then combined according to the prescription of Tinbergen and Rutten (1992) to produce the final polarization degrees and position angles shown in Table 4.96 The advantage of this technique for measuring he polarization is that. since it involves the ratios of the ‘oA and e-ray intensities at cach rotator/hall-wave plate postion. ib is not sensitive to small photometric variations rctwveen the images.," The advantage of this technique for measuring the polarization is that, since it involves the ratios of the `o'­ and `e'-ray intensities at each rotator/half-wave plate postion, it is not sensitive to small photometric variations between the images."97 By combining the intensity ratios from. rotator positions separated by 90 degrees. or half-wave date positions separated by 45 degrees. any instrumental »olarization produced. in the instrument is automatically eliminated.," By combining the intensity ratios from rotator positions separated by 90 degrees, or half-wave plate positions separated by 45 degrees, any instrumental polarization produced in the instrument is automatically eliminated."98 'l'he uncertainties in the individual ‘o’- and οταν intensities were estimated by combining the estimated uncertainty in the subtracteck background. (from the standard deviation in the background measurements). with the uncertainty due to the poissonian [fluctuation in the source|backeround counts in the source aperture.," The uncertainties in the individual `o'- and `e'-ray intensities were estimated by combining the estimated uncertainty in the subtracted background (from the standard deviation in the background measurements), with the uncertainty due to the poissonian fluctuation in the source+background counts in the source aperture."99 These uncertainties were then propagated through the caleulation of the polarization degree and angle., These uncertainties were then propagated through the calculation of the polarization degree and angle.100 The final polarization measurements and upper limits shown in Table 4 have been corrected for the positive bias in the polarization following the prescription of Simmoncds and Stewart (1985)., The final polarization measurements and upper limits shown in Table 4 have been corrected for the positive bias in the polarization following the prescription of Simmonds and Stewart (1985).101 For the 1993 and. 1994 runs. which used the telescope rotator to modulate the polarization. the polarization angles were calibrated using observations of polarization standard stars observed. using the same techniques in the same runs.," For the 1993 and 1994 runs, which used the telescope rotator to modulate the polarization, the polarization angles were calibrated using observations of polarization standard stars observed using the same techniques in the same runs."102 Llowever. for the 1995 run. which used the half-wave plate. it was not possible to derive accurate polarization position angles because of problems with the initialisation of the plate at the end of cach evele: although the degrees of »olarization measured for individual polarized. sources ancl »olarized. standard stars were found to be consistent. [rom one cvcle to the next. large. variations were found in the measured angles between the eveles.," However, for the 1995 run, which used the half-wave plate, it was not possible to derive accurate polarization position angles because of problems with the initialisation of the plate at the end of each cycle; although the degrees of polarization measured for individual polarized sources and polarized standard stars were found to be consistent from one cycle to the next, large variations were found in the measured angles between the cycles."103" For the significantly. »»arized: objects. observed. in this run. the values of the Xxarization listed in ""Table 4 represent the average of the »olarization. values measured independently for cach of the wo eveles of half-wave plate positions."," For the significantly polarized objects observed in this run, the values of the polarization listed in Table 4 represent the average of the polarization values measured independently for each of the two cycles of half-wave plate positions."104 1n the case of objects without significant polarization but two cvceles. of observations from the 199515 run. the clata were analvsed independently for cach evele. and upper limits were derived from one evele of observations only.," In the case of objects without significant polarization but two cycles of observations from the 1995 run, the data were analysed independently for each cycle, and upper limits were derived from one cycle of observations only."105 As a final check on the reliability of the measurements. the individual ‘OCA and οταν intensity measurements for each evele were checked. to determine. whether thev followed the pattern expected for linearly polarized. light.," As a final check on the reliability of the measurements, the individual `o'­ and `e'-ray intensity measurements for each cycle were checked to determine whether they followed the pattern expected for linearly polarized light."106 This allowed: us to check for spurious polarizations which night arise. for example. from a cosmic rav. alfecting one of the images.," This allowed us to check for spurious polarizations which might arise, for example, from a cosmic ray affecting one of the images."107 The degrees of polarization measured for the polarized. standard stars were found to be consistent. with the published values. within the estimated: uncertainties.," The degrees of polarization measured for the polarized standard stars were found to be consistent with the published values, within the estimated uncertainties."108 rerEG). where is the recombination time.," =, where= is the recombination time."109 In our first test we perform an ionized sphere expansion. but we allow the temperature of the eas to vary in. order to test the coupling between the RP and the full non-equilibritun chemistry treatment.," In our first test we perform an ionized sphere expansion, but we allow the temperature of the gas to vary in order to test the coupling between the RT and the full non-equilibrium chemistry treatment."110 As a reference. we compare to the analytical case with constant temperature.," As a reference, we compare to the analytical case with constant temperature."111 We follow the expansion of an ionized) sphere arouncl a source that emits No=5.LOphotonss|.," We follow the expansion of an ionized sphere around a source that emits $\dot N_\gamma = 5 \times 10^{48} \, \rm photons \, s^{-1}$."112 The shape of the source spectrum corresponds to a 3LOtW black bods.," The shape of the source spectrum corresponds to a $3 \times 10^4\, \rm K$ black body."113 The surrounding gas density is p5=L710'gem? 7) and is sampled by 167.5 327. and 64 easticlest.," The surrounding gas density is $\rho = 1.7 \times 10^{-27} \, \rm g \,114cm^{-3}$ $\sim 10^{-3}\,\rm cm^{-3}$ ) and is sampled by $16^3$, $32^3$ , and $64^3$ gas."115. In the 32? case also the shielding of 2. has been adopted. with the values cited in their paper.," In the $32^3$ case also the shielding of \citet{DraineBertoldi1996}116 has been adopted, with the values cited in their paper."117 The initial temperature of the gas is set to 2=107Ix. andl is subject to photoheating and radiative cooling.," The initial temperature of the gas is set to $T = 10^2 \,118\rm K$ and is subject to photoheating and radiative cooling."119 At a temperature of 103Ix. the ease-B recombination cocllicient. is ap2.50.10“emis! (eg 7)..," At a temperature of $10^4 \, \rm K$, the case-B recombination coefficient is $\alpha_{\rm B} = 2.59 \times 10^{-13} \,\rm cm^3 \, s^{-1}$ \cite[e.g.][]{Iliev2009}. ."120" Given these parameters. the recombination time is /,,:=125.127Myr. and the expected Strommeren radius in the isothermal case (assuming LW) is ru=5.1kpe."," Given these parameters, the recombination time is $t_{\rm rec}=125.127 \, \rm Myr$, and the expected Strömmgren radius in the isothermal case (assuming $T = 10^4 \, \rm K$ ) is $r_{\rm S} = 5.4 \,\rm kpc$."121 In Fig. 2..," In Fig. \ref{fig:SST_um_evol},"122 we show the evolution of the radial position of the front with time for the dillerent. resolutions., we show the evolution of the radial position of the I-front with time for the different resolutions.123 As a proxy for the position of the front we take the radius where the neutral ancl tonizecl hydrogen fractions are equal. (see also Fig. 3))., As a proxy for the position of the front we take the radius where the neutral and ionized hydrogen fractions are equal (see also Fig. \ref{fig:SST_um}) ).124 All resolutions agree very well with each other., All resolutions agree very well with each other.125 Phere is no difference in the case with shielding since the simulation never reaches the densities required to produce some effect. as discussed in the introduction.," There is no difference in the case with shielding since the simulation never reaches the densities required to produce some effect, as discussed in the introduction."126 Our results agree within with the analytical ones from equation (15))., Our results agree within with the analytical ones from equation \ref{rI}) ).127 In particular. the simple analytical solution issystematically larger than the fulbsimulation trend. whieh is expected.," In particular, the simple analytical solution issystematically larger than the full-simulation trend, which is expected."128" This can be explained by the missing cooling contributions in the analytical calculations from. c.g.. He. We. H,. HD that lower temperatures. enhance recombination. and make the Strómmeren radius decrease (as visible in the simulated case)."," This can be explained by the missing cooling contributions in the analytical calculations from, e.g., He, $_2$, $_2^+$, HD that lower temperatures, enhance recombination, and make the Strömmgren radius decrease (as visible in the simulated case)."129 In fact. equation. (15)) is computed. by assuming constant temperature for hyelrogen-only eas (seealso ?).. while. in the numerical caleulations the full chemistry treatment of Table 2.. including cooling ancl heating. is considered.," In fact, equation \ref{rI}) ) is computed by assuming constant temperature for hydrogen-only gas \cite[see also][]{Petkova2009}, while, in the numerical calculations the full chemistry treatment of Table \ref{tab:reactions}, including cooling and heating, is considered."130 ?.— find similar results in their one-dimensional ionized sphere , \citet{Pawlik2010} find similar results in their one-dimensional ionized sphere .131simulations?.. In Fig. 3..," In Fig. \ref{fig:SST_um},"132 we show the racial profile of the temperature of the gas at 500 Myr after the source has been switched on., we show the radial profile of the temperature of the gas at 500 Myr after the source has been switched on.133 The temperature inside the ijonized region reaches ~ LOX. consistentlywith photoheating from a stellar source.anclextends bevond 5 kpe.," The temperature inside the ionized region reaches $\sim 10^4\, \rm K$ , consistentlywith photoheating from a stellar-type source,andextends beyond $5\, \rm kpc$ ."134 Even further the temperature begins to drop., Even further the temperature begins to drop.135 Harder photons (withenergies, Harder photons (withenergies136"Telescope Alt-azimuthal (BTA) of the Special Astrophysical Observatory of the Russian Academy οἱ Sciences (0.023"" at the wavelength of 550 nm).",Telescope Alt-azimuthal (BTA) of the Special Astrophysical Observatory of the Russian Academy of Sciences $0.023 ''$ at the wavelength of 550 nm).137 In the present work. we analyse the multiplicity ancl orbital periods distribution lor binary and multiple stars.," In the present work, we analyse the multiplicity and orbital periods distribution for binary and multiple stars."138 We made our analvsis based on own observations and the data adopted [rom other authors., We made our analysis based on own observations and the data adopted from other authors.139 Additionally. an allempl was made to examine (he ratio of binary and multiple stars in the streams of old metal-poor stars located in the solar neighbourhood.," Additionally, an attempt was made to examine the ratio of binary and multiple stars in the streams of old metal-poor stars located in the solar neighbourhood."140 For the observations with high angular resolution. we compiled a sample of 223 field subclwarls of the F. G and early IX spectral classes (Iastegaevetal.2007) [rom the CLLA catalog.," For the observations with high angular resolution, we compiled a sample of 223 field subdwarfs of the F, G and early K spectral classes \citep{rastegaev_2007} from the CLLA catalog."141" The CLLA presents a spectroscopicallv studied sample of the AIx spectral tvpes dwarls from the (Giclas.Burnham 195), which mainlv includes the stars from the Northern Hemisphere with proper motions exceeding 0.26"" per annum and brighter than 16"" in the 2 band."," The CLLA presents a spectroscopically studied sample of the A–K spectral types dwarfs from the \citep*{lpms_1971,lpms_1978}, which mainly includes the stars from the Northern Hemisphere with proper motions exceeding $0.26''$ per annum and brighter than $16^{m}$ in the $B$ band."142" We selected 223 stars from the CLLA using the following criteria: The last criterion was determined bv (he limiting stellar magnitude of our speckle interferometer (Maximovetal.2003).. which was about 13""."," We selected 223 stars from the CLLA using the following criteria: The last criterion was determined by the limiting stellar magnitude of our speckle interferometer \citep{maximov}, which was about $13^{m}$."143 No restrictions were applied on the heliocentric distances of these stars. evenly distributed on the celestial sphere.," No restrictions were applied on the heliocentric distances of these stars, evenly distributed on the celestial sphere."144 The maximum distance to (he sample objects is 250 pe., The maximum distance to the sample objects is 250 pc.145 The median heliocentric distance of the selected stars is approximately LOO pc., The median heliocentric distance of the selected stars is approximately $100$ pc.146 This allows us to take advantage of hish angular, This allows us to take advantage of high angular147environment/container.,.148" As a specific manifestation of this dependence. the sign of v,. that is the sign of the change in the superfIuid spin rate. is determined by thatof IN. or w. in either cases."," As a specific manifestation of this dependence, the sign of $v_r$, that is the sign of the change in the superfluid spin rate, is determined by thatof $N$ , or $\omega$, in either cases."149 As expected 2.4) Eq., As expected 2.4) Eq.150 26 also confirms that. in the absence of external torque Vo (he the superfluidcontainer. the pinned superfluid may eilher retain ils rate or else come to a state of co-rotation wilh the container. dependiusg on the two possibilities considered [or the rotation rate of the vortices upon unpinning.," 26 also confirms that, in the absence of external torque $N$ the the superfluid, the pinned superfluid may either retain its rate or else come to a state of co-rotation with the container, depending on the two possibilities considered for the rotation rate of the vortices upon unpinning."151 The uncertainties in the (micro)phyvsics of individual vortex motion. within a vortex lattice. prevent [rom deciding between the (wo cases.," The uncertainties in the (micro)physics of individual vortex motion, within a vortex lattice, prevent from deciding between the two cases."152 However. (he predicted distinct behaviors. for the case of N=0. might be used in possible laboratory experiments as a clue to disünguish between the two cases.," However, the predicted distinct behaviors, for the case of $N=0$, might be used in possible laboratory experiments as a clue to distinguish between the two cases."153 As a further confirmation. Eq.," As a further confirmation, Eq."154 26 (ease ii) reduces. as it should. to the correct form expected in the absence ofpinning Adams. Cieplak Glaberson 1935: Alpar Sauls 1983: JJahan-Miri 1993). for the limiting ease of £=1 corresponding to values of fw}>way. when the Magnus effect prevents (even temporary) pinning to be realized.," 26 (case ii) reduces, as it should, to the correct form expected in the absence ofpinning \markcite{adam85} Adams, Cieplak Glaberson 1985; \markcite{as88} Alpar Sauls 1988;\markcite{mj98}J Jahan-Miri 1998), for the limiting case of $\xi =1$ corresponding to values of $|\omega| \geq \omega_{\rm crit}$, when the Magnus effect prevents (even temporary) pinning to be realized."155 The above prediction (Eqs 24 or 25) for the superfluid spin-down rate. driven bv random unpinning events wilh agiven probability £. is fundamentally different than the earlier predictions Alpar et.," The above prediction (Eqs 24 or 25) for the superfluid spin-down rate, driven by random unpinning events with agiven probability $\xi$, is fundamentally different than the earlier predictions \markcite{alet84} Alpar et."156 al., al.157 1984: JJahan-Miri 2005a)., 1984; \markcite{MJ05a}J Jahan-Miri 2005a).158" The correct dependence on the cdvnamically relevant (quantities V. iw. τε, and £ assures a (rue and instantaneous dependence of the superfluid spin-cown rate Q. (or equivalently 0.) on the sing and magnitude of the actual torque Gransmitted between the superfIuid ancl its container/environvemnt (the crust)."," The correct dependence on the dynamically relevant quantities $N$, $\omega$, $\tau_v$, and $\xi$ assures a true and instantaneous dependence of the superfluid spin-down rate $\dot\Omega_{\rm s}$ (or equivalently $v_r$ ) on the sing and magnitude of the actual torque transmitted between the superfluid and its container/environvemnt (the crust)."159 li may be noted that even though the steady-state magnitude of w would be set by other denamically independent (quantities. however for a (ransient post-elitch relaxation which is our prime objective here it is indeed an independent evolving quantity. initially determined bv the eliteh.," It may be noted that even though the steady-state magnitude of $\omega$ would be set by other dynamically independent quantities, however for a transient post-glitch relaxation which is our prime objective here it is indeed an independent evolving quantity, initially determined by the glitch."160 The opposite dependence on € in (he two terms at the right hand side of Eq., The opposite dependence on $\xi$ in the two terms at the right hand side of Eq.161" 20 (appearing also in Eqs 24 or 25 )is interesting. aud resembles the similar behavior of the relaxation time 7,."," 20 (appearing also in Eqs 24 or 25 )is interesting, and resembles the similar behavior of the relaxation time $\tau_v$."162 The new prediction reduces to an earlier reported estimate (JJahlan-Miri 2005a). only in the approximate form. as in Eq.," The new prediction reduces to an earlier reported estimate \markcite{MJ05a}J Jahan-Miri 2005a), only in the approximate form, as in Eq."163 26. for the limiting cases indicated (with a correction for the case7 therein).," 26, for the limiting cases indicated (with a correction for the case therein)."164 For a quantitative evaluation of the efficiency of the spinning down of a superfIuid through random unpinning of its pinned vortices. an order of magnitude estimate of the naxinunm spin-dowun rate predicted by the present model (Eqs 24 or 25) may be given. as applicable to the crust. of neutron stars.," For a quantitative evaluation of the efficiency of the spinning down of a superfluid through random unpinning of its pinned vortices, an order of magnitude estimate of the maximum spin-down rate predicted by the present model (Eqs 24 or 25) may be given, as applicable to the crust of neutron stars."165 The spin-down rate indeed depends on the instantaneous munber of (he wunpinned vortices. as determined by the unpiniing probability unction €(w).," The spin-down rate indeed depends on the instantaneous number of the unpinned vortices, as determined by the unpinning probability function $\xi(\omega)$."166 The maximum spin-«down rate would be achieved for values of£ 1. corresponding low~ cua ," The maximum spin-down rate would be achieved for valuesof $\xi \sim 1$ , correspondingto $\omega \sim \omega_{\rm167crit}$ ."168"Adopting a set of parameter values applicable to post-gliteli relaxations in voung jeulron stars. such as rp~105 em. OQ,ον107rads ον N/E©10.Mrads 7. L1~ 0.02."," Adopting a set of parameter values applicable to post-glitch relaxations in young neutron stars, such as $r \sim16910^6 \ {\rm cm}$ , $\Omega_{\rm s} \sim 10^2 \ {\rm rad~s}^{-1}$ , $N/I \sim 10^{-10} \ {\rm rad~s}^{-2}$ , $I_{\rm s}/I \sim 0.02$ ,"170"Two approaches of combining 2N detectors to prove the detection ability to the SGWD are proposed in Allen Romano (1999): (1) correlating the outputs of a pair of detectors. then combining multiple pairs (combining pairs. ""c-p). and (i) directly. combining (hie outputs of 2N detectors (directly combining. ""d-c).","Two approaches of combining 2N detectors to improve the detection ability to the SGWB are proposed in Allen Romano (1999): (i) correlating the outputs of a pair of detectors, then combining multiple pairs (combining pairs, “c-p""), and (ii) directly combining the outputs of 2N detectors (directly combining, “d-c"")."171 For the first approach. the squared SNR. is given by: and for the second one: We show in Table 2 the SNRs calculated for different pairs of LIGOIL. LIGOL. Virgo and GEO. and for (wo combinations of these four IFOs.," For the first approach, the squared SNR is given by: and for the second one: We show in Table 2 the SNRs calculated for different pairs of LIGOH, LIGOL, Virgo and GEO, and for two combinations of these four IFOs."172 We consider here (wo cases representing two real networks of first/second generation IFOs: Case 1 is [or these four IFOs with design sensilivilies: Case 2 consists of (wo advanced LIGO «detectors ancl two advanced. Virgo detectors both with proposed sensitivities., We consider here two cases representing two real networks of first/second generation IFOs: Case 1 is for these four IFOs with design sensitivities; Case 2 consists of two advanced LIGO detectors and two advanced Virgo detectors both with proposed sensitivities.173 Note that SNRs in Table 2 are lower than unity even lor pairs of advanced detectors., Note that SNRs in Table 2 are lower than unity even for pairs of advanced detectors.174 The most promising one (SNR= 0.53) comes from combining pairs of four advanced IFOs., The most promising one $SNR = 0.58$ ) comes from combining pairs of four advanced IFOs.175 If we assume an optimized value of unity. [or 5(f). which is only possible for co-located GW detectors (Fotopoulos&LSC2008).. the SNR. is 11.0 and 4.1 for a pair of advanced LIGO and advanced Virgo IFOs respectively.," If we assume an optimized value of unity for $\gamma(f)$, which is only possible for co-located GW detectors \cite{gamma1}, the SNR is $11.0$ and $4.1$ for a pair of advanced LIGO and advanced Virgo IFOs respectively."176 We note that by considering new detectors wilh comparable sensitivities to advanced LIGO. such as LCGT in Japan (Ixuroda et al.," We note that by considering new detectors with comparable sensitivities to advanced LIGO, such as LCGT in Japan (Kuroda et al."177 1999) and AIGO in Australia (Blair et al., 1999) and AIGO in Australia (Blair et al.178 2008). it could be possible to reach a higher. but still not significant SNR with a network of second-generation IFOs.," 2008), it could be possible to reach a higher, but still not significant SNR with a network of second-generation IFOs."179 In order to obtain some detectable parameter space we need al least one order οἱ magnitude higher SNRs (han those in Case 2 of Table 2., In order to obtain some detectable parameter space we need at least one order of magnitude higher SNRs than those in Case 2 of Table 2.180 Then we reduce the noise power spectral densities of advanced LIGO and advanced: Virgo by a factor of LO by hand. and investigate the role of differential rotation (A) and maximum emitting frequency. (7444) in the detectability of the r-mode background.," Then we reduce the noise power spectral densities of advanced LIGO and advanced Virgo by a factor of 10 by hand, and investigate the role of differential rotation $K$ ) and maximum emitting frequency $\nu_{\rm{max}}$ ) in the detectability of the r-mode background."181 We are motivated here by the fact that detectors like ET can reach a sensitivity roughly an order of magnitude better than that of advanced LIGO (Iild et al., We are motivated here by the fact that third-generation detectors like ET can reach a sensitivity roughly an order of magnitude better than that of advanced LIGO (Hild et al.182 2003)., 2008).183 In Fig., In Fig.184 7 we plot the SNR as a function of A for II-L. II-V. and L-V pairs.," 7 we plot the SNR as a function of $K$ for H-L, H-V and L-V pairs."185 As a natural result [rom Fig., As a natural result from Fig.186 5. the cletectability of SGWB from r-mode instability is drastically reduced to 0 as A approaching 10.," 5, the detectability of SGWB from r-mode instability is drastically reduced to 0 as $K$ approaching 10."187 The higher SNR of ILL pair reflects the lower noise level οἱ advanced LIGO., The higher SNR of H-L pair reflects the lower noise level of advanced LIGO.188 Due to similarity of the overlap reduction functions (see Fie., Due to similarity of the overlap reduction functions (see Fig.189 2 of Fan Zhu 2003) no sienilicant difference is shown between L-V and 1I-V. pairs., 2 of Fan Zhu 2008) no significant difference is shown between L-V and H-V pairs.190SPH code (originallydescribedinSpringel2005)..,SPH code \citep[originally described in][]{Springel05e}.191" Our conventional code includes radiative cooling by H, He, and metals &Nagamine2009a),, heating by a uniform UVB (Choiof a modified Haardt&Madau(1996) spectrum (Katzetal.1996a;Davé1999),, SF, supernova feedback, a phenomenological model for galactic winds, and a sub-resolution model of multiphase interstellar medium (ISM;Springel&Hernquist2003).."," Our conventional code includes radiative cooling by H, He, and metals \citep{Choi09b}, heating by a uniform UVB of a modified \citet{Haardt96} spectrum \citep{Katz96a, Dave99}, SF, supernova feedback, a phenomenological model for galactic winds, and a sub-resolution model of multiphase interstellar medium \citep[ISM;][]{Springel03b}."192" In this multiphase ISM model, high-density ISM is pictured to be a two-phase fluid consisting of cold clouds in pressure equilibrium with a hot ambient phase."," In this multiphase ISM model, high-density ISM is pictured to be a two-phase fluid consisting of cold clouds in pressure equilibrium with a hot ambient phase."193" Cold clouds grow by radiative cooling out of the hot medium, and this material forms the reservoir of baryons available for SF."," Cold clouds grow by radiative cooling out of the hot medium, and this material forms the reservoir of baryons available for SF."194" We use the “Pressure SF” model described by Choi&Nagamine(2010) (which is based on the work by Schaye&DallaVecchia (2008))), but we have checked that the details of the SF model do not change the main conclusions of this paper."," We use the “Pressure SF” model described by \citet{Choi10a} (which is based on the work by \citet{Schaye08}) ), but we have checked that the details of the SF model do not change the main conclusions of this paper."195" For all the simulations used in this paper, we employ a box size of comoving 10h~!Mpc and a total particle number of 2x144° for gas and dark matter."," For all the simulations used in this paper, we employ a box size of comoving $\himpc$ and a total particle number of $2\times 144^3$ for gas and dark matter."196" The initial gas particle mass is Mgas=4.1x10°h-!Mo, and the dark matter particle mass is mam=2.0x10""A!Mo."," The initial gas particle mass is $m_{\rm gas}=4.1\times 10^6\,\himsun$, and the dark matter particle mass is $m_{\rm dm}=2.0\times 10^7\,\himsun$."197" The comoving gravitational softening length is 2.78h.-!kpc, so the physical resolution of our simulation is 0.7 h!kpc at z=3."," The comoving gravitational softening length is $2.78\,\hikpc$, so the physical resolution of our simulation is $\sim$ $\hikpc$ at $z=3$."198" Nagamineetal. showed that increasing the particle number from (2004)2x144? to 2x324? did not change the shape of f(Ngr) very much, therefore our results would not be strongly affected by the resolution effect. "," \citet{Nag04g} showed that increasing the particle number from $2\times 144^3$ to $2\times 324^3$ did not change the shape of $\fn$ very much, therefore our results would not be strongly affected by the resolution effect. ("199see further discussion in Section 4..),But see further discussion in Section \ref{sec:discussion}. .)200" The comoving (Butbox size of 10h!Mpc is somewhat small, however, the number of missed very massive haloes are relatively small, and the impact on f(Nur) is expected to be small."," The comoving box size of $\himpc$ is somewhat small, however, the number of missed very massive haloes are relatively small, and the impact on $\fn$ is expected to be small."201" In fact Nagamineetal.(2004) showed that f(Nmr) did not change very much with increasing box size, except that the lower Ny end of f(Ngi) decreased due to lower resolution."," In fact \citet{Nag04g} showed that $\fn$ did not change very much with increasing box size, except that the lower $\NHI$ end of $\fn$ decreased due to lower resolution."202" In this work, we have not corrected our results for the box size effect."," In this work, we have not corrected our results for the box size effect."203" The adopted cosmological parameters of all simulations are consistent with the latest WMAP result etal.2009, Q4,Q5,(Komatsu2010):: (0.26,0.74,0.044,0.80,0.72,0.96), where (Qm,hh,n.)=H/(100kms~! Mpc-!)."," The adopted cosmological parameters of all simulations are consistent with the latest WMAP result \citep{Komatsu09, Komatsu10}: $(\Om,\Ol,\Ob,\sigma_8, h, n_s)= (0.26, 0.74, 0.044, 0.80, 0.72, 0.96)$ , where $h=H_0 / (100\kms\,\mpc^{-1})$ ."204" With this setup, we run four simulations with different models of UVB: *Fiducial"", *No-UV"", “Half-UV”, and “OTUV” (Optically Thick UV) runs."," With this setup, we run four simulations with different models of UVB: “Fiducial”, “No-UV”, “Half-UV”, and “OTUV” (Optically Thick UV) runs."205" In the Fiducial run, the gas is heated and ionized by the uniform UVB under the optically thin approximation."," In the Fiducial run, the gas is heated and ionized by the uniform UVB under the optically thin approximation."206" In the No-UV run, the UVB strength is set to zero."," In the No-UV run, the UVB strength is set to zero."207" In the Half-UV run, the normalization of UVB is reduced by half."," In the Half-UV run, the normalization of UVB is reduced by half."208" In the OTUV run, we assume that the uniform UVB cannot penetrate into the high-density gas with nga,>NYY, but otherwise it is the same as the Fiducial run at nga,XnU."," In the OTUV run, we assume that the uniform UVB cannot penetrate into the high-density gas with $\ngas > \nuv$, but otherwise it is the same as the Fiducial run at $\ngas \le \nuv$."209" We adopt the threshold density nj=0.01n3F6x107? cem where is theSF threshold density above which the ?,stars are n>allowed to form."," We adopt the threshold density $\nuv = 0.01 \, \nsf = 6\times 10^{-3}$ $^{-3}$, where $\nsf$ is theSF threshold density above which the stars are allowed to form."210" In our simulations, the gas with nga,> is mostly neutral owing to the multiphase ISM model."," In our simulations, the gas with $\ngas > \nsf$ is mostly neutral owing to the multiphase ISM model."211"no We originally arrived at the above value of πι by successively lowering its value from and checking the agreement with the observed f(Nur), n?Fbut will provide further justifications below."," We originally arrived at the above value of $\nuv$ by successively lowering its value from $\nsf$ and checking the agreement with the observed $\fn$, but will provide further justifications below."212 There is evidence that the above value of nj’ is physically appropriate., There is evidence that the above value of $\nuv$ is physically appropriate.213" Tajiri&Umemura(1998) found that the hydrogen cloud becomes fully self-shielded above a critical density of 1.4x107? ccm? through RT calculations for a spherical top-hat sphere, and that the critical density has a mild dependence on the cloud mass and the UVB intensity."," \citet{Tajiri98} found that the hydrogen cloud becomes fully self-shielded above a critical density of $1.4\times 10^{-2}$ $^{-3}$ through RT calculations for a spherical top-hat sphere, and that the critical density has a mild dependence on the cloud mass and the UVB intensity."214" Kollmeieretal. performed a three-dimensional UVB RT calculation(2010) with an isothermal sphere, and showed that the above value of ny” approximately corresponds to the transition density from ttoHr."," \citet{Kollmeier10} performed a three-dimensional UVB RT calculation with an isothermal sphere, and showed that the above value of $\nuv$ approximately corresponds to the transition density from to."215. Faucher-Giguereetal.(2010) postprocessed cosmological SPH simulations with a ray tracing code and found that turning off UVB at Ώρας>0.01 ccm? produces a favorable result., \citet{Faucher10} postprocessed cosmological SPH simulations with a ray tracing code and found that turning off UVB at $\ngas > 0.01$ $^{-3}$ produces a favorable result.216" Furthermore, we also confirmed that the above nj,’ is appropriate by postprocessing our simulations with a RT code, which we will report in detail in a separate paper (H. Yajima et al.,"," Furthermore, we also confirmed that the above $\nuv$ is appropriate by postprocessing our simulations with a RT code, which we will report in detail in a separate paper (H. Yajima et al.,"217" 2011, in preparation)."," 2011, in preparation)."218" For these reasons, we consider that the correct value of π is in the range of 107? to 107? ccm-?, depending on the cloud mass and UVB intensity."," For these reasons, we consider that the correct value of $\nuv$ is in the range of $10^{-2}$ to $10^{-3}$ $^{-3}$, depending on the cloud mass and UVB intensity."219" shows the f(Ngi) in the four runs with different UVB treatment, which was calculated by the same method described in Nagamineetal. (2004).."," \\ref{fig:fn} shows the $\fn$ in the four runs with different UVB treatment, which was calculated by the same method described in \citet{Nag04g}. ."220" In short, we set up a uniform grid around each dark matter halo, and project the gas density field onto face of the grid to compute Nyy."," In short, we set up a uniform grid around each dark matter halo, and project the gas density field onto a face of the grid to compute $\NHI$ ."221" a clearly shows that the Fiducial run reffig:fnunderpredicts the f(Nur), particularly at logNur< 21.2."," \\ref{fig:fn} clearly shows that the Fiducial run underpredicts the $\fn$ , particularly at $\log\NHI < 21.2$ ."222"the forward shock emission are (e...Yostetal.2003) where C,=1Xp—δρ1) for p»2.05. As=(MÁAOOAL.veTyeSOLOcurs1)ft as the wind parameter. 6 is the speed of the wind. AMT is the mass loss rate (Chevalier&Li2000).. aud Y=|1ivlπμ”... aud ως is the factor reflecting the importance of the QKlein-Nishina correction (sec the Appendix A of Piran(2006a) for the expression).","the forward shock emission are \citep[e.g.,][]{Yost03}223 where $C_{p}\equiv 13(p-2)/[3(p-1)]$ for $p>2.05$, $A_{\ast}=(\dot{M}/10^{-5}M_{\odot}~{\rm yr^{-1}})[v_{\rm224w}/(10^{8}~{\rm cm~{\rm s^{-1}}})]^{-1}$ is the wind parameter, $v_{\rm w}$ is the speed of the wind, $\dot{M}$ is the mass loss rate \citep{Chevalier00}, and $\rm Y=[-1+\sqrt{1+4\eta \eta_{_{\rm225KN}}\epsilon_{e}/\epsilon_{B}}]/2$ , $\eta\simeq \rm226min\{1,(\nu_{m}/\nu_{c})^{(p-2)/2}\}$ and $\eta_{_{\rm KN}}$ is the factor reflecting the importance of the Klein-Nishina correction (see the Appendix A of \citet{Fan06a} for the expression)."227" Since my, decreases with time wlile m increases with tine. the current afterglow data suggest that μή=10?κ)Pom ad v(t=6s10bs)>aw~Lot IIz. i... At f10° s the AY band fux is ~34107 Jy (Ciyeiueretal. 2009b).. which gives us another constraiut Substituting Y—HNep (due to the slow cooling and the IWlein-Nishina Vcorrection) in Equations (1) and (5). we have A.=10oe yep210fet. determined."," Since $\nu_{\rm m}$ decreases with time while $\nu_{\rm c}$ increases with time, the current afterglow data suggest that $\nu_{\rm m}(t=10^{5}~{\rm s})\leq \nu_{\rm opt/IR}$ and $\nu_{\rm c}(t=6\times 10^{4}~{\rm s})\geq \nu_{\rm x}\sim 10^{18}$ Hz, i.e., At $t\sim 10^{5}$ s, the $K_{s}$ band flux is $\sim2283\times10^{-5}$ Jy \citep{Greiner09}, , which gives us another constraint Substituting $Y\sim \sqrt{\epsilon_{\rm e}/50\epsilon_{\rm B}}$ (due to the slow cooling and the Klein-Nishina correction) in Equations (4) and (5), we have $A_*\geq 10^{-5}\epsilon_{\rm e,-1}^{2}$, $\epsilon_{\rm B}\geq 10^{-4}\epsilon_{\rm e,-1}^{-1.3}$."229"Though the shock parameters caunot be uniquelv we see that the ""reasonable? parameters (ει,ep.A.)~(0.1.2.5«10.7.0.01) can reproduce the data."," Though the shock parameters cannot be uniquely determined, we see that the “reasonable"" parameters $(\epsilon_{\rm e}, ~\epsilon_{\rm B},~A_*)230\sim (0.1,~2.5\times 10^{-3},~0.01)$ can reproduce the data."231" Tn our data analvsis. before aid after the break at fj~67601|:) s the N-ray declines are fFUFOS and fΤΟΡΟ rospoctively,"," In our data analysis, before and after the break at $t_{\rm b}\sim 676(1+z)$ s the X-ray declines are $t^{-0.72\pm2320.08}$ and $t^{-1.89\pm0.06}$, respectively."233 The X-ray spectrum can be reasonably fitted by FQoxp0, The X-ray spectrum can be reasonably fitted by $F_\nu \propto \nu^{-0.63\pm 0.06}$.234 ο peduced the UVOT data in a standard wav with the aid of reduction threads at http:/pwww.swilt.acuk/UVOT.shtml., We reduced the UVOT data in a standard way with the aid of reduction threads at http://www.swift.ac.uk/UVOT.shtml.235 The combined V-baud aud white lieht curves show a rise since the beginning of UVOT observation to a peak around 1000 5 after the BAT trigeer. which is followed by an apparent decay leading to the optical flux lower than the threshold of UVOT quickly.," The combined V-band and white light curves show a rise since the beginning of UVOT observation to a peak around 1000 s after the BAT trigger, which is followed by an apparent decay leading to the optical flux lower than the threshold of UVOT quickly."236 Our results are generally in aerecet with that of DePasqualeetal.(2009)., Our results are generally in agreement with that of \citet{Pasquale09}.237. Within the standard external shock model the above data are roughly consistent with a slow cooling ejecta expanding iuto the ISM for p2 while the break can be interpreted as the jet effect (Piran1999:Zhane&Mészáros2001).," Within the standard external shock model, the above data are roughly consistent with a slow cooling ejecta expanding into the ISM for $p\sim 2$ while the break can be interpreted as the jet effect \citep{Piran99,ZM04}."238. The slowly riiug optical e1üissiou may sugecst that the observers frequency is below μι., The slowly rising optical emission may suggest that the observer's frequency is below $\nu_{\rm m}$.239 Iu the ISM case. the equations that govern the forward shock cuission are (e... Sari et al.," In the ISM case, the equations that govern the forward shock emission are (e.g., Sari et al."240 1998: Yost et al., 1998; Yost et al.241" 2003) please note that we have ο,~0.23 for p~2.", 2003) please note that we have $C_{p}\simeq0.23$ for $p\sim 2$ .242" The conditions that ο=1281s)>ru. Malt1000«)~5«10 IIz and Fou21.101 Jy (DePasqualeetal.2009). vield The paramcters (Lisi.€p,pἐνqDo)(1.l.7.0.01) satisfy the above coustraits (note that Y«VESep thauks to the Wlein-Nishina correction)."," The conditions that $\nu_{\rm c}(t=1284~{\rm s})>\nu_{\rm x}$, $\nu_{\rm m}(t\sim 1000~{\rm s}) \sim 5\times 10^{14}$ Hz and $F_{\rm \nu,max} \geq 1\times 10^{-4}$ Jy \citep{Pasquale09}243 yield The parameters $(E_{\rm k,54},~\epsilon_{\rm B,-4},~\epsilon_{\rm244e,-1},~n_{0})\sim (1,~1,~7,~0.01)$ satisfy the above constraints (note that $Y\ll \sqrt{\epsilon_{\rm e}/\epsilon_{\rm B}}$ thanks to the Klein-Nishina correction)."245" The jet break tine fi,—1281 sec suggests a halt- ⋅↽∶≽↴∖⊥∖⊥∖⊥∖ ≋∪↑↕∐∖⊓⋅∏↸∖∶↴∙⊾⋜↕⋯⋯⋜⊢↥⋅⋜↕⋅↖↽↸∖↕∐"," The jet break time $t_{\rm b}=1284$ sec suggests a half-opening angle $\theta_{\rm246j}=6\times10^{-3}t_{3.1}^{3/8}E_{\rm247k,54}^{-1/8}\epsilon_{-0.7}^{1/8}n_{0,-2}^{1/8}$."248" jov released. ds Loja=2E-B2=2.110Nλογος, where EL~11.1«aware)107 cre is theOF isotropic-equivalent σαΑΝ energy."," So the true gamma-ray energy released is $E_{\rm \gamma,jet} \simeq \theta_{\rm249j}^{2}E_\gamma/2=2\times10^{48} \rm ergs$, where $E_\gamma \sim2501.4\times 10^{53}$ erg is the isotropic-equivalent gamma-ray energy."251 If the high energyafterglow is due to the IC radiation of the forward shock clectrous. there is a simple method to estimate the mmuber of seed photons. regardless of their origin (either the late prompt cussion from the ceutral engine or the svuchrotron radiation of the forward shock electrous).," If the high energy afterglow is due to the IC radiation of the forward shock electrons, there is a simple method to estimate the number of seed photons, regardless of their origin (either the late prompt emission from the central engine or the synchrotron radiation of the forward shock electrons)."252" Following Fan&Pirauttered(2006b).. the possibility of one seed photon beiug sc (Le. the optical depth) iu the forward shock region cau be estimated as respectively,"," Following \citet{Fan06}, the possibility of one seed photon being scattered (i.e., the optical depth) in the forward shock region can be estimated as respectively."253 With the paramcters derived for GRBs OSOOLGC and 090510. we have respectively.," With the parameters derived for GRBs 080916C and 090510, we have respectively."254" It the detected high euergy afterglow pliotous are indeed the IC radiation of the forward shock oelectrous. the uuuber fux of the seed photons will be For 080916C. in the time interval ~100—1100 «ιο, Af= 13008). Pup~710Pphen?s! (Abdo et al."," If the detected high energy afterglow photons are indeed the IC radiation of the forward shock electrons, the number flux of the seed photons will be For , in the time interval $\sim 100-1400$ s (i.e., $\Delta t=1300$ s), ${ F_{\rm >100 MeV}\sim 7\times 10^{-6}~{\rm255ph~cm^{-2}~s^{-1}}}$ (Abdo et al."256" 20092). so the nuuber of total seed photons is,lÉ ordinost seed aro in the N-rayv baud. the enerev willbe photons~1079 erg.which is too Luge tobe realistic."," 2009a), so the number of total seed photons isIf most seed photons are in the X-ray band, the total energy will be $\sim 10^{56}$ erg,which is too large tobe realistic."257 If the «eed photons are αλα] in optical/intrared band. the total eucrgv willbe ~10” ere.," If the seed photons are mainly in optical/infrared band, the total energy will be $\sim 10^{53}$ erg."258 Thoughbright infrared/optical fare can be produced, Though bright infrared/optical flare can be produced259 g- (e.g..Gossard1975;Gill1982).," $g$ \citep[e.g.,][]{Gossard1975,Gill1982}."260. (Aptetal.1980)., \citep{Young1997} \citep{Apt1980}.261. 107 107 Wom. (~237 m) (e.g..An-etal.1987).. (e.g..Joshietal.Menou&Raucher2009:Showmanetal.2005).," $^{-3}$ $^{-1}$ $^{-2}$ $\sim$ $^{-2}$ \citep[e.g.,][]{Andrews1987}. \citep[e.g.,][]{Joshi1997,Showman2002,Cho2003,Cho2008a,Burkert2005,Cooper2005,Dobbs-Dixon2008,Koskinen2007,Langton2007,Langton2008,Menou2009,Showman2008}."262 as for improving theoretical understanding in general., as for improving theoretical understanding in general.263 For this. the role of eddies and waves in transferring momentum and heat needs to be addressed (Cho2008)..," For this, the role of eddies and waves in transferring momentum and heat needs to be addressed \citep{Cho2008b}."264 This has long been recognized in Solar System planet studies 1990;Fritts&Alexander 2003).," This has long been recognized in Solar System planet studies \citep[e.g.,][]{Lindzen1990,Fritts2003}."265. The plan of the paper is as follows., The plan of the paper is as follows.266 In refsee:theory we derive the governing equation appropriate for linear monochromatic gravity waves on hot extrasolar planets., In \\ref{sec:theory} we derive the governing equation appropriate for linear monochromatic gravity waves on hot extrasolar planets.267 We also discuss a simple parameterization of the key non-linear process. saturation.," We also discuss a simple parameterization of the key non-linear process, saturation."268 In addition. we present solutions to the equation for simple isothermal atmospheres. with and without shear in the background mean flow.," In addition, we present solutions to the equation for simple isothermal atmospheres, with and without shear in the background mean flow."269 In refsec:application we extend the calculation to a physically more realistic situation. by using background flow and temperature profiles derived from a three-dimensional (3-D) hot-Jupiter atmospheric circulation simulation.," In \\ref{sec:application} we extend the calculation to a physically more realistic situation, by using background flow and temperature profiles derived from a three-dimensional (3-D) hot–Jupiter atmospheric circulation simulation."270 This is the first such calculation to have been performed for extrasolar planets., This is the first such calculation to have been performed for extrasolar planets.271 Through this. the significant effects of gravity waves on hot extrasolar planet atmospheric mean flows are demonstrated.," Through this, the significant effects of gravity waves on hot extrasolar planet atmospheric mean flows are demonstrated."272 In this section. we also discuss a way in which gravity waves can transport momentum and heat horizontally—e.g.. from the dayside to nightside on tidally locked planets.," In this section, we also discuss a way in which gravity waves can transport momentum and heat horizontally—e.g., from the dayside to nightside on tidally locked planets."273 In refsec:implications we discuss the implications of our work for current extrasolar planet atmospheric modeling work., In \\ref{sec:implications} we discuss the implications of our work for current extrasolar planet atmospheric modeling work.274 We conclude in refsec:conclusion.., We conclude in \\ref{sec:conclusion}.275 The dynamics of a linear gravity wave 1s describedbythe(TGE).Thisequation is derived from the full. 3-D hydrodynamies equations. (Batchelor 1967)..," The dynamics of a linear gravity wave is describedbythe(TGE).Thisequation is derived from the full, 3-D hydrodynamics equations \citep{Batchelor1967}. ."276 In this work. we restrict the description to. two," In this work, we restrict the description to two"277Iun the automatic application of the aleorithin to the 999 CoRoT svuthetic elt curves. a threshold of the coincidence value was set above which peaks are selected as real transits.,"In the automatic application of the algorithm to the 999 CoRoT synthetic light curves, a threshold of the coincidence value was set above which peaks are selected as real transits."278 As a consequence. some false detections may appear.," As a consequence, some false detections may appear."279 By alse detection we mean any detection that does not correspond to amy trausit-like feature with astroplivsical origin. beige it a planet or some other stellar configuration simulating one.," By false detection we mean any detection that does not correspond to any transit-like feature with astrophysical origin, being it a planet or some other stellar configuration simulating one."280 False detections iu this seuse are therefore detections caused by some random. noise., False detections in this sense are therefore detections caused by some random noise.281 The umiber of false detections depends on how well the voise has been filtered aud on the level of the weshold or the coimecidence on the trials’ results., The number of false detections depends on how well the noise has been filtered and on the level of the threshold for the coincidence on the trials' results.282 With well clioseu hresholds (see section 3. for the selection of thresholds). he rate of false detectious from TRUFAS turus out to be ess than 1*," With well chosen thresholds (see section \ref{sec:disc} for the selection of thresholds), the rate of false detections from TRUFAS turns out to be less than 1."283' The rejection of false detectious is based on the reconstruction of the selected scale based on the snowledee of the spacing of the peaks. by sclecting in the signal's complex Fourier Traustorm only those bius spaced my apart. aud performing an inverse Fourier Trausforui.," The rejection of false detections is based on the reconstruction of the selected scale based on the knowledge of the spacing of the peaks, by selecting in the signal's complex Fourier Transform only those bins spaced $\nu_{0}$ apart, and performing an inverse Fourier Transform."284 The result is a recovered signal with unich better S/N. as it can be secuin Fig. 8..," The result is a recovered signal with much better S/N, as it can be seenin Fig. \ref{figrecovered}."285 This recovered signal can be used or an automatic rejection of false detections., This recovered signal can be used for an automatic rejection of false detections.286 When the amplitude (A) of the recovered signa Is compared with he sigma (0) of the selectec scale. the ratio À/o defines a threshold of higher than 1 for real transits aud less than l for false detections.," When the amplitude (A) of the recovered signal is compared with the sigma $\sigma$ ) of the selected scale, the ratio $\sigma$ defines a threshold of higher than 1 for real transits and less than 1 for false detections."287 This is due to the fact that during he signal recovery. if the selected. bius are not generate wa senal preseut iu the data. their phases do not have he correct relationship to reconstruct the sigual aud oulv roise appears.," This is due to the fact that during the signal recovery, if the selected bins are not generated by a signal present in the data, their phases do not have the correct relationship to reconstruct the signal and only noise appears."288 Iu that case. the amplitude of the recoverce signal is at the level of he recovered noise.," In that case, the amplitude of the recovered signal is at the level of the recovered noise."289 The recoverec roise is lower than the noise present in the original signal. vecamse a significant percentage of bius has been set to zero before recovering the signal: hence the ratio A/o wil © lower than 1.," The recovered noise is lower than the noise present in the original signal, because a significant percentage of bins has been set to zero before recovering the signal; hence the ratio $\sigma$ will be lower than 1."290 For instance. iu the two cases shown. stars 168 and 533. these ratios are 1.58 aud {τὸ respectively whereas al the false detections with level of coiucideuces above 20 % have values of A/a between 0.39 and 0.50.," For instance, in the two cases shown, stars 168 and 533, these ratios are 4.58 and 4.73 respectively whereas all the false detections with level of coincidences above 20 $\%$ have values of $\sigma$ between 0.39 and 0.80."291 Tt is important to keep in iud here. that σ ac Aare not obtained from the same signal but rather from the selected scale before aud after signal recovery.," It is important to keep in mind here, that $\sigma$ and A are not obtained from the same signal but rather from the selected scale before and after signal recovery."292 Although TRUFAS has been tailored to space observations (data without or with rather few eaps. that can be easily interpolated). in the following we slow how the algorithui performs in data with eaps.," Although TRUFAS has been tailored to space observations (data without or with rather few gaps, that can be easily interpolated), in the following we show how the algorithm performs in data with gaps."293 Out of cach of the two light curves that have previously been used as examples. 168 aud #533. we have generated two sets of 100 curves with different dutv-cveles by randonilv introducing gaps ou a 21 hours basis iuterval.," Out of each of the two light curves that have previously been used as examples, 168 and 533, we have generated two sets of 100 curves with different duty-cycles by randomly introducing gaps on a 24 hours basis interval."294 The gaps were uniformly distributed., The gaps were uniformly distributed.295 These sets coutain curves with duty cvcles raneine from 86 to oulv 16," These sets contain curves with duty cycles ranging from 86 to only 16 ,"296results of Paper II (82)).,results of Paper II \ref{sec_simulations}) ).297 We then compare the stellar wind torque to the star-disk spin-down torque in section 3 and then to the star-disk spiu-up torque in section l.. which contains spiu-equilibrimn solutions.," We then compare the stellar wind torque to the star-disk spin-down torque in section \ref{sec_tdsd} and then to the star-disk spin-up torque in section \ref{sec_equilibrium}, which contains spin-equilibrium solutions."298 Section 5 contains a πα and ciscussio-, Section \ref{sec_discussion} contains a summary and discussion.299 This section contaius a brief description of the siuulatiou results of Paper II that we will use for our analysis. aud the reader will &ud details iu that paper.," This section contains a brief description of the simulation results of Paper II that we will use for our analysis, and the reader will find details in that paper."300 The primary purpose of the sinuulations was to commute the spin-down torque on a star. due to the aneular momentum outflow in a wind.," The primary purpose of the simulations was to compute the spin-down torque on a star, due to the angular momentum outflow in a wind."301 We used uunuerical imaenetolivdrodyuaiiüc sinmilatious to directly calculate the torque 7m from steady-state. 2D. (axisviunnetric) winds from isolated stars.," We used numerical magnetohydrodynamic simulations to directly calculate the torque $\tau_{\rm w}$ from steady-state, 2D (axisymmetric) winds from isolated stars."302 We adopted coronal (fherual-pressure-driven) winds as a proxy for the unknown winel dviving imechanisni, We adopted coronal (thermal-pressure-driven) winds as a proxy for the unknown wind driving mechanism.303 Iu the simulations. the torque is entirely deteriiued by the seven key parameters listed in table L..," In the simulations, the torque is entirely determined by the seven key parameters listed in table \ref{tab_parms}."304 These are the stellar mass. Af: stellar radius. Ra streneth of the rotation-axis-aligned dipole maguetic field at the surface aud equator of the star. D.: spin rate expressed as a fraction of brealup speed. where O. is the aneulay spin rate of the star: mass outflow rate in the stellar wiud. M: ratio of the thermal sound speed to the escape speed. evaluated at the base of the wind (just above the stellar surface). οςfeat aud aciabatic index. >.," These are the stellar mass, $M_*$; stellar radius, $R_*$; strength of the rotation-axis-aligned dipole magnetic field at the surface and equator of the star, $B_*$ ; spin rate expressed as a fraction of breakup speed, where $\Omega_*$ is the angular spin rate of the star; mass outflow rate in the stellar wind, $\dot M_{\rm w}$; ratio of the thermal sound speed to the escape speed, evaluated at the base of the wind (just above the stellar surface), $c_{\rm s} / v_{\rm esc}$; and adiabatic index, $\gamma$."305 Table 1 lists the value of cach parameter adopted for a fiducial case., Table \ref{tab_parms} lists the value of each parameter adopted for a fiducial case.306 Paper IE coutained a parameter study iu which cach of the seven parameters were varied relative o the fiducial case. and 14 cases from the parameter study are listed in table 20.001)...," Paper II contained a parameter study in which each of the seven parameters were varied relative to the fiducial case, and 14 cases from the parameter study are listed in table \ref{tab_torques}."307 Iu cach case. six of the parameters were held fixed at the fducial value (as given in table 1)). aud one parameter was varied as indicated by the first colui of table 2..," In each case, six of the parameters were held fixed at the fiducial value (as given in table \ref{tab_parms}) ), and one parameter was varied as indicated by the first column of table \ref{tab_torques}."308" To compare with analytic theory. we also calculated he effective Alfvénn radius (r4). where the poloidal wind velocity equals the poloidal Alfvéóun speed. using an analytic formula for the stellar wind torque. Since our smnimlatious are multi-cdimensional. we have used Gira). Which is the mass-loss-weighted average of ,rm."," To compare with analytic theory, we also calculated the effective Alfvénn radius $r_{\rm A}$ ), where the poloidal wind velocity equals the poloidal Alfvénn speed, using an analytic formula for the stellar wind torque, Since our simulations are multi-dimensional, we have used $\left<309r_{\rm A}^2 \right>$, which is the mass-loss-weighted average of $r_{\rm A}^2$."310" Horeafter,. we'll. rofer. to 66)/21/2 eenericallv. as ray."," Hereafter, we'll refer to $\left< r_{\rm A}^2311\right>^{1/2}$ generically as $r_{\rm A}$."312 Using the sinulation result for nz. equation 2 defines the value of ry. which is tabulated for all cases in the second columu of table 2..," Using the simulation result for $\tau_{\rm w}$, equation \ref{eqn_tw} defines the value of $r_{\rm A}$, which is tabulated for all cases in the second column of table \ref{tab_torques}. ."313 Tn this paper. we iuake use of the seni-analvtic formmlation for the Alfvéuu radius from Paper IL. where A and i are dineusiouless coustants fit to the simulation. and e=(GM./BR)? is the escape speed from the stellar surface.," In this paper, we make use of the semi-analytic formulation for the Alfvénn radius from Paper II, where $K$ and $m$ are dimensionless constants fit to the simulation, and $v_{\rm esc} = (2 G M_* / R_*)^{1/2}$ is the escape speed from the stellar surface."314 Paper IH showed that the values of Asz2.11 aud in50.223 welldescribe (to better than 1'43) the fiducial case aud those eight other cases with variatious on B.. Πο. M. aud AL.," Paper II showed that the values of $K \approx 2.11$ and $m \approx 0.223$ well-describe (to better than ) the fiducial case and those eight other cases with variations on $B_*$, $R_*$, $\dot M_{\rm w}$, and $M_*$."315 Althoueh this is only approximately valid for situations with different wind acceleration rates or different rotation rates (in which case the values of A aud i» are slightly different: see Paper ID). the forumlation of equation 3. serves well as an indication of the approximate dependence of the stellar wiud on parameters. which will be imiportaut for discussing a wide range of possible conditions.," Although this is only approximately valid for situations with different wind acceleration rates or different rotation rates (in which case the values of $K$ and $m$ are slightly different; see Paper II), the formulation of equation \ref{eqn_rasim} serves well as an indication of the approximate dependence of the stellar wind on parameters, which will be important for discussing a wide range of possible conditions."316 The formi of equation (3)) is similar to that derived by for the eeneral theory of ceutritugally diivenu disk wiuds., The form of equation \ref{eqn_rasim}) ) is similar to that derived by for the general theory of centrifugally driven disk winds.317 The quantity in brackets iieasures the magnetization of the wind., The quantity in brackets measures the magnetization of the wind.318" By assuming that the Alfvéónu speed c,4 (at the Alfvéóun radius) is directly proportional to Qury. a relation of the kind eiveu by equation (3)) can be derived1992)."," By assuming that the Alfvénn speed $v_{r,A}$ (at the Alfvénn radius) is directly proportional to $\Omega_*r_A$, a relation of the kind given by equation \ref{eqn_rasim}) ) can be derived."319. In that case. the value of the iudex is a=1/3.," In that case, the value of the index is $m=1/3$."320 While this value is not far from the results of our uunuerical simulations. the differeuce is siguificaut.," While this value is not far from the results of our numerical simulations, the difference is significant."321 One key reasou for this may be that disk winds are in the τοσο of so-called fast mmaguetic rotators. whereas the rather slowly rotating TTS are either slow maguctic rotators (where wind-driving forces dominate over ceutrifueal ones) or are intermediate between these two regimes (see Paper ID).," One key reason for this may be that disk winds are in the regime of so-called fast magnetic rotators, whereas the rather slowly rotating TTS are either slow magnetic rotators (where wind-driving forces dominate over centrifugal ones) or are intermediate between these two regimes (see Paper II)."322 For the discussion that follows. it is useful to highlight how the lever arm (r4) aud wiud torque responds to changing the mass load (tho mass loss rate) of the wind.," For the discussion that follows, it is useful to highlight how the lever arm $r_{\rm A}$ ) and wind torque responds to changing the mass load (the mass loss rate) of the wind."323 The fact that the Alfvéeun lever axi in a livdromagnuetie wind ects siaaller as the mass load of the outflow lnereases. as IS seen d equation (3)). seecnus to suggest that the wind would become ineffective.," The fact that the Alfvénn lever arm in a hydromagnetic wind gets smaller as the mass load of the outflow increases, as is seen in equation \ref{eqn_rasim}) ), seems to suggest that the wind would become ineffective."324 This is certainly uot true however. because equation (2)) assures that an increase du wind iass loss rate leads to a uct increase in the torque that the wind exerts upon the star (the net wind torque scales as AL. 27).," This is certainly not true however, because equation \ref{eqn_tw}) ) assures that an increase in wind mass loss rate leads to a net increase in the torque that the wind exerts upon the star (the net wind torque scales as $\dot325M_w^{1-2m}$ )."326 This is the asic reason Why. by having an outflow rate that is a substantial fraction of the accretion rate. an accretion-oowered stellar wind cau be effective iu countering the accretion torque.," This is the basic reason why, by having an outflow rate that is a substantial fraction of the accretion rate, an accretion-powered stellar wind can be effective in countering the accretion torque."327 It is our goal here to compare the stellar wind torque o the torque expected to arise from the star-dixsk interaction. and the latter has ouly been determined lus far for a dipolar geometry.," It is our goal here to compare the stellar wind torque to the torque expected to arise from the star-disk interaction, and the latter has only been determined thus far for a dipolar geometry."328 So we only consider rerethe cases from: Paper ID with a dipole magnetic Ποια., So we only consider herethe cases from Paper II with a dipole magnetic field.329 We also adoptthe following assumptions., We also adoptthe following assumptions.330 Paper II indicated that the details of the wind driving have a relatively small. but not cutirely negligible. effect on he stellar wind torque.," Paper II indicated that the details of the wind driving have a relatively small, but not entirely negligible, effect on the stellar wind torque."331 In the absence of a detailed, In the absence of a detailed332of Ha.,of $\alpha$.333" A heavy contamination are still K stars with molecular bands of MgH, but since the slope of the spectrum is quite different, they can be identified by visual inspection."," A heavy contamination are still K stars with molecular bands of MgH, but since the slope of the spectrum is quite different, they can be identified by visual inspection."334" This procedure led to the discovery of nine additional DZ white dwarfs, two of which were already in the Dufour sample."," This procedure led to the discovery of nine additional DZ white dwarfs, two of which were already in the Dufour sample."335" Two additional objects, SDSS0143+0113 and SDSS2340+0817, were identified independently by Dufour in a search for DZs."," Two additional objects, SDSS0143+0113 and SDSS2340+0817, were identified independently by Dufour in a search for DZs."336 The complete list of cool DZ (plus one DQ) white dwarfs identified and their ugriz photometry is given in Table 1.., The complete list of cool DZ (plus one DQ) white dwarfs identified and their $ugriz$ photometry is given in Table \ref{objects}.337" All spectral features found in the spectra of the new cool DZ white dwarfs can be identified with lines from Ca, Mg, Na, Fe, Ti, and Cr, broadened predominantly through van der Waals broadening by neutral helium."," All spectral features found in the spectra of the new cool DZ white dwarfs can be identified with lines from Ca, Mg, Na, Fe, Ti, and Cr, broadened predominantly through van der Waals broadening by neutral helium."338" The broadest lines show strongly asymmetric profiles, which were in the case of 5169/5174/5185 originally identified as due to quasi-static broadening by Wehrse&Liebert(1980) in their study of SDSS1330+3029 (= G165-7)."," The broadest lines show strongly asymmetric profiles, which were in the case of 5169/5174/5185 originally identified as due to quasi-static broadening by \cite{Wehrse.Liebert80} in their study of SDSS1330+3029 (= G165-7)."339 The same conclusion was reached by Kawkaetal.(2004) for SDSS1535+1247; both of these stars are in our present sample., The same conclusion was reached by \cite{Kawka.Vennes.ea04} for SDSS1535+1247; both of these stars are in our present sample.340" The width of these lines, as well as that of the resonance lines is far beyond the range of validity of the impact approximation, which is in these cases approximately 8-10 ffrom the line centers (seep.312inUnsóld1968)."," The width of these lines, as well as that of the resonance lines is far beyond the range of validity of the impact approximation, which is in these cases approximately 8-10 from the line centers \citep[see p. 312 in][]{Unsold68}."341". We have used the simple and elegant method of Walkupetal.(1984), who present numerical calculations for the transition range between impact and quasi-static regime, which can in both limits be easily extended with the asymptotic formulae."," We have used the simple and elegant method of \cite{Walkup.Stewart.ea84}, who present numerical calculations for the transition range between impact and quasi-static regime, which can in both limits be easily extended with the asymptotic formulae."342 These profiles are reasonable approximations for the Mel triplet., These profiles are reasonable approximations for the MgI triplet.343 For the much wider resonance lines this approximation fails., For the much wider resonance lines this approximation fails.344 The reason is very likely that for such strong interactions needed to produce a 600 wwide wing the approximation with a simple van der Waals r$ law is not valid., The reason is very likely that for such strong interactions needed to produce a 600 wide wing the approximation with a simple van der Waals $r^{-6}$ law is not valid.345 We have used the quasi-static limit of the semiclassical quasi-molecular broadening theory as described in Allard&Kielkopf(1982)., We have used the quasi-static limit of the semiclassical quasi-molecular broadening theory as described in \cite{Allard.Kielkopf82}.346. This formulation (e.g. their eq., This formulation (e.g. their eq.347 59 in the cited paper) easily allows the incorporation of a Boltzmann factor to account for the variation of the perturbation probability with distance of the perturber in thermal equilibrium., 59 in the cited paper) easily allows the incorporation of a Boltzmann factor to account for the variation of the perturbation probability with distance of the perturber in thermal equilibrium.348" It would also allow us to take a variation in the dipole moments into account, which, however, are apparently not available in the published literature."," It would also allow us to take a variation in the dipole moments into account, which, however, are apparently not available in the published literature."349 Adiabatic potential energy curves for the ground state of the Ca*He quasi-molecule and the two exited states correlated with the resonance term of the ion — (4p)? and (4p)?II — were calculated by Czuchajetal.(1996) and numerical data were presented in a table., Adiabatic potential energy curves for the ground state of the $^+$ He quasi-molecule and the two exited states correlated with the resonance term of the ion – $^2\Sigma$ and $^2\Pi$ – were calculated by \cite{Czuchaj.Rebentrost.ea96} and numerical data were presented in a table.350 Approximate calculations for the spin-orbit interaction show a mixing of the two upper levels of the doublet and a complicated structure of the energy curves (their Fig., Approximate calculations for the spin-orbit interaction show a mixing of the two upper levels of the doublet and a complicated structure of the energy curves (their Fig.351 4)., 4).352 Since no numerical data are given for, Since no numerical data are given for353retaining only the central oof cach of the six orders avoids degradation of wavelength solution accuracy towards the orders ends and so maintains the accuracy of derived radial velocities. ancl (e) due to the Echelle blaze fiction. the instrument response at orders edges falls below of the peak value at ceuter of cach order. thus producing toward order edges both a poorer S/N and a steeper contimmun (harder to normalize to unity before to rum the cross-correlation).,"retaining only the central of each of the six orders avoids degradation of wavelength solution accuracy towards the orders' ends and so maintains the accuracy of derived radial velocities, and $e$ ) due to the Echelle blaze function, the instrument response at orders edges falls below of the peak value at center of each order, thus producing toward order edges both a poorer S/N and a steeper continuum (harder to normalize to unity before to run the cross-correlation)."354 The selected waveleugth interval iucludes the AA=15 rrange centered at 5157 where the highly successful CEA Specdometers have beeu deriviug accurate radial velocities for two decades mow. including a wealth of binaries. as described by Latham (2002. aud references therein).," The selected wavelength interval includes the $\Delta\lambda$ =45 range centered at 5187 where the highly successful CfA Speedometers have been deriving accurate radial velocities for two decades now, including a wealth of binaries, as described by Latham (2002, and references therein)."355 Radial velocities were ieasured with the two-dimensional correlation algorithm) (Zucker aud Alazeh 1991)., Radial velocities were measured with the two-dimensional correlation algorithm (Zucker and Mazeh 1994).356 This is a iuultiple correlation techuique that obtains the Doppler shifts (and the inteusitv ratio) of the two stellar components snmltaneouslhv., This is a multiple correlation technique that obtains the Doppler shifts (and the intensity ratio) of the two stellar components simultaneously.357 It allows for efücieut solution of even bleuded spectra of the two stars with an unknown intensity ratio., It allows for efficient solution of even blended spectra of the two stars with an unknown intensity ratio.358 The aleoritlin has been coded by us iuto a custom IRAF script which makes use of the Fourier correlation routine within the package (Isurtz and Mink 1998. Tourv aud Davis 1979) and builds ou a Frotran code kindly supplied by D. Latham.," The algorithm has been coded by us into a custom IRAF script which makes use of the Fourier correlation routine within the package (Kurtz and Mink 1998, Tonry and Davis 1979) and builds on a Frotran code kindly supplied by D. Latham."359 The code uses template spectra of the two stars as mput., The code uses template spectra of the two stars as input.360 The appropriate templates have been selected among the large svuthetic spectral database computed at 200000 resolving power with I&urucz's codes by Munaini et al. (, The appropriate templates have been selected among the large synthetic spectral database computed at 000 resolving power with Kurucz's codes by Munari et al. (3612003).,2003).362 A subsection of the svuthetic atlas. useful for F aud € main sequence stars aud covering the 16 Asiago Echelle orders from 3200 to 9150 Hs available electronically to interestedusers.," A subsection of the synthetic atlas, useful for F and G main sequence stars and covering the 46 Asiago Echelle orders from 3200 to 9480 is available electronically to interested."363 The accuracy of the racial velocities from the six selected aud trimmed Echelle orders has turned out to be constant over all six selected orders., The accuracy of the radial velocities from the six selected and trimmed Echelle orders has turned out to be constant over all six selected orders.364 Averaged results are summarized in Table 1., Averaged results are summarized in Table 1.365 The mean eror of radial velocities is 1.05 kan | for star 1 (the faiuter of the two). and 0.66 Em 4 for star 2.," The mean error of radial velocities is 1.05 km $^{-1}$ for star 1 (the fainter of the two), and 0.66 km $^{-1}$ for star 2."366" The selected templates have been Z4 26500 IK. logg=15. |Z/Z.]2 0.5 and τος ln | for star 1. and T;g—6250 FK. logg—LO. |Z/Z.]2 0.5 and Yi,—10 kii for star 2."," The selected templates have been $T_{\rm eff}$ =6500 K, $\log g$ =4.5, $_\odot$ $-$ 0.5 and $V_{\rm rot}$ =20 km $^{-1}$ for star 1, and $T_{\rm eff}$ =6250 K, $\log g$ =4.0, $_\odot$ $-$ 0.5 and $V_{\rm rot}$ =40 km $^{-1}$ for star 2."367from the data.,from the data.368" It has its own assumptions, such as Gaussianity, independence of data points and in the specific case analyzed here, cosmologies that obey a FRW metric."," It has its own assumptions, such as Gaussianity, independence of data points and in the specific case analyzed here, cosmologies that obey a FRW metric."369" In the final reconstruction phase, it also exhibits a bias in the"," In the final reconstruction phase, it also exhibits a bias in the"370properties with real observations.,properties with real observations.371 It is therefore timely to investigate further the effects of eutropy generation on the evolution of clu ster scaling relations as the available data for high+vecdshift svstems acctuulates., It is therefore timely to investigate further the effects of entropy generation on the evolution of clu ster scaling relations as the available data for high-redshift systems accumulates.372 Iu this paper. we will use cosmological hydrodvuauuical siuulatiouns described im Muunvousgetal.(2002). hereafter NTTI&SPO2. aud in Wavetal.(200L).. hereafter KTIPOL to trace the evolution of the cluster population to high redshift (2= 1.5).," In this paper, we will use cosmological hydrodynamical simulations described in \citet{Muanwong02}, hereafter MTKP02, and in \citet{Kay04}, hereafter KTJP04, to trace the evolution of the cluster population to high redshift $z=1.5$ )."373" Our results will primarily focus ou three(Radiative,Preheating aud Feedback) models. all able to reproduce the local irclation."," Our results will primarily focus on three, and ) models, all able to reproduce the local relation."374 The aims of this paper are to determine how the scaling relations evolve with redshift in the three models aud to discover what the evolution of scaling relations cau teach us about nou-gravitatioual processes occurrnue iu clusters., The aims of this paper are to determine how the scaling relations evolve with redshift in the three models and to discover what the evolution of scaling relations can teach us about non-gravitational processes occurring in clusters.375 The rest of this paper is outlined as follows., The rest of this paper is outlined as follows.376 In Section 2 we introduce the X-ray scaling relations and suumnaize our preseut observational knowledge of these quantities., In Section \ref{sec:srel} we introduce the X-ray scaling relations and summarize our present observational knowledge of these quantities.377 Details of our simulated cluster populations are prescuted in Section 3.., Details of our simulated cluster populations are presented in Section \ref{sec:sims}.378 In Section | we preseut our main results. fist at 2=0. where the models are in good agreement with each other aud the observations. then as a function of redshift. where the models predict widely different results.," In Section \ref{sec:results} we present our main results, first at $z=0$, where the models are in good agreement with each other and the observations, then as a function of redshift, where the models predict widely different results."379 We discuss the implications of these differences in Section 5 aud demonstrate that the degree of N-rav evolution is driven by the supply of cold. low eutropy gas.," We discuss the implications of these differences in Section \ref{sec:discuss} and demonstrate that the degree of X-ray evolution is driven by the supply of cold, low entropy gas."380 Finally. we stuumarize our conclusions in Section 6..," Finally, we summarize our conclusions in Section \ref{sec:conclude}."381 Isaiscr(1986) derived the following relations for telpcrature aud luminosity assunune the distribution of eas and dark matter iu clusters is perfectlv selfsinilar and the XN-rav ciission is primarily thermal breiisstraliluug radiation., \citet{Kaiser86} derived the following relations for temperature and luminosity assuming the distribution of gas and dark matter in clusters is perfectly self-similar and the X-ray emission is primarily thermal bremsstrahlung radiation.382 Observed clusters do not form a sclfsimuilay population but it is nevertheless convenient to describe their behavior using a generalized power-law form. where Cy.) aud Yy determine the normalization. à is the slope of the relation (in log-space) aud A determines how the relation evolves with redshift.," Observed clusters do not form a self-similar population but it is nevertheless convenient to describe their behavior using a generalized power-law form where $C_0(z)$ and $Y_0$ determine the normalization, $\alpha$ is the slope of the relation (in log-space) and $A$ determines how the relation evolves with redshift."383 Our main results will focus on the determination of A., Our main results will focus on the determination of $A$.384" Observationally. attempts to measure the Tx- Miclationathighredshi ftarccurrentlyiitheirinfancy, asthe dla sothattheirnasscanbees shnilarecolution(A~1. Maughanetal.2005:Vilkshlinin 2005))."," Observationally, attempts to measure the $-M$ relation at high redshift are currently in their infancy, as they require temperature profiles to be measured so that their mass can be estimated, but initial results are consistent with self-similar evolution $A \sim3851$, \citealt{Maughan05,Kotov05}) )."386 Measuring the welation at higher redshift is a somewhat simpler prospect. and has heen attempted by imnauy authors (Mushotzkv&Scharf1997:Fairleyetal.2000:Molden 2005).," Measuring the relation at higher redshift is a somewhat simpler prospect, and has been attempted by many authors \citep{MS97,Fairley00,Holden02,Novicki02,Arnaud02,Vikhlinin02,Lumb04,387Ettori04,Maughan05,Kotov05}."388. We sunmuarize recent results that adopt a low-density flat cosmology in Figure 1.. attempting to iuclude iu the size of the error bars the unecrtainty in οἱ απο to the choice of local relation (when quoted by the authors).," We summarize recent results that adopt a low-density flat cosmology in Figure \ref{fig:ltevolobs}, attempting to include in the size of the error bars the uncertainty in $A$ due to the choice of local relation (when quoted by the authors)."389 Although the preseut situation is by no means clear. takiug all results at face value generally favors positive evolution (0SAz 2) with the latest results being consistent with sel fsimilar evolution (l=3/2).," Although the present situation is by no means clear, taking all results at face value generally favors positive evolution $0 \approxlt A \approxlt3902$ ) with the latest results being consistent with sel f-similar evolution $A=3/2$ )."391 Larecr siuuples of Ligh redshift clusters (such as that expected from the Cluster Survey. Romeretal. 2001)) will be crucial to accurately coustrain the degree of evolution iu therelation.," Larger samples of high redshift clusters (such as that expected from the Cluster Survey, \citealt{Romer01}) ) will be crucial to accurately constrain the degree of evolution in therelation."392" Qur results are drawn from three sinmularl-sized - body/SPI simulations of the AC'DAL ""cosinology. which have already been published iu NTIP02 aud KTJDPO0I."," Our results are drawn from three similarly-sized $N$ -body/SPH simulations of the $\Lambda$ CDM cosmology, which have already been published in MTKP02 and KTJP04."393 The simulation box in MTIKDP02 has a comoving side of 100A!Mpe with 160° particles cach of eas aud dark matter. whose particle masses are set to 2.6«10” and 2.]«1019PALL. respectivelv.," The simulation box in MTKP02 has a comoving side of $100\hMpc$ with $160^3$ particles each of gas and dark matter, whose particle masses are set to $2.6\times 10^9$ and $2.1\times 10^{10}\hMsun$, respectively."394" The box used iu I(TJPOI is bigger with a side of 1207)Mpe usingi 256°y particles cach of eas and dark matter. whose particle masses are 1.3«10"" and τον109?2. TAL. respectively."," The box used in KTJP04 is bigger with a side of $120\hMpc$ using $256^3$ particles each of gas and dark matter, whose particle masses are $1.3\times 10^9$ and $7.3\times 10^9\hMsun$ , respectively."395 Full details can be found in the articles., Full details can be found in the articles.396 The kev difference between the simulations is the model used to raise the eutropy of Mata ΙΓοο) MMM," The key difference between the simulations is the model used to raise the entropy of the intracluster gas, summarized as follows:"397"critical density. £2,,. and the present day value of the reduced Hubble constant. /. over the parameter spaces [0.01. 0.5] and [0.5. 2.5]. respectively.","critical density, $\Omega_{\rm m}$, and the present day value of the reduced Hubble constant, $h$, over the parameter spaces [0.01, 0.5] and [0.5, 2.5], respectively."398" We also put a prior on ΟΙΩΣ so that Q? = 0.019-E0.002. confidence levels. (e.g. Burles ef a£. 2001) and marginalise over the uncertainty range in order to get the likelihoods of £2, and fy,"," We also put a prior on $\Omega_{\rm399b}h^2$ so that $\Omega_{\rm b}h^{2}$ = $\pm$ 0.002, confidence levels, (e.g. Burles $\it et$ $\it al.$ 2001) and marginalise over the uncertainty range in order to get the likelihoods of $\Omega_{\rm m}$ and $h$."400 We note that fixing Qu? to 0.019 tightens the constrains in the Qu. h plane but does not change the best fit points significantly.," We note that fixing $\Omega_{\rm b}h^2$ to 0.019 tightens the constrains in the $\Omega_{\rm m}$, $h$ plane but does not change the best fit points significantly."401 We compute the \7s using Eq., We compute the $\chi^2$ s using Eq.402" B2. in Appendix B: where the sum is over the number of clusters. the baryon fraction is given by fi,=fons|fua and ai, 2 O7."," \ref{chi2_sum} in Appendix B: where the sum is over the number of clusters, the baryon fraction is given by $f_{\rm b} = f_{\rm gas} + f_{\rm gal}$ and $\omega_{\rm b}$ = $\Omega_{\rm b}h^{2}$."403 To obtain a qualititive understanding we consider Eq., To obtain a qualititive understanding we consider Eq.404" |. and use the first cosmological dependence that dominates over the others to an approximate relation between OQ, and {1 For the observed distribution of the gas mass fraction of about Q.08 f+? (e.g. EF99) and reasonable values of Hubble constant. the above relation can be estimated as O,,/D7z0.25."," \ref{eq:fbar}405 and use the first cosmological dependence that dominates over the others to an approximate relation between $\Omega_{\rm m}$ and $h$: For the observed distribution of the gas mass fraction of about 0.08 $h^{-1.5}$ (e.g. EF99) and reasonable values of Hubble constant, the above relation can be estimated as $\Omega_{\rm m} h^{0.5} \approx4060.25$."407 The two datasets do have some clusters in common. however. we see that our conclusions are not affected if we consider the samples separately.," The two datasets do have some clusters in common, however, we see that our conclusions are not affected if we consider the samples separately."408 The results are plotted in Figure 3.., The results are plotted in Figure \ref{fig:clusters}.409 It is seen that in both data sets the value of / is unacceptably high at the684 confidence level (but still lower than Hubble's original value of 500. km/sec/Mpc!), It is seen that in both data sets the value of $h$ is unacceptably high at the$68\%$ confidence level (but still lower than Hubble's original value of 500 km/sec/Mpc!)410" and the best fit values of Qu, are relatively low.", and the best fit values of $\Omega_{\rm m}$ are relatively low.411" The parameter values (Qy,. /) at the best fit points(with 68 per cent confidence limits) are (0.11. 1.73. 75 and (0.18OVSO02 LTο το) for EF99 and MME99 data. respectively."," The parameter values $\Omega_{\rm m}$, $h$ ) at the best fit points(with 68 per cent confidence limits) are $0.11^{+0.03}_{-0.04}$ $1.73^{+0.33}_{-0.48}$ ) and $0.18^{+0.02}_{-0.02}$ $1.17^{+0.10}_{-0.10}$ ) for EF99 and MME99 data, respectively."412 The standard joint analysis of the data sets yields (OQu.. 4) = COAT 551.123. 0753 and with HPs method we obtain (Qu... 9 = (0.15MIS(03. 133OLN so).," The standard joint analysis of the data sets yields $\Omega_{\rm m}$ , $h$ ) = $0.17^{+0.01}_{-0.02}$ $1.23^{+0.08}_{-0.12}$ ) and with HPs method we obtain $\Omega_{\rm m}$, $h$ ) = $0.15^{+0.03}_{-0.03}$, $1.33^{+0.22}_{-0.28}$ )."413" Tt is easy to see from Figure 3. that both separate and joint analyses of the data imply that Qu, = | is ruled out at very high confidence level.", It is easy to see from Figure \ref{fig:clusters} that both separate and joint analyses of the data imply that $\Omega_{\rm m}$ = 1 is ruled out at very high confidence level.414 The standard 47 and HP analyses. shown on bottom left and right panels in Figure 3. yield slightly different results.," The standard $\chi^2$ and HP analyses, shown on bottom left and right panels in Figure \ref{fig:clusters} yield slightly different results."415 The HP values are 0.6 for the EF99 and 0.1 for the MME99 sample., The HP values are 0.6 for the EF99 and 0.1 for the MME99 sample.416 The low weight given to the MME99 data may indicate possible systematic errors. an underestimation of the random errors or incomplete modelling.," The low weight given to the MME99 data may indicate possible systematic errors, an underestimation of the random errors or incomplete modelling."417 The HPs obtained suggest that the EF99 sample is more reliable than the MME99 data., The HPs obtained suggest that the EF99 sample is more reliable than the MME99 data.418 The galaxy clusters in the EF99 sample were selected for ctjeir high X-ray luminosity and relaxed morphology. whereas the selection criteria in MME?99 was to build a flux-limited sample.," The galaxy clusters in the EF99 sample were selected for their high X-ray luminosity and relaxed morphology, whereas the selection criteria in MME99 was to build a flux-limited sample."419 Therefore. we see at least two effects that can make the EF99 sample more robust in providing a stable central value of the gas fraction: (1) the systematies due to non-homogeneous objects are more under control and (ii) the observed dependence of the value of gas mass fraction upon the plasma temperature cand luminosity. as consequence of the tight £97 relation observed in galaxy clusters: e.g. Ettori. Allen Fabian 2001 for an application of HPs o this relation) makes the selection in luminosity (instead of flux) a more robust way to select objects in the upper end of the gas mass Traction distribution.," Therefore, we see at least two effects that can make the EF99 sample more robust in providing a stable central value of the gas fraction: (i) the systematics due to non-homogeneous objects are more under control and (ii) the observed dependence of the value of gas mass fraction upon the plasma temperature (and luminosity, as consequence of the tight $L-T$ relation observed in galaxy clusters; e.g. Ettori, Allen Fabian 2001 for an application of HPs to this relation) makes the selection in luminosity (instead of flux) a more robust way to select objects in the upper end of the gas mass fraction distribution."420 Being concerned about the high Hubble constant. we applied he Bootstrap method (Efron 1982) to baryon mass fraction data o ensure that there are no outlying clusters which could alter he significance of the obtained best fit values.," Being concerned about the high Hubble constant, we applied the Bootstrap method (Efron 1982) to baryon mass fraction data to ensure that there are no outlying clusters which could alter the significance of the obtained best fit values."421 We created 2000 synthetic catalogs selected from the two samples., We created 2000 synthetic catalogs selected from the two samples.422" The histograms of the best fit points for / and ©, for these bootstrap realizations are in very good agreement with the presented results.", The histograms of the best fit points for $h$ and $\Omega_{\rm m}$ for these bootstrap realizations are in very good agreement with the presented results.423 The joint analysis of cosmological probes (e.g. Baheall 1999 and Efstathiou 1999) suggests a flat Universe with Owz0.3., The joint analysis of cosmological probes (e.g. Bahcall 1999 and Efstathiou 1999) suggests a flat Universe with $\Omega_{\rm m} \approx 0.3 $.424" We fix O4, to 0.3 and to 0.2 and plot | dimensional likelihood distributions of .", We fix $\Omega_{\rm m}$ to 0.3 and to 0.2 and plot 1 dimensional likelihood distributions of $h$ .425 These plots are shown in Figure 4.., These plots are shown in Figure \ref{fig:clus1d}. .426" For fixed Qn,=0.3 the best fitpoints of / are 0.64 and 0.78 for EF99 and MME99. respectively."," For fixed $\Omega_{\rm m}427= 0.3 $ the best fitpoints of $h$ are 0.64 and 0.78 for EF99 and MME99, respectively."428 The joint |-dimensional, The joint 1-dimensional429position. using to provide position bins whose energy-dependent extent is always small compared to the PSF. providing a compact representation of the data with minimal information loss.,"position, using to provide position bins whose energy-dependent extent is always small compared to the PSF, providing a compact representation of the data with minimal information loss."430 We verified the results with the ScienceToolgtlike., We verified the results with the ScienceTool.431. The best-fit values are reported in Table 1.. and include a power-law photon index P21.1 and cut-off energy E.= 2.0GGeV. These values apply to the profile as a whole. although Figure 2. suggests that the second gamma-ray peak has a harder spectrum than the first. as is observed for many gamma-ray pulsars (e.g..Abdoetal.2011b).," The best-fit values are reported in Table \ref{tab:parms}, and include a power-law photon index $\Gamma = 1.1$ and cut-off energy $E_c =4322.0$ GeV. These values apply to the profile as a whole, although Figure \ref{fig:prof} suggests that the second gamma-ray peak has a harder spectrum than the first, as is observed for many gamma-ray pulsars \citep[e.g.,][]{awd+11}."433". In addition. to the rescaled IFGL. diffuse model. we also performed the fit with an improved model internal to the LAT collaboration and with ""Pass 7” using the IRFs and the appropriate diffuse model (accompanying V6the 2FGL catalog)."," In addition to the rescaled 1FGL diffuse model, we also performed the fit with an improved model internal to the LAT collaboration and with “Pass 7” using the IRFs and the appropriate diffuse model (accompanying the 2FGL catalog)."434 These values were consistent with those reported in Table 1.. and the scatter has been used to estimate systematic errors on the parameters.," These values were consistent with those reported in Table \ref{tab:parms}, and the scatter has been used to estimate systematic errors on the parameters."435 We have also included uncertainty in the instrument's effective area in the systematic errors through the use of “bracketing” IRFs (Abdoetal.2009¢)., We have also included uncertainty in the instrument's effective area in the systematic errors through the use of “bracketing” IRFs \citep{abdo2009}.436. A short (Gehrelsetal.2004) observation. was obtained on 2010 May 11 to search for an X-ray counterpart toJ203043641., A short \citep{gcg+04} observation was obtained on 2010 May 11 to search for an X-ray counterpart to.437. No emission is observed at the pulsar position in this 3.8kks X-ray Telescope (Burrowsetal.2005) PC mode observation. with a 36 upper limit of 1.710 cetsss7! (O.5-8 keV).," No emission is observed at the pulsar position in this ks X-ray Telescope \citep{bhn+05} PC mode observation, with a $3\,\sigma$ upper limit of $1.7\times10^{-3}$ $^{-1}$ (0.5–8 keV)."438 Assuming a power-law spectrum with photon index [=1.5 for a possible pulsar wind nebula (e.g..Kargaltsev&Pavlov2008) absorbed by a column with Ny=7.4«10°?! cem™ (assuming one free electron for every 10 neutral hydrogen atoms along the line of sight). this corresponds to an unabsorbed flux limit of fy<1.3Εν cem ss7!. or luminosity Ly<1.6«10?!cd/1kpeY s!..," Assuming a power-law spectrum with photon index $\Gamma=1.5$ for a possible pulsar wind nebula \citep[e.g.,][]{kp08} absorbed by a column with $N_H = 7.4\times10^{21}$ $^{-2}$ (assuming one free electron for every 10 neutral hydrogen atoms along the line of sight), this corresponds to an unabsorbed flux limit of $f_X <4391.3\times10^{-13}$ $^{-2}$ $^{-1}$, or luminosity $L_X <4401.6\times10^{31} (d/1\,{\rm kpc})^2$ ."441 For a distance of z2 kkpe (see Table 1)). this corresponds to Ly/E«2x102. which is a reasonably stringent limit. although it would not be a surprise if the actual X-ray flux of this pulsar were about an order of magnitude below the current limit 20110.," For a distance of $\approx4422$ kpc (see Table \ref{tab:parms}) ), this corresponds to $L_X/\dot E <4432\times10^{-3}$, which is a reasonably stringent limit, although it would not be a surprise if the actual X-ray flux of this pulsar were about an order of magnitude below the current limit \citep[see, e.g.,][]{mdc11}."444 The gamma-ray pulsations from uunambiguously identify it as the origin of the gamma rays fromJ2030., The gamma-ray pulsations from unambiguously identify it as the origin of the gamma rays from.445"0+3641.. We note also that a candidate TeV source possibly detected by the Milagro Gamma-Ray Observatory (7C2""inAbdoetal.2007) is positionally coincident withJ2030+3641.", We note also that a candidate TeV source possibly detected by the Milagro Gamma-Ray Observatory \citep[``C2'' in][]{aab+07} is positionally coincident with.446. Its faintness and location near a very bright source precludes further investigation based only on published results (seealsoAbdoetal.2009d).. but the relatively small £ and relatively large age and distance of mmake an association unlikely.," Its faintness and location near a very bright source precludes further investigation based only on published results \citep[see447also][]{milagro09}, but the relatively small $\dot E$ and relatively large age and distance of make an association unlikely."448 With a DM-derived distance of Kkpc. iis located toward the Cygnus region. where until recently very few pulsars were known and where the pulsar distance scale is highly uncertain.," With a DM-derived distance of kpc, is located toward the Cygnus region, where until recently very few pulsars were known and where the pulsar distance scale is highly uncertain."449 Recent discoveries suggest that the Cordes&Lazio(2002) model greatly overpredicts distances in this direction: PSR J2032+4127. located 5° fromJ2030+3641.. with a DM-derived distance of 3.6kkpe. ts thought to be located at half that distance2009b):: and PSR J202143651. less than 2 fromJ203043641.. with a model distance of kkpe. is more likely located at kkpe (Abdoetal.2009e).," Recent discoveries suggest that the \citet{cl02}450 model greatly overpredicts distances in this direction: PSR J2032+4127, located $5\arcdeg$ from, with a DM-derived distance of kpc, is thought to be located at half that distance; and PSR J2021+3651, less than $2\arcdeg$ from, with a model distance of kpc, is more likely located at kpc \citep{abdo15}."451. Also. the RM for iis large and positive. very similar to that of PSR J20214+3651. and this is suggestive of a location closer than the Perseus arm. at kkpe in this direction (seediscussioninHanetal.2006).," Also, the RM for is large and positive, very similar to that of PSR J2021+3651, and this is suggestive of a location closer than the Perseus arm, at kpc in this direction \citep[see discussion in][]{hml+06}."452 Overall. we judge that a likely distance for lis in the range kkpe.," Overall, we judge that a likely distance for is in the range kpc."453 Johnston&Weisberg(2006) noted that the profiles of pulsars with high £ share many common features., \citet{jw06} noted that the profiles of pulsars with high $\dot{E}$ share many common features.454 In particular. the profiles with two components generally show (1) two components with equal width. (11) the trailing component stronger than the leading component. (111) close to linear polarization. (iv) significant circular polarization under the trailing component. and (v) flat position angle swings which appear to steepen at the far trailing edge of the profile.," In particular, the profiles with two components generally show (i) two components with equal width, (ii) the trailing component stronger than the leading component, (iii) close to linear polarization, (iv) significant circular polarization under the trailing component, and (v) flat position angle swings which appear to steepen at the far trailing edge of the profile."455 The profile of cconforms in some ways to these generalizations., The profile of conforms in some ways to these generalizations.456 The profile is symmetrical with the trailing edge brighter., The profile is symmetrical with the trailing edge brighter.457 The PA swing is remarkably flat with a hint of steepening at the trailing edge., The PA swing is remarkably flat with a hint of steepening at the trailing edge.458 However. although the leading component is highly polarized. the trailing edge is not. unlike the majority of the high £ pulsars.," However, although the leading component is highly polarized, the trailing edge is not, unlike the majority of the high $\dot{E}$ pulsars."459 Weltevrede&Johnston(2008) pointed out that the transition between pulsars with low linear polarization and those which are highly polarized oceurs at £—10?sh., \citet{wj08} pointed out that the transition between pulsars with low linear polarization and those which are highly polarized occurs at $\dot{E}\sim 10^{34.5}$.460 ccould be an example| of a pulsar in transition from high to low polarization., could be an example of a pulsar in transition from high to low polarization.461 The interpretation of these profiles by Johnston&Weis-berg(2006) was that the magnetic pole crossing occurs at the (symmetry) center of the profile., The interpretation of these profiles by \cite{jw06} was that the magnetic pole crossing occurs at the (symmetry) center of the profile.462 The PA swing Is significantly shifted to later phase because of aberration (Blaskiewiczetal. 199]).. leading to emission heights close to kkm.," The PA swing is significantly shifted to later phase because of aberration \citep{bcw91}, leading to emission heights close to km."463 This may also be the case inJ2030--3641., This may also be the case in.464. If we assume that the inflexion point of the PA swing is the rise in the PA curve some 20° after the profile center in Figure |.. this implies an emission height of ~800 kkm (close to of the light cylinder). similar to those seen in other high E pulsars.," If we assume that the inflexion point of the PA swing is the rise in the PA curve some $20^{\circ}$ after the profile center in Figure \ref{fig:pol}, this implies an emission height of $\sim465800$ km (close to of the light cylinder), similar to those seen in other high $\dot{E}$ pulsars."466 We also note that a height of ~800 kkm would in turn imply an overall pulse width of some 507. similar to the observed value.," We also note that a height of $\sim467800$ km would in turn imply an overall pulse width of some $50^{\circ}$, similar to the observed value."468 This further suggests that the inclination between the magnetic and rotation axes cannot be too far from orthogonal., This further suggests that the inclination between the magnetic and rotation axes cannot be too far from orthogonal.469 We can use the gamma-ray light curve and polarimetric measurements to test the predictions of magnetosphere beaming models., We can use the gamma-ray light curve and polarimetric measurements to test the predictions of magnetosphere beaming models.470 Such tests are most constraining when the magnetic inclination angle à and the viewing angle c are well determined., Such tests are most constraining when the magnetic inclination angle $\alpha$ and the viewing angle $\zeta$ are well determined.471 The polarization data provide some geometrical constraints., The polarization data provide some geometrical constraints.472 Since the lower frequency data may be affected by interstellar scattering. our primary constraints are based on the GGHz data.," Since the lower frequency data may be affected by interstellar scattering, our primary constraints are based on the GHz data."473 We use PA values from the native 512 observational phase bins with opa«10° and phases 0.1< (relative to the intensity maximum: see Figure |)). and fit to a standard rotating vector model (RVM) polarization sweep.," We use PA values from the native 512 observational phase bins with $\sigma_{\rm PA}<10^\circ$ and phases $-0.1 <\phi <4740.05$ (relative to the intensity maximum; see Figure \ref{fig:pol}) ), and fit to a standard rotating vector model (RVM) polarization sweep."475 The maximum sweep rate is d'/do|max = 1.4 and one obtains good fits in a band of the a—¢ plane. with a best fit V7=37.5 for 55 degrees of freedom (suggesting the PA errors are somewhat overestimated).," The maximum sweep rate is $\Psi$ $\phi |$ max = 1.4 and one obtains good fits in a band of the $\alpha$ $\zeta$ plane, with a best fit $\chi^2 = 37.5$ for 55 degrees of freedom (suggesting the PA errors are somewhat overestimated)."476 Figure 3 shows the RVM fit confidence regions in this plane. after correcting for the," Figure \ref{fig:chi3} shows the RVM fit confidence regions in this plane, after correcting for the"477bands which all lic within the wavelength range covered by the 2dE. spectra.,bands which all lie within the wavelength range covered by the 2dF spectra.478 These indices and the other spectral features described in this section of the paper were measured from the spectra after being smoothed with a 3-pixel box. matching the resolution of the instrument.," These indices and the other spectral features described in this section of the paper were measured from the spectra after being smoothed with a 3-pixel box, matching the resolution of the instrument."479 A J star was for many vears defined as one for which the strength of the οςAGIGS band was at least half that of the 1077€A6122 band (Gordon1968)., A J star was for many years defined as one for which the strength of the $^{13}{\rmn C}^{12}{\rmn C}~\lambda6168$ band was at least half that of the $^{12}{\rmn C}^{12}{\rmn C}~\lambda6122$ band \cite{gordon68}.480".. ""Ehe definition in the revised. classification scheme for carbon stars (Ixecenan1993) is slightly cillerent in that there the j-index is based on the ratios of the bands οCA6168 to στοA6192. POCAGIO2 to 7070A6122 and PCNA6260. to 17CHNA6206."," The definition in the revised classification scheme for carbon stars \cite{keenan93} is slightly different in that there the j-index is based on the ratios of the bands $^{13}{\rmn C}^{12}{\rmn C}~\lambda6168$ to $^{12}{\rmn C}^{12}{\rmn C}~\lambda6192$, $^{13}{\rmn C}^{12}{\rmn C}~\lambda6102$ to $^{12}{\rmn C}^{12}{\rmn C}~\lambda6122$ and $^{13}{\rmn C}^{14}{\rmn N}~\lambda6260$ to $^{12}{\rmn C}^{14}{\rmn N}~\lambda6206$."481 The main dilliculty in determining the j-index of a carbon star. and indeed other spectral parameters. is that defining the continuum is not straightforward.," The main difficulty in determining the j-index of a carbon star, and indeed other spectral parameters, is that defining the continuum is not straightforward."482 The local continuum and pseudo-continuum are greatly dillerent in Group 6 stars for instance. as can be seen in Fig. 5..," The local continuum and pseudo-continuum are greatly different in Group 6 stars for instance, as can be seen in Fig. \ref{sample}."483 Clearly. the huge depression of the local continuum is not due to Bere so the local continuum. is more appropriate [or defining the j-incdex.," Clearly, the huge depression of the local continuum is not due to $^{13}{\rmn C}^{12}{\rmn C}$, so the local continuum is more appropriate for defining the j-index."484 Two measures are used in this paper to define the j-index., Two measures are used in this paper to define the j-index.485 The first is the ratio of the (0.22) bands LOICA6168 and. CECA6192 measured. [rom the loca continuum to the minimum (single pixel) of the band., The first is the ratio of the 2) bands $^{13}{\rmn C}^{12}{\rmn C}~\lambda6168$ and $^{12}{\rmn C}^{12}{\rmn C}~\lambda6192$ measured from the local continuum to the minimum (single pixel) of the band.486 The ratio of the equivalent widths (Wy) of the (4.00). 12CHN ΕΙΝ: : ⋜⋯∠⇂⋟≺↓∖∣⋡⋜⋯∠⇂⊳∖↓≻↓⋅∪∖⇁⊔⇂∢⋅≱∖∣⇂↥⋖⋅≱∖⋖⋅≼∙∩⊔∠⇂⊔↓∢⋅⋜↧⊳∖⊔↓⋅∢⊾⊳∖∖⊓⊐⊓⊔⋜⋯∠ ∖∖⊽, The ratio of the equivalent widths $_\lambda$ ) of the 0) $^{12}{\rmn C}^{14}{\rmn N}$ and $^{13}{\rmn C}^{14}{\rmn N}$ bands provides the second measure.487⊓⊐⋯⋟∖∖⊽∢⊾↓⋅⋖⋅∠⇂∢⊾⇂⋖⋅↓⋅↓↕↓↕↓↕⋖⋅∠⇂⇂⋅↓⋅∪⊔↓⇂↓↕∢⋅∩⋅⊔↓↓≻↓⋜⋯⊾∐⇂⊲↓⊔⋏∙≟↓≻↓⋅⋯∼∢⋅∠⊔⊔⋅⋖⋅ described in Section 3. using the mean J-star template.," $_{6260}$ and $_{6206}$ were determined from the template fitting procedure described in Section 3, using the mean J-star template."488 Fig., Fig.489 9 shows the ratio of €» band depths Dgox DDoao» plottec against the ratio Wiss WWGo»os., \ref{jindex} shows the ratio of $_2$ band depths $_{6168}$ $_{6192}$ plotted against the ratio $_{6260}$ $_{6206}$.490 Lhe two ratios are wel correlated. in fact better than similar ratios based on other continuum levels.," The two ratios are well correlated, in fact better than similar ratios based on other continuum levels."491 So a j-index was defined as the distance along the sequence as marked in the figure., So a j-index was defined as the distance along the sequence as marked in the figure.492 I0 was chosen to be similar to the MIN index (lxeenan.1993) which runs from 3.5 to 7 in à J star (Darnbaunmetal.1996)., It was chosen to be similar to the MK index \cite{keenan93} which runs from 3.5 to 7 in a J star \cite{barnbaum96}.493.. The stars with the lowest. j-indices have CFCA6168 bands slightly stronger than 0.5 times their οσοA6122 bands as is expected. from the older definition of the J star (Cordon 1968)., The stars with the lowest j-indices have $^{13}{\rmn C}^{12}{\rmn C}~\lambda6168$ bands slightly stronger than 0.5 times their $^{12}{\rmn C}^{12}{\rmn C}~\lambda6122$ bands as is expected from the older definition of the J star \cite{gordon68}.494. There is a slight divergence at high j-incdex levels between Group Land Group 5 stars which is probably due to cllliculties in defining the continuum levels for such different types of spectrum., There is a slight divergence at high j-index levels between Group 1 and Group 5 stars which is probably due to difficulties in defining the continuum levels for such different types of spectrum.495 Fig., Fig.496 LO is Fig., \ref{slopes_j} is Fig.497 4. redrawn with symbols representing the jindex as determined. from Fig. 9.., \ref{slopes} redrawn with symbols representing the j-index as determined from Fig. \ref{jindex}.498 Ht is clear. that these spectral parameters are controlled by the j-index. with zones of constant j-index roughly given by sectors defined by straight lines through a point near the lower left-hand corner of the plot. with the j-index increasing in the anti-clockwise direction.," It is clear that these spectral parameters are controlled by the j-index, with zones of constant j-index roughly given by sectors defined by straight lines through a point near the lower left-hand corner of the plot, with the j-index increasing in the anti-clockwise direction."499 As is to be expected. observational errors and probably real Huctuations in these parameters give rise to the considerable overlap between the dillerent svmbols.," As is to be expected, observational errors and probably real fluctuations in these parameters give rise to the considerable overlap between the different symbols."500 No discrimination is possible in the lower Ieft-hand corner where the Croup 1 stars are found., No discrimination is possible in the lower left-hand corner where the Group 1 stars are found.501 The carbon strength can be treated in a similar wav., The carbon strength can be treated in a similar way.502 For J stars. carbon needs to be measured from both isotopic bands rather than just one when the results would clearly be modified by the j-index.," For J stars, carbon needs to be measured from both isotopic bands rather than just one when the results would clearly be modified by the j-index."503 Εις. one measure of carbon strength. is the sum of the (0.22) CHCAGIGS and," Thus, one measure of carbon strength is the sum of the 2) $^{13}{\rmn C}^{12}{\rmn C}~\lambda6168$ and"504Ratios of densiües derived from transit parameters over those from J—A colors (or some other independent measure. such as asteroseismologv) are a useful tool lor the identification of transit exoplanels out of a much Iarger set of candidates.,"Ratios of densities derived from transit parameters over those from $J-K$ colors (or some other independent measure, such as asteroseismology) are a useful tool for the identification of transit exoplanets out of a much larger set of candidates."505 Even rudimentary density measures ((rapezoidal and ./—A densities) appear to identilv exoplanets effectively among the ColtoT candidates., Even rudimentary density measures (trapezoidal and $J-K$ densities) appear to identify exoplanets effectively among the CoRoT candidates.506 More precise density measures [rom detailed (ransil fitting and stellar spectra will be even more effective: these. however. require additional spectral observations.," More precise density measures from detailed transit fitting and stellar spectra will be even more effective; these, however, require additional spectral observations."507 Given data of sullicient quality. densities from asteroseismology might be even more effective. although at this lime the sample of svstems with transiting exoplanets and asteroseismic densities is too small to draw a definitive conclusion.," Given data of sufficient quality, densities from asteroseismology might be even more effective, although at this time the sample of systems with transiting exoplanets and asteroseismic densities is too small to draw a definitive conclusion."508 Significant eccentricities will impact the measured density ratio in the absense of any. knowledee of these orbital parameters: however. (hey will tend to increase the density. ratios of discovered transiting exoplanets. while most false positives have density ratios lower than (vpical planets.," Significant eccentricities will impact the measured density ratio in the absense of any knowledge of these orbital parameters; however, they will tend to increase the density ratios of discovered transiting exoplanets, while most false positives have density ratios lower than typical planets."509 It is important to remember (hat anv (ool can be misused: (he one describe in this paper is no exception. but it does represent an improvement on other techniques currently used to priovilize transit candidates using transit parameters.," It is important to remember that any tool can be misused; the one describe in this paper is no exception, but it does represent an improvement on other techniques currently used to prioritize transit candidates using transit parameters."510 Even a secure. density cut-offs as described in the previous section may cle-priorilize some (rue exoplanets due (o any number of causes: extrenie planet or star characteristics or otherwise inaccurately measured density ratios. [or example.," Even a 'secure' density cut-offs as described in the previous section may de-prioritize some true exoplanets due to any number of causes: extreme planet or star characteristics or otherwise inaccurately measured density ratios, for example."511 However. when used in conjunction with other techniques (ellipsoidal varlalions. presence of secondaries. ete.).," However, when used in conjunction with other techniques (ellipsoidal variations, presence of secondaries, etc.),"512 density ratios can help identify the candidates which are most Likely to be exoplanets and which are most likelv to be [alse positives. increasing the efficiency. of efforts to confirm or reject planet candidates.," density ratios can help identify the candidates which are most likely to be exoplanets and which are most likely to be false positives, increasing the efficiency of efforts to confirm or reject planet candidates."513This is rather surprising since the evolution of the 21-cm signal is stronger in this redshift interval than in the z—11.20 band.,This is rather surprising since the evolution of the 21-cm signal is stronger in this redshift interval than in the $z=11.20$ band.514" For the cube centered around redshift z—9.94 the neutral fraction and the rms change from 0.547 to 0.68 and 10 to 9.4 mK and the power spectrum is amplified by a factor of ~7 at k=0.1Mpc ! (see Table 1 and the last two left panels of Figure 4)), much more than what we see in the cube around z—11.20."," For the cube centered around redshift $z=9.94$ the neutral fraction and the rms change from $0.547$ to $0.68$ and $10$ to $9.4$ mK and the power spectrum is amplified by a factor of $\sim 7$ at $k=0.1 \rm{Mpc}^{-1}$ (see Table \ref{tab:table_L1} and the last two left panels of Figure \ref{fig:ps3de_f10}) ), much more than what we see in the cube around $z=11.20$."515 So we would expect a larger effect than what we see in Figure 4 at z—9.94., So we would expect a larger effect than what we see in Figure \ref{fig:ps3de_f10} at $z=9.94$.516 This trend continues and we see almost no effect for redshift z—9.31 where the neutral fraction and the rms change even more (0.325—0.547 and 9.4—10 mK) and the power spectrum is amplified by a factor of ~5 atk=0.1 Mpc, This trend continues and we see almost no effect for redshift $z=9.31$ where the neutral fraction and the rms change even more $0.325 \rightarrow 0.547$ and $9.4 \rightarrow 10$ mK) and the power spectrum is amplified by a factor of $\sim 5$ at $k=0.1$ $^{-1}$.517" At redshift z=8.76, instead of an enhancement we see suppression!. on all scales with differences up to 3096."," At redshift $z=8.76$, instead of an enhancement we see suppression on all scales with differences up to $30\%$."518 In the L3 simulation this suppression is up to 5096 at redshift z—8.76., In the L3 simulation this suppression is up to $50 \%$ at redshift $z=8.76$.519 All other features are quite similar in the L3 model (Figure 5)) even though the reionization process proceeds faster and the ionized regions are larger in this model., All other features are quite similar in the L3 model (Figure \ref{fig:ps3de_f25}) ) even though the reionization process proceeds faster and the ionized regions are larger in this model.520 Another way to describe the trend we see is that we find a cross-over mode keross—over below which power is enhanced and above which it is suppressed., Another way to describe the trend we see is that we find a cross-over mode $k_{\rm{cross-over}}$ below which power is enhanced and above which it is suppressed.521 The cross-over scales Keross—over shifts towards lower k as the reionization proceeds., The cross-over scales $k_{\rm{cross-over}}$ shifts towards lower $k$ as the reionization proceeds.522 At the end of reionization the cross-over mode is lower than the lowest mode we measure from the simulation box., At the end of reionization the cross-over mode is lower than the lowest mode we measure from the simulation box.523" Above we present results using the entire cubes i.e, for a LOS width corresponding to the size of our simulation volume."," Above we present results using the entire cubes i.e, for a LOS width corresponding to the size of our simulation volume."524" However, it is interesting to explore how the effect changes as one reduces the LOS width."," However, it is interesting to explore how the effect changes as one reduces the LOS width."525" Obviously in the limit of small widths, the light cone effect will disappear, so considering a range a widths allows us to study how it varies with width."," Obviously in the limit of small widths, the light cone effect will disappear, so considering a range a widths allows us to study how it varies with width."526 Here we consider sub-boxes of different LOS widths Az and calculate the quantity (A3p..—Apic)/A3pic for different k modes.," Here we consider sub-boxes of different LOS widths $\Delta z $ and calculate the quantity $(\Delta_{\rm 3Dcc}^2-\Delta_{\rm527 3Dlc}^2)/\Delta_{\rm 3Dlc}^2$ for different $k$ modes."528 Figure 6 shows (A3p..—ASpic)/ASpic as a function of LOS width (and Az) for different k modes at two central redshifts Zc=8.76 and 10.02 for the L3 simulation.," Figure \ref{fig:change-bw} shows $(\Delta_{\rm 3Dcc}^2-\Delta_{\rm529 3Dlc}^2)/\Delta_{\rm 3Dlc}^2$ as a function of LOS width (and $\Delta z $ ) for different $ k$ modes at two central redshifts $z_{\rm530 c}=8.76$ and $10.02$ for the L3 simulation."531" As expected, we see that the quantity (A3p..—Δβριο)/A2pi,decreases for smaller LOS width (and Az)."," As expected, we see that the quantity $(\Delta_{\rm 3Dcc}^2-\Delta_{\rm 3Dlc}^2)/\Delta_{\rm532 3Dlc}^2$decreases for smaller LOS width (and $\Delta z $ )."533" As discussed later in the subsection 4.3, we expect the quantity to increase quadratically with the LOS width."," As discussed later in the subsection 4.3, we expect the quantity to increase quadratically with the LOS width."534" However, due to the smaller number of modes available for the smaller Az, the results are too noisy to test this expectation, although they are roughly consistent with it."," However, due to the smaller number of modes available for the smaller $\Delta z$, the results are too noisy to test this expectation, although they are roughly consistent with it."535" We do not show results for the other two central redshifts of L3 and L1 simulation as the light cone effect is relatively smaller for these, but find similar results there."," We do not show results for the other two central redshifts of L3 and L1 simulation as the light cone effect is relatively smaller for these, but find similar results there."536" These results suggest that measurements of the light cone effect for different LOS widths can, in principle, be used to correct for the effect or at least find the sign of the effect."," These results suggest that measurements of the light cone effect for different LOS widths can, in principle, be used to correct for the effect or at least find the sign of the effect."537 The light cone effect introduces an anisotropy in the full 3D 21 cm power spectrum., The light cone effect introduces an anisotropy in the full 3D 21 cm power spectrum.538" For a fixed k-mode, the power spectrum will depend on the LOS component of k."," For a fixed $k$ -mode, the power spectrum will depend on $k_{\parallel}$, the LOS component of $k$."539" Peculiar velocities and the Alcock-Paczynskikj, effect are the other major sources of anisotropies in the 21 cm power spectrum.", Peculiar velocities and the Alcock-Paczynski effect are the other major sources of anisotropies in the 21 cm power spectrum.540 In order to understand the anisotropic power spectrum and to separate the physics from astrophysics (Barkana&Loeb2005) each effect should be studied in detail., In order to understand the anisotropic power spectrum and to separate the physics from astrophysics \citep{barkana05} each effect should be studied in detail.541" Though the first generation of low frequency radio telescopes (i.g, LOFAR, GMRT, MWA ) are unlikely to able to measure the anisotropies in the 21 cm power spectrum, this will be the ultimate goal of such measurements."," Though the first generation of low frequency radio telescopes (i.g, LOFAR, GMRT, MWA ) are unlikely to able to measure the anisotropies in the 21 cm power spectrum, this will be the ultimate goal of such measurements."542 Fig., Fig.543" 7 plots the ratio A25,/Δβρες as a function of ui? for different k-modes for two central redshifts z.=8.76 (left panel) and 10.02 (right panel) for L3 simulations."," \ref{fig:ps-aniso} plots the ratio $\Delta^2_{\rm544 3Dlc}/\Delta^2_{\rm 3Dcc}$ as a function of $\mu^2$ for different $k$ -modes for two central redshifts $z_{\rm c}=8.76$ (left panel) and $10.02$ (right panel) for L3 simulations."545 Here µ.=ky/k., Here $\mu=k_{\parallel}/k$.546 In the left panel (z.= 8.76) we see that the ratio A3p)./A3pec increases from ~0.7 (at μὲ= 0.1) to 1.1 (at μὲ= 0.9) for k=0.16Mpc!.," In the left panel $z_{\rm c}=8.76$ ) we see that the ratio $\Delta^2_{\rm 3Dlc}/\Delta^2_{\rm 3Dcc}$ increases from $\sim 0.7 $ (at $\mu^2=0.1$ ) to $1.1$ (at $\mu^2=0.9$ ) for $k=0.16 \, {\rm Mpc^{-1}}$."547" For k=0.3Mpc™!, the ratio increases from 0.8 to 1 for the same μ΄ range."," For $k=0.3 \, {\rm Mpc^{-1}}$, the ratio increases from $\sim 0.8$ to $1$ for the same $\mu^2$ range."548 For higher k-modes the degree of anisotropy decreases and the power spectrum is becoming more isotropic., For higher $k$ -modes the degree of anisotropy decreases and the power spectrum is becoming more isotropic.549 We do not see any significant anisotropies for the central redshift z.=10.02 (right panel) where the neutral fraction zie=0.86., We do not see any significant anisotropies for the central redshift $z_{\rm c}=10.02$ (right panel) where the neutral fraction $x_{\rm HIc}=0.86$.550 The other redshifts of the L3 simulation also do not show significant anisotropies and the results for the L1 simulation are similar to L3., The other redshifts of the L3 simulation also do not show significant anisotropies and the results for the L1 simulation are similar to L3.551 We do not try to quantify the anisotropies further as we see the curves are not very smooth due to the small number of modes at large k., We do not try to quantify the anisotropies further as we see the curves are not very smooth due to the small number of modes at large $k$ .552 Our results are sample variance limited and should be considered as qualitative rather than quantitative., Our results are sample variance limited and should be considered as qualitative rather than quantitative.553 Larger simulation volumes are needed to quantify the anisotropies more precisely., Larger simulation volumes are needed to quantify the anisotropies more precisely.554 Barkana&Loeb(2006) (fig., \citet{barkana06} (fig.555 2) reported significant anisotropies, 2) reported significant anisotropies556ooperalions teams [or their rapid ancl effective response to this target of opportunity.,operations teams for their rapid and effective response to this target of opportunity.557 We would also like to thank G. Tavlor. C. Carilli. T. Soifer. and J. Condon for donations of VLA lime.," We would also like to thank G. Taylor, C. Carilli, T. Soifer, and J. Condon for donations of VLA time."558 DLIx is supported by the Fannie John Hertz Foundation., DLK is supported by the Fannie John Hertz Foundation.559Beyond generating tables. there is further possibilities for introducing uncertainties while applying the data.,"Beyond generating tables, there is further possibilities for introducing uncertainties while applying the data."560 First. there is the technical problem of interpolating the tabulatec values.," First, there is the technical problem of interpolating the tabulated values."561 Compared to previously available data. the situation is worse because there are two more dimensions along which to interpolate. that 1s the varying amount of carbon and nitrogen.," Compared to previously available data, the situation is worse because there are two more dimensions along which to interpolate, that is the varying amount of carbon and nitrogen."562 However. on the basis of the above discussion. it is unlikely that too sophisticated interpolation algorithms produce improved accuracy.," However, on the basis of the above discussion, it is unlikely that too sophisticated interpolation algorithms produce improved accuracy."563 This 1s. however. a problem that can in principle be solved by increasing the amount of computer power.," This is, however, a problem that can in principle be solved by increasing the amount of computer power."564 Far more worrying and the largest error source of all is potential misapplication of the data., Far more worrying and the largest error source of all is potential misapplication of the data.565 Strictly speaking. the scope of the tables containing Rosseland mean opacity coefficients are regions where the diffusion approximation for the radiative transfer 1s fulfilled.," Strictly speaking, the scope of the tables containing Rosseland mean opacity coefficients are regions where the diffusion approximation for the radiative transfer is fulfilled."566 In terms of the optical depth. this means r>| for all wavelengths.," In terms of the optical depth, this means $\tau\gg1$ for all wavelengths."567 One of the main applications of our data will be the outermost parts of an AGB star evolution model., One of the main applications of our data will be the outermost parts of an AGB star evolution model.568 The outer boundary condition is usually set somewhere in the atmosphere (logZx 3.6). where by definition tr<|.," The outer boundary condition is usually set somewhere in the atmosphere $\log T\leq3.6$ ), where by definition $\tau\leq1$."569 In some situations. the Rosseland mean might still be a good approximation for evaluating the radiative energy transport.," In some situations, the Rosseland mean might still be a good approximation for evaluating the radiative energy transport."570 However. in general it is necessary to use a non-grey radiative transfer method because. due to the molecular absorbers. the spectral energy distribution is strongly wavelength-dependent.," However, in general it is necessary to use a non-grey radiative transfer method because, due to the molecular absorbers, the spectral energy distribution is strongly wavelength-dependent."571 We refer to the work of Hófneretal.(2003).. who demonstrated the shortcomings of a grey treatment of the radiative transfer for dynamical model atmospheres.," We refer to the work of \citet{2003A&A...399..589H}, who demonstrated the shortcomings of a grey treatment of the radiative transfer for dynamical model atmospheres."572 Harris&Lynas-Grey(2007) investigated the effect of non-grey surface boundary conditions on the evolution of low mass stars and reported noticeable changes to RGB evolution tracks., \citet{2007AIPC..948..195H} investigated the effect of non-grey surface boundary conditions on the evolution of low mass stars and reported noticeable changes to RGB evolution tracks.573 We thus want to emphasise that our mean opacity tables are meant to provide an interim solution until modelling of non-grey radiative transfer in stellar evolution calculations becomes feasible., We thus want to emphasise that our mean opacity tables are meant to provide an interim solution until modelling of non-grey radiative transfer in stellar evolution calculations becomes feasible.574 We have presented a grid of low temperature Rosseland mean opacity tables that take into account variations in the single element abundances of carbon and nitrogen., We have presented a grid of low temperature Rosseland mean opacity tables that take into account variations in the single element abundances of carbon and nitrogen.575 By gradually enhancing the carbon content of a metal mixture. the molecular contribution to opacity changes significantly due to the altered chemistry.," By gradually enhancing the carbon content of a metal mixture, the molecular contribution to opacity changes significantly due to the altered chemistry."576 Already within a certain regime ee. oxygen-rich or carbon-rich). the relative amount of carbon to oxygen has pronounced effects on ag.," Already within a certain regime e. oxygen-rich or carbon-rich), the relative amount of carbon to oxygen has pronounced effects on $\kappa_\mathrm{R}$."577 More distinctive. however. is the comparison between oxygen-rich and carbon-rich regimes.," More distinctive, however, is the comparison between oxygen-rich and carbon-rich regimes."578 Different molecules serve as opacity sources in either case and thus result in a qualitatively and quantitatively different Rosseland mean opacity as a function of temperature and density., Different molecules serve as opacity sources in either case and thus result in a qualitatively and quantitatively different Rosseland mean opacity as a function of temperature and density.579 Changes in the nitrogen abundance also alter the opacity coefficients via certain nitrogen-bearing molecules., Changes in the nitrogen abundance also alter the opacity coefficients via certain nitrogen-bearing molecules.580 The tables are designed such that an incorporation into existing codes that utilised AF94 or FOS data should be straightforward., The tables are designed such that an incorporation into existing codes that utilised AF94 or F05 data should be straightforward.581 Our data cover a wide metallicity range. and the overabundances of carbon and nitrogen are adjusted in each case.," Our data cover a wide metallicity range, and the overabundances of carbon and nitrogen are adjusted in each case."582 We are confident that with these data we provide a tool to simulate the final phases in the evolution of low or intermediate mass stars I more detail., We are confident that with these data we provide a tool to simulate the final phases in the evolution of low or intermediate mass stars in more detail.583 Our data include the effects of the ongoing nucleosynthesis and mixing events in AGB stars in terms of the opacity., Our data include the effects of the ongoing nucleosynthesis and mixing events in AGB stars in terms of the opacity.584 As shown im previous papers (e.g.Cristalloetal.2007).. the incorporation of our tables into stellar evolution codes alters the physical properties of the stellar models.," As shown in previous papers \citep[e.\,g.][]{2007ApJ...667..489C}, the incorporation of our tables into stellar evolution codes alters the physical properties of the stellar models."585 Once the star becomes carbon-rich. molecules form that are more opaque than those in an oxygen-rich regime.," Once the star becomes carbon-rich, molecules form that are more opaque than those in an oxygen-rich regime."586 This in turn results in a steeper temperature gradient., This in turn results in a steeper temperature gradient.587 A consequence is. for instance. a decrease in the effective temperature in stellar evolution models.," A consequence is, for instance, a decrease in the effective temperature in stellar evolution models."588 The stellar radius increases. and the average mass-loss rate increases and erodes the envelope mass at a faster rate.," The stellar radius increases, and the average mass-loss rate increases and erodes the envelope mass at a faster rate."589 Stranieroetal.(2003) showed that a change in the envelope mass (as well as a change in the core mass) affect fundamental properties of AGB stars. gg. the strength of the thermal pulses and the total amount of the mass dredged up.," \citet{2003PASA...20..389S} showed that a change in the envelope mass (as well as a change in the core mass) affect fundamental properties of AGB stars, g. the strength of the thermal pulses and the total amount of the mass dredged up."590 It will also be interesting to see how different mass-loss prescriptions interact with the newly calculated opacity coefficients. since these issues are physically closely coupled.," It will also be interesting to see how different mass-loss prescriptions interact with the newly calculated opacity coefficients, since these issues are physically closely coupled."591 In the future. we plan to extend our tables to contain data about the enrichment in alpha elements.," In the future, we plan to extend our tables to contain data about the enrichment in alpha elements."592 We must emphasise. however. that the data provided in the course of the current and future work must be seen as a transitional solution to the treatment of molecular opacity in AGB star envelopes and atmospheres.," We must emphasise, however, that the data provided in the course of the current and future work must be seen as a transitional solution to the treatment of molecular opacity in AGB star envelopes and atmospheres."593" Due to the band structure of molecular absorption, mean opacities will yield inaccurate results."," Due to the band structure of molecular absorption, mean opacities will yield inaccurate results."594 The past results from static and dynamical model atmosphere calculations demonstrate the importance of a frequency-dependent radiative transfer., The past results from static and dynamical model atmosphere calculations demonstrate the importance of a frequency-dependent radiative transfer.595 Our data promise to bridge the gap until these methods are employed in stellar evolution models., Our data promise to bridge the gap until these methods are employed in stellar evolution models.596 Finally. we emphasise that for forthcoming extensions of this database. 1t would be desirable to obtain extensive response from the community.," Finally, we emphasise that for forthcoming extensions of this database, it would be desirable to obtain extensive response from the community."597 Comments and criticisms that can lead to an improvement in the quality of the data are highly welcome., Comments and criticisms that can lead to an improvement in the quality of the data are highly welcome.598including particle productions. such as pions. are modelled via Monte Carlo sampling using either free-space experimental data or calculated in-mecdium cross sections for the elementary hadron-hadron scatterings (Bertsch&DasGupta1988).,"including particle productions, such as pions, are modelled via Monte Carlo sampling using either free-space experimental data or calculated in-medium cross sections for the elementary hadron-hadron scatterings \citep{Bertsch}."599. Information about the EOS is obtained [rom the underling mean-field potential U which is an input to the transport model., Information about the EOS is obtained from the underlying mean-field potential U which is an input to the transport model.600 By comparing experimental data on some carefully selected observables with transport model predictions using different mean-field) potentials corresponding to various EOSs. one can then constrain the corresponding EOS.," By comparing experimental data on some carefully selected observables with transport model predictions using different mean-field potentials corresponding to various EOSs, one can then constrain the corresponding EOS."601 The specific constrains on the density dependence ol the nuclear svmumetry energy that we are using in this work were obtained by analvzing (he isospin diffusion data (Tsaneetal.2004) within the IDUUOJA version of an isospin and momentum dependenttransport model (Liοἱal.2004)., The specific constrains on the density dependence of the nuclear symmetry energy that we are using in this work were obtained by analyzing the isospin diffusion data \citep{Tsang:2004} within the IBUU04 version of an isospin and momentum dependenttransport model \citep{IBUU04}.602. In (his model. an isospin and momentiunm-dependent interaction (ALDI) (Dasetal.2003) is used.," In this model, an isospin and momentum-dependent interaction (MDI) \citep{Das:2002fr} is used."603 With this interaction. the potential energy density V(p.T.9) at total density. p. temperature 7 and isospin asvimeltry 0 ds In the mean field approximation. Eq. (3))," With this interaction, the potential energy density $V(\rho604,T,\delta )$ at total density $\rho $, temperature $T$ and isospin asymmetry $\delta$ is In the mean field approximation, Eq. \ref{MDIV}) )"605 leads to the following single particle potential for a nucleon with momentum p and isospin 7 where 7=1/2 (—1/2) for neutrons (protons). e. αλ Aric). D. ον ον uo. and A are all parameters given in Ref. (Dasetal.2003)..," leads to the following single particle potential for a nucleon with momentum $\vec{p}$ and isospin $%606\tau where $\tau =1/2$ $-1/2$ ) for neutrons (protons), $x$, $A_{u}(x)$, $A_{\ell }(x)$, $B$ , $C_{\tau ,\tau }$ $C_{\tau ,-\tau607}$, $\sigma $, and $\Lambda $ are all parameters given in Ref. \citep{Das:2002fr}."608 The last (wo terms in Eq. (4)), The last two terms in Eq. \ref{MDIU}) )609" contain ihe momentum dependence of (he single-particle potential. including that of the svuumetry potential if one allows for clilferent interaction strength parameters C,, and C, for a nucleon of isospin 7 interacting. respectively. with unlike and like nucleons in (he background fields."," contain the momentum dependence of the single-particle potential, including that of the symmetry potential if one allows for different interaction strength parameters $C_{\tau ,-\tau }$ and $C_{\tau ,\tau }$ for a nucleon of isospin $\tau $ interacting, respectively, with unlike and like nucleons in the background fields."610" It is worth mentioning (hat (he nucleon isoscalar potential estimated from C;&U,)/2e agrees. with the prediction of variational many-body ealeulations for symmetric nuclear matter (Wiringa1983). in a broad density and momentum range (Lietal.2004).", It is worth mentioning that the nucleon isoscalar potential estimated from $U_{isoscalar}\approx (U_{n}+U_{p})/2$ agrees with the prediction of variational many-body calculations for symmetric nuclear matter \citep{wiringa} in a broad density and momentum range \citep{IBUU04}.611. Moreover. the EOS of sviimetric nuclear matter for this interaction is consistent. with that extracted Irom (he available data on collective flow. aud particle production in relativistic heavy-ion collisions up tofive times the normal nuclear matter(Danielewicz.Lacey.&Lynch 2008).," Moreover, the EOS of symmetric nuclear matter for this interaction is consistent with that extracted from the available data on collective flow and particle production in relativistic heavy-ion collisions up tofive times the normal nuclear matter\citep{Danielewicz:2002pu,KLW2}. ."612. On the other hand. the corresponding isovector (symmetry)," On the other hand, the corresponding isovector (symmetry)"613"the merging event, and this would have an important effect on the possible X-ray emissions from such systems.","the merging event, and this would have an important effect on the possible X-ray emissions from such systems."614 For the above-mentioned reasons the question of a SD vs. DD progenitor cannot be decided based solely on the X-ray brightness (or lack hereof) of a type Ia SN progenitor., For the above-mentioned reasons the question of a SD vs. DD progenitor cannot be decided based solely on the X-ray brightness (or lack hereof) of a type Ia SN progenitor.615" However, a direct detection of X-ray emissions from a progenitor would still be interesting, and would provide much needed observational evidence for the progenitors of type Ia SNe with which to compare theoretical work, something that is sorely lacking at the moment."," However, a direct detection of X-ray emissions from a progenitor would still be interesting, and would provide much needed observational evidence for the progenitors of type Ia SNe with which to compare theoretical work, something that is sorely lacking at the moment."616 We have examined archival pre-explosion images corresponding to the position of ten SNe Ia to determine upper limits to the bolometric luminosities of the progenitors., We have examined archival pre-explosion images corresponding to the position of ten SNe Ia to determine upper limits to the bolometric luminosities of the progenitors.617" Disregarding the ambigious case of SN2007on, our study comprises a complete list of nearby SNe that have pre-explosion images inChandra.."," Disregarding the ambigious case of SN2007on, our study comprises a complete list of nearby SNe that have pre-explosion images in."618 We compared this sample with known SSSs in the Milky Way and Magellanic Clouds., We compared this sample with known SSSs in the Milky Way and Magellanic Clouds.619" While most of the luminosities of our sample SNe are too loosely constrained, two SNe (SN2007sr and SN2011fe) probe the luminosity space of known SSSs."," While most of the luminosities of our sample SNe are too loosely constrained, two SNe (SN2007sr and SN2011fe) probe the luminosity space of known SSSs."620" The results indicate that the progenitors of these SNe were not bright SSSs shortly before they exploded as SNe Ia. However, our upper limits are not constraining enough to rule out less-bright super-soft X-ray progenitors."," The results indicate that the progenitors of these SNe were not bright SSSs shortly before they exploded as SNe Ia. However, our upper limits are not constraining enough to rule out less-bright super-soft X-ray progenitors."621 The theoretical picture concerning the super-soft X-ray characteristics of SN Ia progenitors is less than clear., The theoretical picture concerning the super-soft X-ray characteristics of SN Ia progenitors is less than clear.622" A non-detection does not rule out a SD progenitor, but neither does a positive detection necessarily implicate a SD progenitor or rule out a DD progenitor."," A non-detection does not rule out a SD progenitor, but neither does a positive detection necessarily implicate a SD progenitor or rule out a DD progenitor."623" Regardless, the archival search method of the archive is highly useful in putting much-needed observational constraints on the progenitors, and is a powerful complement to statistical studies of the characteristics of progenitor populations."," Regardless, the archival search method of the archive is highly useful in putting much-needed observational constraints on the progenitors, and is a powerful complement to statistical studies of the characteristics of progenitor populations."624 The method will become increasingly useful as the sky coverage grows., The method will become increasingly useful as the sky coverage grows.625" As SN2011fe shows, if a SN Ia explodes in a nearby galaxy, the chances that several pre-explosion images of the position exist are good, hence affording stringent upper limits to be calculated, or, in the case of an X-ray bright progenitor, a direct detection to be made."," As SN2011fe shows, if a SN Ia explodes in a nearby galaxy, the chances that several pre-explosion images of the position exist are good, hence affording stringent upper limits to be calculated, or, in the case of an X-ray bright progenitor, a direct detection to be made."626 The authors are grateful to the referee Martin Henze for carefully reading our first draft and providing many useful comments and suggestions., The authors are grateful to the referee Martin Henze for carefully reading our first draft and providing many useful comments and suggestions.627 This research made use of data obtained from the Data Archive and the CIAO 4.3 software provided by the X-ray Center., This research made use of data obtained from the Data Archive and the CIAO 4.3 software provided by the X-ray Center.628 We also acknowledge the IAU Central Bureau of Astronomical Telegrams for providing their list of SNe., We also acknowledge the IAU Central Bureau of Astronomical Telegrams for providing their list of SNe.629 This research is supported by NWO Vidi grant 016.093.305., This research is supported by NWO Vidi grant 016.093.305.630" Additionally, we acknowledge Gijs Roelofs for help with this project in its early stages."," Additionally, we acknowledge Gijs Roelofs for help with this project in its early stages."631"We caleulate. the eusenible. average of the squared difference between phasesy; of the nolisc-added realization and the initial one. W,,,: The function Ari) from Eq. (18))","We calculate the ensemble average of the squared difference between phases$\Psi^M_{lm}$ of the noise-added realization and the initial one, $\Psi_{lm}$: The function $\Delta^2(lm)$ from Eq. \ref{eq:squareddifference}) )"632". is. considered separately for different values of the variance of the controlled noise: o;2 iu: the rauge from+ oj,2«ox. up to 1ο level oft pixel: noise: σῃ:2D oS."," is considered separately for different values of the variance of the controlled noise $\sigma_W^2$ in the range from $\sigma_W^2\ll \sigma_N^2$, up to the level of pixel noise $\sigma_W^2\simeq\sigma_N^2$ ."633" We- willH show that the .unctionH τη)2 reflects al asviuuetrie peculiarities of ic juitial signal s,.", We will show that the function $\Delta^2(lm)$ reflects all asymmetric peculiarities of the initial signal $s_p$.634 The results of such a kind of pliase nalvsis are tested nuuercallv aud are presented iu the jext section., The results of such a kind of phase analysis are tested numerically and are presented in the next section.635 Tere we describe the analytical approach to 1e analysis of the phase mixing effect to demonstrate how it is possible to reconstruct the antenma beam shape frou 16 plase distributions in (7717 )-plauc., Here we describe the analytical approach to the analysis of the phase mixing effect to demonstrate how it is possible to reconstruct the antenna beam shape from the phase distributions in $(lm)$ -plane.636 For the E signal the definition ofthe combined pliases y; for each (0) που is simular to Eq. (13)):, For the $s^W_p$ signal the definition of the combined phases $\Psi^{M}_{lm}$ for each $(lm)$ mode is similar to Eq. \ref{eq:tangentequation}) ):637" where 55, is the multipole expansion of the combined sieual(CMD DEAM | PINEL NOISE) at the mode (lin), W,, the correspouding phase. Wy, the controlled noise expansion. and qi its phase."," where $S_{lm}$ is the multipole expansion of the combined signal(CMB $\otimes$BEAM + PIXEL NOISE) at the mode $(lm)$ , $\Psi_{lm}$ the corresponding phase, $W_{lm}$ the controlled noise expansion, and $\Phi^W_{lm}$ its phase."638 The analytical expression for the function A?(ln) cau bo written in the following wav where andl Theinteeral in Eq. (20)), The analytical expression for the function $\Delta^2(lm)$ can be written in the following way where and Theintegral in Eq. \ref{eq:Delta4}) )639" has been tabulated as a function of two variables W;,, aud p aud the result is preseuted in Fig. 2..", has been tabulated as a function of two variables $\Psi_{lm}$ and $\rho$ and the result is presented in Fig. \ref{tabulate}. .640 We will use this tabulation for the munerical experiment m the next section., We will use this tabulation for the numerical experiment in the next section.641 Iu this section we will obtain simple analytical asviuptoties of Eq. (15)., In this section we will obtain simple analytical asymptotics of Eq. \ref{eq:squareddifference}) ).642 From Eq. (203) , From Eq. \ref{eq:Delta4}) )643"one can fud the differeuce Let us determine. the meansquared value AZ,2Um) of the difference between tany; and tanην using Eq. (23))", one can find the difference Let us determine the mean–squared value $\Delta^2_{\tan}(lm)$ of the difference between $\tan \Psi^{M}_{lm}$ and $\tan\Psi_{lm}$ using Eq. \ref{eq:tangentdifference}) )644" One finds that A?(ia)zc—ATQcostViu if Λη)&l ancl after inteerationC» we obtain where oj,=(1Vlir) Yan and Iu the asviuptotic [μες1 we have a;,,=5danKA and from Eq. (21))"," One finds that $\Delta^2_{\tan}(lm) \simeq \Delta^2(lm) /645\cos^4\Psi_{lm}$ if $\Delta^2(lm) \ll 1$ and after integration we obtain where $\alpha_{lm}=(1-\sqrt{1-\beta_{lm}^2})/\beta_{lm}$ , and In the asymptotic $|\beta_{lm}| \ll 1$ we have $\alpha_{lm}=\frac{1}{2}\beta_{lm}\ll 1$ and from Eq. \ref{eq:meansquaredtangent}) )"646 and Eq. (25)), and Eq. \ref{eq:meansqtangentsol}) )647 we ect For our approximation we cau neglect the second tenu in the brackets of Eq. (27)), we get For our approximation we can neglect the second term in the brackets of Eq. \ref{eq:approxmeansquared}) )648 and Properties of ΤΠum1) are the same for any values of ∣⋖⋜⋯≼↧∣⊔⋝∙↕⋟↥, and Properties of ${\langle|W_{lm}|^2\rangle}$ are the same for any values of $l$ (and $m$ ).649"⋅≺∏⋉∖↥⋅↑↕↸∖↴∖↴∪↕⋟↕⊇Sy]?m"" were discussed∙ in| the previous⋅ section⋅ when we discussed⋅ At2 (77).", Properties of$1/2|S_{lm}|^2$ were discussed in the previous section when we discussed $\Delta^2_s(lm)$ .650 It is. obvious. that qualitatively thebehaviors of the function ΔΙ] ave the same as A200)., It is obvious that qualitatively thebehaviors of the function $\Delta^2(lm)$ are the same as $\Delta^2_s(lm)$ .651" Butthere is oue principal difference between the qualitative aud the fullcorrect description of the asviuptotie |S5,|?.> 0.", Butthere is one principal difference between the qualitative and the fullcorrect description of the asymptotic $|S_{lm}|^2\rightarrow 0$ .652 Namely. if [Si]?»0 then Wanοc do audthe asviuptotic Eq. (27))," Namely, if $|S_{lm}|^2\rightarrow 0$ then ${\langle|W_{lm}|^2\rangle}/|S_{lm}|^2 \gg 1$ , andthe asymptotic Eq. \ref{eq:approxmeansquared}) )"653 is, is654"argue. ""most. if not all. of this excess is due to the imperfect knowledge of the PSF for the back-converted gamnma-ravs.""","argue, “most, if not all, of this excess is due to the imperfect knowledge of the PSF for the back-converted gamma-rays.”"655 This argument is based on the observation that the extent of the Crab pulsar is the same as that of AGN. and the excess is different between front and back-converted photons.," This argument is based on the observation that the extent of the Crab pulsar is the same as that of AGN, and the excess is different between front and back-converted photons."656 While we agree wilh Neronovetal.(2010) that it is good to perform other independent tests. we shall show (hat their arguments fail to exclude the physical halos and overturn (he statistical significance of redshift aid spectrum tests discussed above.," While we agree with \citet{Neronov2010b} that it is good to perform other independent tests, we shall show that their arguments fail to exclude the physical halos and overturn the statistical significance of redshift and spectrum tests discussed above."657 To this eund. we have performed an alternative analvsis. using (he observed. Crab profile as a calibrated. PSF template.," To this end, we have performed an alternative analysis, using the observed Crab profile as a calibrated PSF template."658 This confirms our initial conclusion and demonstrates (hat the halos are indeed physical. at 3.50 level.," This confirms our initial conclusion and demonstrates that the halos are indeed physical, at $3.5\sigma$ level."659 For the analvsis. we mainly focus on the 310 GeV band. because the data have more statistical power than in 10100 GeV. as well as the pre-lanuch PSF is better calibrated at lower energies (Burnett.Kerr.&Roth 2009)..," For the analysis, we mainly focus on the 3–10 GeV band, because the data have more statistical power than in 10–100 GeV, as well as the pre-launch PSF is better calibrated at lower energies \citep*{Burnett2009}. ."660 In Fig. 6..," In Fig. \ref{fig:crab},"661 we show surface brightness proliles of our nearby and distant samples of AGN. where one can see clear difference between (the (wo populations of AGN.," we show surface brightness profiles of our nearby and distant samples of AGN, where one can see clear difference between the two populations of AGN."662 In the same figure. we also plot the profile of which appears to be more consistent with the distant AGN than the nearby set.," In the same figure, we also plot the profile of which appears to be more consistent with the distant AGN than the nearby set."663 The backgrounds have been subtracted [rom the sources: μον were estimated based on the large angular regions. where the contributions from both the point sources and halos are expected to be small.," The backgrounds have been subtracted from the sources; they were estimated based on the large angular regions, where the contributions from both the point sources and halos are expected to be small."664 We note that the excess of AGN over Crab seen in Fig., We note that the excess of AGN over Crab seen in Fig.665 4 was not found by Neronovetal.(2010).. who analvzed the data in the 10.100 GeV band. which. as mentioned above. lacks statistical power in comparison with the 310 GeV band used here.," 4 was not found by \citet{Neronov2010b}, who analyzed the data in the 10–100 GeV band, which, as mentioned above, lacks statistical power in comparison with the 3–10 GeV band used here."666 To proceed with a «quantitative analvsis. we use (his Crab prolile as a PSF model in {his energy range. and regard Crab statistical errors as svstematic uncertainties of PSF.," To proceed with a quantitative analysis, we use this Crab profile as a PSF model in this energy range, and regard Crab statistical errors as systematic uncertainties of PSF."667 For example. in angular bin 67=0.225 0.27 deg?. Feri-LAT received 22 photons from Crab. and the background is estimated to be 1.9.," For example, in angular bin $\theta^2 = 0.225$ $0.27$ $^2$, -LAT received 22 photons from Crab, and the background is estimated to be 1.9."668 This is interpreted as systematic uncertainty of PSF in this particular bin., This is interpreted as systematic uncertainty of PSF in this particular bin.669 This method is independent of our previous analysis ancl is free of any uncertainties related to pre-launch PSF calibration., This method is independent of our previous analysis and is free of any uncertainties related to pre-launch PSF calibration.670 A possible source of additional svstematie uncertainties is an energv dependence of PSF., A possible source of additional systematic uncertainties is an energy dependence of PSF.671 In general. gamma-ray spectra are different. between ACN and pulsars. and so are expected PSF sizes.," In general, gamma-ray spectra are different between AGN and pulsars, and so are expected PSF sizes."672" However. the detected. spectra of both stacked AGN and Crab are well approximated by a power law with similar indices: dN/dE,xE77 for nearby AGN (2< 0.5). and xE,7! for Crab. where E, is the gamma-ray energy."," However, the detected spectra of both stacked AGN and Crab are well approximated by a power law with similar indices; $dN/dE_\gamma673\propto E_\gamma^{-2.2}$ for nearby AGN $z < 0.5$ ), and $\propto674E_\gamma^{-2.4}$ for Crab, where $E_\gamma$ is the gamma-ray energy."675 To probe the spectrum dependence of PSF even further. we compare the brightness profiles ofsimulated maps of nearby/hard and distant/soft AGN.," To probe the spectrum dependence of PSF even further, we compare the brightness profiles of maps of nearby/hard and distant/soft AGN."676 Both profiles look very similar. while the profile of hard AGN is slightly less extended.," Both profiles look very similar, while the profile of hard AGN is slightly less extended."677 In angular bin 6?=0.225 0.27 deg?. theseAGN proliles differ," In angular bin $\theta^2 = 0.225$ $0.27$ $^2$, theseAGN profiles differ"678"greater than 13 AL;,,,) or higher. with final orbital radii as large as 800 AU.","greater than 13 $M_{Jup}$ ) or higher, with final orbital radii as large as 800 AU."679 Their results are in general agreement wilh the present results. though the major differences in (he initial disk assumptions preclude a detailed comparison.," Their results are in general agreement with the present results, though the major differences in the initial disk assumptions preclude a detailed comparison."680 Bolev et al. (, Boley et al. (6812010) used an SPII code to demonstrate multiple Iragment formation at —istances [rom ~ 50 AU to — LOO AU from a 0.3 AL. star in a disk with a radius of 510 AU id à mass of 0.19 AZ...,2010) used an SPH code to demonstrate multiple fragment formation at distances from $\sim$ 50 AU to $\sim$ 100 AU from a 0.3 $M_\odot$ star in a disk with a radius of 510 AU and a mass of 0.19 $M_\odot$.682" Given the large disk mass to stellar mass ratio of 0.63. the formation of several chunips with initial masses of 3.3 Mj, and 1.7 Mj, is basically consistent with the present results for moclel 0.5."," Given the large disk mass to stellar mass ratio of 0.63, the formation of several clumps with initial masses of 3.3 $M_{Jup}$ and 1.7 $M_{Jup}$ is basically consistent with the present results for model 0.5."683 The result that champ formation depends on protostellar mass. wilh models 0.1 and 0.5 forming fewer clumps than models 1.0. 1.5. ancl 2.0. is consistent will the resulis presented by Boss (200Gb). who studied the evolution of disks with outer radii of 20 AU around protostars with masses of 0.1 M. and 0.5 M..," The result that clump formation depends on protostellar mass, with models 0.1 and 0.5 forming fewer clumps than models 1.0, 1.5, and 2.0, is consistent with the results presented by Boss (2006b), who studied the evolution of disks with outer radii of 20 AU around protostars with masses of 0.1 $M_\odot$ and 0.5 $M_\odot$."684 Boss (2006b) found that. chimps could form for both protostar masses. but that while several clumps formed for the 0.5 M. protostar. typically onlv a single chump formed for the 0.1 AL. protostar. similar to (he results in models 0.1 and 0.5 for much larger radii disks.," Boss (2006b) found that clumps could form for both protostar masses, but that while several clumps formed for the 0.5 $M_\odot$ protostar, typically only a single clump formed for the 0.1 $M_\odot$ protostar, similar to the results in models 0.1 and 0.5 for much larger radii disks."685 Thus. while not zero. (he chances for giant planet. formation bv disk instability appear to decrease with stellar mass in the range of 0.5 M. to 0.1 ALL.," Thus, while not zero, the chances for giant planet formation by disk instability appear to decrease with stellar mass in the range of 0.5 $M_\odot$ to 0.1 $M_\odot$."686 A simple explanation for this outcome may be that given the assumption of disk masses (hat scale with protostellar masses. (he number of Jupiter-1nass protoplanets (hat could form by disk instability increases with (he number of Jupiter-masses of disk eas available for (heir formation: e.g.. the disk mass for model 2.0 is taken to be 7.5 times that of model 0.1.," A simple explanation for this outcome may be that given the assumption of disk masses that scale with protostellar masses, the number of Jupiter-mass protoplanets that could form by disk instability increases with the number of Jupiter-masses of disk gas available for their formation: e.g., the disk mass for model 2.0 is taken to be 7.5 times that of model 0.1."687 Nero Bjorkman (2009) used analvtieal models to study. lragmentation in suitably massive protoplanetary disks. finding that (heir estimated cooling times were over an order of magnitude shorter than (hose estimates previously by Ralikov (2005). a result consistent with that of Boss (2005).," Nero Bjorkman (2009) used analytical models to study fragmentation in suitably massive protoplanetary disks, finding that their estimated cooling times were over an order of magnitude shorter than those estimates previously by Rafikov (2005), a result consistent with that of Boss (2005)."688 Nero Djorkman (2009) found that the outermost planet around IIR 8799 was likely to have formed by. a disk instabilitw. but that the two closer-in. planets were not. a conclusion at odds with the results of (he present numerical calculations.," Nero Bjorkman (2009) found that the outermost planet around HR 8799 was likely to have formed by a disk instability, but that the two closer-in planets were not, a conclusion at odds with the results of the present numerical calculations."689 The different outcomes appear to be a result of different assumptions about the initial disk density and temperature profiles. dust grain opacities. and use of a cooling time argument rather than detailed radiative transfer ancl hvdrodynamies.," The different outcomes appear to be a result of different assumptions about the initial disk density and temperature profiles, dust grain opacities, and use of a cooling time argument rather than detailed radiative transfer and hydrodynamics."690 Recently the use of cooling times to depict the thermocdwnaniucs of protoplanetary disks has been called in question by the three dimensional hyvcrodvuamiucal models of Meru Bate (2010. 2011). who found (hat previous caleulalions relied on an overly simplistic cooling time argument. and that when sufficiently hieh spatial resolution was emploved. even disks previously thought to be stable underwent fragmentation into chumps.," Recently the use of cooling times to depict the thermodynamics of protoplanetary disks has been called in question by the three dimensional hydrodynamical models of Meru Bate (2010, 2011), who found that previous calculations relied on an overly simplistic cooling time argument, and that when sufficiently high spatial resolution was employed, even disks previously thought to be stable underwent fragmentation into clumps."691 Finally. it is interesting (o note an observational prediction.," Finally, it is interesting to note an observational prediction."692 Ilellel Bodenheimer (2010) have modeled the capture of solids by gas giant. protoplanets formed al distances, Helled Bodenheimer (2010) have modeled the capture of solids by gas giant protoplanets formed at distances693can mimic those of an unreddened old. galaxy. producing a degeneracy of the age and dust. extinction.,"can mimic those of an unreddened old galaxy, producing a degeneracy of the age and dust extinction."694 However. wha happens to the integrated colours of a galaxy when clus extinction is treated more realistically is poorly known.," However, what happens to the integrated colours of a galaxy when dust extinction is treated more realistically is poorly known."695 Witt ct al. (, Witt et al. (6961992) sugeested that the elfects of realistic dust. extinction on the SEDs of high-z galaxies are no strong.,1992) suggested that the effects of realistic dust extinction on the SEDs of $z$ galaxies are not strong.697 However. their claim: was based on a single objec (the radio galaxy B2 0902|34 at 2~ 3.4). and &eneralizec to the whole population of high-z galaxies.," However, their claim was based on a single object (the radio galaxy B2 0902+34 at $z\sim3.4$ ), and generalized to the whole population of $z$ galaxies."698 In addition. the continuum SED of D2 0902|34 turned out to be completely different from that used by Witt et al. (," In addition, the continuum SED of B2 0902+34 turned out to be completely different from that used by Witt et al. ("6991992) because of a strong contamination of the ἐν αμ flux by the redshifted λλες|5007 (Eisenhardt Dickinson 1992).,1992) because of a strong contamination of the $K$ -band flux by the redshifted $\lambda\lambda$ 4959+5007 (Eisenhardt Dickinson 1992).700 lnsteacd. recent. studies (Praneeschini et al.," Instead, recent studies (Franceschini et al."701 1994) have emphasized the role of dust in the carly stages of evolution of galaxies., 1994) have emphasized the role of dust in the early stages of evolution of galaxies.702 “The present optical surveys for high-z galaxies are designed to select objects with strong emission lines. such as Ενα. (see Pritehet 1994 for a review: Thompson et al.," The present optical surveys for $z$ galaxies are designed to select objects with strong emission lines, such as $\alpha$, (see Pritchet 1994 for a review; Thompson et al."703 1995). or galaxies with a flat continuum spectrum and with a sharp Lyman-break (Steidel et al.," 1995), or galaxies with a flat continuum spectrum and with a sharp Lyman-break (Steidel et al."704 1996)., 1996).705 However. because of those selection criteria. these surveys would. miss the putative population of high-z galaxies obscured by. dust. extinction.," However, because of those selection criteria, these surveys would miss the putative population of $z$ galaxies obscured by dust extinction."706 lt is notable that the strongest evolutionary. elfects due to dust extinction are not expected for the galactic disks. or in cisk dominated systems (Mazzei et al.," It is notable that the strongest evolutionary effects due to dust extinction are not expected for the galactic disks, or in disk dominated systems (Mazzei et al."707 1992). but rather in earlv-tvpe galaxies which. under appropriate circumstances. might experience a prolonged. opaque phase (Mazzei De Zotti 1996).," 1992), but rather in early-type galaxies which, under appropriate circumstances, might experience a prolonged opaque phase (Mazzei De Zotti 1996)."708 The whole issue of the ellects of dust. on the SDs of high-z galaxies still remains an important. open question. especially in view of the future ISO ancl sub-mum clata.," The whole issue of the effects of dust on the SEDs of $z$ galaxies still remains an important, open question, especially in view of the future ISO and sub-mm data."709 Extinetion effects become particularly relevant in the case of high-z galaxies with very red colours. also calle extremely red objects (EROs) (AleCarthy et al.," Extinction effects become particularly relevant in the case of $z$ galaxies with very red colours, also called extremely red objects (EROs) (McCarthy et al."710 1992: Llu Ridgeway 1994)., 1992; Hu Ridgway 1994).711 ln fact. these galaxies may be clistant aux old. ellipticals. and could. provide crucial clues on the firs epoch of galaxy formation. {ο and qu. once their ages are derived accurately.," In fact, these galaxies may be distant and old ellipticals, and could provide crucial clues on the first epoch of galaxy formation, $H_0$ and $q_0$, once their ages are derived accurately."712 Llowever. they could also be very dusty igh-z galaxies whose intrinsic colours are stronely reddene w dust extinction.," However, they could also be very dusty $z$ galaxies whose intrinsic colours are strongly reddened by dust extinction."713 Phe main problem is that the degeneracey of the age and the dust extinction. becomes maximized. in his class of objects because of the similarity between the colours of a genuinely old. galaxy anc those induced. by oreground screen reddening., The main problem is that the degeneracy of the age and the dust extinction becomes maximized in this class of objects because of the similarity between the colours of a genuinely old galaxy and those induced by foreground screen reddening.714 Phe main questions are then: row muchrcealisHie dust extinction can mimic the colours of an old galaxy?, The main questions are then: how much dust extinction can mimic the colours of an old galaxy?715 Hf these galaxies are clusty. is it possible to earn something about the spatial distribution of the dust »v modeling their SEDs?," If these galaxies are dusty, is it possible to learn something about the spatial distribution of the dust by modeling their SEDs?"716 AMotivated by the general lack of information on the ellects. of dust extinction on the SEDs of high-: galaxies. we have started an extensive study aimed. at investigating the relevance of these elfects.," Motivated by the general lack of information on the effects of dust extinction on the SEDs of $z$ galaxies, we have started an extensive study aimed at investigating the relevance of these effects."717 In this paper. we focus on the case of spheroidal galaxies. present the first. results. discuss an application to the case of the extremely. red galaxies. and show a serencdipitous result about the strength of the 2200 dust absorption feature in external galaxies.," In this paper, we focus on the case of spheroidal galaxies, present the first results, discuss an application to the case of the extremely red galaxies, and show a serendipitous result about the strength of the 2200 dust absorption feature in external galaxies."718 Alore general results and applications will be presented in a forthcomingὃν paper., More general results and applications will be presented in a forthcoming paper.719 As a first attempt to study the cllects of dust. extinction. we investigate the case of spheroidal galaxies.," As a first attempt to study the effects of dust extinction, we investigate the case of spheroidal galaxies."720 The stellar density profile poor(Qe) is modelled. as a Jatle bulge (see BEG). which reproduces the surface brightness rt! prolile characteristic of elliptical and bulge svstems (de Vaucouleurs 1959).," The stellar density profile $\rho_{star}(r)$ is modelled as a Jaffe bulge (see BFG), which reproduces the surface brightness $r^{1/4}$ profile characteristic of elliptical and bulge systems (de Vaucouleurs 1959)."721" We adopt an elfective racius r7 —4 kpc. representative of nearby. elliptical and bulge svstems (Binney Tremaine 1987). and the distribution Is truncated at a radius Sr,=20 kpe (see BEG for more details)."," We adopt an effective radius $r_e$ =4 kpc, representative of nearby elliptical and bulge systems (Binney Tremaine 1987), and the distribution is truncated at a radius $r_{max}=5 r_e=20$ kpc (see BFG for more details)."722 Dust extinction. has been treated hy using Monte Carlo simulations of realistic radiative transfer in clusty ealaxies (Le. considering the extinction as the combination of absorption and scattering)., Dust extinction has been treated by using Monte Carlo simulations of realistic radiative transfer in dusty galaxies (i.e. considering the extinction as the combination of absorption and scattering).723 The details of the model are not repeated here and can be found in BEC., The details of the model are not repeated here and can be found in BFG.724" However. it is important to recall here that we assume Calactie dust: in our model the grains are supposed to be spherical and. to have à size distribution given by the ALRN model (Mathis. ltumpl Nordsick 1977). (a)xa""where e is the grain radius."," However, it is important to recall here that we assume Galactic dust: in our model the grains are supposed to be spherical and to have a size distribution given by the MRN model (Mathis, Rumpl Nordsiek 1977), $n(a)\propto a^{-3.5}$, where $a$ is the grain radius."725 We consider three materials: astronomical silicates. | eraphite. and L graphite.," We consider three materials: astronomical silicates, $\parallel$ graphite, and $\perp$ graphite."726 The numerical silicates/eraphite ratio is 1:1.12. with 1/3 of the graphite having optical properties measured. parallel (|). and 2/3 perpendicular (1L) to the c-axis.," The numerical silicates/graphite ratio is 1:1.12, with 1/3 of the graphite having optical properties measured parallel $\parallel$ ), and 2/3 perpendicular $\perp$ ) to the c-axis."727 The lower and upper limits of the distribution wea—0.005r μαι and e=0.25 pam. irrespectively of the material.," The lower and upper limits of the distribution are $a_{-}=0.005$ $\mu$ m and $a_{+}=0.25$ $\mu$ m, irrespectively of the material."728 Very small grains and PALL have not been included due to the large uncertainties both in their size distribution and optical constants., Very small grains and PAH have not been included due to the large uncertainties both in their size distribution and optical constants.729 The dielectric constants adopted are the ones given by Draine Lee (1984). recently extended in the far UV and X-rays by Martin Rouleau (1991).," The dielectric constants adopted are the ones given by Draine Lee (1984), recently extended in the far UV and X-rays by Martin Rouleau (1991)."730 AL the relevant optical properties (absorption and scattering cross section. albedo) have been caleulated using Mie formulae.," All the relevant optical properties (absorption and scattering cross section, albedo) have been calculated using Mie formulae."731" We tested three dillerent spatial distributions for the dust within the galaxies: a homogencous disk with constant cust density favs, and with radius re—ros20 kpc equal to that of the stellar. distribution.", We tested three different spatial distributions for the dust within the galaxies: a homogeneous disk with constant dust density $\rho_{dust}$ and with radius $r_d=r_{max}=20$ kpc equal to that of the stellar distribution.732 We considered. three different values of the geometrical half-thickness ofthe disk. ο=10.250.500 pe. and three diferent inclinations to the line of sight. ;=107.457.90. (edge-on): a homogeneous spherical distribution with radius Fgquas=20 kpe equal to that of the stellar bulge. where the dust is intermixed with the stars and has constant density (ρω(1). —constant): a spherical distribution where the dust is intermixed with the stars. but its density follows the same racial distribution of the stellar component (Le. Pats1)= θα).," We considered three different values of the geometrical half-thickness of the disk, $z_d=70, 250, 500$ pc, and three different inclinations to the line of sight, $i=10^\circ, 45^\circ, 90^\circ$ (edge-on); a homogeneous spherical distribution with radius $r_d=r_{max}=20$ kpc equal to that of the stellar bulge, where the dust is intermixed with the stars and has constant density $\rho_{dust}(r)=$ constant); a spherical distribution where the dust is intermixed with the stars, but its density follows the same radial distribution of the stellar component (i.e. $\rho_{dust}(r)=733\rho_{star}(r)$ )."734 Model X can be considered representative of a spheroidal galaxy where the dust is located. in a clisk. similarly to what is actually observed. in a number of nearby. cllipticals (Goudfroij 1996. ancl references therein).," Model A can be considered representative of a spheroidal galaxy where the dust is located in a disk, similarly to what is actually observed in a number of nearby ellipticals (Goudfroij 1996, and references therein)."735 On the other hand. in models 1 and C. the dust is interspersed with the stars.," On the other hand, in models B and C, the dust is interspersed with the stars."736 In particular. model D. although," In particular, model B, although"737]xolmogorov (wpe.,Kolmogorov type.738 Observations of electron-densityw. fluctuations inferred. [rom scintillation measurements exhibit a Ixolmogorov power law. with index approximately equal to 5/3. over 5 orders of magnitude (Armstrongetal.1995).," Observations of electron-density fluctuations inferred from scintillation measurements exhibit a Kolmogorov power law, with index approximately equal to 5/3, over 5 orders of magnitude \citep{a95}."739. Several other observations of magnetic turbulent media. from earth's magnetosphere to galaxy. clusters. validate the Ixolmogorov power spectrum up to a range of 12 orders of magnitude.," Several other observations of magnetic turbulent media, from earth's magnetosphere to galaxy clusters, validate the Kolmogorov power spectrum up to a range of 12 orders of magnitude."740 We mention that solar wind observations show that at scales smaller than the ion thermal gvroradius (~10* em around the earth). much smaller than the scales considered in this paper. the magnetic turbulence spectrum deviates [rom the lIxolmogorov. having an index of —2.12 (Baleοἱal.2005).," We mention that solar wind observations show that at scales smaller than the ion thermal gyroradius $\sim 10^7$ cm around the earth), much smaller than the scales considered in this paper, the magnetic turbulence spectrum deviates from the Kolmogorov, having an index of $-2.12$ \citep{b05}."741. At length-scales larger than the coherence leneth the measured interplanetary magnetic turbulence is well described by a flattening power spectrum (IHedgecock 1994).," At length-scales larger than the coherence length the measured interplanetary magnetic turbulence is well described by a flattening power spectrum \citep{h75,bms94}."742. On the other hand. a consistent comparison wilh the quasi-linear limit requires the power spectrum to be delined at scales larger than coherence length. i.e. for ηςwee up to the physical scale of the svstem a[hi we will adopt here a simplified form: where 2 corresponds to the scale where the dissipation rate of the turbulence overcomes (he energv cascade rate.," On the other hand, a consistent comparison with the quasi-linear limit requires the power spectrum to be defined at scales larger than coherence length, i.e. for $k_\parallel < k_\parallel^{min}$, up to the physical scale of the system $2\pi/k_\parallel ^0$; we will adopt here a simplified form: where $k_\parallel ^{max}$ corresponds to the scale where the dissipation rate of the turbulence overcomes the energy cascade rate."743 The choice of a constant power spectrum at large scales instead of a function smoothly connected to the inertial range already used in the literature is merelv dictated by easier mathematical tractabilityv., The choice of a constant power spectrum at large scales instead of a function smoothly connected to the inertial range already used in the literature is merely dictated by easier mathematical tractability.744 Here q=5/3/ ancl the constant Gn is determined from the normalization implving. using evlindrical coordinate (ας=dhikdk du).," Here $q=5/3$ and the constant $G_\parallel ^0$ is determined from the normalization implying, using cylindrical coordinate $d^3 k = dk_\parallel k_\perp dk_\perp d\psi$ ),"745value of n.,value of $n$.746" Therefore, it is necessary that higher-order non-Gaussianities are taken into account when modelling a non-Gaussian distribution with gwr,<0."," Therefore, it is necessary that higher-order non-Gaussianities are taken into account when modelling a non-Gaussian distribution with $\gnl<0$."747" For instance, including nonzero cumulants Sg and Sg opens up the parameter space to those with S4« 0, as shown in figure pl."," For instance, including nonzero cumulants $S_6$ and $S_8$ opens up the parameter space to those with $S_4<0$ , as shown in figure \ref{s6}."748" In summary, the Edgeworth series should be expanded up to even order in og to produce a well-defined pdf."," In summary, the Edgeworth series should be expanded up to even order in $\sigma_R$ to produce a well-defined pdf."749 The highest cumulant in that case is restricted to non-negative values., The highest cumulant in that case is restricted to non-negative values.750 TheEdgeworth expansion therefore can describe models with gwr<0 if and only if cumulants of order at least 6 or higher are included., TheEdgeworth expansion therefore can describe models with $\gnl<0$ if and only if cumulants of order at least $6$ or higher are included.751" If ονι,=0 and non-Gaussianity is parametrized by fwi, only, the Edgeworth expansion is odd-ordered and the resulting pdf is not well-defined."," If $\gnl=0$ and non-Gaussianity is parametrized by $\fnl$ only, the Edgeworth expansion is odd-ordered and the resulting pdf is not well-defined."752" Although wehave assumed that non-GaussianityBLE) is characterised purely by the ‘local’ fy; and gnz parameters, the results in this section (as summarised in figures have been established in terms of the cumulants, η, and so they hold even if there are other types of non-Gaussianity present."," Although wehave assumed that non-Gaussianity is characterised purely by the `local' $\fnl$ and $\gnl$ parameters, the results in this section (as summarised in figures \ref{scatter}- \ref{s6}) ) have been established in terms of the cumulants, $S_n$, and so they hold even if there are other types of non-Gaussianity present."753 The only difference in this case is that it will be more complicated to translate the cumulants into fwr-type parameters., The only difference in this case is that it will be more complicated to translate the cumulants into $\fnl$ -type parameters.754" For instance, S3 willnow comprise a mixture of local and non-local contributions S3 = where Z; and Zz are some integral expressions."," For instance, $S_3$ willnow comprise a mixture of local and non-local contributions S_3 = where $\mc{I}_1$ and $\mc{I}_2$ are some integral expressions."755 See ?? for the expressions for Z5 in the case where non-Gaussianity is of the so-called folded or equilateral-triangle type.," See \cite{loverde,desjacques2} for the expressions for $\mc{I}_2$ in the case where non-Gaussianity is of the so-called folded or equilateral-triangle type."756" Having understood how to produce well-defined non-Gaussian pdfs using the Edgeworth expansion, we shall now look at two applications, namely, the non-Gaussian prediction for abundances of clusters and voids."," Having understood how to produce well-defined non-Gaussian pdfs using the Edgeworth expansion, we shall now look at two applications, namely, the non-Gaussian prediction for abundances of clusters and voids."757" In what follows, we shall focus on the case where fwr,=0 and ονι,>0."," In what follows, we shall focus on the case where $\fnl=0$ and $\gnl>0$."758 Large-scale structures are sensitive to primordial non-Gaussianity on scales much smaller than the CMB (see ? for α recent, Large-scale structures are sensitive to primordial non-Gaussianity on scales much smaller than the CMB (see \cite{desjacques2} for a recent review).759" On these scales, non-Gaussianity can manifest in the changes in cluster number count and its redshift dependence review). as well as a scale-dependent halo bias (???).."," On these scales, non-Gaussianity can manifest in the changes in cluster number count and its redshift dependence \citep{lucchin,robinson,loverde,oguri} as well as a scale-dependent halo bias \citep{dalal,matarrese,wands}."760" In this work, we use the Edgeworth approach, in its correct (???7)formalism, together with Press-Schechter theory to study the effect of non-zero gwi on the number density of massive clusters."," In this work, we use the Edgeworth approach, in its correct formalism, together with Press-Schechter theory to study the effect of non-zero $\gnl$ on the number density of massive clusters."761 Redshift dependence and the effects on the correlation function will be examined in a later publication., Redshift dependence and the effects on the correlation function will be examined in a later publication.762 Let n(M) be the number density of collapsed objects of mass above M., Let $n(M)$ be the number density of collapsed objects of mass above $M$.763" Press-Schechter theory (?) gives the differential number density of collapsed objects as arn/— where p(v,M) is the pdf smoothed by a window function containing mass M and δεz1.686 is the threshold overdensity for spherical collapse."," Press-Schechter theory \citep{ps} gives the differential number density of collapsed objects as = where $p(\nu,M)$ is the pdf smoothed by a window function containing mass $M$ and $\delta_c\approx1.686$ is the threshold overdensity for spherical collapse."764" For a non-Gaussian, ? suggest that a good fit to N-body simulations can be obtained by using the Press-Schechter mass function modified by the replacement (see ? for a possible theoretical origin.)"," For a non-Gaussian, \cite{grossi} suggest that a good fit to N-body simulations can be obtained by using the Press-Schechter mass function modified by the replacement (see \cite{maggiore3} for a possible theoretical origin.)"765 We make this replacement in our calculations., We make this replacement in our calculations.766" Figure [6] shows the changes in dn/dM for a range of non-Gaussian models with gr,=5x105,1106 and 5x106 (furi,=0 in all cases)."," Figure \ref{figcompare} shows the changes in $dn/dM$ for a range of non-Gaussian models with $\gnl=5\times10^{5},1\times10^{6}$ and $5\times10^6$ $\fnl=0$ in all cases)."767" In these calculations, we keep the Edgeworth expansion up to 10 terms and check that p(v)>0 at least in the range v€[—20,20]."," In these calculations, we keep the Edgeworth expansion up to $10$ terms and check that $p(\nu)>0$ at least in the range $\nu\in[-20,20]$."768" Outside this range, the p(v) is sufficiently small and the contribution to the cluster abundance on this mass scale is negligible (note that for the normal distribution, N(20)~ 10-55)."," Outside this range, the $p(\nu)$ is sufficiently small and the contribution to the cluster abundance on this mass scale is negligible (note that for the normal distribution, $N(20)\sim10^{-88}$ )."769 The values of gri have been chosen to stay within the region of validity (see figure [)., The values of $\gnl$ have been chosen to stay within the region of validity (see figure \ref{scatterlots}) ).770" In our case, we require 0<07.54 0.6, corresponding roughly to 0Sgxr,€ O(108)."," In our case, we require $0\leq\sigma^2 S_4\lesssim0.6$ , corresponding roughly to $0\lesssim\gnl\lesssim\mc{O}(10^8)$ ."771" The general effect of νι,>0 is a boost in the number density of the most massive objects, although significant boost requires the magnitude of gur, to exceed theCMB-derived bound of ?.."," The general effect of $\gnl>0$ is a boost in the number density of the most massive objects, although a significant boost requires the magnitude of $\gnl$ to exceed theCMB-derived bound of \cite{vielva}. ."772" For instance, abundance of objectsa of mass"," For instance, abundance of objects of mass"773ssamples (the darker Madsen et al. (,samples (the darker Madsen et al. (774"2006) points in Figure 7) would then indicate variations with position of abundance and/or of the dominant ionizing star, in addition to variations in U. Variations in aare certainly possible in such a large-scale sampling since there is evidence (O'Dell2001) that the optically thick foreground Veil of the Orion Nebula is probably optically thin to the southwest and this would allow radiation from the hottest star in the region to illuminate ccomponents in that direction.","2006) points in Figure 7) would then indicate variations with position of abundance and/or of the dominant ionizing star, in addition to variations in U. Variations in are certainly possible in such a large-scale sampling since there is evidence \citep{od01} that the optically thick foreground Veil of the Orion Nebula is probably optically thin to the southwest and this would allow radiation from the hottest star in the region to illuminate components in that direction."775" In the case of the WIM samples it is expected that there could be a significant range in photoionizing star temperatures, U, and possibly Z/H. If there is only a single value of the (Z/H) and it is that adopted for our M 43 calculations then most of the aand WIM ratios can be explained by log U values between -3.07 and -3.67, with vvalues of up to slightly more than 35000 K. However, the lower left population of the ssamples and the Barnard’s Loop samples would require unrealistically low vvalues, indicating that there must be regions of higher than average Z/H. We can constrain the likely oof the Barnard Loop samples since they are all illuminated by the same radiation field."," In the case of the WIM samples it is expected that there could be a significant range in photoionizing star temperatures, U, and possibly Z/H. If there is only a single value of the (Z/H) and it is that adopted for our M 43 calculations then most of the and WIM ratios can be explained by log U values between -3.07 and -3.67, with values of up to slightly more than 35000 K. However, the lower left population of the samples and the Barnard's Loop samples would require unrealistically low values, indicating that there must be regions of higher than average Z/H. We can constrain the likely of the Barnard Loop samples since they are all illuminated by the same radiation field."776 Table 2 gives the iin the [N II] emitting zone for all our models., Table 2 gives the in the [N II] emitting zone for all our models.777" The two most closely matching the low-ionization color-color diagram are those with log U=-3.67 and log U=-3.07 with Tstar=31000 K, both with an abundance difference of 0.1 dex, and these have expected oof 5970 K and 5940 K respectively."," The two most closely matching the low-ionization color-color diagram are those with log U=-3.67 and log U=-3.07 with =31000 K, both with an abundance difference of 0.1 dex, and these have expected of 5970 K and 5940 K respectively."778 We will adopt a value of 5960+50 K for comparison with direct determinations., We will adopt a value of $\pm$ 50 K for comparison with direct determinations.779 There is a great uncertainty about the expected oof the other parts of the diagram., There is a great uncertainty about the expected of the other parts of the diagram.780" For example, the T44,—331000 K and log U=-3.07"," For example, the 31000 K and log U=-3.07"781conditions at infinity.,conditions at infinity.782 In field theory. these asvuiptotie boundary conditions asstune conjugate raciative-raciative boundary conditious.," In field theory, these asymptotic boundary conditions assume conjugate radiative-radiative boundary conditions."783 Iu the continuum Iuuit of a plasiua swuch is asviuptoticallv iu charge-separated equilibrium. these become slip-slip boundary couditious: the angular velocities of the fiux-surfaces Q ithe horizon may differ from that of the black hole. aud the angular velocity at infinity may be 10n-zero.," In the continuum limit of a plasma which is asymptotically in charge-separated equilibrium, these become slip-slip boundary conditions: the angular velocities of the flux-surfaces on the horizon may differ from that of the black hole, and the angular velocity at infinity may be non-zero."784 In contrast. a fiux-surfaces supported by barvouic latter are fixed to its angular velocity. namely that of the disk or torus (a boundary coulion).," In contrast, a flux-surfaces supported by baryonic matter are fixed to its angular velocity, namely that of the disk or torus (a no-slip boundary condition)."785 This will hold to within a fair approximation over i Lappreciable scae relative to the svstem size., This will hold to within a fair approximation over an appreciable scale relative to the system size.786 Recall that this well-kuown Cxotation law is based on tl10 slueuar lait of perfect coucductivity: deviatious O order wnity will arise over cistauce scales of order 1/6. upon deviations YOU the corotation charge-deusity to or(Y €.," Recall that this well-known corotation law is based on the singular limit of perfect conductivity; deviations of order unity will arise over distance scales of order $1/\epsilon$, upon deviations from the corotation charge-density to order $\epsilon$."787" Equilibration towards:v force-free state iitroduces al asvuiptotic idition on the current carried by ↑∐↸∖∏∪↖↖⇁∶↴∙⊾∪↕∐∶↴⋁⋯↑∪↑∐↸∖↴⋝↕⋜↧↸⊳↨↘↽∐∪↕↸∖∶⊽∣− ⋅⋅ ∣⋅≻»0 upon approaching the horizon.⋅ where j∣ denotes the fom-curreuta27"" This expresses the colleition that the cirent becQues asvinptotically couvecIve: JntEn jf.ere o denotes the redsüft factor on-axis of the herr black hole."," Equilibration towards a force-free state introduces an asymptotic null-condition on the current carried by the flow going into the black hole: $j^2\rightarrow0$ upon approaching the horizon, where $j^b$ denotes the \cite{pun90,mvp01b}788 This expresses the condition that the current becomes asymptotically convective: $j^r=\pm \alpha j^t$, where $\alpha$ denotes the redshift factor on-axis of the Kerr black hole."789 m apmoaching the Ixxizon. diift-ourreuts are suppressed by a divergent Loreutz factor.," In approaching the horizon, drift-currents are suppressed by a divergent Lorentz factor."790 Here. we swll consider the proposal tiat the boundary concitiolat 1fi vods snilu in an ultrarclativistic outflow.," Here, we shall consider the proposal that the boundary condition at infinity is similar in an ultrarelativistic outflow."791 It would be of interes to study1 this pro»osal selt£-conusistentlv with the micro-pliyvsics in the gap., It would be of interest to study this proposal self-consistently with the micro-physics in the gap.792 Frame-drageIne appears expliciIv in the expression for the electric cliarge-Is]vo pintje equilibrimm charec-separated Li., Frame-dragging appears explicitly in the expression for the electric charge-density $\rho$ in the equilibrium charge-separated limit.793 Indeed. the equilibrium aree-deusitv Is associated with a tine-like coordinate which is orthogonal tlre| azimuthal Willing vecor.," Indeed, the equilibrium charge-density is associated with a time-like coordinate which is orthogonal to the azimuthal Killing vector."794" Ileice. this οjurge-deusitv corresponds to the Is]v-at-iufuty as seen by. ZOTO arelay niouentui observers (ZAMOs): the ""true angular| velocitv of a flux-surface is theut relaive to a local ZAMO with iieular velocity ⋜↧↴∖↴⋜↧⋯∪"," Hence, this charge-density corresponds to the density-at-infinity as seen by zero angular momentum observers (ZAMOs); the “true"" angular velocity of a flux-surface is that relative to a local ZAMO with angular velocity $-\beta$."795≼∐∐↸∖≼⇂≼∶∪↕≼⊔⋅↸∖↕↸⊳∐≓⋅↧↿jueitly. we have t10 expTOSSIOLL p-—(QO|9)B/2x n»la;1 pityxl0 Tje asvinptotical conditiou JQO on the horizou aud infinity now expresses electric current mediated by convection of this modifie Coldreicli-Tlan deuxitv.," Consequently, we have the expression $\rho=-(\Omega+\beta)B/2\pi$ as a modified Goldreich-Julian \cite{gol69,bes97,hir98,mvp01b}796 The asymptotical condition $j^2=0$ on the horizon and infinity now expresses electric current mediated by convection of this modified Goldreich-Julian density."797" lutegratiug over an effective area corresponding 6 a given flux surface AA, Acoust.."," Integrating over an effective area corresponding to a given flux surface $A_\phi=$ const.,"798" we find f=OA, at infu vaudZ,=(QyOQ|jel, on the: horizon.", we find $I_-=\Omega_-A_\phi$ at infinity and $I_+=(\Omega_H-\Omega_+)A_\phi$ on the horizon.799" Here. 9 aud €, denote the Bover-Livlquus aueular velocities of the wo asviuptoticallv equilibrated sections attached to infinity aud the horizon. respectively."," Here, $\Omega_-$ and $\Omega_+$ denote the Boyer-Lindquist angular velocities of the two asymptotically equilibrated sections attached to infinity and the horizon, respectively."800" Current continuity euforces the coition Q-QnQ,.", Current continuity enforces the condition $\Omega_-=\Omega_H-\Omega_+$.801 Clobal current closure nav οtain over the surrouiudiic torus., Global current closure may obtain over the surrounding torus.802 Here. we appeal to a potential similarity f» solar flares. as observed by the Trausieut Reeion Corona Experiment CERACE) and the Solar Heliospherie Observatory (SOIIO).," Here, we appeal to a potential similarity to solar flares, as observed by the Transient Region Corona Experiment (TRACE) and the Solar Heliospheric Observatory (SOHO)."803 While maguetic fheld-liie form closed loops when supported by, While magnetic field-lines form closed loops when supported by804"The best fit solutions for XR) obtained at 1.9 nuu aud 2.8 nuu are shown in Figure 5-— 6 with black aud red curves respectively,",The best fit solutions for $\Sigma(R)$ obtained at 1.3 mm and 2.8 mm are shown in Figure \ref{fig:RYTau_POW}- \ref{fig:DGTau_SIM} with black and red curves respectively.805 The vest fit paralcters are summarized in Table 3 and L., The best fit parameters are summarized in Table \ref{tab:res_clubs} and \ref{tab:res_spades}.806 The quoted uucertainuties correspond to a likelihood of (ie. 30) aud are caleulated x fitting a normal distribution to the measured xobabilitv distributious., The quoted uncertainties correspond to a likelihood of (i.e. $\sigma$ ) and are calculated by fitting a normal distribution to the measured probability distributions.807 For RY Tan. the disk uodel obtained by fitting the two wavoleugthis separately are m agreement within 3e.," For RY Tau, the disk model obtained by fitting the two wavelengths separately are in agreement within $\sigma$."808 For DG Tau he solutious disagree bv imnore than 230 only iu he case of the similarity solution aud high dust opacity., For DG Tau the solutions disagree by more than $\sigma$ only in the case of the similarity solution and high dust opacity.809 Figue 13 shows the radial variation of 3 as defined in Equation ὃ— for both DG Tau and RY Tan., Figure \ref{fig:dbeta} shows the radial variation of $\beta$ as defined in Equation \ref{eq:betar} for both DG Tau and RY Tau.810 The region marked with color iudicates values of > within 30 from the radial profile correspouding to the best fit solution for the surface density iu the case of the similarity solution model., The region marked with color indicates values of $\beta$ within $\sigma$ from the radial profile corresponding to the best fit solution for the surface density in the case of the similarity solution model.811 Values of > outside this region are rejecjected by our observations., Values of $\beta$ outside this region are rejected by our observations.812 The results for RY Tau and DC Tan are clearly consistent with a large variety of radial profiles of jJ, The results for RY Tau and DG Tau are clearly consistent with a large variety of radial profiles of $\beta$.813" For both sources ο) d8 better constrained vetween radii of 20 aud το AU,"," For both sources, $\beta$ is better constrained between radii of 20 and 70 AU."814 However. even iu this interval. the observations constrain possible variation of .} to within oulv AS<0.7.," However, even in this interval, the observations constrain possible variation of $\beta$ to within only $\Delta\beta < 0.7$."815 Nevertheless. across most of the disk the circumstellar dust differs from that observed in the interstellar medium (ISM).," Nevertheless, across most of the disk the circumstellar dust differs from that observed in the interstellar medium (ISM)."816 Dust iu the ΤΟΝΤ is characterized by sub-micron dust erains aud by a mullaueter opacity slope of JJ~1.7., Dust in the ISM is characterized by sub-micron dust grains and by a millimeter opacity slope of $\beta \sim 1.7$.817 In contrast. in both sources. οὐ is naller than 1.7 up to at least SO AU. ggesting that the cireuustellar dust has been processec aud. in particular. has increased its size up to a maxim value that varies between 20 yan aud a few ceutimeters.," In contrast, in both sources, $\beta$ is smaller than 1.7 up to at least 80 AU, suggesting that the circumstellar dust has been processed and, in particular, has increased its size up to a maximum value that varies between 20 $\mu$ m and a few centimeters."818 Although in both sources Jj may be constant throughout the disk (see dashed lines). our results sugecstOO that j| decreases with the radius in DG Tau disk.," Although in both sources $\beta$ may be constant throughout the disk (see dashed lines), our results suggest that $\beta$ decreases with the radius in DG Tau disk."819" As discussed in Section ) depends ou a number of poorly constrained quautities. such as conmosition. structure, aud size of the dust grains."," As discussed in Section \ref{sec:mod}, $\beta$ depends on a number of poorly constrained quantities, such as composition, structure, and size of the dust grains."820 For exiunple. varving > from —1 to ~0.2. simular to what is suggested for DG. Tan between 10 aud 60 AU. mav be due to the iiaxinmuu erain size increasing from 20 µια to 1 cn for q=3. or. alternatively. to a decrease of 4 from { to 3 if the aNd erain size is between 1. and 10 cum.," For example, varying $\beta$ from $\sim$ 1 to $\sim$ 0.2, similar to what is suggested for DG Tau between 10 and 60 AU, may be due to the maximum grain size increasing from $20$ $\mu$ m to 1 cm for $q=3$, or, alternatively, to a decrease of $q$ from 4 to 3 if the maximum grain size is between 1 and 10 cm."821 In short. the interpretation of Jj ouly in terms of the erain size distribution can be verv midsleadius.," In short, the interpretation of $\beta$ only in terms of the grain size distribution can be very misleading."822 It secins most plausible that both dust composition and the relative contributions of smaller aud larger erains chanec through the disk. contributing to the variation of the dust opacity.," It seems most plausible that both dust composition and the relative contributions of smaller and larger grains change through the disk, contributing to the variation of the dust opacity."823 It is clear that better constraints ou the radial profile of .J are required before pushing the investigation further., It is clear that better constraints on the radial profile of $\beta$ are required before pushing the investigation further.824 Iun this reeard. we note that the current constraints on the radial variation of 9 are limited by two factors.," In this regard, we note that the current constraints on the radial variation of $\beta$ are limited by two factors."825 First. although the angular resolution of the observations described here is sienificautly better than hitherto xoswdble. the dust surface density is well) coustraimed ouly between 15 aud 50 AU. where most of the observed flux is ciuitted (see the discussion iu Section 5.3)).," First, although the angular resolution of the observations described here is significantly better than hitherto possible, the dust surface density is well constrained only between 15 and 50 AU, where most of the observed flux is emitted (see the discussion in Section \ref{sec:surf}) )."826 At sinaller and larger radi the surface density is uncertain by almost one order of magnitude., At smaller and larger radii the surface density is uncertain by almost one order of magnitude.827 Second. our analysis is hampered by the small separation iu wavelength between the observations since AGR) is proportional to log{Ay/A4).," Second, our analysis is hampered by the small separation in wavelength between the observations since $\Delta\beta(R)$ is proportional to $log^{-1}(\lambda_1/\lambda_0)$."828 The uncertainties shown iu Figure 13. can be reduced by a factor of 2 by extending the observatious at Tonun., The uncertainties shown in Figure \ref{fig:dbeta} can be reduced by a factor of 2 by extending the observations at 7 mm.829 These observations will become possible with the expanded correlator ou the EVLA., These observations will become possible with the expanded correlator on the EVLA.830 We lave presented CARAIA observations of the dust thermal cussion at the wavelengths of 1.9 nuu aud 2.5 mun from the circumstellar disks around the pre-ain sequence stars RY Tau aud DG Tan., We have presented CARMA observations of the dust thermal emission at the wavelengths of 1.3 mm and 2.8 mm from the circumstellar disks around the pre-main sequence stars RY Tau and DG Tau.831 The observations are characterized bv unprecedented angular resolution of ~0.15” aac aat 1.3 1021 and 2.8 nun respectively. correspouding to spatial scales of 20 and LO AU at the distance of Taurus.," The observations are characterized by unprecedented angular resolution of $\sim$ and at 1.3 mm and 2.8 mm respectively, corresponding to spatial scales of 20 and 40 AU at the distance of Taurus."832 Based on these images. we have addressed three fundamental questions related to the formation of planets in the disk arouud pre-main sequence stars.," Based on these images, we have addressed three fundamental questions related to the formation of planets in the disk around pre-main sequence stars."833 What is the radial density distribution of eircunstellar dust?, What is the radial density distribution of circumstellar dust?834 Does the dust cnussion show any indication of the presence of (proto}-plancts?, Does the dust emission show any indication of the presence of (proto)-planets?835 Do the dust properties vary with orbital radius?, Do the dust properties vary with orbital radius?836 By analyzing the morphology of the surface brightness of the dust cussion aud comparing the observations with theoretical disk models. we male the following conclusions:," By analyzing the morphology of the surface brightness of the dust emission and comparing the observations with theoretical disk models, we make the following conclusions:"837Apart from the geometry. boundary conditious. aud initial couditious. solutions are governed by the following 10 independent dimensionless parameters.,"Apart from the geometry, boundary conditions, and initial conditions, solutions are governed by the following 10 independent dimensionless parameters."838 The Praudtl iuuber aud the magnetic Praudtl uuuber are defined as where xg=fe5pu denotes ai reference value of he thermometric (radiative) diffusivity for region 2., The Prandtl number and the magnetic Prandtl number are defined as where $\chi_0=\kappa_2/\gamma\rho_0$ denotes a reference value of the thermometric (radiative) diffusivity for region 2.839" The xuwanmeter £y determines the pressure scale height at the op of the box. £y=IT,(:4)/df: The initial thermal structure of the GQuasximally) three regions is characterized by the radiative teniperature eracieuts. Tn addition. one often euniplovs the polvtropic index. m=(loVON."," The parameter $\xi_0$ determines the pressure scale height at the top of the box, $\xi_0=H_p(z_1)/d$: The initial thermal structure of the (maximally) three regions is characterized by the radiative temperature gradients, In addition, one often employs the polytropic index, $m=(1-\na)/\na$."840 The adiabatic temperature eracdient is eiven by Vag=(8$15., The adiabatic temperature gradient is given by $\na_{\rm ad}=(\gamma-1)/\gamma$.841 A measure for instability is provided by the superadiabaticity. 6;=V;—Vag. which Is positive in an uustablv stratified medium.," A measure for instability is provided by the superadiabaticity, $\delta_i=\na_i-\na_{\rm ad}$, which is positive in an unstably stratified medium."842" The Ravleigh muuber is defined as where 7,=Sod|O.5d/Une1] is the pressure scale height in the middle of the uustable Iaver. as can be shown using the lvdrostatic equilibria (253)."," The Rayleigh number is defined as where $H_{ph}=\xi_0 d+0.5 d/(m_2+1)$ is the pressure scale height in the middle of the unstable layer, as can be shown using the hydrostatic equilibrium \ref{e0}) )."843" The parameters à» and Z7, refer to the unperturbed stratification. ic. that before the ouset of convection."," The parameters $\delta_2$ and $H_{ph}$ refer to the unperturbed stratification, i.e. that before the onset of convection."844" The Bavleigh το is a measure of the streugth of convection compared to that of viscous aud thermal (radiative) dissipation. as can be seeu by writingM Ra=)focfiaa/fz4,. Where fu=d»fv. had=OF» VIE aud fas>=ΠΠου."," The Rayleigh number is a measure of the strength of convection compared to that of viscous and thermal (radiative) dissipation, as can be seen by writing $\mb{Ra}=t_{\rm visc}t_{\rm rad}/t^2_{\rm conv}$, where $t_{\rm visc}=d^2/\nu$, $t_{\rm rad}=d^2/\chi_0$ , and $t_{\rm conv}^2=H_{ph}/g\delta_2$."845" Alteyuativelv. oue may express Ra in terms of the entropy eracdicut. dsfide=C,of IT,."," Alternatively, one may express $\mb{Ra}$ in terms of the entropy gradient, $ds/dz=C_p\,\delta/H_p$ ."846 According to the Sclavarzschild criterion. a positive value for à. Lc. Ra20. sienifics mstabilitv.," According to the Schwarzschild criterion, a positive value for $\delta$, i.e. $\mb{Ra}>0$, signifies instability."847 Tn reality. Ra aust exceed a finite threshold value for convection to set in.," In reality, Ra must exceed a finite threshold value for convection to set in."848" It should be noted that the value of the Rayleigh uuuboer. d1gà(PNIT,). varies with depth within the unstable laver. becausex. IT, aud. as a result of convection also 6. are z-depoeudenut."," It should be noted that the value of the Rayleigh number, $d^4 g\delta/(\nu\chi H_p)$, varies with depth within the unstable layer, because$\chi$, $H_p$ and, as a result of convection also $\delta$, are $z$ -dependent."849 Typically. the local value is several times smaller than Ra. mainly because à can be strongly reduced by convection.," Typically, the local value is several times smaller than $\mb{Ra}$, mainly because $\delta$ can be strongly reduced by convection."850 The Tavlor uuuber. measures the importance of rotation relative ο VISCOUS dissipation.," The Taylor number, measures the importance of rotation relative to viscous dissipation."851 Finally. oy represeuts the rate at which internal energy is lost from the upper stable laver. aud 0 is the angle between the rotation vector aud tle z-axis.," Finally, $\sigma_0$ represents the rate at which internal energy is lost from the upper stable layer, and $\theta$ is the angle between the rotation vector and the $z$ -axis."852 All other parameters are secondary., All other parameters are secondary.853 The Coriolis nuniber. or inverse Rossby nunber. measures the nuportauce of the Coriolis force aud is defined as where 7=(fuu? is the turnover time.," The Coriolis number, or inverse Rossby number, measures the importance of the Coriolis force and is defined as where $\tau=\ell/u_{\rms}$ is the turnover time."854 The correlation length. f. is taken to be d in the unstable region.," The correlation length, $\ell$ , is taken to be $d$ in the unstable region."855 The Chaudrasckhar umnuuber. nieasures the strength of the imposed magnetic field.," The Chandrasekhar number, measures the strength of the imposed magnetic field."856 Iu the initial state. the 2-component of the radiative energv flux. Frag.=μαςαν. is asstumed to be constant throughout the domain.," In the initial state, the $z$ -component of the radiative energy flux, $F_{{\rm rad},z}=-\kappa de/dz$, is assumed to be constant throughout the domain."857 This determines the radiative conductivities i the three regions according to s;/Wo=Gn;|LeCie1)., This determines the radiative conductivities in the three regions according to $\kappa_i/\kappa_2=(m_i+1)/(m_2+1)$ .858 Iu fact. # is turned iuto a smooth function of depth by allowing it to change coutiuuouslv across thin intermediate lavers between the three regions.," In fact, $\kappa$ is turned into a smooth function of depth by allowing it to change continuously across thin intermediate layers between the three regions."859 An approximate initial stratification. nupertiurbed bv convection. is calculates on the assumption of lvdrostatic equilibrimu. aud this is done iteratively until the condition Pl.=is)py is satisfied.," An approximate initial stratification, unperturbed by convection, is calculated on the assumption of hydrostatic equilibrium, and this is done iteratively until the condition $\rho(z=z_3)=\rho_0$ is satisfied."860 It is also assumed that region lis cooled efficiently enough to become isothermal., It is also assumed that region 1 is cooled efficiently enough to become isothermal.861" The result is then basically a smoothed version of where Qj):Gil} stand for the three regions. ty<2<<te. tySotLois. and isXity. respectively,"," The result is then basically a smoothed version of where $(\mb{i})\cd\cd\cd (\mb{iii})$ stand for the three regions, $z_1\leq z< z_2$, $z_2\leq z< z_3$, and $z_3\leq z\leq z_4$, respectively."862 The actual initial stratification in region 2 is calculated umuerically using the misxine-leneth formalism of convection., The actual initial stratification in region 2 is calculated numerically using the mixing-length formalism of convection.863 The advantage of this approach is that it reduces the amount of time required for relaxation to a fully convective state., The advantage of this approach is that it reduces the amount of time required for relaxation to a fully convective state.864 The internal enerev density at the top equals eq=£ymaagd., The internal energy density at the top equals $e_1=\xi_0 m_{\rm ad}gd$.865 Using (25). it is easily shown that (de/dz);=maag/(Gms| 1).," Using ), it is easily shown that $(de/dz)_4=m_{\rm ad}g/(m_3+1)$ ."866 The radiative. kinetic and maguetic diffusivitics follow from Eqs. (18)," The radiative, kinetic and magnetic diffusivities follow from Eqs. )"867 aud (21)., and ).868 Revnolds wuubers are defined as where (yay. is the rus velocity defined in a suitable way (e.g... by averaging over time and over a partial volume of the box).," Reynolds numbers are defined as where $u_{\rm rms}$ is the rms velocity defined in a suitable way (e.g., by averaging over time and over a partial volume of the box)."869 We enplov a fuite difference scheme. according to which spatial derivatives are calculated with 6tl-order accuracy (Lele 1992).," We employ a finite difference scheme, according to which spatial derivatives are calculated with 6th-order accuracy (Lele )."870 Time-stepping is done using a hircl- πια predictor-corrector method., Time-stepping is done using a third-order Hyman predictor-corrector method.871 Table gives a list of the parameters used for afirst series of ruus in which the influence of rotation is investigatedby varvine the Tavlor uuuber., Table gives a list of the parameters used for afirst series of runs in which the influence of rotation is investigatedby varying the Taylor number.872angular-velocitv perturbations.,angular-velocity perturbations.873 However. Goldreich&Schubert(1967). themselves took the point of view (hat (he saturation occurs with displacements comparable to the pressure scale height. ancl therefore provides a turbulent viscosity ~O17/25.," However, \citet{GoldreichSchubert67} themselves took the point of view that the saturation occurs with displacements comparable to the pressure scale height, and therefore provides a turbulent viscosity $\sim\Omega H_p^2/2\pi$."874 This is something best studied by local rather than global simulations. and (hen represented in the latter by a suberid model.," This is something best studied by local rather than global simulations, and then represented in the latter by a subgrid model."875" IXorveanskyv(1991). simulated the nonlinear outcome of the GSF instability in the special case where 0j/0z=0 and N?»—z""Op/Oz>0."," \citet{Korycansky91} simulated the nonlinear outcome of the GSF instability in the special case where $\partial j/\partial876z=0$ and $N^2>-\varpi^{-3}\partial j^2/\partial\varpi>0$."877 llis results support Goldreich&Schubert (1967)s view of the saturation. but his two-dimensional simulations could not have represented (he nonaxisvnnuetric Ixelvin-IHelmholtz instabilities most likely to limit GSF modes.," His results support \citet{GoldreichSchubert67}' 's view of the saturation, but his two-dimensional simulations could not have represented the nonaxisymmetric Kelvin-Helmholtz instabilities most likely to limit GSF modes."878 Arlt&Urpin(2004) simulated the case 0j?/Ozc>0 and 0j?/0z«0 in (τος dimensions. using ZEUS3D. and concluded that mixing was efficient. but they adopted a barotropic equation of state so that their unperturbed state had to be out of equilibrium.," \citet{Arlt_Urpin04} simulated the case $\partial879j^2/\partial\varpi>0$ and $\partial j^2/\partial z<0$ in three dimensions, using ZEUS3D, and concluded that mixing was efficient, but they adopted a barotropic equation of state so that their unperturbed state had to be out of equilibrium."880 AMenouetal.(2004) added: magnetic effects to the GSF analvsis. but only in the linear regine.," \citet{Menou_Balbus_Spruit04}881 added magnetic effects to the GSF analysis, but only in the linear regime."882 While the growth rate of instabilities that rely on thermal diffusion. should. decrease rapillv wilh increasing pressure. (he rate at which radiative transfer tends to restore the stratification also decreases. so that the outcome for the profiles of entropy. ancl angular velocity is unclear.," While the growth rate of instabilities that rely on thermal diffusion should decrease rapidly with increasing pressure, the rate at which radiative transfer tends to restore the stratification also decreases, so that the outcome for the profiles of entropy and angular velocity is unclear."883 I any of these instabilities is effective at redistributing angular momentum. then (he radiativelv driven circulation max go deeper than present simulations suggest. and the time required for the rotation profile to reach steady state may be very long.," If any of these instabilities is effective at redistributing angular momentum, then the radiatively driven circulation may go deeper than present simulations suggest, and the time required for the rotation profile to reach steady state may be very long."884 We thank Adam Burrows. Ixristen Menou. Jonathan Mitchell. Geoffrev. Vallis. and the Pevton-Hall astro-ph coffee klatsch for helpful discussions.," We thank Adam Burrows, Kristen Menou, Jonathan Mitchell, Geoffrey Vallis, and the Peyton-Hall astro-ph coffee klatsch for helpful discussions."885 This work was supported in part bv the National Science foundation under grant. AST-O707373., This work was supported in part by the National Science foundation under grant AST-0707373.886(Dergerctal.2005).,\citep{brr+05}.887. We also find from a comparison of the radio aud. N-rav data that the magnetic field axis is likely highly inclined relative to the rotation axis of16.. which is interred from the 2-hour period of the Πο cmiission to be about 90° retsec:halpha)).," We also find from a comparison of the radio and X-ray data that the magnetic field axis is likely highly inclined relative to the rotation axis of, which is inferred from the 2-hour period of the $\alpha$ emission to be about $90^\circ$ \\ref{sec:halpha}) )."888 This is au interesting result iu the coutest of mmaenetic dynamo models of fully convective stars., This is an interesting result in the context of magnetic dynamo models of fully convective stars.889 Chabrier&Isiiker(2006) and Dobleretal.(2006) found that the à? dynamo. which relies ou a stratified aud rotating turbulent medi. leads to a non-axisviuuetric field with an overall configuration that lies iu the equatorial plane.," \citet{ck06} and \citet{dsb06} found that the $\alpha^2$ dynamo, which relies on a stratified and rotating turbulent medium, leads to a non-axisymmetric field with an overall configuration that lies in the equatorial plane."890 This secius to be supported by our observations., This seems to be supported by our observations.891 The Xaav enission requires a corona with Tzc10° IS aud a density of p;~1079 7. similar to those of carly AI divarfs," The X-ray emission requires a corona with $T\approx 10^7$ K and a density of $n_e\sim 10^{10}$ $^{-3}$, similar to those of early M dwarfs."892 The interred coronal gas pressure requires a maeguetie feld streneth of at least 1οLO C for confinement. iu eood agreement with the radio-derived feld streusth.," The inferred coronal gas pressure requires a magnetic field strength of at least $\sim 10-40$ G for confinement, in good agreement with the radio-derived field strength."893 The euergv input from the X-rav chutting corona is simul to. or somewhat smaller than. the radiative losses in the Balmer enmuüssion lines. indicating that the chromosphere is at least partly heated by the overlying corona.," The energy input from the X-ray emitting corona is similar to, or somewhat smaller than, the radiative losses in the Balmer emission lines, indicating that the chromosphere is at least partly heated by the overlying corona."894 It is possible. however. that the somewhat elevated chromospheric huninosity is the result of an energv input process that took place before the start of our observations.," It is possible, however, that the somewhat elevated chromospheric luminosity is the result of an energy input process that took place before the start of our observations."895 This latter possibility is supported by he appareutly decreasing level of peak Πα fux during our observation. and the nearly coustaut baseline level traced w the licht curve άλλα.," This latter possibility is supported by the apparently decreasing level of peak $\alpha$ flux during our observation, and the nearly constant baseline level traced by the light curve minima."896 Tudeed. the Πα hnunuinositv during the minima is about half of the X-ray Iuninosity.," Indeed, the $\alpha$ luminosity during the minima is about half of the X-ray luminosity."897 Iu addition to the persistent cussion. we detect a aree number of radio flares with a range of peak fluxes. duratious. and deerees of circular polarization.," In addition to the persistent emission, we detect a large number of radio flares with a range of peak fluxes, durations, and degrees of circular polarization."898 The overall short duratious of the flares and large degree of circular o)blurzation are iudicative of coherent emission., The overall short durations of the flares and large degree of circular polarization are indicative of coherent emission.899 In the context of the electron. cyclotron maser mechanism. the inferred maenetic Ποια is about 3 kG. similar to fields on the most active carly M. dwarfs (Saar&Linsky.1985:Johu--I&rull&Valeuti 1996).," In the context of the electron cyclotron maser mechanism, the inferred magnetic field is about 3 kG, similar to fields on the most active early M dwarfs \citep{sl85,jv96}."900. Suuilar flares have been detected in previous observatious of16.. but with a 2 hour periodicity that is absent iu our data.," Similar flares have been detected in previous observations of, but with a 2 hour periodicity that is absent in our data."901 The 2 hour period was attributed to compact polar regious in a dipolar field rotating iu aud out of our line of sight (Wallanetal.2007)., The 2 hour period was attributed to compact polar regions in a dipolar field rotating in and out of our line of sight \citep{hbl+07}.902. The durations of the flares detected rere. and their random arrival times aud sense of circular volarization. point mstead to a taneled aud imulti-polar field.," The durations of the flares detected here, and their random arrival times and sense of circular polarization, point instead to a tangled and multi-polar field."903 Thus. the conditions required. for coronal coliercut radio flares exist ou lone timescales. but the change iu vchavior may signal a shift iu the feld configuration on zd ovr thuescales.," Thus, the conditions required for coronal coherent radio flares exist on long timescales, but the change in behavior may signal a shift in the field configuration on $\lesssim 1$ yr timescales."904 The inferred multi-polar nature of the field is again iu good aereenient with models of the à? dynamo. which sugsest that the bulk of the energy is in he quadrupolar and higher order componucuts.," The inferred multi-polar nature of the field is again in good agreement with models of the $\alpha^2$ dynamo, which suggest that the bulk of the energy is in the quadrupolar and higher order components."905 Uulike in the radio flares. we do find clear Ho periodicity (Px=2 ly). with a sinusoidal light curve that reveals he presence of a chromosphlerie hot spot. or an exteuded xibble. with a covering fraction of about 50%.," Unlike in the radio flares, we do find clear $\alpha$ periodicity $P\approx 2$ hr), with a sinusoidal light curve that reveals the presence of a chromospheric hot spot, or an extended bubble, with a covering fraction of about $50\%$."906 Tt is nuclear whether this cussion region is stable over timescales ouger than about l1 dax. but the decrease in peal fiux )etwoeen subsequent rotatious may point to a transient ature that may be sinular to the oue now inferred im the radio band.," It is unclear whether this emission region is stable over timescales longer than about 1 day, but the decrease in peak flux between subsequent rotations may point to a transient nature that may be similar to the one now inferred in the radio band."907 The observed 2-hour period is well matched to the measured rotation velocity of16... and indicates a rotation axis iuclinatiou of about 90 deg.," The observed 2-hour period is well matched to the measured rotation velocity of, and indicates a rotation axis inclination of about 90 deg."908 The existence of such au extended structure provides additional support for a large-scale field that dominates the quiesceut radio aud X-ray endssion., The existence of such an extended structure provides additional support for a large-scale field that dominates the quiescent radio and X-ray emission.909 The general wisdom iu the study of maeuetic activity and its impact ou the outer atimosphere is that the iuput of maeuctic energy results in a series of related eveuts that heat the corona and chromosphere aud result iu correlated X-ray. radio. aud optical line emission.," The general wisdom in the study of magnetic activity and its impact on the outer atmosphere is that the input of magnetic energy results in a series of related events that heat the corona and chromosphere and result in correlated X-ray, radio, and optical line emission."910 This idea is supported by observations of the Sun. as well as various saples of carly AL dwarts.," This idea is supported by observations of the Sun, as well as various samples of early M dwarfs."911 The observations presented here show no clear evidence for any correlation between the various activity bauds., The observations presented here show no clear evidence for any correlation between the various activity bands.912 In particular. the quiescent radio Cluission is over-Iumninous by nearly L orders of mmaeitude compared to predictions from the radio/X-ray correlation.," In particular, the quiescent radio emission is over-luminous by nearly 4 orders of magnitude compared to predictions from the radio/X-ray correlation."913 Similarly. the radio flares do not appear to correlate with the Πα variability.," Similarly, the radio flares do not appear to correlate with the $\alpha$ variability."914 Finally. it is possible that the N-ray fiux incident on the chromosphere is uot sufficient to produce the observed Wa huuinositv (particularly if we include the contribution from higher order Baliner nes).," Finally, it is possible that the X-ray flux incident on the chromosphere is not sufficient to produce the observed $\alpha$ luminosity (particularly if we include the contribution from higher order Balmer lines)."915 Taking these various observatious and inferences iuto account woe therefore conclude that the observatious of indicate that: ≋↕⋯∏↕↑⋜⋯↸∖∪∏↴∖↴↕⋯∏↑↕≓↖↖↽⋜∏⇁↸∖↕↸∖∐∶↴⋁∐∪↴⋝↴∖↴↸∖↥⋅↖⇁⋜↧↑↕∪∐↴∖↴∪↕⋟↴∖↴↸∖↖↽↸∖↥⋅⋜↧↕ ⋜↧≼∐∐↑↕∪∐⋜↧↕∏↕⊓⋅⋯⊳∪∪↕≼↧, Taking these various observations and inferences into account we therefore conclude that the observations of indicate that: Simultaneous multi-wavelength observations of several additional ultracool dwarfs are in progress.916↖↖↽⋜∐⋅↕↸∖↴⋜∐⋅↸∖↕∐↻↥⋅∪∶↴⋁↥⋅↸∖↴∖∷∖↴∙↖↖⊽↸∖↸∖⊼↻↸∖↸⊳↑ that with this larger suuple. aud with the longer tine baselines of our observations compared to tvpical studies. we can beein to address in detail the rauge of quiescenut and variable activity. aud the abseuce or presence of the," We expect that with this larger sample, and with the longer time baselines of our observations compared to typical studies, we can begin to address in detail the range of quiescent and variable activity, and the absence or presence of the"917a/Fe| are also similar.,$\alphafe$ are also similar.918 However. Model CK. predicts hat some stars with low oxygen abundance (O/Fo]~L2. 0.3) are distributed at very low ietallicity rauge (Fe/H|< 3.5).," However, Model CK predicts that some stars with low oxygen abundance $\abra{O}{Fe} \sim 0.2-0.3$ ) are distributed at very low metallicity range $\feoh\lesssim-3.5$ )."919 These stars are born du mini halos ornmed at low redshift., These stars are born in mini halos formed at low redshift.920 Tn this model. παν SNe Ia vield iron at lower redshift. aud iron ejected frou nuni halos ower the [D/Fe| of IGAL," In this model, many SNe Ia yield iron at lower redshift, and iron ejected from mini halos lower the $\abra{O}{Fe}$ of IGM."921 Metallicity of the IGM is still ow because ejected matter is diluted in larec mass., Metallicity of the IGM is still low because ejected matter is diluted in large mass.922 Mini idos formed with the ΤΝΤ polluted by SNe Ia have ow |O/Fe] but low ietallicity., Mini halos formed with the IGM polluted by SNe Ia have low $\abra{O}{Fe}$ but low metallicity.923 Obscrvationally. these stars are not detected.," Observationally, these stars are not detected."924 If ejected matter is mixed iu sanaller mmass. iron and oxvecu abundance of polluted TOAD become lareer and these O-poor stars dissipate.," If ejected matter is mixed in smaller mass, iron and oxygen abundance of polluted IGM become larger and these O-poor stars dissipate."925 We note that. oxvecn abundance of these stars can be lower than the detection limit of O. Some stars without detection of O possibly have such an abundance feature.," We note that, oxygen abundance of these stars can be lower than the detection limit of O. Some stars without detection of O possibly have such an abundance feature."926 For Model LK. is obviously lower thau Models KI aud CI in the [O/Fe|whole metallicity range. as secu in Fie. ὃν," For Model LK, $\abra{O}{Fe}$ is obviously lower than Models KK and CK in the whole metallicity range, as seen in Fig. \ref{LK}."927 This is because a slope of the IME is steeper at mass range of stars to be SNe IL, This is because a slope of the IMF is steeper at mass range of stars to be SNe II.928 The relative frequeney of heavier SNe II Cz20 A.) is smaller and a smaller amount of a-clemeuts is ejected., The relative frequency of heavier SNe II $\gtrsim 20\msun$ ) is smaller and a smaller amount of $\alpha$ -elements is ejected.929" The ποσος, distribution of |O/Fe| is much lower than he observations for EMEP stars.", The predicted distribution of $\abra{O}{Fe}$ is much lower than the observations for EMP stars.930 At ΤΟΤΗΕ~2. the abuudances of Me. Si and Na relative to iron are also ower than the observations.," At $\feoh\sim -2$, the abundances of Mg, Si and Na relative to iron are also lower than the observations."931 At |Fe/T]=L. we can see clear decreasing trends for he a-clement abundances as increasing mctallicity for Model CIs aud Lis.," At $\feoh\gtrsim-1$, we can see clear decreasing trends for the $\alpha$ -element abundances as increasing metallicity for Model CK and LK."932 Relative nuubers of SNe In are larger or these 1iodels and they lower the ja/Fe| at higher netallicity., Relative numbers of SNe Ia are larger for these models and they lower the $\alphafe$ at higher metallicity.933" Figures 9.. 10.. aud 11 show abundance ratio distributions for Models WW. KE. aud KC usine SN vields bv Woosley&Weaver(1995).. Francoiset (2001).. and Chief&Limouei(2001).. respectively,"," Figures \ref{KW}, \ref{KF}, , and \ref{KC} show abundance ratio distributions for Models KW, KF, and KC using SN yields by \citet{Woosley95}, \citet{Francois04}, and \citet{Chieffi04}, respectively."934 For Model WW. as Francoisetal.(2001) pointed out. predicted o-elemenut abundances do not agree— with observations.," For Model KW, as \citet{Francois04} pointed out, predicted $\alpha$ -element abundances do not agree with observations."935 Predicted abunudauces of the O. Meg. and Na relative to irou are (0.5dex or more lower than the observational sample.," Predicted abundances of the O, Mg, and Na relative to iron are 0.5dex or more lower than the observational sample."936 For Model KE. since Francoisetal.(2001). inocüfv the uncleosvuthetic vields to match observational data. predicted typical abuudances of EXIP stars show σοος agreement with observations for clemeuts other than Na.," For Model KF, since \citet{Francois04} modify the nucleosynthetic yields to match observational data, predicted typical abundances of EMP stars show good agreement with observations for elements other than Na."937 The decreasinga. treud of [Cr/Fo] at low imoetallicity is also reproduced., The decreasing trend of $\abra{Cr}{Fe}$ at low metallicity is also reproduced.938 They assune that a SN with lavecr initia lnass ejects a naller amount of Cr (sec Fie 2))., They assume that a SN with larger initial mass ejects a smaller amount of Cr (see Fig \ref{yield}) ).939 Since a star with larger mass have shorter lifetime. [Cr/Foe Increases as mactallicity increases with time.," Since a star with larger mass have shorter lifetime, $\abra{Cr}{Fe}$ increases as metallicity increases with time."940 However. al other studies with uucleosvuthesis computations predict that a more massive star vields a larger amount of Cr.," However, all other studies with nucleosynthesis computations predict that a more massive star yields a larger amount of Cr."941 While Model INF πο reproduces the tvpica abuudances. it predicts larger dispersion of the clement abundances than the observations.," While Model KF well reproduces the typical abundances, it predicts larger dispersion of the element abundances than the observations."942 Especially. [O/Fe distributes from 1.5 to 11.5 at οΠ<3.," Especially, $\abra{O}{Fe}$ distributes from $-1.5$ to $+1.5$ at $\feoh<-3$."943 This model also predicts some stars with |Si/Fe|>|1., This model also predicts some stars with $\abra{Si}{Fe}>+1$.944 The predicted scatter is much larger than the observations and it indicates that a one-zone model is inadequate to uiderstaud earliest phases of the chemical evolution aud metal vields of very mctal poor SNe., The predicted scatter is much larger than the observations and it indicates that a one-zone model is inadequate to understand earliest phases of the chemical evolution and metal yields of very metal poor SNe.945 Model KC€ predicts typical abundances in agreement with observational sample. for Mg aud Si.," Model KC predicts typical abundances in agreement with observational sample, for Mg and Si."946 Lower ο abundance than observations is predicted but observed O abunudauces can be lower when non-LTE aud 3D effect taken into account. as mentioned above.," Lower O abundance than observations is predicted but observed O abundances can be lower when non-LTE and 3D effect taken into account, as mentioned above."947 This model predict some stars with very low |O/Fe| and |Mg/Fo| at [PFe/T<3., This model predict some stars with very low $\abra{O}{Fe}$ and $\abra{Mg}{Fe}$ at $\feoh<-3$.948 Such abundance patterns are produced from SNe at low-mass eud of the mass rauge to be SNe IL., Such abundance patterns are produced from SNe at low-mass end of the mass range to be SNe II.949 As seen in Figure 2. stars with 1012M. vield simall amount of O and Mg.," As seen in Figure 2, stars with $10-12\msun$ yield small amount of O and Mg."950 Lower mass limit to be SNe I is assumed to be LOAL.. in this paper but fate of the stars with ~10M.. is not well revealed., Lower mass limit to be SNe II is assumed to be $10\msun$ in this paper but fate of the stars with $\sim10\msun$ is not well revealed.951" Some stars with ~812. thought to become ""super-AGD? stars (Carcia-Berro&Iben1991). and evolve to Me white dwarts or clectron capture supernovae (Herwig2005) with very little ion vield.", Some stars with $\sim 8-12\msun$ thought to become “super-AGB” stars \citep{Garcia94} and evolve to O-Ne-Mg white dwarfs or electron capture supernovae \citep{Herwig05} with very little iron yield.952 A&bseuce of the very a-poor stars possibly indicate that the lower mass μπιτ to be SNe ILis larger than 10AZ. at very low immoetallicity., Absence of the very $\alpha$ -poor stars possibly indicate that the lower mass limit to be SNe II is larger than $10\msun$ at very low metallicity.953 Ivawabataetal.(2005) areue that stars with ο12M. become “faint supernovae” with low iron vield., \citet{Kawabata09} argue that stars with $8-12\msun$ become “faint supernovae” with low iron yield.954 Although Clicth&Limonei(2001) lave assuned ion vield is 0.1AZ... for all SNe. observations indicate that soie SNe vield lower amounts of iron.," Although \citet{Chieffi04} have assumed iron yield is $0.1\msun$ for all SNe, observations indicate that some SNe yield lower amounts of iron."955 Na is overproduced at higher metallicity (|Fe/TII]>2)., Na is overproduced at higher metallicity $\feoh >-2$ ).956 Cr abundance at solar metallicity is consistcut with the observations but the iucreasiue trend is uot reproduced., Cr abundance at solar metallicity is consistent with the observations but the increasing trend is not reproduced.957 Very large scatter of Zu is predicted because they argue that a laree amount of Zu is vielded in à SN II with m13M. but a very little amount of Zu is vielded ina SN with ii>13 M..., Very large scatter of Zn is predicted because they argue that a large amount of Zn is yielded in a SN II with $m\leq13\msun$ but a very little amount of Zn is yielded in a SN with $m>13\msun$ .958" When low mass limit to be SNe II is larger as discussed above, stars with very high ηΤο] is not formed."," When low mass limit to be SNe II is larger as discussed above, stars with very high $\abra{Zn}{Fe}$ is not formed."959 A vield of Zu is scusitive to cutropy duriue explosive Si-burning at SN explosion., A yield of Zn is sensitive to entropy during explosive Si-burning at SN explosion.960 As discussed later. cherectic hvperuovae thought to be required to explain Zu abundance of EMP stars aud their treud.," As discussed later, energetic hypernovae thought to be required to explain Zn abundance of EMP stars and their trend."961 Figures 12. and 19 show a result of Model Kisu without hvperuovae coutribution., Figures \ref{MDFn} and \ref{KKn} show a result of Model KKn without hypernovae contribution.962 The AIDF of Model khu i similar to Model KK., The MDF of Model KKn is similar to Model KK.963 For the abundance ratio distributions. the most plausible difference frou Model IWIN is lower [Zn/Fo].," For the abundance ratio distributions, the most plausible difference from Model KK is lower $\abra{Zn}{Fe}$."964 Since hivperuovae svuthesize a nmch lareer amount of Zu than normal SNe. Zu abundance of Model Iisa is lower than Model KEK and lower than observations for EXIP stars.," Since hypernovae synthesize a much larger amount of Zn than normal SNe, Zn abundance of Model KKn is lower than Model KK and lower than observations for EMP stars."965 o-cleineut abundances predicted by Model KIxu are shelth higher than Model IKIx and [O/Fe| shows better agreement with observations than Model IKK., $\alpha$ -element abundances predicted by Model KKn are slightly higher than Model KK and $\abra{O}{Fe}$ shows better agreement with observations than Model KK.966 But for Meg aud Cr. Model Ίνα predicts slightly higher relative abuudances than the observations.," But for Mg and Cr, Model KKn predicts slightly higher relative abundances than the observations."967 This is because a normal SN vields a sinaller amount of wou than a hiyperuova., This is because a normal SN yields a smaller amount of iron than a hypernova.968 Large explosion cucrey of hyperuovae affects also eas dynamics., Large explosion energy of hypernovae affects also gas dynamics.969 Mauy nini-hialos are blown up by their large explosion euergv aud ejected metal is mixed iu a larec lnass., Many mini-halos are blown up by their large explosion energy and ejected metal is mixed in a large mass.970 Since it averages element abundances. the scatter of the predicted abundance of Model Ids) is smaller than other models.," Since it averages element abundances, the scatter of the predicted abundance of Model KK is smaller than other models."971 The observed sinall scatter of [o/Fe| sugeest that there were many hvperunovae in the carly phases of the chemical evolution., The observed small scatter of $\alphafe$ suggest that there were many hypernovae in the early phases of the chemical evolution.972 We note that. however. Ikobavashietal.(2006). have tuned paramcters intheir colputations to get [O/Fe]=0.5 for all hvperuovae and the scatter of the a-clement abundancesis decreased artificially.," We note that, however, \citet{Kobayashi06} have tuned parameters intheir computations to get $\abra{O}{Fe}=0.5$ for all hypernovae and the scatter of the $\alpha$ -element abundancesis decreased artificially."973in orbital period should be InsertingS values obtained for m41 ancl mà and propagatingS uncertainties appropriately. we obtain the general relativistic predicted value Equations (3) ancl (4) apply in the orbiting svstems relerence frame.,"in orbital period should be Inserting values obtained for $m_1$ and $m_2$ and propagating uncertainties appropriately, we obtain the general relativistic predicted value Equations (3) and (4) apply in the orbiting system's reference frame."974 Relative acceleration of that frame with respect to (he solar svstem barvcenter will cause a small additional contribution to the observed D. Damour, Relative acceleration of that frame with respect to the solar system barycenter will cause a small additional contribution to the observed $\dot{P}_b$.975&Taylor(1991) presented a detailed discussion of this effect and other possible contributions to D., \citet{dt91} presented a detailed discussion of this effect and other possible contributions to $\dot{P}_b$.976" Recent progress in determining the ealactic-struceture parameters allows us to update the relevant quantities and compute a new value [or the kinematie correction to ""n", Recent progress in determining the galactic-structure parameters allows us to update the relevant quantities and compute a new value for the kinematic correction to $\dot{P}_b$.977" Using 2y=8.4z0.6 kpe for the distance to the galactic center and O,=254+16 kan | for the circular velocity of the local standard of rest (Ghezetal.2008:Gillessen2009:Reid2009)... and d=9.923.1 kpe For the pulsar distance (Weisbergοἱal.2008).. we obtain the kinematic contribution. AL},ca Thus. we lind the ratio of observed to predicted rate of orbital period decay to be Agreement between the observed orbital decay and the general relativistic prediction is illustrated in Fie. 3.."," Using $R_0=8.4\pm 0.6$ kpc for the distance to the galactic center and $\Theta_0=254\pm16$ km $^{-1}$ for the circular velocity of the local standard of rest \citep{ghez08,get09,ret09}, and $d=9.9\pm3.1$ kpc for the pulsar distance \citep{wet08}, we obtain the kinematic contribution, $\Delta\dot{P}_{\rm b, gal}$: Thus, we find the ratio of observed to predicted rate of orbital period decay to be Agreement between the observed orbital decay and the general relativistic prediction is illustrated in Fig. \ref{fig:parabola},"978 which shows how excess orbital phase (relative to an unchanging orbit) has accumulated since the pulsar's discovery in 1974., which shows how excess orbital phase (relative to an unchanging orbit) has accumulated since the pulsar's discovery in 1974.979 We note that the overall experimental uncertainty embocied in Eq. (, We note that the overall experimental uncertainty embodied in Eq. (9806) is now dominated by uncertainties in the galactic parameters and pulsar distance. not the pulsar üming measurements.,"6) is now dominated by uncertainties in the galactic parameters and pulsar distance, not the pulsar timing measurements."981" Even better agreement between observed and expected values of D, would be obtained if the true value of £j or d were slightly smaller. or Oy slishtlv larger."," Even better agreement between observed and expected values of $\dot{P}_b$ would be obtained if the true value of $R_0$ or $d$ were slightly smaller, or $\Theta_0$ slightly larger."982 For example. observed. and expected. values agree if d—6.9 kpc. which is within the Weisbergetal.(2008) error envelope.," For example, observed and expected values agree if $d=6.9$ kpc, which is within the \citet{wet08} error envelope."983 It will be interesting to see whether improved future estimates of these quantities will show one or more of these conditions to be true., It will be interesting to see whether improved future estimates of these quantities will show one or more of these conditions to be true.984"parameters of proton and He, which produce the main part of the electrons/positrons, are almost unchanged.","parameters of proton and He, which produce the main part of the electrons/positrons, are almost unchanged."985" In summary we use the pair production interaction model between CR nuclei and ambient radiation field proposed in Paper I to explain the features of the CR spectra, including the sharp knee and fine structures."," In summary we use the pair production interaction model between CR nuclei and ambient radiation field proposed in Paper I to explain the features of the CR spectra, including the sharp knee and fine structures."986 Results show that the spectra of CRs agree well with the observations., Results show that the spectra of CRs agree well with the observations.987" In our model, the He composition dominates around the knee at ~4 PeV. The sharp knee observed by Tibet air shower array and confirmed by more and more experiments, can be well reproduced through the pile-up of He particles."," In our model, the He composition dominates around the knee at $\sim 4$ PeV. The sharp knee observed by Tibet air shower array and confirmed by more and more experiments, can be well reproduced through the pile-up of He particles."988" In addition, this model can explain the fine structures of CR spectrum through the pile-up effects of CNO"," In addition, this model can explain the fine structures of CR spectrum through the pile-up effects of CNO"989We note that photometric redshifts for star forming galaxies are cdillicult due to the fatness of their spectrum. and four band. photometry is a minimum requirement for determining photometric redshifts.,"We note that photometric redshifts for star forming galaxies are difficult due to the flatness of their spectrum, and four band photometry is a minimum requirement for determining photometric redshifts."990 Additional photometric points in the Infra-red (LR) and. near-UV (NUM) help to tightly constrain photometric recshilts (Alargonier.Con-nolly&Tyson 2005)., Additional photometric points in the Infra-red (IR) and near-UV (NUV) help to tightly constrain photometric redshifts \citep{Marg05}.991. No candidate galaxies [for the =00.8426 system are observed in the field., No candidate galaxies for the 0.8426 system are observed in the field.992 The limiting 7 |xuxdl magnitude of of~25 correspondsls to a limiting luminositylu[ of this galaxy of LZO0.1L in the observed frame ; band., The limiting $i$ band magnitude of $\sim25$ corresponds to a limiting luminosity of this galaxy of $\la$ $^{\star}$ in the observed frame $i$ band.993 No object at z0.8426 was observed in the LEU observations of this QSO either (Pérouxetal.2010)., No object at $z\sim0.8426$ was observed in the IFU observations of this QSO either \citep{Per10}.994.. The only. other »ossible source in this field is a faint object south of the QSO which is minimally visible in the à and { frames. as well as he colour combined frame in Figure 2..," The only other possible source in this field is a faint object south of the QSO which is minimally visible in the $r$ and $i$ frames, as well as the colour combined frame in Figure \ref{Fig:RGB}."995 The object was not detected at. >206 with however. and was not included in the final catalogue.," The object was not detected at $>2\sigma$ with however, and was not included in the final catalogue."996 A second. possibility is that he z=0.8426 galaxy could be at à small impact parameter o the QSO and not have significant star formation., A second possibility is that the $z=0.8426$ galaxy could be at a small impact parameter to the QSO and not have significant star formation.997 The oevious IPU observations would. not. likely detect. such a galaxy. and higher quality PSE subtraction or space based imagine would be necessary to rule out such a scenario.," The previous IFU observations would not likely detect such a galaxy, and higher quality PSF subtraction or space based imaging would be necessary to rule out such a scenario."998" AX sub-DLA system is observed in the spectrum of this QSO ad 245,7200.9376 with log —119.41z50.04 (Rao.Turn-shek&Nestor 2006).", A sub-DLA system is observed in the spectrum of this QSO at 0.9376 with log $\pm$ 0.04 \citep{Rao06}.999.. Although the Zn Ll 2026.2062 lines were not detected in our earlier spectra. the system does have a high metallicity based on the depleted element Ee of 0.31+0.02 and a kinematical width 1116 (Meiringetal.2008).," Although the Zn II 2026,2062 lines were not detected in our earlier spectra, the system does have a high metallicity based on the depleted element Fe of $-0.31\pm0.02$ and a kinematical width 116 \citep{Mei08}."1000 This field. was observed in the rz filters with the exposure times given in Table 1.., This field was observed in the $riz$ filters with the exposure times given in Table \ref{Tab:Obs}.1001 Phe final combined frames are shown in the third. row of Figure. 1.. and the colour combined image composed of the rz frames is shown in Figure 2..," The final combined frames are shown in the third row of Figure \ref{Fig:Fig1}, and the colour combined image composed of the $riz$ frames is shown in Figure \ref{Fig:RGB}."1002" The seeing in the final combined frames was 0.8""OS and. 15""in the r.i. and z filters respectively."," The seeing in the final combined frames was $\sim$, and in the $r,i,$ and $z$ filters respectively."1003 Limiting magnitudes of ~25.0.24.5. and 23 were reached in the 2.4.z filters.," Limiting magnitudes of $\sim25.0,24.5,$ and 23 were reached in the $r,i,z$ filters."1004 Two galaxies are seen northwest. of the QSO. at projected impact. parameters of 38 and 66 kpe with / band magnitudes of 22.08 and 22.70 respectively., Two galaxies are seen northwest of the QSO at projected impact parameters of 38 and 66 kpc with $i$ band magnitudes of 22.08 and 22.70 respectively.1005 Two other objects are also seen in the r band image of this field. but they were notdetected above à 2a significance with and are not included in the final object catalogues.," Two other objects are also seen in the $r$ band image of this field, but they were notdetected above a $\sigma$ significance with and are not included in the final object catalogues."1006" A metal rich sub-DLA svstem is observed in the spectrum of this QSO at z,5,200.7160 with log =220.21-60.20 (Pérouxetal.2006a).", A metal rich sub-DLA system is observed in the spectrum of this QSO at 0.7160 with log $\pm$ 0.20 \citep{Per06a}.1007. From high resolution VLT spectra of this object. metallicities based on Zn of. 0.6140.20 and based on Fe of 0.5140.20 and. a kinematical width Aroy=991 have been determined. (Ixhare )..," From high resolution VLT spectra of this object, metallicities based on Zn of $\pm$ 0.20 and based on Fe of $-0.51\pm$ 0.20 and a kinematical width 91 have been determined \citep{Kh04, Per06a}."1008 This field. was observed in the qr filters with the exposure times given in Table 1.., This field was observed in the $gri$ filters with the exposure times given in Table \ref{Tab:Obs}. .1009 Phe final combined frames are shown in the fourth row of Figure 1.. and the colour combined image composed of the gr frames is shown in Figure 2..," The final combined frames are shown in the fourth row of Figure \ref{Fig:Fig1}, , and the colour combined image composed of the $gri$ frames is shown in Figure \ref{Fig:RGB}."1010" Phe secing in the final combined frames was ~0.7. O.S. and 0.7 "" in the gor. and i filters respectively."," The seeing in the final combined frames was $\sim$ 0.7, 0.8, and 0.7 $\arcsec$ in the $g,r,$ and $i$ filters respectively."1011 Limiting magnitudes of ~25.5. and 25 were reached in the q.1.7 filters.," Limiting magnitudes of $\sim25.5,25.5,$ and 25 were reached in the $g,r,i$ filters."1012 Three objects are detected in the field. with one object detected in the 7 band image to the northeast of the QSO.," Three objects are detected in the field, with one object detected in the $i$ band image to the northeast of the QSO."1013 After PSE subtraction of the QSO. the nearby. object. is more visible (labelled. 2 in Figure 1. and is in the same position as the object that was detected in the A band Li imaging of this QSO in Llewett&Wild.(2007) and adaptive optics imaging of Chunctal.(2010).," After PSF subtraction of the QSO, the nearby object is more visible (labelled 2 in Figure \ref{Fig:Fig1}, and is in the same position as the object that was detected in the $K$ band IR imaging of this QSO in \citet{HW07} and adaptive optics imaging of \citet{Chun10}."1014.. The quality of the PSE subtraction of the QSO is not adequate to obtain a magnitude of this object in the ὁ band image. and we note only its position in Table 2..," The quality of the PSF subtraction of the QSO is not adequate to obtain a magnitude of this object in the $i$ band image, and we note only its position in Table \ref{Tab:Mags}."1015 It is interesting to note that no L-o emission is detecte in this galaxy (Pérouxetal.2010)., It is interesting to note that no $\alpha$ emission is detected in this galaxy \citep{Per10}.1016. Ehe lack of H-6 emission and the non-detections in the g and ik images of this fiel (even though the seeing and depths were similar) indicates that this galaxy is of moderately carly type. with few voung stars producing emission in the near UW and u band a the redshift of the absorber.," The lack of $\alpha$ emission and the non-detections in the $g$ and $r$ images of this field (even though the seeing and depths were similar) indicates that this galaxy is of moderately early type, with few young stars producing emission in the near UV and u band at the redshift of the absorber."1017Indeed. Pérouxetal. determine a SER of «0.1NL; vet for this object. base on the non-detection of H-o.,"Indeed, \citet{Per10} determine a SFR of $<$ $_{\sun}$ $^{-1}$ for this object based on the non-detection of $\alpha$."1018 Magnitudes for the remaining objects are also given in Table 2.., Magnitudes for the remaining objects are also given in Table \ref{Tab:Mags}.1019 Two systems are observed in the spectrum of this QSO al 00.031 anc 0.0281 with log —220.0840.11 and log is. Srespeclivelg., Two systems are observed in the spectrum of this QSO at 0.7377 and 0.9281 with log $\pm$ 0.11 and log $<$ 18.8 respectively.1020"Dolhsystemshavehighmelallicilies. wilhthelowerredsh ifi having 0.05-x0.12 and 0.61-20.11 with Λο]. while the svstem at. z,4,""00.9281 is highly enriched with Zn/ll]z |0.86 and Fe/l]»—0.07 and =662Ll."," Both systems have high metallicities, with the lower redshift system at 0.7377 having $-0.05\pm$ 0.12 and $-0.61\pm$ 0.11 with 71, while the system at 0.9281 is highly enriched with $>$ +0.86 and $>-0.07$ and 62."1021" Both systems show Ca LL 3934 absorption lines. with 0.98x0.03 and 0.7940.04 [or the οςτοντ and 245,7200.9281 systems respectively (Meiringetal.2008)."," Both systems show Ca II 3934 absorption lines, with $-0.98\pm0.03$ and $-0.79\pm0.04$ for the 0.7377 and 0.9281 systems respectively \citep{Mei08}."1022". The field of this QSO was observed in the gris filters with the exposure times given in ""Table 1.", The field of this QSO was observed in the $griz$ filters with the exposure times given in Table \ref{Tab:Obs}.1023 The final combined frames are shown in fifth row of Figure 1.. and the colour combined image composed. of the gr frames is shown in Figure 2..," The final combined frames are shown in fifth row of Figure \ref{Fig:Fig1}, and the colour combined image composed of the $gri$ frames is shown in Figure \ref{Fig:RGB}."1024 Phe secing in the final combined frames was 0.8. 0.8. 0.6 ancl 1.4 aresec in the g.r7. and > filters respectively.," The seeing in the final combined frames was $\sim$ 0.8, 0.8, 0.6 and 1.4 arcsec in the $g,r,i,$ and $z$ filters respectively."1025 Limiting magnitudes of ~26.5.25.5.25. and 24 were reached in the g.οἐς filters.," Limiting magnitudes of $\sim26.5,25.5,25,$ and 24 were reached in the $g,r,i,z$ filters."1026 Several objects are detected: within 10 aresee of the QSO. as can be seen in Figure 1..," Several objects are detected within 10 arcsec of the QSO, as can be seen in Figure \ref{Fig:Fig1}."1027 Objects labelled 5. 6 and 7T are the brightest galaxies in the region. with 523.86. m;=20.00 and m;=2189.," Objects labelled 5, 6 and 7 are the brightest galaxies in the region, with $m_i$ =23.86, $m_i=20.90$ and $m_i=21.89$."1028 Object 6 and 7 appear to be interacting., Object 6 and 7 appear to be interacting.1029 ALL of these three objects have relatively [lat spectral energy distributions. tvpical of actively star forming ealaxics at the redshift) of the absorbers.," All of these three objects have relatively flat spectral energy distributions, typical of actively star forming galaxies at the redshift of the absorbers."1030 Photometric redshifts for these three objects determine ρω~ 0.10. consistent with these being members ofa group.," Photometric redshifts for these three objects determine $z_{phot}\sim0.70$ , consistent with these being members ofa group."1031 We notethat the Le error on the photometric redshift of object 5 is 0.11. re. the photometric redshift determined from is only 2o away [rom the redshift of the higher z svstem at =00.9281.," We notethat the $\sigma$ error on the photometric redshift of object 5 is $\sim0.11$ , i.e. the photometric redshift determined from is only $\sigma$ away from the redshift of the higher $z$ system at 0.9281."1032 The extremely blue colors of objects labelled three and four in Figure 1. likely exclude these galaxies of being at the recshift of either absorber., The extremely blue colors of objects labelled three and four in Figure \ref{Fig:Fig1} likely exclude these galaxies of being at the redshift of either absorber.1033" determines photometric redshifts of thro,=0.25c0.10.0.18+0.10 respectively."," determines photometric redshifts of $z_{phot}=0.25\pm0.10,0.18\pm0.10$ respectively."1034of the point spread function improves (he agreement between the data and (he models slightly in the lower slope of the gamma-ray spectrum.,of the point spread function improves the agreement between the data and the models slightly in the lower slope of the gamma-ray spectrum.1035 The proton spectrum TrialdGl. combined with model A (Fig.s. curve) produces a E2F(5) spectrum consistent with that of the EGRET data in the GeV range.," The proton spectrum Trial4GR combined with model A (Fig.8, ) produces a $E^2_\gamma F(\gamma)$ spectrum consistent with that of the EGRET data in the GeV range."1036" The higher z"" vield in model A relative to model B implies higher anti-proton vield.", The higher $\pi^0$ yield in model A relative to model B implies higher anti-proton yield.1037 Qur study. (T. Kamae et al., Our study (T. Kamae et al.1038 2005. in preparation) shows that Pythia 6.2 with the higher order terms. with the model A cross-section. and with the LIS proton spectrum produces ~1.5—2.0 times more secondary. anti-protons (han that without the higher order teris. with the model B cross-section. aud with the LIS proton spectrum. for E(p)=1—20 GeV (see Fig.9).," 2005, in preparation) shows that Pythia 6.2 with the higher order terms, with the model A cross-section, and with the LIS proton spectrum produces $\sim1.5-2.0$ times more secondary anti-protons than that without the higher order terms, with the model B cross-section, and with the LIS proton spectrum, for $E(\bar{p})=1-20$ GeV (see Fig.9)."1039 Several comments are in order., Several comments are in order.1040" The non-diffractive inelastic process is expected to produce p even Lor T,«62.5 GeV. However our low energy model based on Stephens& and Dlattnigetal.(2000) has not been implemented with the pp—p inclusive process.", The non-diffractive inelastic process is expected to produce $\bar{p}$ even for $T_p<62.5$ GeV. However our low energy model based on \citet{SB81} and \citet{Blattnig00} has not been implemented with the $pp \rightarrow \bar{p}$ inclusive process.1041" Hence we have used Pythia 6.2 with the higher order terms aud. Pythia 6.1 to T,=10 GeV [or models A and D. respectively. to obtain the p yield shown in Fig.9."," Hence we have used Pythia 6.2 with the higher order terms and Pythia 6.1 to $T_p=10$ GeV for models A and B, respectively, to obtain the $\bar{p}$ yield shown in Fig.9."1042" We conclude on the analvses presented here that an accurate modeling of (he p-p interaction (model A) with the dilfractive process and the Fevnman sealing violation makes (he gamma-ray spectrum harder and produces 30-80% more gamma-ravs (Figs.6. 7. and 8) than previous predictions (Strongοἱal.1978:Stephens&Dadhwar19831:Dermer1986:Stecker1989:Mori1997) for incident protons with T,>LOO GeV. Combination of the (wo can explain e50 of the “GeV Excess” in the EGRET Galactic ridge spectrum within the conventional cosmic proton and electron spectra as shown in Fig.3."," We conclude on the analyses presented here that an accurate modeling of the $p$ $p$ interaction (model A) with the diffractive process and the Feynman scaling violation makes the gamma-ray spectrum harder and produces $-$ more gamma-rays (Figs.6, 7, and 8) than previous predictions \citep{Strong78,SB81,Dermer86,Stecker89,Mori97}1043 for incident protons with $T_p>100$ GeV. Combination of the two can explain $\sim 50$ of the “GeV Excess” in the EGRET Galactic ridge spectrum within the conventional cosmic proton and electron spectra as shown in Fig.8."1044" The above statement is only relative to other pp—x"" production models: the absolute prediction of the Galactic ridge ganmuna-ray spectrum is conüngent on the absolute normalization. or the absolute cosmic rav. [hixes. the absolute ISAT density. and the absolute radiation field densitv."," The above statement is only relative to other $pp \rightarrow \pi^0$ production models: the absolute prediction of the Galactic ridge gamma-ray spectrum is contingent on the absolute normalization, or the absolute cosmic ray fluxes, the absolute ISM density, and the absolute radiation field density."1045 As [far as (he gamma-ray spectral shape is concerned. the remaining cliserepancy )) requires some moclilication to the conventional cosmic ray spectra: one possibility is to assume (he proton spectrum in the Galactic ridge to be a little harder than that of the solar neighborhood. eg.," As far as the gamma-ray spectral shape is concerned, the remaining discrepancy ) requires some modification to the conventional cosmic ray spectra: one possibility is to assume the proton spectrum in the Galactic ridge to be a little harder than that of the solar neighborhood, eg."1046 ~2.5 in power-law index as TrailtGh in Fig.s., $\sim 2.5$ in power-law index as Trail4GR in Fig.8.1047 We have compared model A critically with data [rom accelerator experiments (Figs.La. 3. 4. and 5) and confirmed that important aspects of experimental data are reproduced much better bv model A than model D which erudely reflects the Fevnman scaling hypothesis.," We have compared model A critically with data from accelerator experiments (Figs.1a, 3, 4, and 5) and confirmed that important aspects of experimental data are reproduced much better by model A than model B which crudely reflects the Feynman scaling hypothesis."1048 We believe that all future cosmic p-p interaction models must include the diffractive process aud incorporate the scaling violation., We believe that all future cosmic $p$ $p$ interaction models must include the diffractive process and incorporate the scaling violation.1049already assumed to be fairly mocest. aud even adopting a face-on inclination would not brighten the predicted maguitude appreciably.,"already assumed to be fairly modest, and even adopting a face-on inclination would not brighten the predicted magnitude appreciably."1050 However. the more accurate HST FCS parallax 2000) briugs the empirical absolute magnitude to 3.5. much closer to the predicted value.," However, the more accurate HST FGS parallax \citep{harrison00} brings the empirical absolute magnitude to 3.8, much closer to the predicted value."1051 Harrisonetal.(2003a) discuss the Ady) (παν) - πμ relation at greater leneth using the HST parallaxes. aud confirm that the relatiouship appears to hold.," \citet{harrison03a} discuss the $M_V$ (max) - $P_{\rm orb}$ relation at greater length using the HST parallaxes, and confirm that the relationship appears to hold."1052 The parallax of AM Her agrees well with distances based on the spectrum of the secondary., The parallax of AM Her agrees well with distances based on the spectrum of the secondary.1053 EF Eri is uot accurately. determined but comes in a little farther away than the white dwarf atmosphere (Beuermanunetal.2000) would suggest., EF Eri is not accurately determined but comes in a little farther away than the white dwarf atmosphere \citep{beuermanneferi} would suggest.1054 Harrisonetal.(2003) have recently ujeasured aud iuodeled iufrared spectra aud light curves of EF Eri. but do not comment on how the mocels are uormalized to the data (that is. the distance): the infrared light curve is quite complicated aud so model dependeucies are likely to creep into such determinations in αν case.," \citet{harrison03}1055 have recently measured and modeled infrared spectra and light curves of EF Eri, but do not comment on how the models are normalized to the data (that is, the distance); the infrared light curve is quite complicated and so model dependencies are likely to creep into such determinations in any case."1056 GP Com was the only δια CV. included. but it appears to be the first to have au accurate distance determination.," GP Com was the only helium CV included, but it appears to be the first to have an accurate distance determination."1057 Taking our measured V.=16.1 as typical. the measured distauce modulus am—M=1240.2 yields Ady=411.9.," Taking our measured $V = 16.1$ as typical, the measured distance modulus $m - M = 4.2 \pm 0.2$ yields $M_V = +11.9$."1058 The main couclusious are as follows. (, The main conclusions are as follows. (10591) As USNOO9? assert. interestingly accurate parallaxes cau be derived without special equipment. provided the instrumentation is stable. (,"1) As USNO92 assert, interestingly accurate parallaxes can be derived without special equipment, provided the instrumentation is stable. ("10602) Over the years a fair amount of conventional wisdom has grown up arouud cataclysmic distauces. based ou detectious of secoucary stars. kinematical evidence. aud the like.,"2) Over the years a fair amount of conventional wisdom has grown up around cataclysmic distances, based on detections of secondary stars, kinematical evidence, and the like."1061 This study largelye corroborates this couventional wisdom: a one-line sumaiuary mieht[we be uo biee surprises’. (, This study largely corroborates this conventional wisdom; a one-line summary might be `no big surprises'. (10623) Even so. there are some small surprises.,"3) Even so, there are some small surprises."1063" WZ See is a little closer that some previous estimates liac suggested. aud a little farther away than predicted by the My (max) - 2, relation."," WZ Sge is a little closer than some previous estimates had suggested, and a little farther away than predicted by the $M_V$ (max) - $P_{\rm orb}$ relation."1064 Although the result for EF Eri is impre‘ise. it appears to be a little farther away than anticipated. (," Although the result for EF Eri is imprecise, it appears to be a little farther away than anticipated. ("10651) GP Com is evidently the first ——heliuui CV. with a reliable clistauce.,4) GP Com is evidently the first helium CV with a reliable distance.1066 It is intrinsically faint (My= 411.9)., It is intrinsically faint $M_V = +11.9$ ).1067 Furthermore. its transverse velocity is 110 kim | outside the rather sinall velocity dispersion of the main CV population.," Furthermore, its transverse velocity is 110 km $^{-1}$, outside the rather small velocity dispersion of the main CV population."1068 Special thauks go to Dave Monet for encouragement aud free advice. which was lufinitely many times more valuable than its price. aud lor his role in pioneering this powerful techuique.," Special thanks go to Dave Monet for encouragement and free advice, which was infinitely many times more valuable than its price, and for his role in pioneering this powerful technique."1069 Conard Dalin. communicated a USNO parallax for WZ See while this paper was iu preparation. and it was a great conlidence-buikler to find it was essentially. identical to tliat presented here.," Conard Dahn communicated a USNO parallax for WZ Sge while this paper was in preparation, and it was a great confidence-builder to find it was essentially identical to that presented here."1070 Also. Tom Harrison kiudly communicated the wouderfully accurate HST parallaxes just as L was completing this paper.," Also, Tom Harrison kindly communicated the wonderfully accurate HST parallaxes just as I was completing this paper."1071 Tom Marsh suggested GP Com as a target., Tom Marsh suggested GP Com as a target.1072 After I had begun development of the Bayesian distauce estimation techniques I discovered that Haywood 5$1uitl, After I had begun development of the Bayesian distance estimation techniques I discovered that Haywood Smith1073 After I had begun development of the Bayesian distauce estimation techniques I discovered that Haywood 5$1uitli, After I had begun development of the Bayesian distance estimation techniques I discovered that Haywood Smith1074the various classes of objects are probably not homologous.,the various classes of objects are probably not homologous.1075 jut the [aet that the dwarf spheroidal galaxies deviate significantly from this FP is consistent with MOND., But the fact that the dwarf spheroidal galaxies deviate significantly from this FP is consistent with MOND.1076 These are deep MOND low-surface-brightness objects with a large discrepancy: in this deep MOND limit the length scale has dropped out as a parameter. and the mass is related only to the velocity. dispersion.," These are deep MOND low-surface-brightness objects with a large discrepancy; in this deep MOND limit the length scale has dropped out as a parameter, and the mass is related only to the velocity dispersion."1077 The high surface brightness objects defining the Newtonian FP must. ceviate from an isothermal state. as they do in the case of the bright ellipticals ancl the globular clusters: both classes of objects exhibit a line-of-steht velocity dispersion that declines with radius. at. least within 1.5 Hj.," The high surface brightness objects defining the Newtonian FP must deviate from an isothermal state, as they do in the case of the bright ellipticals and the globular clusters; both classes of objects exhibit a line-of-sight velocity dispersion that declines with radius, at least within 1.5 $\mathit{R_{eff}}$."1078 At laveecr radii. the radial profile of the 7 is highly clependent upon the form of the anisotropy parameter 1. but a continuing decline is consistent with a trend toward more racial orbits in the outer regions.," At larger radii, the radial profile of the $\sigma$ is highly dependent upon the form of the anisotropy parameter $\beta$, but a continuing decline is consistent with a trend toward more radial orbits in the outer regions."1079 In order to produce a high surface density Newtonian object. the required. deviation. from. an isothermal state is relatively small.," In order to produce a high surface density Newtonian object, the required deviation from an isothermal state is relatively small."1080 “Pypically. theJalle models which are Newtonian within an elfective radius are equivalent to polvtropes of index 12 to 16: thus the density changes by many orders of magnituce while the velocity dispersion changes by a factor of two.," Typically, the Jaffe models which are Newtonian within an effective radius are equivalent to polytropes of index 12 to 16; thus the density changes by many orders of magnitude while the velocity dispersion changes by a factor of two."1081 In other words. the requirements [or producing objects which obey the Newtonian virial relation are that they should have high internal accelerations (I ay) ancl be near-isothermal with a racially declining velocity clispersion.," In other words, the requirements for producing objects which obey the Newtonian virial relation are that they should have high internal accelerations $\ge a_0$ ) and be near-isothermal with a radially declining velocity dispersion."1082 One might argue that this again bees the question: why are cllipticals and globular clusters near-isothermal objects with high internal accelerations?, One might argue that this again begs the question: why are ellipticals and globular clusters near-isothermal objects with high internal accelerations?1083 Does this not push the existence of the FP back to contingencies of structure formation?, Does this not push the existence of the FP back to contingencies of structure formation?1084 ‘To some extent. this is. the case. but the requirement of a near-isothermal state is rather mild.," To some extent, this is the case, but the requirement of a near-isothermal state is rather mild."1085 Violent relaxation. even in spherical collapse. typically produces a near-isothermal virialized structure.," Violent relaxation, even in spherical collapse, typically produces a near-isothermal virialized structure."1086 For example. with modified dynamics just such objects with high internal accelerations do result. from. the spherically svnumetric dissipationless collapse out of a medium initially expanding with the Llubble flow (Sanders 2008).," For example, with modified dynamics just such objects with high internal accelerations do result from the spherically symmetric dissipationless collapse out of a medium initially expanding with the Hubble flow (Sanders 2008)."1087 In. non-spherical MONDian clissipationless collapse calculations. the final virializecl objects with low internal accelerations (< ay) are essentially isothermal. but also those with higher internal accelerations are near-isothermal with a radial velocity. dispersion. which. compared. with density. declines slowly with radius (Nipoti. Londrillo Ciotti 2007).," In non-spherical MONDian dissipationless collapse calculations, the final virialized objects with low internal accelerations $\le a_0$ ) are essentially isothermal, but also those with higher internal accelerations are near-isothermal with a radial velocity dispersion which, compared with density, declines slowly with radius (Nipoti, Londrillo Ciotti 2007)."1088 Viewed in this context. the cdwarl spheroidal galaxies become the anomalous objects requiring an alternative formation scenario.," Viewed in this context, the dwarf spheroidal galaxies become the anomalous objects requiring an alternative formation scenario."1089 lt is the FJ relation. in spite of its large scatter. that emerges as the more fundamental and more universal scaling relation for hot systems. embodving both high and. low surface brightness systems.," It is the FJ relation, in spite of its large scatter, that emerges as the more fundamental and more universal scaling relation for hot systems, embodying both high and low surface brightness systems."1090 The amplitude of the relation is even more significant than its slope because this is related directly to the magnitude of ay., The amplitude of the relation is even more significant than its slope because this is related directly to the magnitude of $a_0$.1091 Lt is easily demonstrated that pure Newtonian systems (obeving the Newtonian virial theorem) with a constant mean surface density will also fall on a ALxa? relation., It is easily demonstrated that pure Newtonian systems (obeying the Newtonian virial theorem) with a constant mean surface density will also fall on a $M\propto \sigma^4$ relation.1092 The essential point is the sets this characteristic value of the surface density (20/0) ftfor all near-isothermal svstenms., The essential point is that $a_0$ sets this characteristic value of the surface density $a_0/G$ ) for all near-isothermal systems.1093 The appearance of a universal mass-velocity dispersion relation as an aspect of dynamics cirecthy rellects the presence of this new dimensional constant in the structure equation., The appearance of a universal mass-velocity dispersion relation as an aspect of dynamics directly reflects the presence of this new dimensional constant in the structure equation.1094 Phe fact that the magnitude of this constant (=107 eni/s7) is the same as that required by the scale of spiral galaxy rotation curves (the Tullv-Fisher relation) is one more powerful indication that such à. fundamental acceleration scale exists in the Universe and is operative in eravitational physics., The fact that the magnitude of this constant $\approx 10^{-8}$ $^2$ ) is the same as that required by the scale of spiral galaxy rotation curves (the Tully-Fisher relation) is one more powerful indication that such a fundamental acceleration scale exists in the Universe and is operative in gravitational physics.1095 lam grateful to Moti Milgrom and Joe Wolf lor useful comments and to Scott Trager for a critical. reading. of the paper., I am grateful to Moti Milgrom and Joe Wolf for useful comments and to Scott Trager for a critical reading of the paper.1096 This paper. in content ancl presentation. has benefitted from the comments of an anonvmous referee.," This paper, in content and presentation, has benefitted from the comments of an anonymous referee."1097(2007).. not differentiating [BITB2007| 1 and 2 which are unresolved iu the data due to the large off-axis angle.,", not differentiating [BHB2007] 1 and 2 which are unresolved in the data due to the large off-axis angle."1098 Additionally. [DIIB2007| 7 appears to have a weak N-vay counterpart that is uot listed in the 2NAIG catalog. but was identified iu our wavelet source detection.," Additionally, [BHB2007] 7 appears to have a weak X-ray counterpart that is not listed in the 2XMMi catalog, but was identified in our wavelet source detection."1099 One N-ray detected YSO — |BIID2007] 20 is located outside of the on-core region. and the deeply οοσα protostar |DIID2007] 11. while N-rayvdetected. is filtered due to its weak 2MÁSS counterpart.," One X-ray detected YSO – [BHB2007] 20 – is located outside of the on-core region, and the deeply embedded protostar [BHB2007] 11, while X-ray–detected, is filtered due to its weak 2MASS counterpart."1100 In the iunerinost. nost deeply cimbedded part of the Spitzer—identified vouug cluster (Brookeetal.2007).. no rew candidate members were detected.," In the innermost, most deeply embedded part of the -identified young cluster \citep{bro07}, no new candidate members were detected."1101 However. a 2MASS source south of |DIID2007]. 6 and 7 (not among the identified YSOs) was found to ave a weal. soft N-ray counterpart.," However, a 2MASS source south of [BHB2007] 6 and 7 (not among the identified YSOs) was found to have a weak, soft X-ray counterpart."1102 The X-rav properties of the known YSOs in B559 are ciseussed m more detail iu Section 3.3.., The X-ray properties of the known YSOs in 59 are discussed in more detail in Section \ref{sec_b59}.1103 Since we undoubtedly again detect backeround sources in the Calactic bulee next to putative sources im the cloud as well as foreground sources. we again analyze the density of X-ray sources du he on-core aud the off-core regions.," Since we undoubtedly again detect background sources in the Galactic bulge next to putative sources in the cloud as well as foreground sources, we again analyze the density of X-ray sources in the on-core and the off-core regions."1104 In 665. all A-rav sources with NIR counterparts lie in off-core regions: this is not the case in BSd9 and he PAIR.," In 68, all X-ray sources with NIR counterparts lie in off-core regions; this is not the case in 59 and the PMR."1105 Iu the absence of a class TID source »pulatiou in the Pipe region. we would expect o fiud a source density that is lower than or equal o the source density iu the offcore region due o the additional extinction.," In the absence of a class III source population in the Pipe region, we would expect to find a source density that is lower than or equal to the source density in the off-core region due to the additional extinction."1106 Iu. 559. with its suown cluster of ¥YSOs. we find that the source density in the on-core regions is indeed slightly ugher than the source density in the surrounding off-core regions of the X-rav sources with NIR counterparts lie in the ou-core regions which cover of the field of view).," In 59, with its known cluster of YSOs, we find that the source density in the on-core regions is indeed slightly higher than the source density in the surrounding off-core regions of the X-ray sources with NIR counterparts lie in the on-core regions which cover of the field of view)."1107 Tn the PAIR. in strikiue contrast. we find that ouly of these sources are in the on-core regious even though these cover of the field of view.," In the PMR, in striking contrast, we find that only of these sources are in the on-core regions even though these cover of the field of view."1108 Note that the source deusitv in 559 turus into an uudoerdeusitv without the counterparts of known YSOs., Note that the source density in 59 turns into an underdensity without the counterparts of known YSOs.1109 This conrparison of X-ray source deusitics iu the on-core and off-core regions shows that there is no indication for a significant. previously unknown population of PMS objects.," This comparison of X-ray source densities in the on-core and off-core regions shows that there is no indication for a significant, previously unknown population of PMS objects."1110 Tn the on-core regions of the observations. we therefore find an uppoer mit of 6 new evolved YSOs since this is the nuuber ofX- rav sources with appropriate As-band counterparts. rot counting the known YSOs.," In the on-core regions of the observations, we therefore find an upper limit of 6 new evolved YSOs since this is the number of X-ray sources with appropriate $K_S$ -band counterparts, not counting the known YSOs."1111 However. the fact hat the two regions with any detectious in the ou-core regions. 559 aud the PAIR. both show underdeusities with respect to the surounudius vackeround source densities (uot takius iuto account the known YSOs iu 559) suggests that a nore realistic upper limit is closer to zero.," However, the fact that the two regions with any detections in the on-core regions, 59 and the PMR, both show underdensities with respect to the surrounding background source densities (not taking into account the known YSOs in 59) suggests that a more realistic upper limit is closer to zero."1112 A more stringent upper lanit results when additionally requiring detections at 21g. assuming that this selects ~SO Finally. we can additionally eive strict upper Πιν for anv evolved YSO population in the three eutire fields to account for auv more distributed »pulatious.," A more stringent upper limit results when additionally requiring detections at $\mu$ m, assuming that this selects $\sim80$ Finally, we can additionally give strict upper limits for any evolved YSO population in the three entire fields to account for any more distributed populations."1113 For this purpose. we cannot treat he off-core source density as cutirely uurelated o the cloud.," For this purpose, we cannot treat the off-core source density as entirely unrelated to the cloud."1114 While we have found that all sources in the B6GS and rine fields can be explained bx a combination of chance aliguiments and weal vackeround sources. there are 23 selected X-ray sources in the 559 area when only 3.5 would ο expected from chance aligumnenuts;," While we have found that all sources in the 68 and ring fields can be explained by a combination of chance alignments and weak background sources, there are 23 selected X-ray sources in the 59 area when only 3.5 would be expected from chance alignments."1115 Subtracting he expected uuuber of chance aliguiuecuts and he muuber of known YSOs among the selected sources (7). we derive an upper luit of ~13 new candidate YSOs in the ecutive 559 field.," Subtracting the expected number of chance alignments and the number of known YSOs among the selected sources (7), we derive an upper limit of $\sim13$ new candidate YSOs in the entire 59 field."1116 Note that among the selected sources. the field coutaius six detectious at 21 nu apart frou he known YSOs. again suggesting a more modest upper limit for anv additional more evolved YSOs.," Note that among the selected sources, the field contains six detections at 24 $\mu$ m apart from the known YSOs, again suggesting a more modest upper limit for any additional more evolved YSOs."1117 These sources would be in addition to the upper iuit of 15 previously known cauclidate YSOs iu [1559 (Brookeetal.2007:Forbrich2009).," These sources would be in addition to the upper limit of 15 previously known candidate YSOs in 59 \citep{bro07,for09}."1118. Tn addition. to the analysis in the previous section. which focused on finding candidate YSOs other than the ones already kuown from. iul-infrared imagine. we now take a more detailed N-vay look at the sample of YSOs identified by Brookeetal.(2007).. using Spitzer.," In addition to the analysis in the previous section, which focused on finding candidate YSOs other than the ones already known from mid-infrared imaging, we now take a more detailed X-ray look at the sample of YSOs identified by \citet{bro07}, using ."1119. It turus out that half of their sources have N-ray counterparts (Table 3))., It turns out that half of their sources have X-ray counterparts (Table \ref{tab_brookeX}) ).1120 Note that |DIID2007] 1 aud 2 are far off-axis in the data and detected as a relatively bright unresolved X-ray source., Note that [BHB2007] 1 and 2 are far off-axis in the data and detected as a relatively bright unresolved X-ray source.1121 As corroborated by near-infrared spectroscopy (Covey et al., As corroborated by near-infrared spectroscopy (Covey et al.1122 2010. 51512.)). sources [BIID2007] 5," 2010, ), sources [BHB2007] 5"1123Using the most straightforward. of these methocls. directly applying the boundaries as in Table 1.. consider a quasar at 1077AL. and Lgs at LS&z<2.0. fy=3.5 Gyr (2=L.85 using cosmological parameters from ?7)).,"Using the most straightforward of these methods, directly applying the boundaries as in Table \ref{table:boundaries}, consider a quasar at $10^{8.5} M_\odot$ and $L_{Edd}$ at $1.8 < z < 2.0$, $t_0 = 3.5$ Gyr $z = 1.85$ using cosmological parameters from \citet{WMAP3}) )."1124 Evolving his quasar forward. while constrained to lie within the Table l parameters. restricts the allowed slope & and conversion actor & to narrow bands for both power-law (Figure 8)) and exponential (Figure 9)) decavs.," Evolving this quasar forward, while constrained to lie within the Table \ref{table:boundaries} parameters, restricts the allowed slope $k$ and conversion factor $\kappa$ to narrow bands for both power-law (Figure \ref{fig:8.5pl}) ) and exponential (Figure \ref{fig:8.5exp}) ) decays."1125 The allowed parameters orm roughly a one-dimensional locus., The allowed parameters form roughly a one-dimensional locus.1126 As indicated by the test parameters in 3.. the turnoll ime /r and final mass Al; are sensitive to cach of these parameters.," As indicated by the test parameters in \ref{sec:tracks}, the turnoff time $t_f$ and final mass $M_f$ are sensitive to each of these parameters."1127 Requiring that the turnolf happen at a specilic time or mass restricts the possibilities to a narrower set of possible parameters (e.g.. 0.5<logAJ/M.9.6 in Figure 93).," Requiring that the turnoff happen at a specific time or mass restricts the possibilities to a narrower set of possible parameters (e.g., $9.5 < \log M/M_\odot < 9.6$ in Figure \ref{fig:8.5exp}) )."1128 Solutions with larger & correspond to SALBLI that gain mass more slowly at a given luminosity and/or are more often quiescent. resulting in slower growth ancl a smaller mass at turnoll.," Solutions with larger $\kappa$ correspond to SMBH that gain mass more slowly at a given luminosity and/or are more often quiescent, resulting in slower growth and a smaller mass at turnoff."1129 Solutions as &0 rapidly produce hieh-mass SMDAIL that then turns olf., Solutions as $\kappa \rightarrow 0$ rapidly produce high-mass SMBH that then turns off.1130 Phese solutions therefore correspond. to solutions in which growth is primarily non-luminous. and thus are disallowed by the requirement that most SAIBLL mass was aceuired during a luminous quasar phase (???).. and so are not plausible candidates for SALBIL erowth.," These solutions therefore correspond to solutions in which growth is primarily non-luminous, and thus are disallowed by the requirement that most SMBH mass was acquired during a luminous quasar phase \citep{Soltan1982,Yu2002,Elvis2002}, and so are not plausible candidates for SMBH growth."1131 Individual quasars in SDSS are observed to undergo ~0.3 dex variations in the optical on timescales of months to vears (2)..., Individual quasars in SDSS are observed to undergo $\sim 0.3$ dex variations in the optical on timescales of months to years \citep{structurefunction}.1132 “Phe luminosities on the model tracks represent he characteristic luminosity of the quasar averaged over onger timescales., The luminosities on the model tracks represent the characteristic luminosity of the quasar averaged over longer timescales.1133 However. the observed: distribution. of quasars includes a dispersion. due to this intrinsic short-erm variability.," However, the observed distribution of quasars includes a dispersion due to this intrinsic short-term variability."1134 the boundaries in Table 1 are similarly oadened. so the proper track must lie well within these xuncdaries.," the boundaries in Table \ref{table:boundaries} are similarly broadened, so the proper track must lie well within these boundaries."1135 Individual quasars might spend a small fraction of their time across a boundary(5%... see 3)).," Individual quasars might spend a small fraction of their time across a boundary, see \ref{sec:tracks}) )."1136 A vestriction to lie 0.2 dex away from cach boundary wocluces no non-trivial solutions at fy=3.5.Aly8.5.," A restriction to lie $0.2$ dex away from each boundary produces no non-trivial solutions at $t_0 = 3.5, M_0 = 8.5$."1137 This might be because (1) the objects observed at 107M. are. due to intrinsic. variability. above their characteristic uminositv. (2) the redshift bins are too wide. or (3) quasar evolution does not lie on a simply-parametrizecl track of the sort we are fitting.," This might be because (1) the objects observed at $10^{8.5} M_\odot$ are, due to intrinsic variability, above their characteristic luminosity, (2) the redshift bins are too wide, or (3) quasar evolution does not lie on a simply-parametrized track of the sort we are fitting."1138 HE Ady is allowed to vary. keeping fy=3.5 ," If $M_0$ is allowed to vary, keeping $t_0 = 3.5$ "1139total proper motion greater than zero.,total proper motion greater than zero.1140 It shows a weak but noteworthy trend for the high variability group to have lower proper motion than the low vartability group., It shows a weak but noteworthy trend for the high variability group to have lower proper motion than the low variability group.1141 We also tested the significance of these differences using two-sample KS tests. and parameterised the shape of the distributions. the results of which can be seen in Table 3..," We also tested the significance of these differences using two-sample KS tests, and parameterised the shape of the distributions, the results of which can be seen in Table \ref{table:pm_tab}."1142 The KS test results show that with the exception of A stars. and to some extent F. the proper motion values for the high and low variability groups are very unlikely to be drawn from the same distribution. while the shape parameters highlight more subtle differences in shape and trends between spectral types.," The KS test results show that with the exception of A stars, and to some extent F, the proper motion values for the high and low variability groups are very unlikely to be drawn from the same distribution, while the shape parameters highlight more subtle differences in shape and trends between spectral types."1143 This is consistent with the view that higher variability stars are younger and therefore have lower proper motions., This is consistent with the view that higher variability stars are younger and therefore have lower proper motions.1144 This conclusion is dependant on the stars being at the same distance and location on the sky., This conclusion is dependant on the stars being at the same distance and location on the sky.1145 In our samples. the magnitude and spatial distributions are approximately equal for the high and low variability subsets.," In our samples, the magnitude and spatial distributions are approximately equal for the high and low variability subsets,"1146motion (expansion).,motion (`expansion').1147" The average surface deusity of sources in tie. Galactic plane. assuiniug au anuulus of 0.5 kpe ceitred on 3.5 kpe. is 6 αιd 7 sources per >- [orJ the near aud far+ portious"" of the arms (415° lougitude) res»ectively."," The average surface density of sources in the Galactic plane, assuming an annulus of 0.5 kpc centred on 3.5 kpc, is 6 and 7 sources per ${^2}$ for the near and far portions of the arms $\pm$ $^{\circ}$ longitude) respectively."1148 This is comparable to tle expected ‘smeared? density of sources iu the spiral arus (?).., This is comparable to the expected `smeared' density of sources in the spiral arms \citep{caswell10mmb1}.1149 Tie average ceisity along tlie taugeit (exeludiug sources associated with other structural eatiJes. eee. limiting the velocity range to —G0 + to —85 kkniss!j is 22 sources per sper.," The average density along the tangent (excluding sources associated with other structural features, i.e. limiting the velocity range to $-$ $^{-1}$ to $-$ $^{-1}$ ) is 22 sources per ${^2}$."11502 This higler density ca1 be accounted for yy the presence of a spiral aria origin. whic1 we examine |1 Section ??," This higher density can be accounted for by the presence of a spiral arm origin, which we examine in Section \ref{armorigins}."1151 The existing uodels o “thre ¢vnanies on tle iuuer Galaxy account. [or cU31% of the 3-kpe arm sources., The existing models of the dynamics on the inner Galaxy account for $\le$ of the 3–kpc arm sources.1152 In compa‘ison. a simple elli»tic‘al ring or ‘expatiug circular ring account for of the order o," In comparison, a simple elliptical ring or `expanding' circular ring account for of the order of."1153"ugl there a‘e several nxxlels for an ""expaicine” circular rine close to the centre of our Galaxy (within a Galactocenutric radius of «] | kpe) (e.g.?2???).. and munerous examples of barred exteral galaxies with rines (e.g.ο)??7).. dvianica models of the Milky Way since tlie early examples ii he 1970s do not [avo rosuch a feattre."," Although there are several models for an `expanding' circular ring close to the centre of our Galaxy (within a Galactocentric radius of $<$ 1 kpc) \citep[e.g.][]{scoville72, kaifu72, kaifu74, bally87}, and numerous examples of barred external galaxies with rings \citep[e.g.][]{buta86, buta96,treuthardt09}, dynamical models of the Milky Way since the early examples in the 1970s do not favour such a feature."1154 Soue radial motion may be a resut of the influence of the radius of corotatio Jesolialice: a product of the transition between the elliptical orbits which ollow the bar inside t eraclius of corotatio1 resonance aud he circular orbits which exlst outside. wit ithe 3-kpe rine te interface region between tlie two. pi{lin© elliptically orbiting inaterial iuto a ci‘cular orbit (an early example is hat of ?)).," Some radial motion may be a result of the influence of the radius of corotation resonance: a product of the transition between the elliptical orbits which follow the bar inside the radius of corotation resonance and the circular orbits which exist outside, with the 3–kpc ring the interface region between the two, pulling elliptically orbiting material into a circular orbit (an early example is that of \citealt{shane72}) )."1155 The more favotred picwet in teris of dyiamical moclelli1g) of the elliptical ring Or 5ream lines cau account for tlie parallel sections and tο some cee'ee he negative tarscent. but. cannot 'eadily account for tle positive longitude llase* with large veocities.," The more favoured picture (in terms of dynamical modelling) of the elliptical ring or stream lines can account for the parallel sections and to some degree the negative tangent, but cannot readily account for the positive longitude masers with large velocities."1156 The 6.7-GHz masers. as 1‘acers of the structure. have he potenti: to fully celine t eosyatial and kiueimalic structure of the 3-kpe ring. since further astrometr lneasturenentiswill alow parallax cistances (thus a direc measure of the ellipticity of the rine) a the fll three cii16113]onal velocity belavlour.," The 6.7–GHz masers, as tracers of the structure, have the potential to fully define the spatial and kinematic structure of the 3–kpc ring, since further astrometric measurements will allow parallax distances (thus a direct measure of the ellipticity of the ring) and the full three dimensional velocity behaviour."1157 The spiral arms are believed to originate at approximately the radius of corotation resona of the Galactic bar fe.o.?? where the Galactic material is rotating at tLe sale speed as j»atteru speed o ‘the bar. aia racial oscillation is zero (?)..," The spiral arms are believed to originate at approximately the radius of corotation resonance of the Galactic bar \citep[e.g.][]{lopez99,englmaier99}, where the Galactic material is rotating at the same speed as the pattern speed of the bar, and radial oscillation is zero \citep{lindblad74}. ."1158 Highly elliptical orbits exist wit he radius of co‘olatlol resonance. in contrast to cireular orbits outside (?ον," Highly elliptical orbits exist within the radius of corotation resonance, in contrast to circular orbits outside \citep{englmaier06}."1159 This requires t he 3-kpc aums should be eitlier a more elliptical structure interior o the radius of corotation 'esOllallce. With orbits followiug the bar (e.g.??) Or a more circular sructu'e close to the radius of corotation resonaice. similar to resolance rings seen ii exterual galaxies. sich as NGC9523 aud GC1215) (e.(e.g.72).e," This requires that the 3–kpc arms should be either a more elliptical structure interior to the radius of corotation resonance, with orbits following the bar \citep[e.g.][]{contopoulos80, englmaier00} or a more circular structure close to the radius of corotation resonance, similar to resonance rings seen in external galaxies, such as NGC2523 and NGC4245 \citep[e.g.][]{buta99,treuthardt09}."1160 As discussed in Sec‘ious ?? aud ??.. the maser clisribution leads us to believe he lone thin bar is he most iufluentia on star formation. with a bar semi-major axis of ~3.1 kpe and orieitation of  127. and the 3 kpe arms appear to be well approximatecd by an elliptical ring (or cireular with racial velocity Comporents resulting [ron the resonance).," As discussed in Sections \ref{3kpctan} and \ref{3kpcstrutfit}, the maser distribution leads us to believe the long thin bar is the most influential on star formation, with a bar semi-major axis of $\sim$ 3.4 kpc and orientation of $\sim$ $^{\circ}$, and the 3 kpc arms appear to be well approximated by an elliptical ring (or circular with radial velocity components resulting from the resonance)."1161 This indicates a racius of corotation resoliaice of ~ LO kpe. ard a possible location for the origins of thespiral aruis.," This indicates a radius of corotation resonance of $\sim$ 4.0 kpc, and a possible location for the origins of thespiral arms."1162To understand the role of low and intermediate mass stars within the cosmic matter cycle the efficiency of the third dredge up is a critical quantity.,To understand the role of low and intermediate mass stars within the cosmic matter cycle the efficiency of the third dredge up is a critical quantity.1163 During the short but decisive asymptotic giant branch (AGB) phase the third dredge up is responsible for mixing the burning products and the material produced via the s-process to the surface from where it can be ejected into the interstellar medium by stellar mass loss (see e.g. Busso et citeBusso99 for a review).," During the short but decisive asymptotic giant branch (AGB) phase the third dredge up is responsible for mixing the burning products and the material produced via the s-process to the surface from where it can be ejected into the interstellar medium by stellar mass loss (see e.g. Busso et \\cite{Busso99}1164 for a review)."1165 Current stellar evolution models (e.g. Straniero et al. citestra97:;, Current stellar evolution models (e.g. Straniero et al. \\cite{stra97};1166 Herwig 2000:: Busso et citeBusso01:: Stancliffe et citestancliffeO4:; Straniero et al. 2006:, Herwig \cite{Herwig00}; Busso et \\cite{Busso01}; ; Stancliffe et \\cite{stancliffe04}; Straniero et al. \cite{stra06};1167 Karakas Lattanzio 2007) provide quite detailed predictions for the surface abundance changes during the AGB phase., Karakas Lattanzio \cite{KL07}) ) provide quite detailed predictions for the surface abundance changes during the AGB phase.1168 Different models agree qualitatively., Different models agree qualitatively.1169 The dependency of dredge up on various parameters like mass and metallicity has been explored in the models (ben Renzini 1983; Straniero et al. 2003)., The dependency of dredge up on various parameters like mass and metallicity has been explored in the models (Iben Renzini \cite{ib83}; Straniero et al. \cite{SDCG03}) ).1170 Quantitative checks of the model predictions for third dredge-up efficiency have been so far restricted to AGB stars in the solar neighborhood LLebzelter Hron 2003.. Busso et citeBussoO1)) or to indirect methods like the study of the progeny of AGB stars or synthetic stellar evolution (e.g. van Eck et citevaneckO1.. Marigo et citeMarigo99)).," Quantitative checks of the model predictions for third dredge-up efficiency have been so far restricted to AGB stars in the solar neighborhood Lebzelter Hron \cite{LH03}, Busso et \\cite{Busso01}) ) or to indirect methods like the study of the progeny of AGB stars or synthetic stellar evolution (e.g. van Eck et \\cite{vaneck01}, Marigo et \\cite{Marigo99}) )."1171 However. for studying ongoing nucleosynthesis and the third dredge-up itself. observations of AGB stars are needed.," However, for studying ongoing nucleosynthesis and the third dredge-up itself, observations of AGB stars are needed."1172 Among the material dredged to the surface. °C is of special interest as mixing of this element changes an oxygen-rich star (C/O«D) into a carbon-rich one (C/O>1).," Among the material dredged to the surface, $^{12}$ C is of special interest as mixing of this element changes an oxygen-rich star $<$ 1) into a carbon-rich one $>$ 1)."1173 This leads to significant changes in. the chemistry and. às à result. in the atmospheric structure and the mass loss properties of the star.," This leads to significant changes in the chemistry and, as a result, in the atmospheric structure and the mass loss properties of the star."1174 The value of the C/O ratio is thus an indicator of the nucleosynthesis and mixing processes inside the star., The value of the C/O ratio is thus an indicator of the nucleosynthesis and mixing processes inside the star.1175 For a few bright field AGB stars. measurements of the abundance of C and its isotopes exist (Lambert et citelambert86:; Harris et citeharris87:; Smith Lambert 1990)).," For a few bright field AGB stars, measurements of the abundance of C and its isotopes exist (Lambert et \\cite{lambert86}; Harris et \\cite{harris87}; Smith Lambert \cite{SL90}) )."1176 Values for C/O range between 0.25 and 1.6 (see 99 of Smith Lambert 1990))., Values for C/O range between 0.25 and 1.6 (see 9 of Smith Lambert \cite{SL90}) ).1177 Comparing the findings from field stars with nucleosynthesis and mixing models is hampered by the rather large uncertainty in luminosity and mass. two very critical parameters for the models.," Comparing the findings from field stars with nucleosynthesis and mixing models is hampered by the rather large uncertainty in luminosity and mass, two very critical parameters for the models."1178 Clusters of stars offer an excellent possibility to investigate several questions of stellar astronomy., Clusters of stars offer an excellent possibility to investigate several questions of stellar astronomy.1179 They provide samples of stars that are homogeneous in age and. in general. also in. metallicity located at the same distance.," They provide samples of stars that are homogeneous in age and, in general, also in metallicity located at the same distance."1180 Thus it is possible to determine their evolutionary status and their mass more accurately than for field stars., Thus it is possible to determine their evolutionary status and their mass more accurately than for field stars.1181 This provides an important advantage for comparison with models of stellar atmospheres and evolution., This provides an important advantage for comparison with models of stellar atmospheres and evolution.1182 To investigate highly evolved stars on the AGB. globular clusters seem the best choice due to the number of potential targets they include and due to the age range in which they are found.," To investigate highly evolved stars on the AGB, globular clusters seem the best choice due to the number of potential targets they include and due to the age range in which they are found."1183 Globular clusters of the Milky Way are not good candidates when studying the effect of the third dredge up., Globular clusters of the Milky Way are not good candidates when studying the effect of the third dredge up.1184 They are. indeed. too old so that their present generation of AGB stars should have a very low envelope mass. too low for the occurrence of a substantial dredge up.," They are, indeed, too old so that their present generation of AGB stars should have a very low envelope mass, too low for the occurrence of a substantial dredge up."1185 The Magellanie Clouds. however. contain a population of intermediate age clusters (e.g. Girardi et citegirardi95)) with AGB stars in the mass range 1.5 to Mo.," The Magellanic Clouds, however, contain a population of intermediate age clusters (e.g. Girardi et \\cite{girardi95}) ) with AGB stars in the mass range 1.5 to $M_{\sun}$."1186 In this paper we present measurements of the C/O ratio and the isotopic ratio C/C for a sample of AGB stars in the cluster NGC 1846., In this paper we present measurements of the C/O ratio and the isotopic ratio $^{12}$ $^{13}$ C for a sample of AGB stars in the cluster NGC 1846.1187 In a previous paper (Lebzelter Wood 2007)). the variability of the AGB stars in this cluster was discussed.," In a previous paper (Lebzelter Wood \cite{LW07}) ), the variability of the AGB stars in this cluster was discussed."1188 We refer to this paper for a recent overview of the literature on this cluster and will only repeat a short summary here. listingthe values for the global parameters used in the present paper.," We refer to this paper for a recent overview of the literature on this cluster and will only repeat a short summary here, listingthe values for the global parameters used in the present paper."1189 NGC 1846 ts an intermediate age cluster belonging to the LMC., NGC 1846 is an intermediate age cluster belonging to the LMC.1190 It has a metallicity of [Fe/H|2 —0.49 (Grocholski et, It has a metallicity of $=-$ 0.49 (Grocholski et1191"In our simulations. the masses of Jupiter 4; and Saturn Γης are initiated with values of ny;=mg;10 Ma: and the cores of Jupiter and Saturn are placed on circular orbits at a,=2 and ας=2.65. just exterior to their mutual 3:2 mean motion resonance.","In our simulations, the masses of Jupiter $m_J$ and Saturn $m_S$ are initiated with values of $m_{J,i}=m_{S,i}=10$ $\mearth$; and the cores of Jupiter and Saturn are placed on circular orbits at $a_J=2$ and $a_S=2.65$, just exterior to their mutual 3:2 mean motion resonance."1192" In an isothermal disk. the type I migration timescale of a planet with mass Ημ. semimajor axis a, and on a circular orbit with angular frequency Q, can be estimated by (Paardekooper et al."," In an isothermal disk, the type I migration timescale of a planet with mass $m_p$, semimajor axis $a_p$ and on a circular orbit with angular frequency $\Omega_p$ can be estimated by (Paardekooper et al."1193 2010): Because of Eq. 1..," 2010): Because of Eq. \ref{eq:taumig},"1194 we expect Jupiter and Saturn's cores. embedded in a disk model with o«3/2 . to undergo convergent migration and become eventually trapped in the 3:2 resonance.," we expect Jupiter and Saturn's cores, embedded in a disk model with $\sigma<3/2$ , to undergo convergent migration and become eventually trapped in the $3:2$ resonance."1195 In contrast. a disk model with c>3/2 should lead to divergent migration.," In contrast, a disk model with $\sigma > 3/2$ should lead to divergent migration."1196 Once the cores have evolved for ~500 orbits of the innermost embryo. we allow Jupiter’s core to acerete gas from the disk.," Once the cores have evolved for $\sim 500$ orbits of the innermost embryo, we allow Jupiter's core to accrete gas from the disk."1197 For each timestep Af. aceretion is modeled by reducing the surface density in the grid cells located within a distance R4.acc of the planet by a factor 1—f;Ar.," For each timestep $\Delta t$, accretion is modeled by reducing the surface density in the grid cells located within a distance $R_{acc}$ of the planet by a factor $1 -f_J \Delta t$."1198 Following Paardekooper Mellema (2008). we set f;=5/3 in our simulations.," Following Paardekooper Mellema (2008), we set $f_J=5/3$ in our simulations."1199" Furthermore. we choose R,4.=0.1 Ry; where Αμ 1s the Hill radius of the planet (8j;=a;G1;/3M. jy this value i5 small enough to ensure that the accretion procedure is independent of our choice of f; (Tanigawa Watanabe 2002)."," Furthermore, we choose $R_{acc}=0.1$ $R_{H,J}$ where $R_{H,J}$ is the Hill radius of the planet $R_{H,J} = a_J 1200\left(m_J/3 M_\odot \right)^{1/3}$ ); this value is small enough to ensure that the accretion procedure is independent of our choice of $f_J$ (Tanigawa Watanabe 2002)."

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