ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 However. in this paper we show that this is not the case for current observational estimates. and other authors have reached similar conclusions (Nagamineetal.2004:OuchivanDokkum2008:Wilkinsetal.Davé 2008).," However, in this paper we show that this is not the case for current observational estimates, and other authors have reached similar conclusions \citep{Nagamine.etal:04, Ouchi.etal:04, vanDokkum:08, Wilkins.etal:08, Dave:08}."3. Over the past decade. larec samples of color. selected high-z galaxies such as Lyman break galaxies (LBCGs) have enabled. us to measure the cosmic SERD at 3=26 from rest-frame UV luminosity density1999).," Over the past decade, large samples of color selected $z$ galaxies such as Lyman break galaxies (LBGs) have enabled us to measure the cosmic SFRD at $3 \lesssim z \lesssim 6$ from rest-frame UV luminosity density."4 X number of near-infrarecl observations have also constrained the galaxy stellar mass function. (GSME) at 256g.Marchesinietal.2009).," A number of near-infrared observations have also constrained the galaxy stellar mass function (GSMF) at $z\lesssim 4$ \citep[e.g.,][]{Marchesini.etal:09}."5. Furthermore. the advent of theο CWECH) on board the CHST) has dramatically improved. our ability to measure the rest-frame UV light from galaxies at ο2.6.," Furthermore, the advent of the ) on board the ) has dramatically improved our ability to measure the rest-frame UV light from galaxies at $z \gtrsim 6$."6 Combined with the measurement of rest-D[rame optical light by the (LIAC) onTelescope. it is now possible tomeasure the characteristic stellar mass of galaxies at 2Z6 using stacked spectra (Yanetal. 2010)..," Combined with the measurement of rest-frame optical light by the ) on, it is now possible tomeasure the characteristic stellar mass of galaxies at $z \gtrsim 6$ using stacked spectra \citep{Yan.etal:09,Bouwens.etal:10,Labbe.etal:10,Gonzalez.etal:10}."7 llowever. the sources ato.=>6 are verv faint. alc so [ar we have only detected. the massive end of GSME.," However, the sources at $z>6$ are very faint, and so far we have only detected the massive end of GSMF."8" In addition. there are sill sienificant uncertainties in the estimates of SERD and p,."," In addition, there are still significant uncertainties in the estimates of SFRD and $\rhostar$."9 Given this situation. it would. be απο to obtain oedictions on SERD and ps trom theoretical models.," Given this situation, it would be useful to obtain predictions on SFRD and $\rhostar$ from theoretical models."10 In. particular. cosmological hvdrodvnamüc simulations have been widely used to investigate cosmic star formation (o.g..Con&Ostrikeretal.2006:Davé2008:Schave 2010).," In particular, cosmological hydrodynamic simulations have been widely used to investigate cosmic star formation \citep[e.g.,][]{Cen.Ostriker:92,Katz.etal:96,Springel.Hernquist:03_SFR,Nagamine.etal:06,Dave:08,Schaye.etal:10}."11". 1n thisLeffler, we focus on the cosmic SE history at 2l2 using cosmological simulations."," In this, we focus on the cosmic SF history at $z>2$ using cosmological simulations."12 Phe remaining of this paper is organized as follows., The remaining of this paper is organized as follows.13 In Section 2.. we describe the," In Section \ref{sec:method}, , we describe the"14these features are consistent with a significant contribution from voung stellar populations (see Tadhunter ct al.,these features are consistent with a significant contribution from young stellar populations (see Tadhunter et al.15 1996. Robinson et al.," 1996, Robinson et al."16 2000)., 2000).17 Therefore we have attempted to model the continua of the three objects with various combinations of old and. voung stellar populations (using the instantaneous burst models of Bruzual Charlot 1993) and power-laws., Therefore we have attempted to model the continua of the three objects with various combinations of old and young stellar populations (using the instantaneous burst models of Bruzual Charlot 1993) and power-laws.18 We have also tried. models in which the voung stellar populations were reddened by varving degrees., We have also tried models in which the young stellar populations were reddened by varying degrees.19 The best fitting models are shown in Table 9. and compared with the data in Figure 3.," The best fitting models are shown in Table 9, and compared with the data in Figure 3."20 In the case of PINS1549-79 and. PINS2135-20 we obtained an adequate fit using models which combine an old (15Civr) and voung stellar populations (reddened in the case of PISS1549-79)., In the case of PKS1549-79 and PKS2135-20 we obtained an adequate fit using models which combine an old (15Gyr) and young stellar populations (reddened in the case of PKS1549-79).21 On the other hand. in the case of DPIX82314103. the best. fit comprised a combination of voung stellar populations with two starburst ages plus a power-law.," On the other hand, in the case of PKS2314+03 the best fit comprised a combination of young stellar populations with two starburst ages plus a power-law."22 Given that the spectrum of PINS2135-20 has a relatively low S/N. that. of PINS1549-79 has a relatively small spectral coverage. and that of PINS2314|03 may be alfected by dillerential atmospheric refraction effects (sce section 3.1). the modelling estimates of the ages of the voung stellar populations should not be regarded definitive.," Given that the spectrum of PKS2135-20 has a relatively low S/N, that of PKS1549-79 has a relatively small spectral coverage, and that of PKS2314+03 may be affected by differential atmospheric refraction effects (see section 3.1), the modelling estimates of the ages of the young stellar populations should not be regarded definitive."23 Nonetheless. these results provide strong evidence that the optical/UV. continua of all three objects are dominated. by the light of voung stellar populations with ages in the range 0.1]. 2€.," Nonetheless, these results provide strong evidence that the optical/UV continua of all three objects are dominated by the light of young stellar populations with ages in the range 0.1 – 2Gyr."24 This CSS radio galaxy has a large UV excess. but a low polarization. and no sign of broad. permitted lines in its spectrum.," This CSS radio galaxy has a large UV excess, but a low polarization, and no sign of broad permitted lines in its spectrum."25 A possible starburst candidate., A possible starburst candidate.26 l'he strength of the broad permitte lines in this DLIW: suggests that much. of its UV. excess is due to direct. AGN light., The strength of the broad permitted lines in this BLRG suggests that much of its UV excess is due to direct AGN light.27 However. given the significan polarization detected at both UV wavelengths (this paper) and. optical wavelengths Clachiunter et al.," However, given the significant polarization detected at both UV wavelengths (this paper) and optical wavelengths (Tadhunter et al."28 1992). scatterec AGN σαι may also. contribute.," 1992), scattered AGN light may also contribute."29 Optical synchrotron emission is a plausible alternative to scattered AGN ligh in this source. given the distorted S-shaped radio structure. ancl relatively strong core-jet visible in high resolution racio maps (Morganti et al.," Optical synchrotron emission is a plausible alternative to scattered AGN light in this source, given the distorted S-shaped radio structure, and relatively strong core-jet visible in high resolution radio maps (Morganti et al."30 1999)., 1999).31 Direct AGN light is likely to contribute much of the UV excess in this DLIG which has alow UV polarization., Direct AGN light is likely to contribute much of the UV excess in this BLRG which has a low UV polarization.32 This FRIL radio galaxy has a large UV. excess. significant UV. polarization. but no. broad. permitted. lines.," This FRII radio galaxy has a large UV excess, significant UV polarization, but no broad permitted lines."33 Although the scattered. AGN light. is likely to be significant. given the relatively low. level of intrinsic polarization (Table 4). it is unlikely that this component dominates the UV. continuum.," Although the scattered AGN light is likely to be significant, given the relatively low level of intrinsic polarization (Table 4), it is unlikely that this component dominates the UV continuum."34 A possible starburst candidate., A possible starburst candidate.35 This FRIL radio galaxy has a modest UV excess. no significant UV. polarization. and no clear detection of broad. permitted. lines.," This FRII radio galaxy has a modest UV excess, no significant UV polarization, and no clear detection of broad permitted lines."36 The origin of its UV excess is not clear., The origin of its UV excess is not clear.37 This high redshift PRU racio galaxy is one of the most highly polarized objects in our sample., This high redshift FRII radio galaxy is one of the most highly polarized objects in our sample.38 Given the high intrinsic polarization (Table 4). it is likely that scattered AGN light dominates the UY excess in this SOULCC.," Given the high intrinsic polarization (Table 4), it is likely that scattered AGN light dominates the UV excess in this source."39 This FRI radio galaxy shows a laree UV. excess. but has a low UV. polarization.," This FRII radio galaxy shows a large UV excess, but has a low UV polarization."40 Weak broad. wings are marginally detected to the LE3 and Mell(2800) permitted lines. but deeper spectroscopic observations are required to confirm that this is a BLRG in which the UV excess is dominated by direct ACGN light.," Weak broad wings are marginally detected to the $\beta$ and MgII(2800) permitted lines, but deeper spectroscopic observations are required to confirm that this is a BLRG in which the UV excess is dominated by direct AGN light."41 Contamination of images and. spectra by a forgrouncl galaxy. preclude detailed: study of the optical continuum in this CSS radio galaxy., Contamination of images and spectra by a forground galaxy preclude detailed study of the optical continuum in this CSS radio galaxy.42 This unusual EIL radio galaxy has broad permitted. lines but only weak narrow lines. (di Serego Alighieri et al., This unusual FRII radio galaxy has broad permitted lines but only weak narrow lines (di Serego Alighieri et al.43 1994)., 1994).44 Although it has not been possible to model the continuum of this object in detail because of a poor sky subtraction. given the low level of UV polarization.," Although it has not been possible to model the continuum of this object in detail because of a poor sky subtraction, given the low level of UV polarization,"45In addition. because the running spectral index model predicts a significant lower power ol density (netuation on small scales Chan the standard PL-ACDM model (??).. it should also attract considerable attention in studies on weak lensing hy large-scale structure (?).. especially on skewness (??) which characterizes (he non-Gaussian property of & field in the nonlinear regime.,"In addition, because the running spectral index model predicts a significant lower power of density fluctuation on small scales than the standard $\Lambda$ CDM model \citep{2003ApJS..148..175S,2003ApJ...598...73Y}, it should also attract considerable attention in studies on weak lensing by large-scale structure \citep{2003astro.ph..8446I}, especially on skewness \citep{2003ApJ...592..664P,2003ApJ...598..818Z}46 which characterizes the non-Gaussian property of $\kappa$ field in the nonlinear regime."47star. yy is the X-ray albedo of the disk. and H is the disk’s scale height.,"star, $\eta_{\rm d}$ is the X-ray albedo of the disk, and $H$ is the disk's scale height."48 Πο may be determined from the condition of hydrostatic equilibrium. as in a standard Shakura-Sunyaev disk model (see. e.g.. Frank. King. Raine 1992).," $H(r)$ may be determined from the condition of hydrostatic equilibrium, as in a standard Shakura-Sunyaev disk model (see, e.g., Frank, King, Raine 1992)."49 The first term in equation (2) is due to internal viscous heating in the disk. and the second term is due to X-ray heating.," The first term in equation (2) is due to internal viscous heating in the disk, and the second term is due to X-ray heating."50 For SAX J1808.4-3658. many of these model parameters are well-constrained.," For SAX J1808.4–3658, many of these model parameters are well-constrained."51 We may adopt the distance D=2.5 kpe inferred from radius-expansion X-ray bursts (in t Zand et al., We may adopt the distance $D=2.5$ kpc inferred from radius-expansion X-ray bursts (in 't Zand et al.52 2001)., 2001).53" Since this is a disk-accreting pulsar, we may assume that the inner disk is truncated by the pulsar's magnetosphere at a radius 5j of order the corotation radius Feo(GM,Psi/[A7)3230 km (Psaltis Chakrabarty 1999); in fact. the optical spectrum is not very sensitive to the exact value of this parameter. since the optical emission. primarily arises from radit in excess of 10° em."," Since this is a disk-accreting pulsar, we may assume that the inner disk is truncated by the pulsar's magnetosphere at a radius $r_{\rm in}$ of order the corotation radius $r_{\rm co}=(GM_{\rm x}P_{\rm54spin}^2/4\pi^2)^{1/3} \approx 30$ km (Psaltis Chakrabarty 1999); in fact, the optical spectrum is not very sensitive to the exact value of this parameter, since the optical emission primarily arises from radii in excess of $10^8$ cm."55 The outer disk will be eut off sharply near the neutron star's tidal radius. zReoene (Frank et al.," The outer disk will be cut off sharply near the neutron star's tidal radius, $\approx R_{\rm Roche}$ (Frank et al."56 1992). which will in turn depend upon the mass ratio and thus the binary inclination (Eggleton 1983).," 1992), which will in turn depend upon the mass ratio and thus the binary inclination (Eggleton 1983)."57" We may infer the X-ray luminosity from the X-ray flux Ly=AzDF,. and hence deduce the mass transfer rate M. throu"," We may infer the X-ray luminosity from the X-ray flux through $L_{\rm x}=4\pi D^2 F_{\rm x}$, and hence deduce the mass transfer rate $\dot M$."58ghFinally. for the X-ray albedo of the disk. we use the results of previous studies of X-ray reprocessing in LMXBs which found that jjj20.90. indicating that only a small fraction of the incident X-ray flux is absorbed by the aceretion disk and reprocessed into the optical band (Kallman. Raymond. Vrtilek 1991: de Jong. van Paradijs. Augusteijn 1996).," Finally, for the X-ray albedo of the disk, we use the results of previous studies of X-ray reprocessing in LMXBs which found that $\eta_{\rm59d}\gtrsim 0.90$, indicating that only a small fraction of the incident X-ray flux is absorbed by the accretion disk and reprocessed into the optical band (Kallman, Raymond, Vrtilek 1991; de Jong, van Paradijs, Augusteijn 1996)."60 With the model parameters set as described above. we fit the heated disk model to the observed photometry with two free parameters. cos/ and the optical V-band extinction Ay.," With the model parameters set as described above, we fit the heated disk model to the observed photometry with two free parameters, $\cos 61i$ and the optical $V$ -band extinction $A_V$."62 We computed our model fits on a grid with 99 values of cosi in the range 0.01—0.99 and 501 values of Ay in the range 0.00—5.00., We computed our model fits on a grid with 99 values of $\cos i$ in the range 0.01–0.99 and 501 values of $A_V$ in the range 0.00--5.00.63 We computed the extinction in the other bands using the interstellar reddening law of Rieke Lebofsky (1985)., We computed the extinction in the other bands using the interstellar reddening law of Rieke Lebofsky (1985).64 For each (Ay.cos/) grid point. we fit the data for 10 different values of iq in the range 0.90-0.99 and used only the best-fit value for that grid point.," For each $(A_V, \cos i)$ grid point, we fit the data for 10 different values of $\eta_{\rm d}$ in the range 0.90–0.99 and used only the best-fit value for that grid point."65 In order to ensure that we were working in the regime where X-ray heating is important (and the X-ray flux is well determined). we confined our fitting to the optical data prior to the break in the X-ray light curve at MJD 50929.," In order to ensure that we were working in the regime where X-ray heating is important (and the X-ray flux is well determined), we confined our fitting to the optical data prior to the break in the X-ray light curve at MJD 50929."66 The fitting was performed simultaneously to all the data in Table | prior to that date., The fitting was performed simultaneously to all the data in Table 1 prior to that date.67 Our simple disk model was able to provide a good simultaneous solution to these data., Our simple disk model was able to provide a good simultaneous solution to these data.68 The best-fit parameters were Ay20.6853; and eos20.65στον with reduced 4720.81 (9 degrees of freedom). where the uncertainties are quoted at the 90%--contidence level.," The best-fit parameters were $A_V=0.68^{+0.37}_{-0.28}$ and $\cos i= 0.65^{+0.23}_{-0.38}$, with reduced $\chi^2=0.81$ (9 degrees of freedom), where the uncertainties are quoted at the -confidence level."69 The spectral model for two epochs is shown by the solid curves in Figure 2. and a contour plot of the allowed parameter space is shown in Figure 3.," The spectral model for two epochs is shown by the solid curves in Figure 2, and a contour plot of the allowed parameter space is shown in Figure 3."70 The confidence levels indicated by the contours in Figure 3 are determined. as described by Lampton. Margon. Bowyer (1976).," The confidence levels indicated by the contours in Figure 3 are determined as described by Lampton, Margon, Bowyer (1976)."71 The hashed regions in Figure 3 reflect the additional lower limit of Ay>0.53 set by the measured Galactic dust extinction through the Galactic disk along the line of sight, The hashed regions in Figure 3 reflect the additional lower limit of $A_V>0.53$ set by the measured Galactic dust extinction through the Galactic disk along the line of sight72While the observed strengths of the 1667 and 1665 MIIz lines agree well with our line strength: predictions. the observed OII line shapes are in verv poor agreement wilh our predictions.,"While the observed strengths of the $1667$ and $1665\,$ MHz lines agree well with our line strength predictions, the observed OH line shapes are in very poor agreement with our predictions."73" The observed line profiles are neither ""top hats” nor double-peaked: indeed. they are nol even svimneltric about ezsg=—26.5kins|. the systemic velocity of IRC2-10216."," The observed line profiles are neither “top hats” nor double-peaked; indeed, they are not even symmetric about $v_{LSR}=-26.5\,{\rm km\, s^{-1}}$, the systemic velocity of IRC+10216."74 This asvinmetry is - every other molecule observed in the outer envelope of IRC+10216 has a profile which is svinmetric about the svstemic velocity (e.g. Cernicharo et al., This asymmetry is - every other molecule observed in the outer envelope of IRC+10216 has a profile which is symmetric about the systemic velocity (e.g. Cernicharo et al.75 2000)., 2000).76 Rather. the 1667 and 1665 MlIz emission features are blueshifted with respect to the svstemic velocity. and they ive central velocities which differ shehtly (see Table 1)).," Rather, the $1667$ and $1665\,$ MHz emission features are blueshifted with respect to the systemic velocity, and they have central velocities which differ slightly (see Table \ref{linefit}) )."77 Based on the errors quoted in Table 1.. we might conclude that the velocities of the (wo features differ at a statistically significant evel.," Based on the errors quoted in Table \ref{linefit}, we might conclude that the velocities of the two features differ at a statistically significant level."78 ILowever. we note that the errors are based on fitting a Gaussian profile to a line which is not likely to be a true Gaussian.," However, we note that the errors are based on fitting a Gaussian profile to a line which is not likely to be a true Gaussian."79 A more appropriate (and conservative) estimate of the error associated with the line center determination is simply (the velocity. resolution of our spectrum., A more appropriate (and conservative) estimate of the error associated with the line center determination is simply the velocity resolution of our spectrum.80 For the 1665 and 1667 MlIE lines. the size of a resolution element alter smoothing is Likms !.," For the $1665$ and $1667\,$ MHz lines, the size of a resolution element after smoothing is $1.1\,{\rm km\,s^{-1}}$ ."81 Given this error estimate. we conclude that the 1665 and 1667 MIIz lines may have the same central velocity.," Given this error estimate, we conclude that the $1665$ and $1667\,$ MHz lines may have the same central velocity."82 For comparison with our pre-observation models. we plot our “best fit model over the data for the 1667 MIIz line in Figure 5..," For comparison with our pre-observation models, we plot our “best fit” model over the data for the $1667\,$ MHz line in Figure \ref{datamod}."83 Our “best fit is model R38. except that. we must assume a fractional water abundance of 2.4x10°6 in order to match the line fluxes for velocities between —40 and —30kins!.," Our “best fit” is model R3, except that we must assume a fractional water abundance of $2.4 \times 10^{-6}$ in order to match the line fluxes for velocities between $-40$ and $-30\,{\rm km\,s^{-1}}$."84 Also. in order to match the velocity of the observed line with the blueshifted peak of the model. we assume a (jsg=—23.5kms|. which represents a redshift of 3kms.| with respect to prior measurements of the (54; using other species (e.g. Cernicharo et al.," Also, in order to match the velocity of the observed line with the blueshifted peak of the model, we assume a $v_{LSR}=-23.5\,{\rm km\, s^{-1}}$, which represents a redshift of $3\,{\rm km\, s^{-1}}$ with respect to prior measurements of the $v_{LSR}$ using other species (e.g. Cernicharo et al."85 2000)., 2000).86 It is obvious [rom the plot that the blueshifted peak of the model fits the data reasonably well. but the redshilted peak of the moclel is entirelv missing from the data.," It is obvious from the plot that the blueshifted peak of the model fits the data reasonably well, but the redshifted peak of the model is entirely missing from the data."87 The observed shapes of the 1667 and 1665 MIIz OLI lines are quite unexpected.," The observed shapes of the $1667$ and $1665\,$ MHz OH lines are quite unexpected."88 There are onlv three general mechanisms which might create the observed line profiles: these mechanisms are: 1) absorption. 2) masing or 2) an intrinsic asymmetry in (he spatial distribution ol the OIL," There are only three general mechanisms which might create the observed line profiles; these mechanisms are: 1) absorption, 2) masing or 3) an intrinsic asymmetry in the spatial distribution of the OH."89 In thefollowing sections. we examine each mechanism in detail and discuss its plausibility.," In thefollowing sections, we examine each mechanism in detail and discuss its plausibility."9010mm,10mm91taken during the science demonstration phase of the mission.,taken during the science demonstration phase of the mission.92" For details of the observations and data reduction process, we refer to ?.."," For details of the observations and data reduction process, we refer to \citet{Berta10}."93 Fluxes were extracted using MIPS 24 um sources with 3 c detections or better as priors (?).., Fluxes were extracted using }-MIPS 24 $\mu$ m sources with 3 $\sigma$ detections or better as priors \citep{Magnelli09}.94" The priors are matched to bviz (ACS), JHK (FLAMINGO), and Spitzer-IRAC photometry."," The priors are matched to bviz (ACS), JHK (FLAMINGO), and -IRAC photometry."95 Spectroscopic redshifts are from ? and photometric redshifts were derived using the code EAZY (?).. TheCha, Spectroscopic redshifts are from \citet{Barger08} and photometric redshifts were derived using the code EAZY \citep{Brammer08}.96ndra 2Ms catalog (?) is matched to the PACS sources and is used to flag X-ray sources., The 2Ms catalog \citep{Alexander03} is matched to the PACS sources and is used to flag X-ray sources.97" One source without an X-ray detection but which exhibits a clear power-law SED in the IRAC bands, was also flagged as an AGN."," One source without an X-ray detection but which exhibits a clear power-law SED in the IRAC bands, was also flagged as an AGN."98" In this study, we are interested in 1.5«z«2.5 range and require redshift information."," In this study, we are interested in $<$ $<$ 2.5 range and require redshift information."99"selections. In addition, we require that in a 10"" radius around a 24 um prior there is no more than one other 24 um source and it may have no more than of the prior flux."," In addition, we require that in a 10"" radius around a 24 $\mu$ m prior there is no more than one other 24 $\mu$ m source and it may have no more than of the prior flux."100 This condition ensures that the sample does not experience significant flux confusion between MIR priors and/or FIR fluxes due to neighbors., This condition ensures that the sample does not experience significant flux confusion between MIR priors and/or FIR fluxes due to neighbors.101" These criteria result in a sample of 23 detected sources in total, 17 classified as SFGs, and 4 of which have a spectroscopic redshift."," These criteria result in a sample of 23 detected sources in total, 17 classified as SFGs, and 4 of which have a spectroscopic redshift."102 306 24 um priors without a PACS detection are available for stacking analysis (see below)., 306 24 $\mu$ m priors without a PACS detection are available for stacking analysis (see below).103" We calculate SFRs by assuming that they are proportional to the integrated infrared luminosity (LIR,typically ?).."," We calculate SFRs by assuming that they are proportional to the integrated infrared luminosity \citep[LIR, typically 8-1000~$\mu$m][]{Kennicutt98}."104" We convert PACS 160 um fluxes into LIR by fitting the flux using the ?,hereafter:CEO1 SED library, in which for a given redshift and band flux, a unique solution to LIR exists."," We convert PACS 160 $\mu$ m fluxes into LIR by fitting the flux using the \citet[][hereafter: CE01]{CE01} SED library, in which for a given redshift and band flux, a unique solution to LIR exists."105" The 100 um filter is not used because at z~2, emission at rest-frame wavelengths may already be affected by hot dust and suffer the same systematic effects as the 24 um based SFR."," The 100 $\mu$ m filter is not used because at $\sim$ 2, emission at rest-frame wavelengths may already be affected by hot dust and suffer the same systematic effects as the 24 $\mu$ m based SFR."106" In addition, at these redshifts 100 um is on the same side of the SED peak and too close to 160 um to provide meaningful temperature constraints, without longer wavelength data."," In addition, at these redshifts 100 $\mu$ m is on the same side of the SED peak and too close to 160 $\mu$ m to provide meaningful temperature constraints, without longer wavelength data."107 Combined PACS and SPIRE sub-mm data show that fitting CE01 SEDs to the 160 um flux provides a reliable estimate of the total 8—1000 um luminosity (LIR) of the large-grain dust for z~2 galaxies (?).., Combined PACS and SPIRE sub-mm data show that fitting CE01 SEDs to the 160 $\mu$ m flux provides a reliable estimate of the total 8–1000 $\mu$ m luminosity (LIR) of the large-grain dust for $\sim$ 2 galaxies \citep{Elbaz10}.108" To explore the relationship between direct FIR luminosities, 24 um extrapolated luminosities, and UV-SFRs to lower luminosities and SFRs, we also perform a stacking analysis."," To explore the relationship between direct FIR luminosities, 24 $\mu$ m extrapolated luminosities, and UV-SFRs to lower luminosities and SFRs, we also perform a stacking analysis."109 We stack the 160 µπι image centered on the prior positions and measure a mean flux for the stack., We stack the 160 $\mu$ m image centered on the prior positions and measure a mean flux for the stack.110" The mean luminosity of the stack, LIR(160 j4m);4:4, is defined as the luminosity that will result in the 160 um stacked flux, for the redshift distribution of the sources in the stack and the adopted CE01 SEDs."," The mean luminosity of the stack, LIR(160 $\mu$ $_{stack}$, is defined as the luminosity that will result in the 160 $\mu$ m stacked flux, for the redshift distribution of the sources in the stack and the adopted CE01 SEDs."111" In this way, both k-corrections and luminosity distances are accounted for without bias."," In this way, both k-corrections and luminosity distances are accounted for without bias."112 The error in the mean luminosity is calculated using a bootstrap method., The error in the mean luminosity is calculated using a bootstrap method.113 The same number of sources are resampled with replacements from the original stack to produce a new stacked image., The same number of sources are resampled with replacements from the original stack to produce a new stacked image.114 The new mean luminosity is then calculated., The new mean luminosity is then calculated.115 The error is finally calculated from the distribution of luminosities in the repeated resampling., The error is finally calculated from the distribution of luminosities in the repeated resampling.116 Spitzer-MIPS 24 um fluxes are converted to LIR by fitting the 24 um flux to CE01 SEDs using the same method we use for the, Spitzer-MIPS 24 $\mu$ m fluxes are converted to LIR by fitting the 24 $\mu$ m flux to CE01 SEDs using the same method we use for the117DE-FGO03-91ER40662 and NASA ATP grant NNNOSALI8G. Α.Α. thanks Aspen Center for Physics lor hospitality.,DE-FG03-91ER40662 and NASA ATP grant NNX08AL48G. A.K. thanks Aspen Center for Physics for hospitality.118after the collapse commenses. the clump is not. virialized while it is optically thin.,"after the collapse commenses, the clump is not virialized while it is optically thin."119 The temperature cannot be much smaller than 7. since otherwise the cooling rate would. be much smaller than the rate of release of the gravitational binding energy. and the gas would heat up by quasi-adiabatie compression.," The temperature cannot be much smaller than $\tilde{T}$, since otherwise the cooling rate would be much smaller than the rate of release of the gravitational binding energy, and the gas would heat up by quasi-adiabatic compression."120 Theinequality in Ίσα. (20)), Theinequality in Eq. \ref{T1}) )121 should be substituted by an approximate equality. ancl therefore we have curing optically-thin collapse The optical depth scales as and hence rises sharply as the clumip’s radius decreases: as the clump shrinks it. becomes. opticallythick.," should be substituted by an approximate equality, and therefore we have during optically-thin collapse The optical depth scales as and hence rises sharply as the clump's radius decreases; as the clump shrinks it becomes optically."122. It is possible to show that once the clump is optically thick. it virializes quickly with it’s temperature Pox70.," It is possible to show that once the clump is optically thick, it virializes quickly with it's temperature $T\propto R^{-1}$."123 For κον17 (icegrains). the cooling time of an optically thick chump scales with the clump radius as The characteristic timescale for the clump to collide with another clump scales with the clump radius as From Eqs. (23))," For $\kappa\propto T^2$ (icegrains), the cooling time of an optically thick clump scales with the clump radius as The characteristic timescale for the clump to collide with another clump scales with the clump radius as From Eqs. \ref{tcool}) )"124 and (24)). we see that the collision rate decreases less steeply than the coolling rate as a function of the radius of an optically thick clump.," and \ref{tcoll}) ), we see that the collision rate decreases less steeply than the coolling rate as a function of the radius of an optically thick clump."125 Therefore. merger can be an ellicient way of increasing the clump's mass.," Therefore, merger can be an efficient way of increasing the clump's mass."126 This conclusion is no longer valid when the temperature of the clump becomes larger than ~ 200K: then the opacity is dominated by metal dust with sx27/7., This conclusion is no longer valid when the temperature of the clump becomes larger than $\sim 200$ K; then the opacity is dominated by metal dust with $\kappa\propto T^{1/2}$.127 In this case the cooling time scales as AoixA.07., In this case the cooling time scales as $t_{\rm cool}\propto R^{-1.5}$.128 Lhe collision timescale increases faster than the cooling time as the clump shrinks. and naively one would expect that mergers may. not. be ellicient in growing the clump masses.," The collision timescale increases faster than the cooling time as the clump shrinks, and naively one would expect that mergers may not be efficient in growing the clump masses."129 Llowever. we have neglected the rotational suppor within a chump.," However, we have neglected the rotational support within a clump."130 Each clump is initially rotating with angular requency comparable to the clump's inverse dynanica imeseale: for example. in a Weplerian disc each clump's initial angular velocity is 7/2.," Each clump is initially rotating with angular frequency comparable to the clump's inverse dynamical timescale; for example, in a Keplerian disc each clump's initial angular velocity is $\sim \Omega/2$."131 TPherefore cach clump wil shrink and. collapse into a rotationally supported clise. anc he size of this disc is comparable to the size of the origina chump (this picture scems to be in agreement with Ciammie's simulations).," Therefore each clump will shrink and collapse into a rotationally supported disc, and the size of this disc is comparable to the size of the original clump (this picture seems to be in agreement with Gammie's simulations)."132 Fhus rotational support generally slows down he collapse of an individual fragment ancl makes mergers »etween cdiferent. [ragments to be ellicient., Thus rotational support generally slows down the collapse of an individual fragment and makes mergers between diferent fragments to be efficient.133 Alagnetic braking is one of the wavs for the clump to ose its rotational (sec. e.g. Spitzer 1978).," Magnetic braking is one of the ways for the clump to lose its rotational (see, e.g., Spitzer 1978)."134 One gencrally expects a horizontal magnetic field to be present in a clillercntially rotating disc due to the MIU (Balbus and Lawley. 1991).," One generally expects a horizontal magnetic field to be present in a differentially rotating disc due to the MRI (Balbus and Hawley, 1991)."135 lonization fraction in the disc is expected. to be small. so the magnetic field is saturated at a subequipartition value B=GDa. with ««1l.," Ionization fraction in the disc is expected to be small, so the magnetic field is saturated at a subequipartition value $B=\beta B_{\rm eq}$, with $\beta<<1$."136 Horizontal magnetic Geld will couple inner and outer parts of the differentially rotating clump on the Alfven crossing timescale GarconΓΙ and the collapse will proceed on this timescale as well.," Horizontal magnetic field will couple inner and outer parts of the differentially rotating clump on the Alfven crossing timescale $t_{\rm alfven}\sim t_{\rm dynamical}/\beta$, and the collapse will proceed on this timescale as well."137 What is the maximum mass that the clump can achieve?, What is the maximum mass that the clump can achieve?138" ""his issue has been analyzed for the similar situation of a protoplanetary core accreting from a disc of planetesimals (Ralikov 2001 and references therein).", This issue has been analyzed for the similar situation of a protoplanetary core accreting from a disc of planetesimals (Rafikov 2001 and references therein).139" Lhe growing clump cannot accrete more mass than is present in its ""feeding annulus.", The growing clump cannot accrete more mass than is present in it's “feeding annulus”.140 This gives the maximum “isolation” mass of a clump: where. as above. M=Movil2cup is Che mass scale of the irst clumps to form from a disc: see. c.g.. Ίσα. (," This gives the maximum “isolation” mass of a clump: where, as above, $\bar{M}_{\rm cl}=\Sigma_{\rm crit}h_{\rm crit}^2$ is the mass scale of the first clumps to form from a disc; see, e.g., Eq. ("1412) of Ralikoy (POOL).,2) of Rafikov (2001).142 Llowever. numerical work of Ida and Makino (1993) ancl analytical calculations of Ralikoy (2001) indicate that he isolation mass mav be hard to reach.," However, numerical work of Ida and Makino (1993) and analytical calculations of Rafikov (2001) indicate that the isolation mass may be hard to reach."143 The consider a massive body moving on a circular orbit through a disc of eravitationallv interacting particles. and they find that when he mass of the body exceeds some critical value. an annular gap is opened in the particle disc around the body's orbit.," The consider a massive body moving on a circular orbit through a disc of gravitationally interacting particles, and they find that when the mass of the body exceeds some critical value, an annular gap is opened in the particle disc around the body's orbit."144 We can idealize a disc consisting of [fragments as a disc of xwticles of a typical fragment mass Mg., We can idealize a disc consisting of fragments as a disc of particles of a typical fragment mass $M_{\rm fr}$.145 Once a growing clump opens a gap in a disc of gravitationally interacting ragments. the clump's growth may become quenched.," Once a growing clump opens a gap in a disc of gravitationally interacting fragments, the clump's growth may become quenched."146 This gap-opening mass of the clump A is given by Eq. (, This gap-opening mass of the clump $M_{\rm gap}$ is given by Eq. (14725) of valikov (2001): We use the numerical factor 2τουxHI=15 appropriate for thin discs.,25) of Rafikov (2001): We use the numerical factor $2^{-7/6}\pi^{-1/2}I=1.5$ appropriate for thin discs.148 By taking Q=1 we ect In Figure 4 the masses Adi. ancl Mai are plotted: as a function of radius for a 3«LOPAL. black hole: when we calculate Ma we conservatively set Ady=Ma: and. not to the larger value Ma., By taking $Q=1$ we get In Figure 4 the masses $M_{\rm is}$ and $M_{\rm gap}$ are plotted as a function of radius for a $3\times 10^6M_{\odot}$ black hole; when we calculate $M_{\rm gap}$ we conservatively set $M_{\rm fr}=\bar{M}_{\rm cl}$ and not to the larger value $\tilde{M}_{\rm cl}$.149 lt is likely that the most. massive clumps will reach Mi. but it will be more difficult to form a clump with the mass A.," It is likely that the most massive clumps will reach $M_{\rm gap}$, but it will be more difficult to form a clump with the mass $M_{\rm is}$."150 From Fig., From Fig.151 4 we see that the most massive clumps can reach tens huncereds of solar masses., $4$ we see that the most massive clumps can reach tens hundereds of solar masses.152 Phe maximum mass would be even larger if we included the heating of the disc w external irradiation or internal starburst., The maximum mass would be even larger if we included the heating of the disc by external irradiation or internal starburst.153 Lt is plausible hat these very massive clumps will form massive stars: the masses of the stars may be comparable to the masses of the original clumps: see Melxee and Tan (2002) and. references herein., It is plausible that these very massive clumps will form massive stars; the masses of the stars may be comparable to the masses of the original clumps; see McKee and Tan (2002) and references therein.154 Stars with masses of a few tens of solar masses will produce black holes as the end product of their rapid (« LO°vr) evolution: the characteristic mass of these black roles is believed to be around 107..., Stars with masses of a few tens of solar masses will produce black holes as the end product of their rapid $<10^6$ yr) evolution; the characteristic mass of these black holes is believed to be around $10M_{\odot}$ .155 X recent work by, A recent work by156Over the past vears. the implications of clustered star formation have touched a range of astrophysical disciplines. from the scales of the star formation process itself (seethereviewby?). to the fundamental properties of young star clusters (e.g.222). or possibly even the global stellar mass assembly of galaxies ??)..,"Over the past years, the implications of clustered star formation have touched a range of astrophysical disciplines, from the scales of the star formation process itself \citep[see the review by][]{mckee07} to the fundamental properties of young star clusters \citep[e.g.][]{mcmillan07,allison09,moeckel09}, or possibly even the global stellar mass assembly of galaxies \citep[see e.g.][]{pflamm07,bastian10}."157 While it seems evident that most stars form in a clustered setting (e.g.2).. estimations of the exact fraction are hampered by the substantial dissociation of stellar structure that occurs during (but is not necessarily related to) the transition from the phase to classical. gas-poor star clusters €?2)..," While it seems evident that most stars form in a clustered setting \citep[e.g.][]{parker07}, estimations of the exact fraction are hampered by the substantial dissociation of stellar structure that occurs during (but is not necessarily related to) the transition from the phase to classical, gas-poor star clusters \citep{lada03,portegieszwart10}."158 The traditional interpretation that gas expulsion leading to their early disruption (infantmortality’.see22?) has recently been challenged by observational studies suggesting that stars form with a continuous distribution of densities. of whieh only the tail eventually leads to bound stellar clusters (22)..," The traditional interpretation that gas expulsion leading to their early disruption \citep[`infant mortality', see][]{lada03,bastian06b,goodwin06} has recently been challenged by observational studies suggesting that stars form with a continuous distribution of densities, of which only the tail eventually leads to bound stellar clusters \citep{bressert10,gieles11}."159 Current advancements in numerical calculations of turbulent fragmentation in star-forming regions enable the study of clustered star formation in increasing detail (e.g.2222)..," Current advancements in numerical calculations of turbulent fragmentation in star-forming regions enable the study of clustered star formation in increasing detail \citep[e.g.][]{bonnell98,klessen00,bate03,bonnell08}."160 However. theoretical investigations of the response of stellar structure to gas expulsion are still largelybased on the assumption of," However, theoretical investigations of the response of stellar structure to gas expulsion are still largelybased on the assumption of"161lis based on the diserepaucy between the| observed and snuulated redshift distribution.,is based on the discrepancy between the observed and simulated redshift distribution.162 The quality aud flexibilityo of the siuulation is illustrated 1du Figs 2- Pa-3..," The quality and flexibility of the simulation is illustrated in Figs. \ref{fig:ovdatasim_flux}- \ref{fig:ovdatasim_fluxerr},"163 which show data-simulation comparisous for the measured fiux aud its ffor four different surveys., which show data-simulation comparisons for the measured flux and its for four different surveys.164 For the o'conrparisou (Fig. 3)).," For the comparison (Fig. \ref{fig:ovdatasim_fluxerr}) ),"165 there are some cliscrepancies —hat may be due to a nüsiuterpretation o| the noise ctermunation from the inage-subtraction pi»eliue., there are some discrepancies that may be due to a mis-interpretation of the noise determination from the image-subtraction pipeline.166 Although superuovi-based. cosmology resuts have all sed rest-frame SN Ia iiodels of optical (BVRI) light curves. there is a growing interest m obtaiuiic mfrared helt curves in order to reduce the effect of jost-galaxv extinction.," Although supernova-based cosmology results have all used rest-frame SN Ia models of optical $UBVRI$ ) light curves, there is a growing interest in obtaining infrared light curves in order to reduce the effect of host-galaxy extinction."167 To study such possibilities iu futire SULVOVA. rest-frame infrared light curves cau be si.ated using an extended version of Hu which light curve teimplates for YJIIAN have been constructed based on recent observaions from PAIRITEL (?)..," To study such possibilities in future surveys, rest-frame infrared light curves can be simulated using an extended version of in which light curve templates for $YJHK$ have been constructed based on recent observations from PAIRITEL \citep{WV08IR}."168 To study the determination of SN Ia protometyic redshifts (photo-Z). the simulation iuclude ‘Sal ealaxy library (HOSTLIB) so hat the host-ealaxy cca be used as à prior iu a fait.," To study the determination of SN Ia photometric redshifts ), the simulation includes a host-galaxy library ) so that the host-galaxy can be used as a prior in a fit."169 The lis not create bySNANA.. aud therefore the nuuust be created externally from citlieYo another si.ation. or frou a aanalvsis of host-galaxies with ivedshifts.," The is not created by, and therefore the must be created externally from either another simulation, or from a analysis of host-galaxies with redshifts."170 The sunulatiou simply finds a host ealaxy with a redshift matching the SN redshift. and stores the host-galaxy to be used by the light curve fitter.," The simulation simply finds a host galaxy with a redshift matching the SN redshift, and stores the host-galaxy to be used by the light curve fitter."171 To estimate SN. Ia. sample contamination. the station can generate non-la SN light curves.," To estimate SN Ia sample contamination, the simulation can generate non-Ia SN light curves."172 While the Type Ia light curve iiodels are based on a parametric equation or photometric templates. there are no such models for non-Ia types.," While the Type Ia light curve models are based on a parametric equation or photometric templates, there are no such models for non-Ia types."173 To allow for a large diversity of nou-Ia SNe. the simulation uses a library of spectral templates that specify the SN flux as a function of epoch and waveleneth.," To allow for a large diversity of non-Ia SNe, the simulation uses a library of spectral templates that specify the SN flux as a function of epoch and wavelength."174 A spectral template can be a siootlied average based on an eusenmible of SNe. or a template can correspond to a particular (well-observed) supernova where a composite spectrum is warped to match the observed plotometric colors.," A spectral template can be a smoothed average based on an ensemble of SNe, or a template can correspond to a particular (well-observed) supernova where a composite spectrum is warped to match the observed photometric colors."175 Since the spectral templates are mterpolated to cover all waveleneths aud epochs. ouly wellsampled photometric light curves are used.," Since the spectral templates are interpolated to cover all wavelengths and epochs, only well-sampled photometric light curves are used."176 The current library coutaius composite auc individual cluplates for types IIP. IIu. Ib. aud Thc.," The current library contains composite and individual templates for types IIP, IIn, Ib, and Ibc."177 The simulation of the non-Ia diversity will eradually iuprove as more well-observed: uou-la light curves become available., The simulation of the non-Ia diversity will gradually improve as more well-observed non-Ia light curves become available.178 A iuütation of ls that there is curentlv uo utility to convert 10ni-Ta ight curves mto spectral surfaces., A limitation of is that there is currently no utility to convert non-Ia light curves into spectral surfaces.179 A trigecr simulation is inchided to mimic algoritlins hat are used to discover SNe In in real time., A trigger simulation is included to mimic algorithms that are used to discover SNe Ia in real time.180 Although he offline selection criteria should in principle be more stringent than the search trigecr. if may be useful to use the simulation to make more rigorous crosschecks.," Although the offline selection criteria should in principle be more stringent than the search trigger, it may be useful to use the simulation to make more rigorous crosschecks."181 The trigger sinulation is also useful to anticipate SN discovery rates in the design of future surveys., The trigger simulation is also useful to anticipate SN discovery rates in the design of future surveys.182 The trigecrao simulation is based ou user-supplied tables that depend either ou observed inaguitudes or ou the signal-to-noise ratio (SNR)., The trigger simulation is based on user-supplied tables that depend either on observed magnitudes or on the signal-to-noise ratio (SNR).183 These ttables could be made. for example. by injecting fake SNe iuto real images. and then passing these inages through the object-finding pipeline.," These tables could be made, for example, by injecting fake SNe into real images, and then passing these images through the object-finding pipeline."184 Since a discovery typically requires observations in multiple filters and/or multiple epochs. one can specifv arbitrary detection logic.," Since a discovery typically requires observations in multiple filters and/or multiple epochs, one can specify arbitrary detection logic."185 For exaniple. the SSN Survey required a detection in at least two of the gr filters. and required a detection at two or more epochs: this logic is simulated by specifving the trigger to be 72 er|r|el”," For example, the SN Survey required a detection in at least two of the $gri$ filters, and required a detection at two or more epochs; this logic is simulated by specifying the trigger to be “2 gr+ri+gi.”"186 A inore difficult aspect of the trigger is the target selection for oohservations., A more difficult aspect of the trigger is the target selection for observations.187 Since sselection is based on human decisions and telescope availability. there is no clear software algorithi to describe this part of theefficieucy.," Since selection is based on human decisions and telescope availability, there is no clear software algorithm to describe this part of the."188. As described iu 62.1 of ?.. the observed and suunlated redshift distributions can be used to emipiricallv determine the sselectionefficiency.," As described in 6.2.1 of \citet{K09}, the observed and simulated redshift distributions can be used to empirically determine the selection."189.. After all quantifiable sources ofrefficiency are ducluded in the simulation. the sinuulated --codshift distribution will typically not match that of the data.," After all quantifiable sources of are included in the simulation, the simulated redshift distribution will typically not match that of the data."190 In the specific case of ?.. the observed. redshift distribution always has a deficit at ligher redshifts compared o the simulation. aud this deficit is assumed to be a result of the (éspec} ," In the specific case of \citet{K09}, the observed redshift distribution always has a deficit at higher redshifts compared to the simulation, and this deficit is assumed to be a result of the $\effspec$ )."191Iu general e depends on two types of paranieters.," In general, $\effspec$ depends on two types of parameters."192 The first set of parameters are those determined bv the simulation (denoted yay). such as intrinsic or observed brightuess. host-galaxy extinction. and host-SN separation.," The first set of parameters are those determined by the simulation (denoted $\simpar$ ), such as intrinsic or observed brightness, host-galaxy extinction, and host-SN separation."193 The second set of paraiieters (denoted μωμα) are those introduced by the analysis team based on their kuowledge ofsurvey operations. or in sole cases based on a guess.," The second set of parameters (denoted $\modpar$ ) are those introduced by the analysis team based on their knowledge ofsurvey operations, or in some cases based on a guess."194 A simple example is fccmexp].frny)ru]. where Tain= ris the observed rband inaguitude. aud iq= are the model paranueters.," A simple example is $\effspec = \exp[-(r-r_0)/\tau_r]$, where $\simpar=r$ is the observed $r$ -band magnitude, and $\modpar = \{ r_0,\tau_r \}$ are the model parameters."195 The μοα paraueters tro.are7} determined by solving where οταντε) is the umber of observed SNe. after all selection criteria. in the redshift lin centered at ij. aud πο wmuuber of simulated SNe in he sane redshift bin and within the iuteeration cell denoted bv di.," The $\modpar$ parameters are determined by solving where $\NDATA(z_i)$ is the number of observed SNe, after all selection criteria, in the redshift bin centered at $z_i$, and $\NSIM(z_i,\simpar)$ is the number of simulated SNe in the same redshift bin and within the integration cell denoted by $d\simpar$."196 cca be used to determine Napqtz.αμα) and Npavra( 2). mt the extraction of μιας requires specific software hat is currently not part ofSNANA.," can be used to determine $N_{\rm SIM}(z,\simpar)$ and $N_{\rm DATA}(z)$ , but the extraction of $\modpar$ requires specific software that is currently not part of."197". It mav be couvenicut o determine the model parameters iu redshft bius. Juodat6;) and then ft cach parameter to a smooth ""nuctiou of redshift."," It may be convenient to determine the model parameters in redshfit bins, $\modpar(z_i)$, and then fit each parameter to a smooth function of redshift."198 With cach uew definition of yoda xwanmeters. the snulatiou is easily modified to compute poolLoVana nodo).," With each new definition of $\modpar$ parameters, the simulation is easily modified to compute $\effspec(z,\simpar,\modpar)$ ."199 Finally. we uote that the precision iu cetermuning €ye 1 Huütedby the precision iu the SN rate as a function of redshift.," Finally, we note that the precision in determining $\effspec$ is limitedby the precision in the SN rate as a function of redshift."200computed spectra for columns of outflowing gas with a variety of density and velocity profiles.,computed spectra for columns of outflowing gas with a variety of density and velocity profiles.201 They demonstrated that outflows can imprint a wide variety of features on X-ray spectra. depending on the outflow conditions and that very high outflow velocities would be required if absorption in outflows is to explain soft excesses in AGN spectra.," They demonstrated that outflows can imprint a wide variety of features on X-ray spectra, depending on the outflow conditions and that very high outflow velocities would be required if absorption in outflows is to explain soft excesses in AGN spectra."202 More recently. a similar approach to that adopted by ? has been used for the calculation of transmission spectra in dynamical models of AGN outflows by ?..," More recently, a similar approach to that adopted by \citet{schurch07} has been used for the calculation of transmission spectra in dynamical models of AGN outflows by \citet{dorodnitsyn08}."203 In this paper. we extend the study of ? to incorporate a more realistic and more versatile description of a disk wind geometry including both rotation and off-axis lines-of-sight.," In this paper, we extend the study of \citet{sim05b} to incorporate a more realistic and more versatile description of a disk wind geometry including both rotation and off-axis lines-of-sight."204 We retain the use of MC method owing to its versatility for multi-dimensional radiative thetransfer., We retain the use of the MC method owing to its versatility for multi-dimensional radiative transfer.205 Our method is complementary to that of ? since We account for geometric effects directly (e.g. scattering of radiation between lines-of-sight in multi-dimensional outflow geometries) but make some simplitications in the treatment of atomic processes., Our method is complementary to that of \citet{schurch07} since we account for geometric effects directly (e.g. scattering of radiation between lines-of-sight in multi-dimensional outflow geometries) but make some simplifications in the treatment of atomic processes.206 We focus on highly ionized winds and the interpretation of observable features in the Fe K band., We focus on highly ionized winds and the interpretation of observable features in the Fe K band.207 Although other spectral lines are expected to form in outflows. Fe Ka absorption is the most relevant for the interpretation of observed spectra since it is the clearest signature of a highly ionized flow: although more abundant. the lighter elements are fully ionized more easily than Fe so that any spectral features they imprint are weaker.," Although other spectral lines are expected to form in outflows, Fe $\alpha$ absorption is the most relevant for the interpretation of observed spectra since it is the clearest signature of a highly ionized flow: although more abundant, the lighter elements are fully ionized more easily than Fe so that any spectral features they imprint are weaker."208 Furthermore. identification of features in the Fe K energy band is relatively secure since only K shell transitions of heavy ions are expected a energies <5 keV. At lower energies. where Ka transitions of ligh or intermediate mass elements might arise. line identification is more ambiguous. particularly if large velocity shifts are considered.," Furthermore, identification of features in the Fe K energy band is relatively secure since only K shell transitions of heavy ions are expected at energies $\simgt2095$ keV. At lower energies, where $\alpha$ transitions of light or intermediate mass elements might arise, line identification is more ambiguous, particularly if large velocity shifts are considered."210 Although we regard Fe Ka absorption features as the bes diagnostic for a highly ionized flow. we will also investigate the ormation of emission components in the Fe K arising from line scattering or recombination in the outflow.," Although we regard Fe $\alpha$ absorption features as the best diagnostic for a highly ionized flow, we will also investigate the formation of emission components in the Fe K arising from line scattering or recombination in the outflow."211 Such features are of articular interest since they may explain possible P-Cygni-like line orofiles (e.g. 2.. 2) and may affect the interpretation of Fe emission eutures commonly associated with disk reflection We begin in Section 2. by defining the class of outflow models which we will consider.," Such features are of particular interest since they may explain possible P-Cygni-like line profiles (e.g. \citealt{done07}, \citealt{turner08}) ) and may affect the interpretation of Fe emission features commonly associated with disk reflection We begin in Section \ref{sect_model} by defining the class of outflow models which we will consider."212 In Section ὁ we describe our radiative ransfer method and discuss the adopted atomic data., In Section \ref{sect_RT} we describe our radiative transfer method and discuss the adopted atomic data.213 We present a sample calculation for one model in Section + and then extend our discussion to a a grid of outflow models in Section 5..The implications of our models for observations of Fe Ka absorption are described in Section 6 and for other spectral features in Section 7.., We present a sample calculation for one model in Section \ref{sect_example} and then extend our discussion to a a grid of outflow models in Section \ref{sect_grid}.The implications of our models for observations of Fe $\alpha$ absorption are described in Section \ref{sect_obs} and for other spectral features in Section \ref{sect_beyondka}.214 In Section 8 we illustrate the value of our models by comparing them in detail with observations of a well-known AGN. Mrk 766.," In Section \ref{sect_mrk766} we illustrate the value of our models by comparing them in detail with observations of a well-known AGN, Mrk 766."215 We draw conclusions and discuss further work in Section 9.., We draw conclusions and discuss further work in Section \ref{sect_conc}.216 Our radiative transfer calculations were performed using a simply-parameterised model for an outflow launched from an accretion disk around a supermassive black hole., Our radiative transfer calculations were performed using a simply-parameterised model for an outflow launched from an accretion disk around a supermassive black hole.217 In this section. we describe the properties of the model and the parameters which must be specitied to define a particular realisation of the model.," In this section, we describe the properties of the model and the parameters which must be specified to define a particular realisation of the model."218 We adopt a standard disk wind geometry. namely the “displaced dipole” model of ?..," We adopt a standard disk wind geometry, namely the “displaced dipole” model of \citet{knigge95}. ."219 This geometry has been adopted in radiative transfer studies of accretion disk winds for a variety of systems including cataclysmic variables (22). and massive young stellar objects (2)..," This geometry has been adopted in radiative transfer studies of accretion disk winds for a variety of systems including cataclysmic variables \citep{knigge95,220 long02} and massive young stellar objects \citep{sim05}."221 The geometry is illustrated in Fig., The geometry is illustrated in Fig.222 |. and is defined by the following three parameters (each of which is marked in the figure) The accretion disk is assumed to lie in the .-y-plane., \ref{fig_geo} and is defined by the following three parameters (each of which is marked in the figure): The accretion disk is assumed to lie in the $xy$ -plane.223 The wind is symmetric under rotation about the z-axis and under reflection in the .ry-plane., The wind is symmetric under rotation about the $z$ -axis and under reflection in the $xy$ -plane.224 The velocity is specified at every point in the wind following the parameterisation of 2?) (see also 2))., The velocity is specified at every point in the wind following the parameterisation of \citet{knigge95} (see also \citealt{long02}) ).225 Although this velocity law is not based on self-consistent hydrodynamical outflow models (cf. 2)).," Although this velocity law is not based on self-consistent hydrodynamical outflow models (cf. \citealt{dorodnitsyn08}) ),"226 it provides a simple and reasonably flexible description of possible steady-state flows which we use for our exploratory radiative transfer simulations., it provides a simple and reasonably flexible description of possible steady-state flows which we use for our exploratory radiative transfer simulations.227 The wind rotates about the z-axis., The wind rotates about the $z$ -axis.228 The rotational velocity is obtained by assuming that parcels of matter conserve specific angular momentum about the z-axis as they flow outwards., The rotational velocity is obtained by assuming that parcels of matter conserve specific angular momentum about the $z$ -axis as they flow outwards.229 The angular momentum at the base of a streamline is set at the Keplerian value for the radius at which the streamline crosses the .ry-plane., The angular momentum at the base of a streamline is set at the Keplerian value for the radius at which the streamline crosses the $xy$ -plane.230 Thus the rotational velocity is determined only by the choice of wind geometry (see above) and the mass of the central object. Aij. The outflow velocity points directly away from the focus point of thewind.," Thus the rotational velocity is determined only by the choice of wind geometry (see above) and the mass of the central object, $M_{\mbox{\scriptsize bh}}$ The outflow velocity points directly away from the focus point of thewind."231 Its magnitude is given by, Its magnitude is given by232Measuring precisely the polarization of the Cosmic Microwave Background (CMB) is one of the major challenges of contemporary observationnal cosmology.,Measuring precisely the polarization of the Cosmic Microwave Background (CMB) is one of the major challenges of contemporary observationnal cosmology.233 It has already led to spectacular results concerning the cosmological model Kovacetal..2002.Readhead2004.Dunkleyetal..2008.NoltaAde2008 describing our Universe.," It has already led to spectacular results concerning the cosmological model \cite{DASI, CBI, WMAPa, WMAPb, QUAD}] ] describing our Universe."234 Even more challenging i$. the detection of the so-called B-modes in the CMB polarization. associated with pure tensor modes originating from primordial gravitational waves enhanced by inflation.," Even more challenging is the detection of the so-called B-modes in the CMB polarization, associated with pure tensor modes originating from primordial gravitational waves enhanced by inflation."235 Discovering these modes would give direct information on inflation as the amplitude of the B-modes is proportional to the tensor to sealar ratio for the amplitude of the primordial density perturbations which is a direct product of inflationary scenari. [LiddleandLyth. 2000]]., Discovering these modes would give direct information on inflation as the amplitude of the B-modes is proportional to the tensor to scalar ratio for the amplitude of the primordial density perturbations which is a direct product of inflationary scenarii \cite{refBmodesinflation}] ].236 Furthermore. it seems that most of the inflationary models arising in the context of string theory (brane inflation. ...) predict an undetectably small scalar to tensor ratio [KalloshandLinde. 200711.," Furthermore, it seems that most of the inflationary models arising in the context of string theory (brane inflation, ...) predict an undetectably small scalar to tensor ratio \cite{KalloshBmodes}] ]."237" The ""Siscovery of B-modes in the CMB may therefore appear as the only present way to falsify string theories.", The discovery of B-modes in the CMB may therefore appear as the only present way to falsify string theories.238 Cosmic strings and other topological defects are also sources of density perturbations. of both scalar and tensor nature., Cosmic strings and other topological defects are also sources of density perturbations of both scalar and tensor nature.239 They are however largely dominated by the adiabatic inflationary perturbations in TT. TE and EE power spectra therefore hard to detect.," They are however largely dominated by the adiabatic inflationary perturbations in TT, TE and EE power spectra and therefore hard to detect."240" It is only in the B-mode sector (BB power spectrum) that the tensor topological defects perturbation could be large [Bevisetal.. 2007]] and have a different) shape [Urrestillaetal.. 2008]] from those originating from inflation and hence be ""Setectable |PogosranandWyman. 2007].", It is only in the B-mode sector (BB power spectrum) that the tensor topological defects perturbation could be large \cite{BevisBmodes}] ] and have a different shape \cite{UrrestillaBmodes}] ] from those originating from inflation and hence be detectable \cite{PogosianBmodes}] ].241 Unfortunately. the inflationary tensor to scalar ratio seems to be rather small so that the B-modes are expected at a low level as compared to the E-modes.," Unfortunately, the inflationary tensor to scalar ratio seems to be rather small so that the B-modes are expected at a low level as compared to the E-modes."242 The quest for the B-modes ts a therefore tremendous experimental challenge: one requires exquisitely sensitive detectors with an unprecedented control of the instrumental systematics. observing at a number of different frequencies to be able to remove foreground contamination.," The quest for the B-modes is a therefore tremendous experimental challenge: one requires exquisitely sensitive detectors with an unprecedented control of the instrumental systematics, observing at a number of different frequencies to be able to remove foreground contamination."243 Various teams have decided to joi the quest. most of them with mstrumental designs based on the imager concept (BICEP. EBEX. QUIET. SPIDER. CLOVER).," Various teams have decided to join the quest, most of them with instrumental designs based on the imager concept (BICEP, EBEX, QUIET, SPIDER, CLOVER)."244 Another possible instrumental concept is an interferometer that has many advantages from the point of view of systematic effects (no optics for instance) and that directly measures the Fourier modes of the sky., Another possible instrumental concept is an interferometer that has many advantages from the point of view of systematic effects (no optics for instance) and that directly measures the Fourier modes of the sky.245 Let us recall that the first nmetections of polarization of the CMB were performed with —nterferometers [Kovacetal..2002.Readhead 2004]].," Let us recall that the first detections of polarization of the CMB were performed with interferometers \cite{DASI,CBI}] ]."246 Interferometers are however often considered as less sensitive than imagers mainly because of the additional noise induced by the amplifiers required for heterodyne interferometry whereas imagers use background limited bolometers., Interferometers are however often considered as less sensitive than imagers mainly because of the additional noise induced by the amplifiers required for heterodyne interferometry whereas imagers use background limited bolometers.247 Another drawback of heterodyne interferometry is that it requires a number of correlators that scales as the square of the number of input channels limiting the number of channels actually achievable [CMBTaskForcereport. 2006]]., Another drawback of heterodyne interferometry is that it requires a number of correlators that scales as the square of the number of input channels limiting the number of channels actually achievable \cite{cmbtaskforce}] ].248" A new concept of instrument. called ""Bolometric Interferometer"" is currently under developpement (MBI Timbieetal.. 2003]. BRAIN [Polentaetal..2003.Charlassieretal.. 2008]."," A new concept of instrument called ""Bolometric Interferometer"" is currently under developpement (MBI \cite{MBI}] ], BRAIN \cite{Brain, BrainRomain}] ])."249 In such an instrument. the interference fringes are “imaged using bolometers.," In such an instrument, the interference fringes are ""imaged"" using bolometers."250 We believe that such an instrument could combine the advantages of interferometry in terms of systematic effects and data analysis and those of bolometers in terms of sensitivity., We believe that such an instrument could combine the advantages of interferometry in terms of systematic effects and data analysis and those of bolometers in terms of sensitivity.251 The goal of this article is to investigate ways to reconstruct the Fourier modes on the sky (the so-called visibilities) of the Stokes parameters with a bolometric interferometer., The goal of this article is to investigate ways to reconstruct the Fourier modes on the sky (the so-called ) of the Stokes parameters with a bolometric interferometer.252 In particular. we focus our attention on the necessary phase-shifting schemes required to modulate the fringe patterns observed with the bolometer array.," In particular, we focus our attention on the necessary phase-shifting schemes required to modulate the fringe patterns observed with the bolometer array."253" We show that one can construct phase-sequences that allow to achieve an excellent sensitivity on the visibilitites: scaling as VN;/Na (where Nj, is the number of horns and Na, is the number of couples of horns separated by identical vectors hereafter called baselines) whereas it would scale as. ΥΛΗJ/N&, for a non optimal phase-shifting sequence.", We show that one can construct phase-sequences that allow to achieve an excellent sensitivity on the visibilitites: scaling as $\sqrt{N_h}/N_\mathrm{eq}$ (where $N_h$ is the number of horns and $N_\mathrm{eq}$ is the number of couples of horns separated by identical vectors hereafter called ) whereas it would scale as $\sqrt{N_h}/\sqrt{N_\mathrm{eq}}$ for a non optimal phase-shifting sequence.254 This article is organised as follows: in section I we describe the assumptions that we make on the hardware design and on the properties of the various parts of the detector., This article is organised as follows: in section \ref{design} we describe the assumptions that we make on the hardware design and on the properties of the various parts of the detector.255 In section 2 we describe how the signal measured by such an instrument can be expressed in terms of the Stokes parameter visibilities., In section \ref{stokes} we describe how the signal measured by such an instrument can be expressed in terms of the Stokes parameter visibilities.256 We show how to invert the problem in an optimal way in section 3. and show how the phase-shifting scheme, We show how to invert the problem in an optimal way in section \ref{reco} and show how the phase-shifting scheme257wilh a rest-Irame line-of-sight velocity dispersion of 935 km | and a mass of ~2xLOY AL..,with a rest-frame line-of-sight velocity dispersion of 935 km $^{-1}$ and a mass of $\sim 2 \times 10^{15}$ $_\odot$.258 These clusters are bevond (he range of sensitivity of the Subaru weak lensing map (see Section 3.1))., These clusters are beyond the range of sensitivity of the Subaru weak lensing map (see Section \ref{newmap}) ).259 In 1999. Dressler et al. (," In 1999, Dressler et al. ("2601999) included (he cluster CI16012-42 in (heir spectroscopic catalog of 10 distant rich clusters of galaxies.,1999) included the cluster Cl1601+42 in their spectroscopic catalog of 10 distant rich clusters of galaxies.261 Girardi Mezzetti (2001) analvzed the redshift distribution for the 46 cluster members., Girardi Mezzetti (2001) analyzed the redshift distribution for the 46 cluster members.262 They obtained a mean redshilt of 0.54 and a rest frame line-ol-sight velocity dispersion of 22 km |., They obtained a mean redshift of 0.54 and a rest frame line-of-sight velocity dispersion of $^{+84}_{-87}$ km $^{-1}$.263 They compute a cluster mass of ~2.5xLOM ALS., They compute a cluster mass of $\sim 2.5 \times 10^{14}$ $_\odot$.264 This cluster is well within the sensilivilv range of the weak lensing map and we compare these results wilh our own estimate in Section 4.2.., This cluster is well within the sensitivity range of the weak lensing map and we compare these results with our own estimate in Section \ref{clusters}.265 In contrast with the observations of small patches of the original GIIO field geared toward studying individual clusters at reasonably high redshift. (he wider field Mivazaki et al (2002) observation provides (he basis for a weak lensing convergence map of the region.," In contrast with the observations of small patches of the original GHO field geared toward studying individual clusters at reasonably high redshift, the wider field Miyazaki et al (2002) observation provides the basis for a weak lensing convergence map of the region."266 The weak lensing convergence map is sensitive to systems al lower redshifts ranging from ~0.2 to ~0.7., The weak lensing convergence map is sensitive to systems at lower redshifts ranging from $\sim 0.2$ to $\sim 0.7$.267 In Section 4.2.. we show that the cluster CII6012—42 (previously studied by Dressler (1999) ancl Girardi Mezzetti (2001) appears as one of the (wo most significant peaks in the weak lensing map.," In Section \ref{clusters}, we show that the cluster Cl1601+42 (previously studied by Dressler (1999) and Girardi Mezzetti (2001) appears as one of the two most significant peaks in the weak lensing map."268 Tlamana et al (2009) carried out multüi-object spectroscopy. along four lines-ol-sight in the GTO2deg? field., Hamana et al (2009) carried out multi-object spectroscopy along four lines-of-sight in the $^2$ field.269 They observed with a single 6’ diameter slit mask in each of four patches and measured a total of 92 redshifts., They observed with a single $^{\prime}$ diameter slit mask in each of four patches and measured a total of 92 redshifts.270 On the basis of 15 of these galaxies coincicent in redshilt. SL J1602.34-4335 is a cluster at a redshift of 0.42 with a rest-Irame line-of-sight velocity dispersion of G75 kins I: this cluster is the other of the (wo most significant weak lensing peaks in the Mivazaki οἱ al. (," On the basis of 15 of these galaxies coincident in redshift, SL J1602.8+4335 is a cluster at a redshift of 0.42 with a rest-frame line-of-sight velocity dispersion of 675 km $^{-1}$; this cluster is the other of the two most significant weak lensing peaks in the Miyazaki et al. ("2712007) map.,2007) map.272 We compare (his measurement will our redshift survey results in Section 4.2. and Table 3.., We compare this measurement with our redshift survey results in Section \ref{clusters} and Table \ref{tbl:VDisp}.273 We investigate the association between convergence peaks and clusters (halos) in the ealaxy distribution based on a densely sampled redshift survey., We investigate the association between convergence peaks and clusters (halos) in the galaxy distribution based on a densely sampled redshift survey.274 Our goal is identification of the svstems of galaxies (hat should produce a weak lensing signal., Our goal is identification of the systems of galaxies that should produce a weak lensing signal.275 We (hus seek to identilv candidate svstems in the redshift survey with rest hane line-ol-sight velocity dispersion Z500 km + consistent with the sensitivity of the Subaru map., We thus seek to identify candidate systems in the redshift survey with rest frame line-of-sight velocity dispersion $\gtrsim 500$ km $^{-1}$ consistent with the sensitivity of the Subaru map.276 We constinetec the galaxy catalog from the Sloan Digital Skv Survey (SDSS. 2008) r-bancl galaxy list for the GTO2deg? field.," We constructed the galaxy catalog from the Sloan Digital Sky Survey (SDSS, Adelman-McCarthy 2008) r-band galaxy list for the $^2$ field."277" The field covers the region 240.05*<A000249329° ancl 42.55*<Ouon 43.83""."," The field covers the region $240.05^\circ \leq \alpha_{2000} \leq278242.32^\circ$ and $42.55^\circ \leq \delta_{2000} \leq 43.83^\circ$ ."279Asymptotic Giant Braneh (AGB) stars. are. generally Jassified to be oxvgen-rich (M-tvpe) or carbon-rich (C-type) ased on the chemistry of the photosphere and/or the outer envelope (e... Busso. Gallino Wasserburg 1999: Lerwig 2005).,"Asymptotic Giant Branch (AGB) stars are generally classified to be oxygen-rich (M-type) or carbon-rich (C-type) based on the chemistry of the photosphere and/or the outer envelope (e.g., Busso, Gallino Wasserburg 1999; Herwig 2005)."280 Chan Ixwok (1990) argued that a Al-type star may become a carbon star when the star goes through € cdredge-up processes and thus the abundance of C is larger than that of O. S stars are generally. regarded: as intermediate between Al-twpe and carbon stars in their properties (e.g.. Lloyd Evans Little-Marenin. 1999).," Chan Kwok (1990) argued that a M-type star may become a carbon star when the star goes through C dredge-up processes and thus the abundance of C is larger than that of O. S stars are generally regarded as intermediate between M-type and carbon stars in their properties (e.g., Lloyd Evans Little-Marenin 1999)."281 Only the S stars with Te (also called intrinsic S stars) are believed. to be actually in the AGB phase following the evolution sequence M-S-€ (Iben Renzini 1983: Jorissen Mayor 1988. 1992).," Only the S stars with Tc (also called intrinsic S stars) are believed to be actually in the AGB phase following the evolution sequence M-S-C (Iben Renzini 1983; Jorissen Mayor 1988, 1992)."282 Llowever. Chan Ixwok (1990) and Cuandalini Busso (2008) pointed out that the M-S-C evolutionary sequence is not a certain thing for all the AGB stars.," However, Chan Kwok (1990) and Guandalini Busso (2008) pointed out that the M-S-C evolutionary sequence is not a certain thing for all the AGB stars."283 The two-colour diagram. (2€D) of stellar sources. in the Znfrared Astronomical Satellite (LRAS) Point Source Catalog (PSC) has. been useful. in. characterizing the circumstellar environment. of ACD stars., The two-colour diagram (2CD) of stellar sources in the $Infrared$ $Astronomical$ $Satellite$ $IRAS$ ) Point Source Catalog (PSC) has been useful in characterizing the circumstellar environment of AGB stars.284 van cer Veen Labbing (1988) divided the £4.15 2CD into eight areas in such a way that cach area contains a more or less homogeneous group., van der Veen Habbing (1988) divided the $IRAS$ 2CD into eight areas in such a way that each area contains a more or less homogeneous group.285 The 2CD statistically distinguishes between C-rich and O-rich ACD stars., The 2CD statistically distinguishes between C-rich and O-rich AGB stars.286 For many. studies since the /RAS mission. the JAS 2€D has been the starting point for colour selection of ssumples: not onky to select. AGB or red. giant branch (ROB) stars. but also to select. postACID. stars. voung stellar objects ancl starburst ealaxies.," For many studies since the $IRAS$ mission, the $IRAS$ 2CD has been the starting point for colour selection of samples; not only to select AGB or red giant branch (RGB) stars, but also to select post-AGB stars, young stellar objects and starburst galaxies."287 The £RAS PSC (version 2.1) contains useful photometric data at four bands (12. 25. 50 and 100 pea) for 245.880. sources.," The $IRAS$ PSC (version 2.1) contains useful photometric data at four bands (12, 25, 50 and 100 $\mu$ m) for 245,889 sources."288 {15 photometric data at. four bands as well as near infrared (NI) photometric data at A and L bands have been used to make various infrared 2€Ds for AGB stars (e... Sub Ixwon 2009).," $IRAS$ photometric data at four bands as well as near infrared (NIR) photometric data at $K$ and $L$ bands have been used to make various infrared 2CDs for AGB stars (e.g., Suh Kwon 2009)."289 The τς Low Resolution Spectrograph (LAS: A = S 22 jm) data are useful to identify important features of O-rich ancl C-rich, The $IRAS$ Low Resolution Spectrograph (LRS; $\lambda$ = $-$ 22 $\mu$ m) data are useful to identify important features of O-rich and C-rich290"2009a, 2009b, Molodtsova et al.","2009a, 2009b, Molodtsova et al."291 2010) In such vibrations the rate of differentially rotational material displacements of stellar matter is described by nodeless toroidal vector field which is identical to that for torsion node-free vibrations restored by Hooke’s elastic force (Bastrukov et al., 2010) In such vibrations the rate of differentially rotational material displacements of stellar matter is described by nodeless toroidal vector field which is identical to that for torsion node-free vibrations restored by Hooke's elastic force (Bastrukov et al.292" 2007a, 2007b)."," 2007a, 2007b)."293" In the last equation, P(cos@) stands for Legendre polynomial of degree { specifying the overtone of toroidal a-mode; the amplitude a(t) describes time evolution of vibrations (both global and locked in the crust)."," In the last equation, $P_\ell(\cos\theta)$ stands for Legendre polynomial of degree $\ell$ specifying the overtone of toroidal $a$ -mode; the amplitude $\alpha(t)$ describes time evolution of vibrations (both global and locked in the crust)."294" In computing discrete spectrum of such vibrations, the magnetic field can be conveniently represented in the form: B(r)—Bb(r), where B is the intensity and b(r) is dimensionless vector-function of magnetic field distribution over the star volume."," In computing discrete spectrum of such vibrations, the magnetic field can be conveniently represented in the form: ${\bf B}({\bf r})=B\,{\bf b}({\bf r})$, where $B$ is the intensity and ${\bf b}({\bf r})$ is dimensionless vector-function of magnetic field distribution over the star volume."295" Similar representation can be used for the bulk density p(r) pó(r), where p is the density at the star center and g(r) describes the radial profile of density which can be taken from computations of neutron star structure relying on realistic equations of state accounting for non-uniform mass distribution in the star interior (e.g., Weber 1999)."," Similar representation can be used for the bulk density $\rho(r)=\rho\phi(r)$ , where $\rho$ is the density at the star center and $\phi(r)$ describes the radial profile of density which can be taken from computations of neutron star structure relying on realistic equations of state accounting for non-uniform mass distribution in the star interior (e.g., Weber 1999)."296" Scalar product of (3)) with the following separable representation of u(r,t)=a(r)o(t) and integration over the star volume leads to equation for a(t) having the form of equation of harmonic oscillator 'The amplitude of oscillations with constant in time frequency wy is given by where over-bar stands for averaging over period of vibrations: a?(t)=(1/2)og."," Scalar product of \ref{e1.2}) ) with the following separable representation of ${\bf u}({\bf r},t)={\bf a}({\bf r})\,{\alpha}(t)$ and integration over the star volume leads to equation for $\alpha(t)$ having the form of equation of harmonic oscillator The amplitude of oscillations with constant in time frequency $\omega_\ell$ is given by where over-bar stands for averaging over period of vibrations: $\bar{\alpha^2}(t)=(1/2)\alpha^2_0$."297" This suggests, if all the energy Epurst of x-ray outburst goes in the quake-induced vibrations and, i.e. when [νε=Ea, the amplitude αρ can be extracted from the last equation."," This suggests, if all the energy $E_{\rm burst}$ of x-ray outburst goes in the quake-induced vibrations and, i.e. when $E_{\rm burst}=E_A$, the amplitude $\alpha_0$ can be extracted from the last equation."298" In the reminder of the paper we remove index 6 and confine our analysis to the case of quadrupole overtone of a-mode, i.e., putting w=wee."," In the reminder of the paper we remove index $\ell$ and confine our analysis to the case of quadrupole overtone of $a$ -mode, i.e., putting $\omega=\omega_{\ell=2}$ ."299 The important outcome of assumption about constant in time undisturbed magnetic field is the vibration energy conservation and also that the fundamental frequency v4—wa/2m (where w4=v4/R) and the period P4=vil of global Alfvénn oscillations remain constant in time., The important outcome of assumption about constant in time undisturbed magnetic field is the vibration energy conservation and also that the fundamental frequency $\nu_A=\omega_A/2\pi$ (where $\omega_A=v_A/R$ ) and the period $P_A=\nu_A^{-1}$ of global Alfvénn oscillations remain constant in time.300 The magnitudes of basic frequency of toroidal a mode in neutron stars with magnetic fields typical to radio-pulsars By2=B/(10!? G and magnetars (soft gamma repeaters) G are, The magnitudes of basic frequency of toroidal $a$ mode in neutron stars with magnetic fields typical to radio-pulsars $B_{12} = B/(10^{12} $ G and magnetars (soft gamma repeaters) $B_{14} = B/(10^{14}$G are301The ‘tilts’ of the velocity vectors from the E-W direction. seen most strongly on the poleward side of the band. are of particular interest.,"The 'tilts' of the velocity vectors from the E-W direction, seen most strongly on the poleward side of the band, are of particular interest."302 In both antisolar and solar cases they implv angular momentum transport toward the equator., In both antisolar and solar cases they imply angular momentum transport toward the equator.303 In the antisolar case. (his implies angular momentum transport down the angular velocity gradient. which feeds kinetic energy to the disturbances away from (he band. aud would reduce the differential rotation.," In the antisolar case, this implies angular momentum transport down the angular velocity gradient, which feeds kinetic energy to the disturbances away from the band, and would reduce the differential rotation."304 By contrast the (ilis in the solar case imply angular momentum (ransport up the gradient. whieh would actually increase the differential rotation.," By contrast the tilts in the solar case imply angular momentum transport up the gradient, which would actually increase the differential rotation."305 The energv [or this increase comes from the toroidal field., The energy for this increase comes from the toroidal field.306 So there will be futher tendeney lor antisolar differential rotation to be cdestvovecl by this instability., So there will be further tendency for antisolar differential rotation to be destroyed by this instability.307 In the solar case. these high latitude hydrodynamic perturbations must be driven by the low latitude JxD forces and associated {hnicl pressure eradients. because they are giving up energy (o the differential rotation.," In the solar case, these high latitude hydrodynamic perturbations must be driven by the low latitude $\mathbf{J \times B}$ forces and associated fluid pressure gradients, because they are giving up energy to the differential rotation."308 Panels e) and [) displav the velocity and pressure perturbations for a weaker peak toroidal field parameter a=1. which is much closer to (hie value for onset of this instability.," Panels e) and f) display the velocity and pressure perturbations for a weaker peak toroidal field parameter $a=1$, which is much closer to the value for onset of this instability."309 lere we see the Ults have largely. disappeared., Here we see the tilts have largely disappeared.310 The velocity. patterns still show the near eeostrophic balance. but are largely present only in high latitudes in the antisolar case. mostly in equatorial latitudes in the solar case.," The velocity patterns still show the near geostrophic balance, but are largely present only in high latitudes in the antisolar case, mostly in equatorial latitudes in the solar case."311 Figures 4 and 5 show planforms lor unstable disturbances in (he overshoot tachocline of a G-star. with effective gravity G=0.01. for modes that are svimmetric about the equator.," Figures 4 and 5 show planforms for unstable disturbances in the overshoot tachocline of a G-star, with effective gravity $G=0.01$, for modes that are symmetric about the equator."312 Figure 4 is lor a strong; toroidal field case. namely α=0.6. for both antisolar ancl solar tvpe differential rotations.," Figure 4 is for a strong toroidal field case, namely $a=0.6$, for both antisolar and solar type differential rotations."313 Figure 5Hr is for a weak field case. à=0.1. for whieh. from Figure 1. only the antisolar case is unstable.," Figure 5 is for a weak field case, $a=0.1$, for which, from Figure 1, only the antisolar case is unstable."314 For α=0.6 in Figure 4. we see the perturbation fIuid pressure and velocity. structures (frames ο) and d))are very different from the case of the radiative tachocline.," For $a=0.6$ in Figure 4, we see the perturbation fluid pressure and velocity structures (frames c) and d))are very different from the case of the radiative tachocline."315 Peaks ancl troughs of fluid pressure occur at nearly the same longitude. ancl (here are (wo latituclinally narrow additional fluid pressure perturbations on (the poleward sicle of the baud. one near il and the other near the poles.," Peaks and troughs of fluid pressure occur at nearly the same longitude, and there are two latitudinally narrow additional fluid pressure perturbations on the poleward side of the band, one near it and the other near the poles."316 Most of the magnetic perturbations (Iyvames a) and b)) of both signs occur on the poleward side of the toroidal band., Most of the magnetic perturbations (frames a) and b)) of both signs occur on the poleward side of the toroidal band.317 High {hud pressure is still on the left of the perturbation field arrows. low pressure on the right. but the perturbation fields are not closed ovals.," High fluid pressure is still on the left of the perturbation field arrows, low pressure on the right, but the perturbation fields are not closed ovals."318 Rather there are strong points of horizontal convergence and divergence of field., Rather there are strong points of horizontal convergence and divergence of field.319 This means (he vertical fields are equite significant., This means the vertical fields are quite significant.320 Similarly. the flow fields are not simply counterclockwise around lows ancl clockwise around highs.," Similarly, the flow fields are not simply counterclockwise around lows and clockwise around highs."321 Instead there is much flow both up and down the fluid. pressure gradients. ancl substantial areas of horizontal convergence and divergence.," Instead there is much flow both up and down the fluid pressure gradients, and substantial areas of horizontal convergence and divergence."322 This implies the vertical motions are substantial., This implies the vertical motions are substantial.323lt is well known that. if g(2)4f(2) and the boundary-terminal data is discontinuous. (hen one can not expect the unique solution of continuous up to the boundary.,"It is well known that, if $g(\beta) \neq f(\beta)$ and the boundary-terminal data is discontinuous, then one can not expect the unique solution of continuous up to the boundary."324 Furthermore. the discontinuity and the singularity ad the corner propagate (he numerical errors quickly throughout its entire domain lor the numerical PDE methods. such as finite element method (FIM) or finite difference method (FDAI). see more discussions in 10 and the references therein.," Furthermore, the discontinuity and the singularity at the corner propagate the numerical errors quickly throughout its entire domain for the numerical PDE methods, such as finite element method (FEM) or finite difference method (FDM), see more discussions in \cite{SYZ07} and the references therein."325 Therefore. the unique solvability and the regularity of the solution are crucial to make use of the existing PDE nunerical methods.," Therefore, the unique solvability and the regularity of the solution are crucial to make use of the existing PDE numerical methods."326 To avoid this error propagation due to the discontinuity of the boundary-terminal data. we provide an alternative choice to bv revising the terminal pavofE: Consider a rebate option of barrier 3 with In this case. the rebate option price is associated to PDE Observe that. the revised terminal data f? not only makes the terminal-boundary data continuous al the corner (2.Z7). but also preserves Hóllder regularityv of the original terminal data f regardless how large the value 9 is.," To avoid this error propagation due to the discontinuity of the boundary-terminal data, we provide an alternative choice to by revising the terminal payoff: Consider a rebate option of barrier $\beta$ with In this case, the rebate option price is associated to PDE Observe that, the revised terminal data $f^\beta$ not only makes the terminal-boundary data continuous at the corner $(\beta, T)$, but also preserves Höllder regularity of the original terminal data $f$ regardless how large the value $\beta$ is."327 Although PDE is degenerate al 7=0. one can still has unique classical solution by utilizing Shauder's interior estimate.," Although PDE is degenerate at $x=0$, one can still has unique classical solution by utilizing Shauder's interior estimate."328 Also. its solution is indeed equal to the revised rebate option price V! of(3.7).. see Lemma 9..," Also, its solution is indeed equal to the revised rebate option price $\widetilde V^\beta$ of, see Lemma \ref{lem:app1}."329 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."330 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."331 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."332 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."333 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."334 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."335 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."336 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."337 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."338 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."339 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."340 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."341 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."342 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."343 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."344 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."345 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."346 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."347 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅∐," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."348 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅∐≼," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."349 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅∐≼↲," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."350 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅∐≼↲≼," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."351 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅∐≼↲≼⇂," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."352 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅∐≼↲≼⇂≸," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."353 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅∐≼↲≼⇂≸↽," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."354 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅∐≼↲≼⇂≸↽↔," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."355 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅∐≼↲≼⇂≸↽↔↴," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."356 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅∐≼↲≼⇂≸↽↔↴↕," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."357 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅∐≼↲≼⇂≸↽↔↴↕∐," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."358 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅∐≼↲≼⇂≸↽↔↴↕∐≸," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."359 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅∐≼↲≼⇂≸↽↔↴↕∐≸≟," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."360 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅∐≼↲≼⇂≸↽↔↴↕∐≸≟↕," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."361 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅∐≼↲≼⇂≸↽↔↴↕∐≸≟↕↽," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."362 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅∐≼↲≼⇂≸↽↔↴↕∐≸≟↕↽≻," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."363 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅∐≼↲≼⇂≸↽↔↴↕∐≸≟↕↽≻∏," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."364 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅∐≼↲≼⇂≸↽↔↴↕∐≸≟↕↽≻∏≺," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."365 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅∐≼↲≼⇂≸↽↔↴↕∐≸≟↕↽≻∏≺∢," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."366 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅∐≼↲≼⇂≸↽↔↴↕∐≸≟↕↽≻∏≺∢≼," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."367 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅∐≼↲≼⇂≸↽↔↴↕∐≸≟↕↽≻∏≺∢≼↲," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."368 Moreover. by using comparison principle twice on (wo dillerent truncated domains. one can show its unique solution V must be convergent to the desired value V. of(2.3).. ↴⊺∐≀↧↴∐↳↽⊳∖⇁↥∪⊔∐↲↴⊺∐≼↲∪↕⋅≼↲∐↓⊑↽⊰⋅⋅∪∐≼↲≺∢≀↧↴∐∏⊳∖⇁≼↲≼↲↕⊔∐↲↕⋅∖∖↽≼↲∐≼↲⊳∖⇁↥≀↧↴∣↽≻∐⋝∖⊽↥∐↲≼⇂⇪∐⇀∖↕∪↕⋅∏⋮⇀∖↕∪∐↥↴↻⊏ ≼↜⋮⋅↽⊰⋅⋖↽∖⋟⋮⊔⋟∪↕⋅≀↧↴↥≀↧↴↕⋅≸≟≼↲↽≳⋟↥∪≼↲⋟∖⊽∐∐⋯↴∩↲⊔∐↲⋟∖⇁∐↓≀↧↴∐≼↲⋟∖⊽↥⋟∖⊽∏↕↽≻≼↲↕⋅∐≼↲≼⇂≸↽↔↴↕∐≸≟↕↽≻∏≺∢≼↲⋅," Moreover, by using comparison principle twice on two different truncated domains, one can show its unique solution $\widetilde V^\beta$ must be convergent to the desired value $V$ of, Thanks to the Theorem \ref{thm:contbd}, one can use either well established FDM or FEM on PDE for a large $\beta$ to estimate the smallest superhedging price."369Because HD 209458 is a bright star (A.=6.31) and the background at these shorter wavelengths is minimal. we calculate the flix from the star in each image using aperture photometry will a radius of five pixels.,"Because HD 209458 is a bright star $K=6.31$ ) and the background at these shorter wavelengths is minimal, we calculate the flux from the star in each image using aperture photometry with a radius of five pixels."370 We determine the position of the star in each image as the posilion-weightecd sum of the flix in à 7x pixel box centered on the approximate position of (he star., We determine the position of the star in each image as the position-weighted sum of the flux in a $7\times7$ pixel box centered on the approximate position of the star.371 We estimate (he background in each image by selecting a subset of pixels from the corners of (he image where the point spread funcüon of the star is faintest. making a histogram of (he fIux values in (hese pixels. and fitting a Gaussian function to the center of (his distribution.," We estimate the background in each image by selecting a subset of pixels from the corners of the image where the point spread function of the star is faintest, making a histogram of the flux values in these pixels, and fitting a Gaussian function to the center of this distribution."372 We calculate the JD value for each image as the Gime at mid-exposure. aud apply a correction to convert these JD values to the appropriate ILJD. taking into account Spitzers orbital position at each point during the observations.," We calculate the JD value for each image as the time at mid-exposure, and apply a correction to convert these JD values to the appropriate HJD, taking into account Spitzer's orbital position at each point during the observations."373 As a check we repeat our analvsis using apertures ranging [rom 3.5—1 pixels. aud obtain consistent results in all cases.," As a check we repeat our analysis using apertures ranging from $3.5-7$ pixels, and obtain consistent results in all cases."374 Fluxes measured at these (wo wavelengths show a strong correlation with the changing position of the star on (he array. al a level comparable to the depth of the secondary eclipse.," Fluxes measured at these two wavelengths show a strong correlation with the changing position of the star on the array, at a level comparable to the depth of the secondary eclipse."375 This effect is due to a well-documented intra-pixel sensitivity (Reachetal.2005:Charbon-neaοἱal.2005:Morales-Calderonet 2006).. and can be removed bv fitting the data with a quadratic function of x aud y position. where position is measured as the distance between the peak of the stars point spread function and the center of (he pixel containing (liis peak: where / is the original flux from the star. {+ is the measured flux. x and y denote the location of (he center of the star on the array. and ei—ὃς are the five [ree parameters in (he fit.," This effect is due to a well-documented intra-pixel sensitivity \citep{reach05,char05,mor06}, and can be removed by fitting the data with a quadratic function of x and y position, where position is measured as the distance between the peak of the star's point spread function and the center of the pixel containing this peak: where $f$ is the original flux from the star, $f^1$ is the measured flux, $x$ and $y$ denote the location of the center of the star on the array, and $c_1-c_5$ are the five free parameters in the fit."376 We find that adding higher-order terms (o this equation does not improve the fit. nor does adding a linear or quadratic fanction of time.," We find that adding higher-order terms to this equation does not improve the fit, nor does adding a linear or quadratic function of time."377 We fit this fanction to the out-ol-transil data alone and also simultaneously with the (transit curve. and obtain consistent results in both cases.," We fit this function to the out-of-transit data alone and also simultaneously with the transit curve, and obtain consistent results in both cases."378 We chose to use the simultaneous fit. as it allows us to accurately estimate the additional uncertainty in (he depth of the eclipse introduced by (his correction.," We chose to use the simultaneous fit, as it allows us to accurately estimate the additional uncertainty in the depth of the eclipse introduced by this correction."379 We fit the correction for the intra-pixel sensitivity of the array and the (ransit curve simultaneously to the data using a Markov Chain Monte Carlo method with LO’ steps.," We fit the correction for the intra-pixel sensitivity of the array and the transit curve simultaneously to the data using a Markov Chain Monte Carlo method \citep{ford05,winn07} with $10^6$ steps."380 We set the uncertainty on individual points equal to the standard deviation of the out-of-transit data alter correction for (he intra-pixel variations. ancl remove outliers of 5o or more as ealeulated using the residuals from the best-fit light curve.," We set the uncertainty on individual points equal to the standard deviation of the out-of-transit data after correction for the intra-pixel variations, and remove outliers of $\sigma$ or more as calculated using the residuals from the best-fit light curve."381 We allow both the depth and timine of the secondary. eclipse to vary independently for (he eclipses, We allow both the depth and timing of the secondary eclipse to vary independently for the eclipses382in our sample would have somewhat lower coutinutun veiliugs than those calculated based ou the observed VSSC 17 spectrum.,in our sample would have somewhat lower continuum veilings than those calculated based on the observed VSSG 17 spectrum.383 We have calculated these reduced values. aud in Table 2 we present all of these estimated veilines for the observed sources. usiug our best estimates of their intrinsic spectral types.," We have calculated these reduced values, and in Table 2 we present all of these estimated veilings for the observed sources, using our best estimates of their intrinsic spectral types."384 We now discuss how the results of this veiling / rotation analysis and pre-existing data constrain the possible physical natures of these sources., We now discuss how the results of this veiling / rotation analysis and pre-existing data constrain the possible physical natures of these sources.385 The flat-spectrum YSOs IRS 63 aud IRS 21 were both fouud to have broad. weak CO absorptions which matched those expected for late-type stellar photospheres rotating at e sin? ~50 kins fF.," The flat-spectrum YSOs IRS 63 and IRS 51 were both found to have broad, weak CO absorptions which matched those expected for late-type stellar photospheres rotating at $v$ sin $i \simeq 50$ km $^{-1}$."386 The weak CO absorptions of these two YSOs are consistent. with their not being detected in our initial low-resolution survey (Paper I)., The weak CO absorptions of these two YSOs are consistent with their not being detected in our initial low-resolution survey (Paper I).387" We estimate the contiuuuim veiling of IRS 63 to ber, ~1 provided that it is à PMS YSO near MO spectral type.", We estimate the continuum veiling of IRS 63 to be $r_{k} \simeq 4$ provided that it is a PMS YSO near M0 spectral type.388 Lulunan&Rieke find that the spectral type of IRS 51 is C - IT. earlier than our MO template VSSG 17.," \citeauthor{LR99} find that the spectral type of IRS 51 is G5 – K7, earlier than our M0 template VSSG 17."389 Thus their derived veiling 7j = 1-3 is lower than ours because a Cio — IXY PMS star has less intrinsic CO absorption than a MO oue (see 83.2)., Thus their derived veiling $r_{k}$ = 1 – 3 is lower than ours because a G5 – K7 PMS star has less intrinsic CO absorption than a M0 one (see 3.2).390 It is likely that IRS 21 is indeed au embedded low-mass YSO because its bolometric luninosity is only Lf L.. (WLY)., It is likely that IRS 51 is indeed an embedded low-mass YSO because its bolometric luminosity is only 1.4 $_{\odot}$ (WLY).391 The birthliue mass for this luminosity is approximately 0.5 M... correspouding to a spectral type of 5-7 and a true veiling of 7j223.," The birthline mass for this luminosity is approximately 0.5 $_{\odot}$, corresponding to a spectral type of K5–7 and a true veiling of $r_{k} \simeq 3$."392 Thus it is likely that both IRS 63 and IRS 51 are similar to the quickly rotating flat-spectruui YSOs which we analyzed in Paper IL. but these uew objects have even greater veiliug (Le. rj — 3- [ versus rj~1 for the Paper II Y50).," Thus it is likely that both IRS 63 and IRS 51 are similar to the quickly rotating flat-spectrum YSOs which we analyzed in Paper II, but these new objects have even greater veiling (i.e. $r_{k}$ = 3 – 4 versus $r_{k} \simeq 1$ for the Paper II YSOs)."393 Luhiuau&Rieke [found GSS 26 to have variable veiling. rj; = 0.75 aud rj = Lat epochs of 1991 July aud 1996 May. respectively.," \citeauthor{LR99} found GSS 26 to have variable veiling, $r_{k}$ = 0.75 and $r_{k}$ = 4 at epochs of 1994 July and 1996 May, respectively."394 Our spectrum of GSS 26 (in Figure 1) was taken in 1997 May. oue vear alter the latest Luliman&Rieke spectrum.," Our spectrum of GSS 26 (in Figure 1) was taken in 1997 May, one year after the latest \citeauthor{LR99} spectrum."395 We estimate that ryoZ11 when our spectrum was acquired. aud our assumption of a MO spectral type is consistent. with the determination of I5 — M2.," We estimate that $r_{k} \gtrsim 11$ when our spectrum was acquired, and our assumption of a M0 spectral type is consistent with the \citeauthor{LR99} determination of K5 – M2."396 This rapid increase in veiling - a factor of 2 each vear - is perhaps suggestive of a similarly rapid increase in accretion., This rapid increase in veiling - a factor of 2 each year - is perhaps suggestive of a similarly rapid increase in accretion.397 Luliuiau&Rieke also uote that this n¢wce increased tu brightuess by A~ 1.2 image between epochs., \citeauthor{LR99} also note that this source increased in brightness by $K \simeq$ 1.2 mag between epochs.398 Our spectra are not photometrically calibrated. but comparisons with other «jects support that this source was at least as bright as when observed by Lulunan&Rieke the previous year.," Our spectra are not photometrically calibrated, but comparisons with other objects support that this source was at least as bright as when observed by \citeauthor{LR99} the previous year."399 This is oue of the YSOs observed whose HI Br ~ emissiou line flux increased as its veiling increased. implying that the excess continuum emission is associated with a cireumstellar accretion disk if the Br + emission arises [roi disk accretion.," This is one of the YSOs \citeauthor{LR99} observed whose HI Br $\gamma$ emission line flux increased as its veiling increased, implying that the excess continuum emission is associated with a circumstellar accretion disk if the Br $\gamma$ emission arises from disk accretion."400 The rapid variability of this objects veiling also suggests that its {ναι veiliug is produced by accretion [rom inner disk distances (several AU) aud not from an outer disk, The rapid variability of this object's veiling also suggests that its $K$ -band veiling is produced by accretion from inner disk distances (several AU) and not from an outer disk401"where mj, is the mass of the II» molecule (the dominant atmospheric constituent). 5 is (he gas acliabatic index and e; is (he corresponding adiabatie sound speed.","where $m_{\rm H_2}$ is the mass of the ${\rm H_2}$ molecule (the dominant atmospheric constituent), $\gamma$ is the gas adiabatic index and $c_s$ is the corresponding adiabatic sound speed."402 This scaling illustrates how the Doppler width is reduced for radiative constituents which are typically more massive (han molecular hydrogen., This scaling illustrates how the Doppler width is reduced for radiative constituents which are typically more massive than molecular hydrogen.403 Note that the linear sealing of Avy with the central wavelength Ag implies significant. Doppler width variations across the relevant optical-IB spectral range., Note that the linear scaling of $\Delta \nu_D$ with the central wavelength $\lambda_0$ implies significant Doppler width variations across the relevant optical-IR spectral range.404 Substantial variations in temperature on constant pressure levels are founcl. [rom clay- {ο nieht-side. in current. atmospheric circulation models for hot Jupiters 2009).," Substantial variations in temperature on constant pressure levels are found, from day- to night-side, in current atmospheric circulation models for hot Jupiters ."405. Here. for simplicity. we choose T=1500 IX and 1000 IX as representative temperature values at the 1 bar and 10.7? bar levels. respectively2009).," Here, for simplicity, we choose $T=1500$ K and $1000$ K as representative temperature values at the $1$ bar and $10^{-2}$ bar levels, respectively."406".. The ratio of Doppler to pressure broadening widths is given bv For relevant molecules. typical values of the mass ratio factor. (mg,/mg)!7. are (CIL). 1/3 (HH50). 1/4.7(COs) and 1/5.6(TiO)."," The ratio of Doppler to pressure broadening widths is given by For relevant molecules, typical values of the mass ratio factor, $(m_{\rm H_2}/m_{\rm mol})^{1/2}$, are $\simeq 1/2.8{\rm ~(CH_4)} $ , $1/3~{\rm (H_2O)}$ , $1/4.7{\rm ~(CO_2)}$ and $1/5.6{\rm ~(TiO)}$."407" At 1 bar. for T'=1500 IN. the tvpical broadening ratio is (hus Avy)/Av,c0.5—2 at 1jun and 0.05—0.2 at LOjim."," At 1 bar, for $T=1500$ K, the typical broadening ratio is thus $\Delta408\nu_D /\Delta \nu_p \simeq 0.5-2$ at ${\rm 1~\mu m}$ and $0.05-0.2$ at ${\rm 10~\mu m}$."409" At LO> bar and TZ=1000 k. the ratio becomes Avy/Av,c30—130 at 1jm and 3—13 at 10jn."," At $10^{-2}$ bar and $T=1000$ K, the ratio becomes $\Delta \nu_D /\Delta \nu_p \simeq 30-130$ at ${\rm 1~\mu m}$ and $3-13$ at ${\rm 10~\mu m}$."410 Doppler broadening is thus signilicant at the 1 bar level. especially in the near-IR. ancl the optical. and it becomes increasinely domüinant across the entire oplical-LR. spectral range hieher up in the atmosphere.," Doppler broadening is thus significant at the 1 bar level, especially in the near-IR and the optical, and it becomes increasingly dominant across the entire optical-IR spectral range higher up in the atmosphere."411 The sizable contribution of thermal Doppler broadening to the width of radiative lines at photospheric levels in hot Jupiter atmospheres. together with the scaling Avy«e;xm/e from Eq. (10)).," The sizable contribution of thermal Doppler broadening to the width of radiative lines at photospheric levels in hot Jupiter atmospheres, together with the scaling $\Delta \nu_D < c_s \times \nu_0 / c$ from Eq. \ref{eq:DnuD}) ),"412 suggests that bulk Doppler shifts from atmospheric motions near (he sound speed could modify the shapes of radiative lines sienilicantlv., suggests that bulk Doppler shifts from atmospheric motions near the sound speed could modify the shapes of radiative lines significantly.413" By contrast. much deeper in the atmosphere. where Avp/Av,<1. Doppler shifts fom bulk atmospheric motions near the sound speed would only amount to small shifts over comparatively wide. pressure-broadened lines."," By contrast, much deeper in the atmosphere, where $\Delta \nu_D / \Delta \nu_p \ll 1$, Doppler shifts from bulk atmospheric motions near the sound speed would only amount to small shifts over comparatively wide, pressure-broadened lines."414 Furthermore. wind speeds themselves may be reduced al these deeper levels (see. e.g... Fig.1)).," Furthermore, wind speeds themselves may be reduced at these deeper levels (see, e.g., \ref{fig:one}) )."415 These qualitative arguments are not. very informative about the possible consequences of bulk Doppler shifts on radiation transport in a dynamic aümosphere., These qualitative arguments are not very informative about the possible consequences of bulk Doppler shifts on radiation transport in a dynamic atmosphere.416" li particular. since the Doppler coresof radiative lines are often. verv optically. thick. (saturated"")in hot Jupiter and other planetary atmospheres. (hey do not necessarily contribute much to the"," In particular, since the Doppler coresof radiative lines are often very optically thick (“saturated”)in hot Jupiter and other planetary atmospheres, they do not necessarily contribute much to the"417dinuuest having PSPC counterparts). aud we present full source lists for these. detailing their N-rav properties.,"dimmest having PSPC counterparts), and we present full source lists for these, detailing their X-ray properties."418 2., 2.419 The brightest source (Ly(0.1-2.lee)=107 core s+) is likely a DIIXRD. while a highly variable source nearby is seen to be a supersoft source.," The brightest source $L_{X} (0.1$ $2.4\,keV) = 2.2\times10^{38}$ erg $^{-1}$ ) is likely a BHXRB, while a highly variable source nearby is seen to be a supersoft source."420 Other bright sources coincident with known SNRs aud regions are discussed. as aro foreground. stars and backeround. ACN.," Other bright sources coincident with known SNRs and regions are discussed, as are foreground stars and background AGN."421 ὃν, 3.422 The presen analvsis attaius a ereater scusitivity than previous studies. and the number of believable. X-rav sources within NCC 300 has been iuereased almost twofold.," The present analysis attains a greater sensitivity than previous studies, and the number of believable X-ray sources within NGC 300 has been increased almost twofold."423 That said. no further X-ray counterparts to new candidate SNRs have been detected.," That said, no further X-ray counterparts to new candidate SNRs have been detected."424 1l., 4.425 Residual N-ray enuüsson is observed within NGC 300. due probably to unresolved sources aud eeuuiue diffuse eas.," Residual X-ray emission is observed within NGC 300, due probably to unresolved sources and genuine diffuse gas."426 This cmission (Ly=12.0 ecre i) accounts for approximately of the total X-ray DIuuinuositv of NCC 300 (5.8«10NS OCTOanaso S Ly., This emission $L_{X} = 1.2\times10^{38}$ erg $^{-1}$ ) accounts for approximately of the total X-ray luminosity of NGC 300 $5.8\times10^{38}$ erg $^{-1}$ ).427 5., 5.428" Detailed PSPC aud URI ποιος lists are also preseuted for sources detected outside of NCC 200, and we briefly discuss a ο of hem. notably the galaxy cluster 00053-37."," Detailed PSPC and HRI source lists are also presented for sources detected outside of NGC 300, and we briefly discuss a number of them, notably the galaxy cluster 0053-37."429 6., 6.430 The N-ray source hDnuninositv cüstributiou of NGC 300 is in no wav unusual when compared with other nearby spiral galaxies., The X-ray source luminosity distribution of NGC 300 is in no way unusual when compared with other nearby spiral galaxies.431 The observed lack of highly Dhuuimous N-ray sources is entirely consisteut with other normal. quiescent spirals.," The observed lack of highly luminous X-ray sources is entirely consistent with other normal, quiescent spirals."432 T., 7.433 In terms of how the N-ray properties of NGC 300 conrpare with hose of its ucighbours in the SculpY ealaxy group. NGC 300 appears to be the nost unrenirkable of all the uorial growp members.," In terms of how the X-ray properties of NGC 300 compare with those of its neighbours in the Sculptor galaxy group, NGC 300 appears to be the most unremarkable of all the normal group members."434 It shows no unusual X-rav properties. nor oddities iu inulti-waveleugth luminosities or ratios.," It shows no unusual X-ray properties, nor oddities in multi-wavelength luminosities or ratios."435 It may the best example of a typical normal quiesceut late-type spiral ealaxy., It may the best example of a typical normal quiescent late-type spiral galaxy.436 Tere are tabulated the X-ray properties of the PSPC iux IIRI sources detected outside of the NGC 300 D25 ellipsc., Here are tabulated the X-ray properties of the PSPC and HRI sources detected outside of the NGC 300 D25 ellipse.437 Table Al lists. the PSPC values. as follows: source number 11). corrected right ascension ik declination 22.33). error on the source position LL including a 2799 svstematic attitude solution error). likelihood of existence 55). net broad bau counts and error 66). and count rates aud errors after applving deadtine and vignetting corrections 77). hardness ratios TRL aud IIB2 88 9: see Sect. 2)).," Table \ref{table_PsrcA} lists the PSPC values, as follows: source number 1), corrected right ascension and declination 3), error on the source position 4, including a 9 systematic attitude solution error), likelihood of existence 5), net broad band counts and error 6), and count rates and errors after applying deadtime and vignetting corrections 7), hardness ratios HR1 and HR2 8 9; see Sect. \ref{sec_obse}) )."438 Finally. the 2.1 kkeV flux aud δαν hDnuuinosity. ASS]niue a 5kkeV thermal brenisstralhluug model aud a ποιος distance of MMpe to NGC 300. which is here unlikely to be valid. heuce the bracketed values). are eiven in 110 11.," Finally, the $-$ keV flux and X-ray luminosity, assuming a keV thermal bremsstrahlung model and a source distance of Mpc to NGC 300, which is here unlikely to be valid, hence the bracketed values), are given in 10 11."439 Table A2 lists the IRI values in the same wav as Table Al.. except that no hardness ratios are given. hence the 2.tkkeW flux aud the (again bracketed) Noaav huuinosity are given in ὃς 9.," Table \ref{table_HsrcA} lists the HRI values in the same way as Table \ref{table_PsrcA}, except that no hardness ratios are given, hence the $-$ keV flux and the (again bracketed) X-ray luminosity are given in 8 9."440 A final identification coluun is eiven 110). listing which PSPC source Gf amv) is a likely counterpart. whether any DSS2 candidates (as for Table 5)). aud the naues of any known counerparts (see Sect. 3.2)).," A final identification column is given 10), listing which PSPC source (if any) is a likely counterpart, whether any DSS2 candidates (as for Table \ref{table_iden}) ), and the names of any known counterparts (see Sect. \ref{sec_res2}) )."441 Neptune’s thermal emission has been initally explored from the ground in the 8-13 uim window and in the millimeter range and by theVovager spacecraft in 1989. but detailed views of its spectrum had to await sensitive instrumentation. onboard [50 (see review in Bezzard et al.," Neptune's thermal emission has been initally explored from the ground in the 8-13 $\mu$ m window and in the millimeter range and by the spacecraft in 1989, but detailed views of its spectrum had to await sensitive instrumentation onboard ISO (see review in Bézzard et al."442 19992). (Meadows et al.," 1999a), (Meadows et al."443 2008) and recently AKARI (Fletcher et al., 2008) and recently AKARI (Fletcher et al.444 2010)., 2010).445 Altogether. these observations have revealed a surprisingly rich composition of Neptune’s stratosphere. including numerous hydrocarbons H;. 1Η». 2 Hs. Hs. ΣΗ 1. NENH5C oH. C4H»?). oxygen-bearing species (CO. CO». and HO). HCN. as well as deutertum species CH;D and HD.," Altogether, these observations have revealed a surprisingly rich composition of Neptune's stratosphere, including numerous hydrocarbons $_4$ , $_2$ $_2$ , $_2$ $_6$, $_3$ , $_2$ $_4$, $_3$ $_2$ H, $_4$ $_2$ ), oxygen-bearing species (CO, $_2$, and $_2$ O), HCN, as well as deuterium species $_3$ D and HD."446 Favorable factors for observing minor species in. Neptune's atmosphere are (i) its relatively warm. stratosphere (140 K at | mbar) that enhances IR emission: and (11) Neptune's large internal heat source that results in rapid convection updrafting minor disequilibrium species. notably CO. up to observable levels.," Favorable factors for observing minor species in Neptune's atmosphere are (i) its relatively warm stratosphere $\sim$ 140 K at 1 mbar) that enhances IR emission; and (ii) Neptune's large internal heat source that results in rapid convection updrafting minor disequilibrium species, notably CO, up to observable levels."447 Neptune's submillimeter spectrum longwards of 50 jm has jeen observed by ISO/LWS (Buredorf et al., Neptune's submillimeter spectrum longwards of 50 $\mu$ m has been observed by ISO/LWS (Burgdorf et al.448 2003). but the signal-to-noise ratio in the data was not high enough to reveal spectral features.," 2003), but the signal–to–noise ratio in the data was not high enough to reveal spectral features."449 In this paper. we report the first results from observations of Neptune at 51-220 jm (195-45 !) with the PACS instrument onboardHerschiel(Pilbratt et al.," In this paper, we report the first results from observations of Neptune at 51-220 $\mu$ m (195–45 $^{-1}$ ) with the PACS instrument onboard(Pilbratt et al."450" 2010). in.the3 framework ofcthe4 KP-GT ""Waterκ... provand Related"," 2010), performedin the frameworkof the KP-GT “Water and Related"451" 2010). in.the3 framework ofcthe4 KP-GT ""Waterκ... provand Related "," 2010), performedin the frameworkof the KP-GT “Water and Related"452" 2010). in.the3 framework ofcthe4 KP-GT ""Waterκ... provand Related i"," 2010), performedin the frameworkof the KP-GT “Water and Related"453" 2010). in.the3 framework ofcthe4 KP-GT ""Waterκ... provand Related im"," 2010), performedin the frameworkof the KP-GT “Water and Related"454" 2010). in.the3 framework ofcthe4 KP-GT ""Waterκ... provand Related imp"," 2010), performedin the frameworkof the KP-GT “Water and Related"455" 2010). in.the3 framework ofcthe4 KP-GT ""Waterκ... provand Related impo"," 2010), performedin the frameworkof the KP-GT “Water and Related"456" 2010). in.the3 framework ofcthe4 KP-GT ""Waterκ... provand Related impor"," 2010), performedin the frameworkof the KP-GT “Water and Related"457" 2010). in.the3 framework ofcthe4 KP-GT ""Waterκ... provand Related import"," 2010), performedin the frameworkof the KP-GT “Water and Related"458" 2010). in.the3 framework ofcthe4 KP-GT ""Waterκ... provand Related importa"," 2010), performedin the frameworkof the KP-GT “Water and Related"459" 2010). in.the3 framework ofcthe4 KP-GT ""Waterκ... provand Related importan"," 2010), performedin the frameworkof the KP-GT “Water and Related"460" 2010). in.the3 framework ofcthe4 KP-GT ""Waterκ... provand Related important"," 2010), performedin the frameworkof the KP-GT “Water and Related"461the frame of the shock downstream.,the frame of the shock downstream.462" The value of £(x=0) decreases with increasing %panay because when protons are accelerated to higher energies. the number of nonthermal protons between which the available energy ~€,Ey 18 partitioned decreases. while the lower energy nonthermal protons are confined closer to the shock. both of which decrease the density of nonthermal protons far from the shock where the Amperre force-driven acceleration takes place."," The value of $\xi(x=0)$ decreases with increasing $\gamma_{p,{\rm max}}$ because when protons are accelerated to higher energies, the number of nonthermal protons between which the available energy $\sim \epsilon_{\rm nt}E_{\rm tot}$ is partitioned decreases, while the lower energy nonthermal protons are confined closer to the shock, both of which decrease the density of nonthermal protons far from the shock where the Ampèrre force-driven acceleration takes place."463 Under what circumstances will the transverse displacement result in à nonlinear density contrast on scales A?, Under what circumstances will the transverse displacement result in a nonlinear density contrast on scales $\lambda$?464 This requires £C)~A before the fluid element is overtaken by the shock at x=0., This requires $\xi(x) \sim \lambda$ before the fluid element is overtaken by the shock at $x=0$.465 However. before the fluid arrives at the shock transition. some assumptions entering the derivation of equation (19)) may be compromised: its motion may become relativistic (4&/dr~ c). it may enter the region in which the pressure transfered by the nonthermal protons to the upstream fluid starts to accelerate the upstream fluid in the original rest frame of the shock upstream. and it may also enter the region containing accelerated nonthermal electrons where the return current vanishes.," However, before the fluid arrives at the shock transition, some assumptions entering the derivation of equation \ref{eq:fluid_y}) ) may be compromised: its motion may become relativistic $d\xi/d\tau\sim c$ ), it may enter the region in which the pressure transfered by the nonthermal protons to the upstream fluid starts to accelerate the upstream fluid in the original rest frame of the shock upstream, and it may also enter the region containing accelerated nonthermal electrons where the return current vanishes."466 The latter problem arises when x~xo where x«t=AcCremay)/((R/ST7) is given in equation (2)).," The latter problem arises when $x \sim x_{\rm cool}$ where $x_{\rm cool} \equiv \Delta_e(\gamma_{e,{\rm max}}) / (R/8\Gamma^2)$ is given in equation \ref{eq:Delta_ratio}) )."467 It is evident from equation (4)) that the return current vanishes only in the region populated by the lowest-energy nonthermal protons (55% 10°). which for panas>10°. as expected. will be confined very close to the shock transition.," It is evident from equation \ref{eq:x_cool}) ) that the return current vanishes only in the region populated by the lowest-energy nonthermal protons $\gamma_p\lesssim 10^3$ ), which for $\gamma_{p,{\rm max}}\gg 10^3$, as expected, will be confined very close to the shock transition."468 We are not able determine the value of x at which the upstream starts to be accelerated in its own frame but we do assume that it ts smaller than Que., We are not able determine the value of $x$ at which the upstream starts to be accelerated in its own frame but we do assume that it is smaller than $x_{\rm cool}$.469 To assess the distance at which the transverse motion of the fluid becomes relativistic. we focus on the special case of a tangled deflecting field; the case of a coherent deflecting field is qualitatively similar.," To assess the distance at which the transverse motion of the fluid becomes relativistic, we focus on the special case of a tangled deflecting field; the case of a coherent deflecting field is qualitatively similar."470" The time at which the upstream motion becomes relativistic is obtained by setting —R/SI""? (Le. d£/dr2 c) to find.(23) for panas(Ssσοιcrit where sin(24) "," The time at which the upstream motion becomes relativistic is obtained by setting $d\xi/dx = -R/8\Gamma^2$ (i.e., $d\xi/d\tau = c$ ) to find, for $\gamma_{p,{\rm max}}\leq \gamma_{\rm rel,crit}$, where 10^6 ) ."471"110""ου (Gir)! (28) When(CE)5,>(peep)?relat the fluid does not attain relativistic transverse velocity before it reaches the shock."," When$\gamma_{p,{\rm max}}>\gamma_{\rm rel,crit}$, the fluid does not attain relativistic transverse velocity before it reaches the shock."472 Then. the numerical estimate in equation (21)) at x=0 where g(v)~I. which was derived assuming Newtonian motion. shows that the transverse displacement decreases with mas.," Then, the numerical estimate in equation \ref{eq:xi_numerical}) ) at $x=0$ where $g(x) \sim 1$, which was derived assuming Newtonian motion, shows that the transverse displacement decreases with $\gamma_{p,{\rm max}}$."473 Conversely. for ~pinay&Arete the fluid +)motion formally becomes relativistic well before the fluid reaches the shock.," Conversely, for $\gamma_{p,{\rm max}}\ll\gamma_{\rm rel,crit}$, the fluid motion formally becomes relativistic well before the fluid reaches the shock."474 The maximum transverse displacement that can be attained in the Newtonian regime can be evaluated by substituting x2x4 in equation (19)) to obtain Gua) fracR8E (Gis) να .(31) for(Crenp ~pinay)toic," The maximum transverse displacement that can be attained in the Newtonian regime can be evaluated by substituting $x=x_{\rm rel}$ in equation \ref{eq:fluid_y}) ) to obtain ) ) , for $\gamma_{p,{\rm max}}\ll \gamma_{\rm rel,crit}$."475: Acceleration of the fluid may not stop in the Newtonian regime: indeed. it will likely continue into the transrelativistic regime. where the equation of motion is simply d£/dr~c.," Acceleration of the fluid may not stop in the Newtonian regime; indeed, it will likely continue into the transrelativistic regime, where the equation of motion is simply $d\xi/d\tau\sim c$."476 Then. however. the motion will not be purely perpendicular to the direction of shock propagation and the fluid will start accelerate. in the upstream frame. in the parallel direction.," Then, however, the motion will not be purely perpendicular to the direction of shock propagation and the fluid will start accelerate, in the upstream frame, in the parallel direction."477 Here we do not take into account this behavior and conservatively restrict our attention to the maximum transverse displacement that the fluid reaches while its motion remains Newtonian., Here we do not take into account this behavior and conservatively restrict our attention to the maximum transverse displacement that the fluid reaches while its motion remains Newtonian.478" Since the transverse displacement increases with >)imax when the transverse motion becomes transrelativistic. and decreases with 75,54, When it does not. the largest Newtonian displacement is possible when the maximum proton Lorentz factor is about equal to 7,444 1n equation (24)) and is simply given by £i,~IR8°. which is much larger than the proton plasma skin depth —c(4re7nny)? of the shock upstream."," Since the transverse displacement increases with $\gamma_{p,{\rm max}}$ when the transverse motion becomes transrelativistic and decreases with $\gamma_{p,{\rm max}}$ when it does not, the largest Newtonian displacement is possible when the maximum proton Lorentz factor is about equal to $\gamma_{\rm rel,crit}$ in equation \ref{eq:gamma_rel_crit}) ) and is simply given by $\xi_{\rm max}\sim \frac{1}{3}R/8\Gamma^2$, which is much larger than the proton plasma skin depth $c/\omega_{\rm p}\equiv c/(4\pi e^2 n/m_p)^{1/2}$ of the shock upstream."479 Of course.c/u the maximum transverse displacement is achieved only if a magnetic field that reverses on scales A~Snax IS present.," Of course, the maximum transverse displacement is achieved only if a magnetic field that reverses on scales $\lambda\sim \xi_{\rm max}$ is present."480 We speculate about the origin of the reversing field in 2.4. below., We speculate about the origin of the reversing field in \ref{sec:bell} below.481 Note that Gy. 1s close to the maximal value allowed by causality. R/8I7.," Note that $\xi_{max}$ is close to the maximal value allowed by causality, $R/8\Gamma^2$."482 Here. we study the evolution of an initially uniform density fluid in response to the Lorentz force-driven transverse motion discussed in. 82.2..," Here, we study the evolution of an initially uniform density fluid in response to the Lorentz force-driven transverse motion discussed in \ref{sec:eom}."483 If the magnetic field reverses itself on scales ~A. the average linear density contrast arising from the transverse motion. for linear displacements. ©«A. will be given by(," If the magnetic field reverses itself on scales $\sim \lambda$, the average linear density contrast arising from the transverse motion, for linear displacements, $\xi\ll \lambda$, will be given by."484"32) We expect nonlinear density contrast on scales A provided that £C)2A. where x,=max[oorv4)."," We expect nonlinear density contrast on scales $\lambda$ provided that $\xi(x_{\rm max}) \gtrsim \lambda$, where $x_{\rm max}={\rm max} \{x_{\rm cool},x_{\rm rel}\}$."485 This condition places an upper limit on the magnetic. field reversal length scales A on which a nonlinear density contrastcan build up before the fluid reaches the shock., This condition places an upper limit on the magnetic field reversal length scales $\lambda$ on which a nonlinear density contrastcan build up before the fluid reaches the shock.486 When fluid with nonlinear density contrast reaches the shock transition. provided that the width of the density jump of the shock transition is smaller than the length scale associated with the contrast.vorticity is generated at the transition.," When fluid with nonlinear density contrast reaches the shock transition, provided that the width of the density jump of the shock transition is smaller than the length scale associated with the contrast,vorticity is generated at the transition."487 Siront&Goodman(2007) have calculated the fraction of shock energy that is converted into vortical energy for an ultrarelativistic blastwave propagating into a clumpy medium., \citet{Sironi:07} have calculated the fraction of shock energy that is converted into vortical energy for an ultrarelativistic blastwave propagating into a clumpy medium.488" They provide a fitting formula for vortical energy fraction. é.o, as a function of clump size L. peak density contrast das. and volume-filling factor Προ. which reads"," They provide a fitting formula for vortical energy fraction $\epsilon_{\rm vort}$ as a function of clump size $L$ peak density contrast $\delta_{\rm max}$ , and volume-filling factor $n_{\rm clump}L^3$ , which reads"489LURES/RKECI samples. of highresolution spectra.,HIRES/KECK samples of high–resolution spectra.490 The characteristics of the low and high-resolution data sets are very dillerent. (the number of SDSS spectra is about a [actor 200 larger than that of high-resolution samples. but the latter probes smaller scales due to the higher spectral resolution).," The characteristics of the low and high-resolution data sets are very different (the number of SDSS spectra is about a factor $\sim 200$ larger than that of high-resolution samples, but the latter probes smaller scales due to the higher spectral resolution)."491 Measurements based on forest. data have reached a level of accuracy where an understanding of svsteniatic uncertainties at the percent level or below (the magnitude of statistical errors associated. with the SDSS sample) has become important., Measurements based on forest data have reached a level of accuracy where an understanding of systematic uncertainties at the percent level or below (the magnitude of statistical errors associated with the SDSS sample) has become important.492 In this Letter. we will revisit he Hux PDE. which has been investigated: previously by several authors either on its own (e.g. 22227773). or jointly with the flux power spectrum (227)...," In this Letter, we will revisit the flux PDF, which has been investigated previously by several authors either on its own (e.g. \citealt{mcdonald00,jena,Becker:2006qj,lidz06,tkim,Bolton08}) ), or jointly with the flux power spectrum \citep{meiksin01,zaroubi06,desjacques07}."493 We shall focus on he flux PDE of the UVES/VLYT data as recently measured w 7 (hereafter IeW): the svstematic ancl statistical errors or this sample have been addressed: in. detail., We shall focus on the flux PDF of the UVES/VLT data as recently measured by \cite{tkim} (hereafter K07); the systematic and statistical errors for this sample have been addressed in detail.494" Recently. roth 2 (from the Wo UVISS/VLTI data) and ? (from independent: LILESIXIx spectra) have found: evidence or a densitv-tempoerature relation of the LGAL which appears inverted. if approximated as a powerlaw ο«1 for Lo=μα|0)"" )."," Recently, both \cite{Bolton08} (from the K07 UVES/VLT data) and \cite{Becker:2006qj} (from independent HIRES/KECK spectra) have found evidence for a density-temperature relation of the IGM which appears inverted if approximated as a power–law $\gamma<1$ for $T=T_0(1+\delta)^{\gamma-1}$ )."495 Here. we will improve on the analysis xerformed in ?. (hereafter IXYS) and check its robustness by ‘ally exploring the cosmological and astrophysical parameter space.," Here, we will improve on the analysis performed in \cite{Bolton08} (hereafter B08) and check its robustness by fully exploring the cosmological and astrophysical parameter space."496 In addition. we briefly. discuss a joint analysis of the flux PDE and. SDSS flux power spectrum. and he possible implications for constraints on cosmological raranietors describing the linear matter power spectrum and he thermal history of the IGM.," In addition, we briefly discuss a joint analysis of the flux PDF and SDSS flux power spectrum, and the possible implications for constraints on cosmological parameters describing the linear matter power spectrum and the thermal history of the IGM."497 We use simulations performed with the parallel hivelrodynamical CIrecsSPLHI) code —(7) to calculate the Hux statistics for models with a wide range of cosmological and astrophysical parameters by expanding around a reference model., We use simulations performed with the parallel hydrodynamical (TreeSPH) code \citep{springel} to calculate the flux statistics for models with a wide range of cosmological and astrophysical parameters by expanding around a reference model.498 For the reference model we choose here the 20-256 simulation of BOs., For the reference model we choose here the 20-256 simulation of B08.499 We refer the reader to this paper for further details. including resolution and box size convergence tests (see 2? for recent convergence tests on SPILL simulations).," We refer the reader to this paper for further details, including resolution and box size convergence tests (see \cite{bb09} for recent convergence tests on SPH simulations)."500 We will compare these simulations to improved. measurements of the PDE made by WOT in three redshift bins at £2?=2.07. £2)=2.52 and £2)=2.94 based on a set of 18 high. resolution (2~45 000). high signaltonoise (S/N x30 50) VLI/UVIZS. spectra.," We will compare these simulations to improved measurements of the PDF made by K07 in three redshift bins at $\langle z \rangle =2.07$, $\langle z \rangle =2.52$ and $\langle z501\rangle =2.94$ based on a set of 18 high resolution $R \sim 45~000$ ), high signal–to–noise (S/N $\geq 30-50$ ) VLT/UVES spectra."502 Further details regarding the observational data and. its reduction. with particular emphasis on metal removal and continuum [fitting errors. may be found in WOT.," Further details regarding the observational data and its reduction, with particular emphasis on metal removal and continuum fitting errors, may be found in K07."503 In all instances the mock QSO spectra have been processed. to ave the same instrumental properties as the observed data: ic. the same signaltonoise. resolution and. pixel size.," In all instances the mock QSO spectra have been processed to have the same instrumental properties as the observed data: i.e. the same signal–to–noise, resolution and pixel size."504 We explore the following cosmological ancl astrophysical xwameters: O4. ni. Ho. ax for the cosmological part ancl qus⋅ ⋎↽⋝⊽↿∖∶∶∆⊰∃⇂∪↓⋅↿↓↥⋖⋅↓≺↳∖↓↿↓↥⋖⊾↓⋅⊔⋯↓ s ⋅⋅ ⋠ history. where↙∩↿∖∶∶∆∫≻⊐⋜⋯∠⇂ ef and S indicate the amplitude ancl slope for the emperat ureand 5 relations normalised at z =3(y= (1I z).," We explore the following cosmological and astrophysical parameters: $\Omega_{\rm m}$, $n_{\rm s}$, $H_0$, $\sigma_8$ for the cosmological part and $T_0^{A,S}(z=3)$ and $\gamma^{A,S}(z=3)$ for the IGM thermal history, where $A$ and $S$ indicate the amplitude and slope for the temperature and $\gamma$ relations normalised at $z=3$ $y=A[(1+z)/4]^S$ )."505 The amplitude and. slope of the elfective optical depth evolution. zr=L5. are varied assuming a poweraw evolution with redshift in order to conservatively span he observed range suggested by. high-resolution ancl low-resolution data sets.," The amplitude and slope of the effective optical depth evolution, $\tau_{\rm eff}=-\langle F \rangle$, are varied assuming a power--law evolution with redshift in order to conservatively span the observed range suggested by high-resolution and low-resolution data sets."506" We furthermore varied the reionization redshift (ο=9 in our reference model) but found this had no impact on the Dux PDP at z<3 (although the differences in “Jeans smoothing"" will be important at redshifts close to ne. 6m. 7))."," We furthermore varied the reionization redshift $z_{\rm re}=9$ in our reference model) but found this had no impact on the flux PDF at $z<3$ (although the differences in “Jeans smoothing” will be important at redshifts close to $z_{\rm re}$, e.g. \cite{Pawlik09}) )."507 For the clleet on the flux power we refer to ? ancl ?.., For the effect on the flux power we refer to \cite{mcdonald05} and \cite{vielhaehnelt06}.508 We also consider the clleet of a misplaced continuum evel by adding an extra. parameter fi. (he tus following a continuum correction is assumed to be £«(1|f)., We also consider the effect of a misplaced continuum level by adding an extra parameter $f_{\rm c}$ (the flux following a continuum correction is assumed to be $F\times (1+f_{\rm c})$ ).509 We compute derivatives of the [lux statistics from. he 20-256 model at second order using between two and our simulations for each cosmological ancl astrophysical xwameter., We compute derivatives of the flux statistics from the 20-256 model at second order using between two and four simulations for each cosmological and astrophysical parameter.510 For the thermal history we explore a wide range of possible Zi and > values by the original erid of simulations presented in BOs., For the thermal history we explore a wide range of possible $T_0$ and $\gamma$ values by extending the original grid of simulations presented in B08.511 Theextending 20-256 model has ο1.8 xlow z=3 and the temperature at mean density in the hree PDP redshift bins are Z5=14.8.17.6.20.8.10° Is. This model was shown to be a poor fit to m WOT data in the analysis performed by DOS.," The 20-256 model has $\gamma \sim 1.3$ below $z=3$ and the temperature at mean density in the three PDF redshift bins are $T_0=14.8,17.6,20.8\,\times 10^3$ K. This model was shown to be a poor fit to the K07 data in the simple analysis performed by B08."512 Here we will calculate the 7 uxof vmour models varvingalf the parameters that allect the PDE and not just the effective optical depth. enabling us ο expand around this model.," Here we will calculate the $\chi^2$ of our models varying the parameters that affect the flux PDF and not just the effective optical depth, enabling us to expand around this model."513 This simple Tavlor.expansion method was introduced in ? in order to explore constraints or the SDSS flux power spectrum., This simple Taylor–expansion method was introduced in \cite{vielhaehnelt06} in order to explore constraints for the SDSS flux power spectrum.514 It has the advantage of enabling the exploration of the parameter space close to he reference model with an accurate set o£ hydrodynamical simulations., It has the advantage of enabling the exploration of the parameter space close to the reference model with an accurate set of hydrodynamical simulations.515 However. the full parameter space cannot. be xobed in this way with the same high accuracy (see ο for a dillerent approach).," However, the full parameter space cannot be probed in this way with the same high accuracy (see \citealt{mcdonald05} for a different approach)."516 We obtain the best fit to the observed ux PDE for three Dux intervals /=0.1.OS). P—0.40.9]. f=οI].," We obtain the best fit to the observed flux PDF for three flux intervals $F=[0.1-0.8]$, $F=[0.1-0.9]$, $F=[0-1]$."517 Dilferent Hux levels are subject to different svstematic cllects. such as the presence of noise and strong absorption systems at PF—0 and the ellect of continuum fitting errors at £F—1 (see WOT for details).," Different flux levels are subject to different systematic effects, such as the presence of noise and strong absorption systems at $F\sim 0$ and the effect of continuum fitting errors at $F\sim 1$ (see K07 for details)."518 Since the PDE error bars are correlated we expect these systematic errors to nevertheless impact on the PDF over the full Dux range., Since the PDF error bars are correlated we expect these systematic errors to nevertheless impact on the PDF over the full flux range.519 The level of consistency between the fits to these three flux intervals should indicate, The level of consistency between the fits to these three flux intervals should indicate520[or p=2.4.,for $p=2.4$.521 As we can see. vi is below the N-ray frequency v~LOM Iz for typical parameters.," As we can see, $\nu_{a}^{\rm{IC}}$ is below the X-ray frequency $\nu\sim10^{18}$ Hz for typical parameters."522 We thus do not consider this frequency in our estimation of the IC: component in the N-rav lieht curve in (he slow-cooling phase., We thus do not consider this frequency in our estimation of the IC component in the X-ray light curve in the slow-cooling phase.523 The inverse Compton spectrum is where we have neglected the logarithmic term for p>£F and also do not consider the lowest spectral segment below © for simplicity., The inverse Compton spectrum is where we have neglected the logarithmic term for $\nu>\nu_{c}^{\rm{IC}}$ and also do not consider the lowest spectral segment below $\nu_{a}^{\rm{IC}}$ for simplicity.524 The relation between the peak {lux density ol the SSC spectral component and (hat of the svuchrotvon component is (Sari Esin 2001] The critical Irequeney corresponding to the crossing point of (he svnchirotron spectra component and the SSC component is where we include the coefficient co=Οία(1—€)tpk—etp-ον2p1)!1/352. which is much larger than unity (by at least one order of magnitude). but was neglected in equation(5.1) of Sari. Esin. (2001).κSince. 5135 is. always smaller than unity.. zl can be determined. directly. by pl=maxiiultY without judging whether pl.<UK“an or nol.," The relation between the peak flux density of the SSC spectral component and that of the synchrotron component is (Sari Esin 2001) The critical frequency corresponding to the crossing point of the synchrotron spectral component and the SSC component is where we include the coefficient $c_2=\displaystyle\frac{(1-\epsilon)^2(p-1/3)^2(p+1)^4}{9x_{0}^2(4-k-\epsilon)^2(p-2)^2(p+1/3)^2}$, which is much larger than unity (by at least one order of magnitude), but was neglected in equation(5.1) of Sari Esin (2001).Since $\displaystyle\frac{3}{2+3p}$ is always smaller than unity, $\nu_{\times}^{\rm{IC}}$ can be determined directly by $\nu_{\times}^{\rm{IC}}=\rm{max}\{\nu_{\times,<}^{\rm{IC}},\nu_{\times,>}^{\rm{IC}}\}$ without judging whether $\nu_{\times}^{\rm{IC}}<\nu_{m}^{\rm{IC}}$ or not."525 We have numerically caleulated the temporal evolution of pl. and ον case. ," We have numerically calculated the temporal evolution of $\nu_{\times,<}^{\rm{IC}}$ and $\nu_{\times,>}^{\rm{IC}}$ . ,"526the expression for vi. is," the expression for $\nu_{\times,<}^{\rm{IC}}$ is"527obtained when considered. a dipole magnetic field. should remain valicl.,obtained when considered a dipole magnetic field should remain valid.528 In the previous sections we compared the structure of the magnetic fields of V2129 Oph and DP Tau to that of a dipole., In the previous sections we compared the structure of the magnetic fields of V2129 Oph and BP Tau to that of a dipole.529 1n this section. we select out only those field. lines which would be able to interact with the accretion disc ancl carry material on to the star., In this section we select out only those field lines which would be able to interact with the accretion disc and carry material on to the star.530 In order to select such. field. lines we follow the algorithm discussed. by 2?.. which we only stummarise here.," In order to select such field lines we follow the algorithm discussed by \citet{gre06a,gre07}, which we only summarise here."531 We consider a thin accretion disc and for V2129 Oph assume that the disc normal is parallel to the stellar rotation axis. such that the clise mid-plane is aligned with the stars equatorial plane.," We consider a thin accretion disc and for V2129 Oph assume that the disc normal is parallel to the stellar rotation axis, such that the disc mid-plane is aligned with the stars equatorial plane."532 By extrapolating the field of BP Tau. ? argued that a flat cise model could not explain the observec location of accretion hotspots.," By extrapolating the field of BP Tau, \citet{don08a} argued that a flat disc model could not explain the observed location of accretion hotspots."533 For material to accrete into the observed hotspot locations. either the dise must be tiltec relative to the stellar rotation axis (i.e. aligned. with the stellar magnetic equator - similar to the scenario. founc during the 3D ANID simulations of 2)). or the inner disc must be warped.," For material to accrete into the observed hotspot locations, either the disc must be tilted relative to the stellar rotation axis (i.e. aligned with the stellar magnetic equator - similar to the scenario found during the 3D MHD simulations of \citealt{rom03}) ), or the inner disc must be warped."534 Itadio CO maps of BP Tau’s dise sugges a cise inclination of 30ollset from the stellar inclination of (?).. although both values are rather uncertain.," Radio CO maps of BP Tau's disc suggest a disc inclination of offset from the stellar inclination of \citep*{sim00}, although both values are rather uncertain."535 Analytic arguments suggest that a large scale tiltecl magnetosphere (as possessed by BP Pau) will warp the inner disc. allowing material to accrete on to latitudes which are inaccessible if accretion were to proceed. from a flat. wedge-shaped. disc (?)..," Analytic arguments suggest that a large scale tilted magnetosphere (as possessed by BP Tau) will warp the inner disc, allowing material to accrete on to latitudes which are inaccessible if accretion were to proceed from a flat, wedge-shaped, disc \citep{ter00}."536 Furthermore. the 3D. MILD. simulations of ?.. suggest hat complicated. inner disc warps may arise due to the interaction of the magnetosphere with the disc.," Furthermore, the 3D MHD simulations of \citet{rom03}, suggest that complicated inner disc warps may arise due to the interaction of the magnetosphere with the disc."537" Phere is also strong evidence for the stellar field warping the disc in at cast one other star. AA ""Tau (e.g. 2)). which is inclined such hat our linc-of-sight to the star looks through the inner disc."," There is also strong evidence for the stellar field warping the disc in at least one other star, AA Tau (e.g. \citealt{bou07}) ), which is inclined such that our line-of-sight to the star looks through the inner disc."538 Given the smaller inclination of BP Tau (7= 45°). however. ohoetometric eclipses due to a dense inner disc warp crossing our linc-of-sight are not expected.," Given the smaller inclination of BP Tau $i = 45\degr$ ), however, photometric eclipses due to a dense inner disc warp crossing our line-of-sight are not expected."539 For BP Tau we therefore assume that the cisc is slighth tilted. or equivalently that he inner disc has been warped by the stellar.," For BP Tau we therefore assume that the disc is slightly tilted, or equivalently that the inner disc has been warped by the stellar."540sphere?.. An obvious question to ask. however. is why did 7 [ind that a Hat disc model was sullicient to explain the observed hotspot locations on V2129 Oph. but 7. find that a small inner disc warp was required for BP Tau?," An obvious question to ask, however, is why did \citet{don07} find that a flat disc model was sufficient to explain the observed hotspot locations on V2129 Oph, but \citet{don08a} find that a small inner disc warp was required for BP Tau?"541 This is likely related to the strength of the dipole component on both stars. which is almost 4-times stronger on BP Tau than V2129 Oph.," This is likely related to the strength of the dipole component on both stars, which is almost 4-times stronger on BP Tau than V2129 Oph."542 At the inner disc. at a distance of a few stellar radii the dipole component is likely dominant. with the strength of the higher order field components dropping Faster with height above the star.," At the inner disc, at a distance of a few stellar radii, the dipole component is likely dominant, with the strength of the higher order field components dropping faster with height above the star."543 Phe larger scale magnetosphere of BP Tau is therefore more likely to cistort the circumstellar disc., The larger scale magnetosphere of BP Tau is therefore more likely to distort the circumstellar disc.544 Indeed to explain the hotspot locations on BP Tau the disc had. to be tilted in the same cdirection as the dipole moment., Indeed to explain the hotspot locations on BP Tau the disc had to be tilted in the same direction as the dipole moment.545 Tilting the disc in a similar way for V2129 Oph makes little. difference to the hotspot location. suggesting that it is the strength of the dipole that is alfecting the inner disc.," Tilting the disc in a similar way for V2129 Oph makes little difference to the hotspot location, suggesting that it is the strength of the dipole that is affecting the inner disc."546 Further numerical simulations of how magnetic fields with a realistically complexity can distort the structure of the dise will be required in future to confirm this. ancl are currently being undertaken.," Further numerical simulations of how magnetic fields with a realistically complexity can distort the structure of the disc will be required in future to confirm this, and are currently being undertaken."547 1n order to compare the structure of the complex fields of V2129 Oph and DP Tau with that of a dipole we consider how fast the field strength drops. with height above the stellar surface., In order to compare the structure of the complex fields of V2129 Oph and BP Tau with that of a dipole we consider how fast the field strength drops with height above the stellar surface.548 We therefore compare how the ratio D(r)/D; varies with i. where D(r) is the strength of the field at some position r along the path of a field line anc D; the field streneth at the field line footpoint.," We therefore compare how the ratio $B(r)/B_{\ast}$ varies with $r$, where $B(r)$ is the strength of the field at some position $r$ along the path of a field line and $B_{\ast}$ the field strength at the field line footpoint."549 7 is the spherical radius measured from the centre of the star., $r$ is the spherical radius measured from the centre of the star.550 Figs., Figs.551 T and 8. show such plots for both V2129 Oph and BP Tau., \ref{bratio_big} and \ref{bratio_small} show such plots for both V2129 Oph and BP Tau.552 All D(r)/D. values are plotted from the disc mid-plane to the field line [ootpoint at the stellar surface., All $B(r)/B_{\ast}$ values are plotted from the disc mid-plane to the field line footpoint at the stellar surface.553 Accretion is assumed. to occur along all field. lines threading the mid-plane of the disc across a range of radii., Accretion is assumed to occur along all field lines threading the mid-plane of the disc across a range of radii.554 ln Fig., In Fig.555" T we assume that accretion is occuring from the corotation radius. down to Ro (95OTR, for V2129 Oph and ~5.5TAR, for BP Tau). whereas in Fig."," \ref{bratio_big} we assume that accretion is occuring from the corotation radius, down to $\,R_{co}$ $\sim 5 - 6.7\,R_{\ast}$ for V2129 Oph and $\sim 5.5 - 7.4\,R_{\ast}$ for BP Tau), whereas in Fig."556 S we assume that accretion is occuring from a range of radii about the disc truncation radius caleulated in 855.1., \ref{bratio_small} we assume that accretion is occuring from a range of radii about the disc truncation radius calculated in 5.1.557 Por V2129 Oph. where the disc truncation radius was calculated to be 2.822. (see Fig. 6)).," For V2129 Oph, where the disc truncation radius was calculated to be $2.8\,R_{\ast}$ (see Fig. \ref{rt}) ),"558 the accreting field is assumed to span the range of radii ~24324 for BP Tau. with a disc truncation radius of 48 FI. aceretion is assumed to occur from 4.4.5.2fH.," the accreting field is assumed to span the range of radii $\sim 2.4 - 3.2\,R_{\ast}$; for BP Tau, with a disc truncation radius of $\sim 4.8\,R_{\ast}$ , accretion is assumed to occur from $\sim 4.4 - 5.2\,R_{\ast}$."559 In practise little cillerence is found in the structure of the accreting field when these values are varied., In practise little difference is found in the structure of the accreting field when these values are varied.560 Figs., Figs.561 7 and S also show the behaviour of a dipole magnetic field. tilted by 10for comparison with the DP Tau data (whose dipole component is tilted by relative to the stellar. rotation axis). and by 307for comparison with the V2129 Oph data.," \ref{bratio_big} and \ref{bratio_small} also show the behaviour of a dipole magnetic field, tilted by for comparison with the BP Tau data (whose dipole component is tilted by relative to the stellar rotation axis), and by for comparison with the V2129 Oph data."562 tots such as Figs., Plots such as Figs.563 7 and S allow a comparison of 10w the field complexity varies with height above the stellar surface., \ref{bratio_big} and \ref{bratio_small} allow a comparison of how the field complexity varies with height above the stellar surface.564 We note. however. that we do not account for how 1e structure of the magnetic field will evolve in time due to 1e interaction with the disc.," We note, however, that we do not account for how the structure of the magnetic field will evolve in time due to the interaction with the disc."565 However. this will be less of an issue if aceretion proceeds. [rom close to corotation. where 1e. dilTerential rotation of field line footpoints anchored in 1e disc and on the stellar surface is much less than if the isc is truncated. well within corotation.," However, this will be less of an issue if accretion proceeds from close to corotation, where the differential rotation of field line footpoints anchored in the disc and on the stellar surface is much less than if the disc is truncated well within corotation."566 As the strength X the dipole component decreases with height more slowly jan the higher order field components. the behaviour of the ield on the largest scales should be somewhat simpler than wt of the surface field.," As the strength of the dipole component decreases with height more slowly than the higher order field components, the behaviour of the field on the largest scales should be somewhat simpler than that of the surface field."567" This is the case for the magnetic ied. of V2129 Oph where the field. behaves more like a ipole above 2.52, (see Fig. τι, "," This is the case for the magnetic field of V2129 Oph where the field behaves more like a dipole above $\sim 2.5R_{\ast}$ (see Fig. \ref{bratio_big}, ,"568right panel). after an initial fast drop within the strong complex field region close o the stellar surface.," right panel), after an initial fast drop within the strong complex field region close to the stellar surface."569 For BP Tau the Geld is generally more dipolar. even closer to the stellar surface (see Fig. 7..," For BP Tau the field is generally more dipolar, even closer to the stellar surface (see Fig. \ref{bratio_big},"570 eft. panel). rellecting the much stronger dipole component of its magnetic field. found to be 1.2kG. ancl containing about 50% of the magnetic energv (2)..," left panel), reflecting the much stronger dipole component of it's magnetic field, found to be $1.2\,{\rm kG}$ and containing about $50\%$ of the magnetic energy \citep{don08a}."571 For V2129 Oph if we assume that accretion. occurs from. around the disc runcation radius as calculated in the previous section. see Fig. S.," For V2129 Oph if we assume that accretion occurs from around the disc truncation radius as calculated in the previous section, see Fig. \ref{bratio_small},"572 we find that the structure of the accreting field. is much more complex than a simple dipole., we find that the structure of the accreting field is much more complex than a simple dipole.573 7. found that the σης of accretion in the visible hemisphere of V2129 Oph occured into a single magnetic spot at high latitude., \citet{don07} found that the bulk of accretion in the visible hemisphere of V2129 Oph occured into a single magnetic spot at high latitude.574 Using he algorithm discussed in ? and ? we calculate that about of the mass supplied. by the cise would. accrete into he highlatitude northern hemisphere spot on V2129 Oph. with a similiar amount to an unseen southernhemisphere," Using the algorithm discussed in \citet{gre07} and \citet{jar08} we calculate that about of the mass supplied by the disc would accrete into the highlatitude northern hemisphere spot on V2129 Oph, with a similiar amount to an unseen southernhemisphere"575at an optical depth of around. #=0.05. while at optical depths approaching zero the point masses should. behave independently (in terms of microlensing). producing an ellectiveness parameter of ανω=I.,"at an optical depth of around $\kappa=0.05$, while at optical depths approaching zero the point masses should behave independently (in terms of microlensing), producing an effectiveness parameter of $a_{tot}=1$."576 As the optical depth is increased. the population of caustics becomes more dense.," As the optical depth is increased, the population of caustics becomes more dense."577 This increase in density corresponds to an increase in the proportion of large ligh curve derivatives. as well as a decrease in the. proportion of low derivatives.," This increase in density corresponds to an increase in the proportion of large light curve derivatives, as well as a decrease in the proportion of low derivatives."578 The increase in the contribution of Fold. caustics is rellected in both the increased. elfectiveness parameter. as well as the location of the derivative where the minimum IWS cilference is found.," The increase in the contribution of fold caustics is reflected in both the increased effectiveness parameter, as well as the location of the derivative where the minimum KS difference is found."579 Phe relatively small size of this derivative highlights the fact that the total elfectiveness parameter is à representation of microlensing Lux variations ol all levels., The relatively small size of this derivative highlights the fact that the total effectiveness parameter is a representation of microlensing flux variations of all levels.580 -revious work has demonstrated that the characteristic imce-scale for variability scales as vAm. but is independent of the form of the microlens mass function (Witt. Kaiser telsdal 1993: Lewis Irwin 1996).," Previous work has demonstrated that the characteristic time-scale for variability scales as $\sqrt{\langle m \rangle}$, but is independent of the form of the microlens mass function (Witt, Kaiser Refsdal 1993; Lewis Irwin 1996)."581 Also. the probability distribution of magnifications is a function only of the xwameters of optical depth and shear (eg.," Also, the probability distribution of magnifications is a function only of the parameters of optical depth and shear (eg."582 Lewis Irwin 995)., Lewis Irwin 1995).583" ""his is demonstrated for the case of models 5 ancl 10 in the left hand. plot of Figure 5..", This is demonstrated for the case of models 5 and 10 in the left hand plot of Figure \ref{amp_dist}.584" We therefore expect that he distribution of mucrolensed light curve derivatives is a 'unction of Vm. but that e, is independent of the mass unction."," We therefore expect that the distribution of microlensed light curve derivatives is a function of $\sqrt{\langle m \rangle}$, but that $a_{tot}$ is independent of the mass function."585 We investigate this by repeating some of the simulations of section ο with a microlensing model of tvpe SALPETERB (models 9-13λ in Table 12)., We investigate this by repeating some of the simulations of section \ref{opt_sect} with a microlensing model of type $SALPETER$ (models 9-13 in Table \ref{parameters}) ).586 With the introduction of the mass function the mean mass of stars in the model has en Lowered., With the introduction of the mass function the mean mass of stars in the model has been lowered.587 Phere is therefore an increase in the number density of stars in this model. and a corresponding increase in the number density of caustics.," There is therefore an increase in the number density of stars in this model, and a corresponding increase in the number density of caustics."588 The increase in caustic, The increase in caustic589the Infrared Processing and. Analysis Center/California Institute of Technology. funded by ihe National Aeronauties and Space Achuinistration and the National Science Foundation.,"the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation."590 (Doruckietal., \citep{Borucki:11b}.591"2001b).. HQ,<ΣΠ). I)."," $1.25\,R_{\earth} < R_p <5922\,R_{\earth}$ )."593 The wealth of uew information promises to revolutionize our knowledge of extrasolar plaucts., The wealth of new information promises to revolutionize our knowledge of extrasolar planets.594 Although strictly speaking these are still oulv since confirmation by spectroscopic or oter means is not vet in haud. expectatious are high that the rate of false positives in this list is relatively small (seeDoruckietal.2001b:Morton&Johuson2011).," Although strictly speaking these are still only since confirmation by spectroscopic or other means is not yet in hand, expectations are high that the rate of false positives in this list is relatively small \citep[see][]{Borucki:11b, Morton:11}."595 Consequeutly. results. from lis sample conceruiug the Sreneral properties of exoplanets have already beera- to cmerege. including studies of the architecture aud (lvnamics of multiple transiting svstems (Lissaucrctal. 2011h).. an investigation of the statistical distribution of ¢secontricities (Moorhleadetal.2011)... ancl first estimates 6ft the rate of occurrence of plaucts larger than 2R with orbital xeriods up to 50 davs (Howardetal.2011).. iuuong others.," Consequently, results from this sample concerning the general properties of exoplanets have already begun to emerge, including studies of the architecture and dynamics of multiple transiting systems \citep{Lissauer:11b}, an investigation of the statistical distribution of eccentricities \citep{Moorhead:11}, and first estimates of the rate of occurrence of planets larger than $R_{\earth}$ with orbital periods up to 50 days \citep{Howard:11}, among others."596" For good reasous the confirmation or ""validation"" of sul transiting (Eartlesize or super-Earth-size) has attracted considerable attention. but has proven o be non-trivial i many cases because of the cifieultv 6oft detecting the tiny radial-volocitv (RV) signatures that hese objects cause on their parent stars. as exeniplified w the cases of CoRoT-7 (Légeretal.2009).. Odd (Torresetal.2011).. bbaud. aogg (Lissaucrot201 1aj."," For good reasons the confirmation or “validation” of small transiting (Earth-size or super-Earth-size) has attracted considerable attention, but has proven to be non-trivial in many cases because of the difficulty of detecting the tiny radial-velocity (RV) signatures that these objects cause on their parent stars, as exemplified by the cases of b \citep{Leger:09}, d \citep{Torres:11}, and g \citep{Lissauer:11a}."597. Iu fact. such spectroscopic signals are often oo πια to detect with current iustruuentation. aud the," In fact, such spectroscopic signals are often too small to detect with current instrumentation, and the"598contains 362 sources.,contains 362 sources.599 Compared to Sub Ixwon (2009). the number has been increased by 75.," Compared to Suh Kwon (2009), the number has been increased by 75."600 Silicate carbon stars are the carbon stars with silicate dust. features., Silicate carbon stars are the carbon stars with silicate dust features.601 For the sample of silicate carbon stars in ACGD phase. we use the same list as presented in Suh Ixwon (2009) except that one silicate carbon star (22AS 04496-6958) is excluded because it is not in our Galaxy.," For the sample of silicate carbon stars in AGB phase, we use the same list as presented in Suh Kwon (2009) except that one silicate carbon star $IRAS$ 04496-6958) is excluded because it is not in our Galaxy."602 The list of S stars and silicate carbon stars is shown in Table 3., The list of S stars and silicate carbon stars is shown in Table 3.603 For the ACD stars listed in our new catalog. we have tried to collect all the available NIR data atA and £ bands obtained from ground based observations.," For the AGB stars listed in our new catalog, we have tried to collect all the available NIR data at$K$ and $L$ bands obtained from ground based observations."604 We have mace revisions to the list of ΝΑ data in Suh Ixwon (2009) by verifving the position information ancl added 2ALASS data for many objects., We have made revisions to the list of NIR data in Suh Kwon (2009) by verifying the position information and added $2MASS$ data for many objects.605" We cross-identifv the 287.159 source by [inding the nearest one in the position within 10"" by using the position information in version 2.1 of the 74S PSC.", We cross-identify the $2MASS$ source by finding the nearest one in the position within $\arcsec$ by using the position information in version 2.1 of the $IRAS$ PSC.606" We have found the 247,485 counterparts for 2840 O-rich stars. 1090 C-rich stars. 456 8 stars and 32 silicate carbon stars."," We have found the $2MASS$ counterparts for 2840 O-rich stars, 1090 C-rich stars, 356 S stars and 32 silicate carbon stars."607" We use only the good. quality 2474,4S5. NIR data at. dvs band. for this paper.", We use only the good quality $2MASS$ NIR data at $K_S$ band for this paper.608 Variations of the fv band (2.2 jii) are designated: as As (2.0-2.3 pam: 2.17 pim for 2ALASS)., Variations of the $K$ band (2.2 $\mu$ m) are designated as $K_S$ (2.0-2.3 $\mu$ m; 2.17 $\mu$ m for $2MASS$ ).609 For analyzing the large sample of data in a single 2€CD. we need to ignore the slight variations of the AV anc £ bands depending on the observation systems.," For analyzing the large sample of data in a single 2CD, we need to ignore the slight variations of the $K$ and $L$ bands depending on the observation systems."610 In this paper. we assume the sume band wavelengths for A. (2.2 pim) and £ (3.5 jim) bands for all variations.," In this paper, we assume the same band wavelengths for $K$ (2.2 $\mu$ m) and $L$ (3.5 $\mu$ m) bands for all variations."611 “Phere could be minor errors for this assumption., There could be minor errors for this assumption.612 ‘Table 4 lists the numbers of collected NIR data at A and L bands for the sample ACB stars., Table 4 lists the numbers of collected NIR data at $K$ and $L$ bands for the sample AGB stars.613 Some stars are observed more than one time., Some stars are observed more than one time.614 ὃν using the position information in version 2.1 of the {1115 PSC. we cross-identify the AACGAAZ and AMS.N counterparts bv finding the nearest source for each object in the new catalog of AGB stars.," By using the position information in version 2.1 of the $IRAS$ PSC, we cross-identify the $AKARI$ and $MSX$ counterparts by finding the nearest source for each object in the new catalog of AGB stars."615" bor AAA PSC. we lind the closest. counterpart in the position within 10""."," For $AKARI$ PSC, we find the closest counterpart in the position within $\arcsec$."616 For AALLAL BSC. we find the closest source in the position within 1’.," For $AKARI$ BSC, we find the closest source in the position within $\arcmin$ ."617 We have cross-identified the ACA PSC counterparts for 2356 O-rich stars (detection rate: 78.5 '4)). 1012 C-rich stars ((86.6 %)). 336 8 stars (92.8 '4)) and 31 silicate carbon," We have cross-identified the $AKARI$ PSC counterparts for 2356 O-rich stars (detection rate: 78.5 ), 1012 C-rich stars (86.6 ), 336 S stars (92.8 ) and 31 silicate carbon"618minimum light RS Car would therefore appear at V (min) x15.1 at the standard inclination.,minimum light RS Car would therefore appear at $V$ (min) $\approx 18.1$ at the standard inclination.619 For a nova with /»=32 d and standard. inclination. the range of eruption should be —13.1 (Figure 5.4 o£ Warner 1995) whieh would make RS Car V—5.0 at maximum. which adds support to the suspicion that maximum light was missed (Duerbeck 1987).," For a nova with $t_2 = 32$ d and standard inclination, the range of eruption should be $\sim$ 13.1 (Figure 5.4 of Warner 1995) which would make RS Car $V \sim 5.0$ at maximum, which adds support to the suspicion that maximum light was missed (Duerbeck 1987)."620 V365 Car was Nova Carinac 1948. a very slow nova reaching mpg=10.1 at maximum.," V365 Car was Nova Carinae 1948, a very slow nova reaching $m_{pg} = 10.1$ at maximum."621 Lt is listed in the Downes. Webbing Shara (1007) catalogue as m;=21.6 at minimum. but photometry by Zwitter Munari (1996) in 1995 gave Vo=j 1831. |D=—0.51] and D.V=0.63. and Downes Duerbeck (2000) give V—18.47 in 1998.," It is listed in the Downes, Webbing Shara (1997) catalogue as $m_j = 21.6$ at minimum, but photometry by Zwitter Munari (1996) in 1995 gave $V = 18.31$ , $U-B = -0.51$ and $B-V = 0.63$, and Downes Duerbeck (2000) give $V = 18.47$ in 1998."622 The eruption range of 9 mag is normal for the speed class., The eruption range of $\sim 9$ mag is normal for the speed class.623 The spectrum obtained by Zwitter Munari shows strong Hell and moderate Balmer emission: the slope of the continuum is shallow because of reddening of this distant low Galactic latitude object., The spectrum obtained by Zwitter Munari shows strong HeII and moderate Balmer emission; the slope of the continuum is shallow because of reddening of this distant low Galactic latitude object.624 Phere is no X-ray detection., There is no X-ray detection.625 Our high speed. photometric runs on V365. Car are listed in Table 1: and the two longest light curves. spaced two days apart. are presented in Fig. 3.," Our high speed photometric runs on V365 Car are listed in Table 1 and the two longest light curves, spaced two days apart, are presented in Fig. \ref{lcv365car}."626 The Fourier transform of these light curves shows no features other than the fundamental and harmonics associated. with the slight upward convexity in the two long runs and the slow lickering., The Fourier transform of these light curves shows no features other than the fundamental and harmonics associated with the slight upward convexity in the two long runs and the slow flickering.627 However. the two light curves seen in Fig.," However, the two light curves seen in Fig."628 3. show a strong resemblence to each other. which could be the result of à modulation period that is near to a submultiple of the wo day spacing. e.g.. 6.86 h or 8.0 h. These light. curves illustrate a [limitation of our photometric survey: despite wo long runs of good. quality of ~9 h each. no definitive moculation was detected. and it was deemed not σους use of available time to continue on this star.," \ref{lcv365car}629 show a strong resemblence to each other, which could be the result of a modulation period that is near to a submultiple of the two day spacing, e.g., 6.86 h or 8.0 h. These light curves illustrate a limitation of our photometric survey: despite two long runs of good quality of $\sim$ 9 h each, no definitive modulation was detected, and it was deemed not good use of available time to continue on this star."630 In ellect. we are insensitive to low amplitude modulations with periods z 5 h. V436 Car was identified as the optical counterpart (Y 15.3) of the οΛΙ source. JJ0744.0-5257 having strong Balmer. moderate el anc weak Hell emission lines. together withevidence for long term variations in brightness," In effect, we are insensitive to low amplitude modulations with periods $\ga$ 8 h. V436 Car was identified as the optical counterpart $V \sim 15.3$ ) of the ROSAT source J0744.9-5257, having strong Balmer, moderate HeI and weak HeII emission lines, together withevidence for long term variations in brightness"631"While the density contrast in Equation (17)) is defined in three dimensions, the amplitude we obtained from the simulation is one-dimensional because it is the contrast of the radially averaged surface density.","While the density contrast in Equation \ref{eq:rho3}) ) is defined in three dimensions, the amplitude we obtained from the simulation is one-dimensional because it is the contrast of the radially averaged surface density."632" Therefore, we define the amplitude of a spiral arm as From Equations (17)) and (18)), the amplitude relates with Q as The black curve in Figure 12 shows (0.144)? obtained from Equation (19)), where we assumed C— 1.0."," Therefore, we define the amplitude of a spiral arm as From Equations \ref{eq:rho3}) ) and \ref{eq:amp}) ), the amplitude relates with $Q$ as The black curve in Figure \ref{fig:Q_tp} shows $(0.1A_m)^2$ obtained from Equation \ref{eq:amp2}) ), where we assumed $C=1.0$ ."633" Although Equation (19)) qualitatively explains the amplitude as a function of Q after it reaches the maximum, the amplitude obtained from the simulations is smaller than that obtained from Equation (19)) by a factor of 10."," Although Equation \ref{eq:amp2}) ) qualitatively explains the amplitude as a function of $Q$ after it reaches the maximum, the amplitude obtained from the simulations is smaller than that obtained from Equation \ref{eq:amp2}) ) by a factor of 10."634 The possible reasons are as follows. (, The possible reasons are as follows. (635"1) We assumed that a homogeneous region collapses to estimate the density contrast, but this is not the case in a disk.","1) We assumed that a homogeneous region collapses to estimate the density contrast, but this is not the case in a disk."636" Especially, the scale height of the disk is much smaller than ro, which we assumed as the initial radius. ("," Especially, the scale height of the disk is much smaller than $r_0$, which we assumed as the initial radius. ("6372) We used the radially averaged surface density to calculate the Fourier amplitude from the simulations.,2) We used the radially averaged surface density to calculate the Fourier amplitude from the simulations.638 This treatment may underestimate the local amplitude of spiral arms because the averaged density depends on the radial width for averaging., This treatment may underestimate the local amplitude of spiral arms because the averaged density depends on the radial width for averaging.639 We chose a radial width smaller than the critical wavelength., We chose a radial width smaller than the critical wavelength.640" However, the amplitudes increased ~10% when we halved the width. "," However, the amplitudes increased by $\sim 10$ when we halved the width. ("641Growth of byspiral arms does not complete because the (3)galactic shear breaks up the spiral arms before they are virialized.,3) Growth of spiral arms does not complete because the galactic shear breaks up the spiral arms before they are virialized.642" We do not insist that our simple model gives fully correct description of the mechanism through whicha Q controls the amplitude of spiral arms, but it is clear from Figure 12 that Q determines the amplitude."," We do not insist that our simple model gives a fully correct description of the mechanism through which $Q$ controls the amplitude of spiral arms, but it is clear from Figure \ref{fig:Q_tp} that $Q$ determines the amplitude."643" Thus, the spiral arms evolve in a self-regulated manner as follows."," Thus, the spiral arms evolve in a self-regulated manner as follows."644 Spiral arms grow from small density perturbations by the swing amplification (Toomre to their maximum amplitudes limited Q., Spiral arms grow from small density perturbations by the swing amplification \citep{Toomre81} to their maximum amplitudes limited by $Q$.645" The 1981) arms scatter disk stars, and as a result bythe velocity spiraldispersion of the disk star increases."," The spiral arms scatter disk stars, and as a result the velocity dispersion of the disk star increases."646" The heating rate, dQ/dt, is proportional to the squared amplitudes of spiral arms (see Equation (11)))."," The heating rate, $dQ/dt$, is proportional to the squared amplitudes of spiral arms (see Equation \ref{eq:dQdt2}) ))."647" This heating mechanism increases Q, and therefore the amplitude of spiral arms decreases."," This heating mechanism increases $Q$, and therefore the amplitude of spiral arms decreases."648" As a result, the heating rate decreases as Q increases."," As a result, the heating rate decreases as $Q$ increases."649" Through this evolution, the spiral arms become asymptotically faint as qualitatively shown by the black line in Figure 12,, but its timescale is comparable to the cosmological time, i.e., 10 Gyr."," Through this evolution, the spiral arms become asymptotically faint as qualitatively shown by the black line in Figure \ref{fig:Q_tp}, but its timescale is comparable to the cosmological time, i.e., 10 Gyr."650" In order to see how the initial Q, and disk mass fraction affect the evolution and morphology of spiral arms, we performed three additional runs: an unstable disk (Qo=0.5; model g), a massive disk (Ma/My=0.075, model h), and a less massive disk (Ma/Mn=0.03, model i)."," In order to see how the initial $Q$, and disk mass fraction affect the evolution and morphology of spiral arms, we performed three additional runs: an unstable disk $Q_0=0.5$ ; model g), a massive disk $M_{\rm d}/M_{\rm h} = 0.075$, model h), and a less massive disk $M_{\rm d}/M_{\rm h} = 0.03$ , model i)."651" In all models, the number of particles is 3x109."," In all models, the number of particles is $3\times 10^6$."652" Figure shows the snapshots of models f-i. Model f is a model with a large initial Q, Qo—1.8 and shown in Section 3.2."," Figure \ref{fig:snapshot_all} shows the snapshots of models f–i. Model f is a model with a large initial $Q$, $Q_0=1.8$ and shown in Section 3.2."653 We show it again as an example of a model with a large Qo., We show it again as an example of a model with a large $Q_0$.654" Model g is initially cold and unstable, therefore strong spiral arms develop in the first 0.5 Gyr."," Model g is initially cold and unstable, therefore strong spiral arms develop in the first 0.5 Gyr."655" As shown in top panel of Figure 14,, the disk is soon heated up to ~1.6, and the Q keeps "," As shown in top panel of Figure \ref{fig:3M_all}, the disk is soon heated up to $Q \sim 1.6$, and the $Q$ keeps increasing."656"As from ourQ theory in Section 3.3, theincreasing. amplitude ofexpected spirals then decreases quickly, and they are very weak at t=6 Gyr."," As expected from our theory in Section 3.3, the amplitude of spirals then decreases quickly, and they are very weak at $t=6$ Gyr."657 The final density and velocity profiles are quite different from original ones., The final density and velocity profiles are quite different from original ones.658" In model f, whose disk is initially hot (Qo= 1.8), spiral arms do not develop, and therefore Q (or the velocity dispersion) stays nearly constant (see the left panels of Figure 9))."," In model f, whose disk is initially hot $Q_0= 1.8$ ), spiral arms do not develop, and therefore $Q$ (or the velocity dispersion) stays nearly constant (see the left panels of Figure \ref{fig:three}) )."659" Models h and i have the same parameters as those of model b (standard model) except the disk mass ratio to halo, Ma/Mny. Carlberg&F"," Models h and i have the same parameters as those of model b (standard model) except the disk mass ratio to halo, $M_{\rm d}/M_{\rm h}$."660"reedman(1985) showed that the number of spiral arms in numerical simulation is consistent with that predicted by the swing amplification theory (Toomre1981),, and massive disks have a smaller number of spiral arms."," \citet{CF85} showed that the number of spiral arms in numerical simulation is consistent with that predicted by the swing amplification theory \citep{Toomre81}, and massive disks have a smaller number of spiral arms."661 Our results are consistent with this previous result., Our results are consistent with this previous result.662 We can estimate the number of spiral arms as follows., We can estimate the number of spiral arms as follows.663" The swing amplification is characterized by a parameter, X=ky where ker is the critical wavenumberR/m (Binney&?R/2nGYm,&Tremaine 2008)."," The swing amplification is characterized by a parameter, $X\equiv {k_{\rm cr}R}/{m} = {\kappa^2R}/{2\pi G\Sigma m}$, where $k_{\rm cr}$ is the critical wavenumber \citep{BT08}."664. Spiral arms develop most effectively when 1<2 (Toomre1981)., Spiral arms develop most effectively when $1<X<2$ \citep{Toomre81}.665". Therefore, we can estimate the dominating number of spiral arms, m, as where we adopted X~ 2."," Therefore, we can estimate the dominating number of spiral arms, $m$, as where we adopted $X\simeq2$ ."666" In the case of model b, we obtain m=6 at 8 kpc, which roughly agrees with the result of the simulation."," In the case of model b, we obtain $m=6$ at 8 kpc, which roughly agrees with the result of the simulation."667 This estimate is applicable for other models with different disk mass fractions., This estimate is applicable for other models with different disk mass fractions.668" Since the halo mass, My, is fixed in our models, the surface density, X is proportional to the disk mass fraction, Ma/My."," Since the halo mass, $M_{\rm h}$, is fixed in our models, the surface density, $\Sigma$, is proportional to the disk mass fraction, $M_{\rm d}/M_{\rm h}$."669" The numbers of spiral arms of models h and i are estimated as m—4 and m—9 at 8 kpc, and they also agree with the results of the simulations."," The numbers of spiral arms of models h and i are estimated as $m=4$ and $m=9$ at 8 kpc, and they also agree with the results of the simulations."670" Figure14 shows the time evolution of Q averaged within 5-10 kpc (top) and the totalpower at R=7.5 kpc (bottom), respectively."," Figure\ref{fig:3M_all} shows the time evolution of $Q$ averaged within 5–10 kpc (top) and the totalpower at $R=7.5$ kpc (bottom), respectively."671" As was the case with models a-f, the large total to the increase of Q."," As was the case with models a–f, the large total powers correspond to the rapid increase of $Q$ ."672 We investigated powersthe time correspondevolutionsof rapiddQ/dt from, We investigated the time evolutionsof $dQ/dt$ from673"Based on photometric data presented here. the first unambieuous substellar companion to a white dwarf mav have been discovered. within 0.3"" (~12 AU) of GD1400 (DAÀ4.4).","Based on photometric data presented here, the first unambiguous substellar companion to a white dwarf may have been discovered within $0.3''$ $\sim12$ AU) of GD1400 (DA4.4)."674 llowever. (he near infrared spectroscopy may indicate a CO temperature that is hieher (han the photospheric temperature indicated by the photometry.," However, the near infrared spectroscopy may indicate a CO temperature that is higher than the photospheric temperature indicated by the photometry."675 This could be the result of close binary interactions causing the CO bandheacds to appear more strongly (han in isolated L cwarfs or may be due to errors in the models used to remove the flux of the primary., This could be the result of close binary interactions causing the CO bandheads to appear more strongly than in isolated L dwarfs or may be due to errors in the models used to remove the flux of the primary.676 From a direct comparison with the GD165 binary svstem (relving on the same white cwarf and brown dwarf models). it appears that GDIL00B is cooler than spectral (wpe L4.," From a direct comparison with the GD165 binary system (relying on the same white dwarf and brown dwarf models), it appears that GD1400B is cooler than spectral type L4."677 The deconvolved magnitudes and colors of GD1400D are most consistent with spectral tvpe L6. indicativeof a GOAL) brown dwarf at an estimated age of 1.25 Gyr.," The deconvolved magnitudes and colors of GD1400B are most consistent with spectral type L6, indicativeof a $60M_{\rm J}$ brown dwarf at an estimated age of 1.25 Gyr."678 Its (rue nature and origins remain uncertain until more is known about the binary svstem., Its true nature and origins remain uncertain until more is known about the binary system.679 A trigonometic parallax determination. radial velocity measurements. or verv high resolution imaging should be able to further constrain the properties of this system.," A trigonometic parallax determination, radial velocity measurements, or very high resolution imaging should be able to further constrain the properties of this system."680 Both authors owe a debt of gratitude to M. Cushing for kindly providing us with his spectra for analvsis here and to N. Scoville for donating some of his Keck NIRSPEC time to observe GD1400., Both authors owe a debt of gratitude to M. Cushing for kindly providing us with his spectra for analysis here and to N. Scoville for donating some of his Keck NIRSPEC time to observe GD1400.681 J. Farihi wishes (ο express sincere (hanks to D. Zuckerman for his assistance in acquiring the optical data. to E. Gates of Lick Observatory [or taking the optical data. to L. Prato M. MeGovern for securing follow up near inlrared images ancl many helplul discussions. and to EZ. E. Becklin D. Zuckerman lor careful readings of the manuscript and constructive comments.," J. Farihi wishes to express sincere thanks to B. Zuckerman for his assistance in acquiring the optical data, to E. Gates of Lick Observatory for taking the optical data, to L. Prato M. McGovern for securing follow up near infrared images and many helpful discussions, and to E. E. Becklin B. Zuckerman for careful readings of the manuscript and constructive comments."682 Some of the data presented herein were obtained al Keck Observatory. which is operated as a scientilic partnership among (he California Institute ol Teehnologv (CIT). the University of California and the National Aeronauties and Space Administration (NASA).," Some of the data presented herein were obtained at Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology (CIT), the University of California and the National Aeronautics and Space Administration (NASA)."683 Some data used in this paper are part of the Two Micron. All sky Survey. a joint project of the University of Massachusetts aud the Infrared Processing and Analysis Center (IDACO/CIT. funded by NASA and the National Science Foundation (NSF).," Some data used in this paper are part of the Two Micron All Sky Survey, a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center (IPAC)/CIT, funded by NASA and the National Science Foundation (NSF)."684 2MASS data were retrieved from the NASA/IPAC Infrared Science Archive. which is operated by the Jet Propulsion Laboratory. CIT. under contract with NASA.," 2MASS data were retrieved from the NASA/IPAC Infrared Science Archive, which is operated by the Jet Propulsion Laboratory, CIT, under contract with NASA."685 J. Farihi has been supported in part by grants from NASA to UCLA and M. Christopher by NSF eranl AST02-28955., J. Farihi has been supported in part by grants from NASA to UCLA and M. Christopher by NSF grant AST02-28955.686 Facilities:Nickel.. IXeck..," Facilities:, ."687 , 688where (02). is the nth cumulant.,where $\bkta{\delta_R^n}_c$ is the $n$ th cumulant.689" For a distribution with zero mean, the relationships between the first few cumulants and moments are ο. (Rime -=(53), o=(64)--30, Throughout this work we shall often make references to the andkurtosis,, which are definedrespectively as and (6p)/o%."," For a distribution with zero mean, the relationships between the first few cumulants and moments are _c 0, _c= _R^2, _c = , _c= Throughout this work we shall often make references to the and, which are definedrespectively as $\bkta{\delta_R^3}/\sigma_R^3$ and $\bkta{\delta_R^4}/\sigma_R^4$."690" The is defined as (5%)/o%—3, with 3 being the kurtosis of the Gaussian distribution."," The is defined as $\bkta{\delta_R^4}/\sigma_R^4-3$, with 3 being the kurtosis of the Gaussian distribution."691"(5$)/o} At leading order, fwi, is related to the skewness via the relation derived in ? ο. FAQs )P(S) A(k2)P(((i)E where 108k2='Mpe.+2ukyko."," At leading order, $\fnl$ is related to the skewness via the relation derived in \cite{desjacques}692 ^4 S_3(R) = A(k_1) (k_1) A(k_2) (k_2), where $k_3^2=k_1^2+k_2^2+2\mu k_1k_2$."693 Figure [I] shows the cumulant $5 as a function of og in the mass range 1013—h- , Figure \ref{figcum} (upper curve) shows the cumulant $S_3$ as a function of $\sigma_R$ in the mass range $10^{13}-10^{16}\ff h^{-1}$ Mpc.694"On these scales, the weak (uppercurve) scale-dependencein $3 can be accurately fitted by a simple formula $3 with sub-percent accuracy."," On these scales, the weak scale-dependence in $S_3$ can be accurately fitted by a simple formula S_3 with sub-percent accuracy."695" This fitting orm offers an easy way to calculate the observational signatures of fwr, without resorting to the integralsin", This fitting formula offers an easy way to calculate the observational signatures of $\fnl$ without resorting to the integrals in.696" If fur= 0, we can similarly derive the leading-order relation between gny and the excess kurtosis °S4(R)_39"," If $\fnl=0$ , we can similarly derive the leading-order relation between $\gnl$ and the excess kurtosis ^6S_4(R)&=&"697" If fur= 0, we can similarly derive the leading-order relation between gny and the excess kurtosis °S4(R)_39N"," If $\fnl=0$ , we can similarly derive the leading-order relation between $\gnl$ and the excess kurtosis ^6S_4(R)&=&"698" If fur= 0, we can similarly derive the leading-order relation between gny and the excess kurtosis °S4(R)_39NL"," If $\fnl=0$ , we can similarly derive the leading-order relation between $\gnl$ and the excess kurtosis ^6S_4(R)&=&"699fitting the spectrum with a single gaussian curve are determining the area under that curve. using stancdare routines in the ASAP softwarep,"fitting the spectrum with a single gaussian curve and determining the area under that curve, using standard routines in the ASAP software."700ackages. Figure 3. shows the distribution of measured integrate intensities for both radio recombination lines throughout the observations., Figure \ref{rrlplot} shows the distribution of measured integrated intensities for both radio recombination lines throughout the observations.701 Filled circles indicate integrated intensities for the I169a line and open squares indicate integrate intensities for the L62e line., Filled circles indicate integrated intensities for the $\alpha$ line and open squares indicate integrated intensities for the $\alpha$ line.702 We might expect that if there is significant atmospheric attenuation. then the integrate intesities might be correlated. with elevation and/or svsteni temperature.," We might expect that if there is significant atmospheric attenuation, then the integrated intesities might be correlated with elevation and/or system temperature."703 However. Figure 3. shows that the distribution of integrated. intensities for cach line does not appear to correlate with either elevation or svsteni temperature.," However, Figure \ref{rrlplot}704 shows that the distribution of integrated intensities for each line does not appear to correlate with either elevation or system temperature."705 But ligure 3. does show a scatter of integrated intensities., But Figure \ref{rrlplot} does show a scatter of integrated intensities.706 We calculate the standard deviation of integrated intensities is 15 per cent for LW69e and 16 per cent for I162a., We calculate the standard deviation of integrated intensities is 15 per cent for $\alpha$ and 16 per cent for $\alpha$.707 ‘Thus. about 95 per cent (6wo standard deviations) of all integrated intensities are within 30 per cent of the mean integrated intesitv.," Thus, about 95 per cent (two standard deviations) of all integrated intensities are within 30 per cent of the mean integrated intesity."708 We assign 30 per cent as the uncertainty in the intensities of the LODS data., We assign 30 per cent as the uncertainty in the intensities of the HOPS data.709 Since the radio recombination line emission in Orion is extended. ib is possible hat the actual uncertainty is less then this as some of the scatter in Figure 3. may be due to small pointing errors of the telescope.," Since the radio recombination line emission in Orion is extended, it is possible that the actual uncertainty is less then this as some of the scatter in Figure \ref{rrlplot} may be due to small pointing errors of the telescope."710 Thus we consider30 per cent as an upper limit., Thus we consider30 per cent as an upper limit.711 Figure 3 does show a significant cdillerence in the integrated. intensities of the two radio recombination lines. with the όσα line weaker than the L69e line. on average.," Figure \ref{rrlplot} does show a significant difference in the integrated intensities of the two radio recombination lines, with the $\alpha$ line weaker than the $\alpha$ line, on average."712 Figure 4. shows the distribution of the ratio of H60a/1162a integrated. intensities for simultaneous observations., Figure \ref{rrlratio} shows the distribution of the ratio of $\alpha$ $\alpha$ integrated intensities for simultaneous observations.713 The mean of this distribution is 1.37. with a standard deviation of 0.07.," The mean of this distribution is 1.37, with a standard deviation of 0.07."714 This shows that the ratio of intensities appears stable over time., This shows that the ratio of intensities appears stable over time.715 Therefore. whilst the absolute intensity scale may be uncertain by a factor of 30 per cent. the relative intensity scale of dilferent spectral lines measured. using simultaneous observations is likely to be no worse than 5 per cent.," Therefore, whilst the absolute intensity scale may be uncertain by a factor of 30 per cent, the relative intensity scale of different spectral lines measured using simultaneous observations is likely to be no worse than 5 per cent."716 We note that the higher intensity of the E690 line. compared to the Πόλα line is most likely because the beam at 19.6CiLIz (the L69e line frequency) is larger than at 26.9CiCllz (the 1162a line frequency) and encompassess more extended racio recombination line emission.," We note that the higher intensity of the $\alpha$ line, compared to the $\alpha$ line is most likely because the beam at GHz (the $\alpha$ line frequency) is larger than at GHz (the $\alpha$ line frequency) and encompassess more extended radio recombination line emission."717 Previous observations of the Galactic plane in continuum (Schullerctal. 2009).. thermal line," Previous observations of the Galactic plane in continuum \citep{schuller09}, , thermal line"718slope of the V-band PL relation are found at the level around a median value of about -2.75 among nearby galaxies (excluding the poorly populated Sextans A/D data point) in which Cepheids have been discovered.,slope of the V-band $PL$ relation are found at the level around a median value of about -2.75 among nearby galaxies (excluding the poorly populated Sextans A/B data point) in which Cepheids have been discovered.719 If one were to rely exclusively on V-band PL relations for Cepheid distances that might be cause for concern., If one were to rely exclusively on V-band $PL$ relations for Cepheid distances that might be cause for concern.720 Bul such is not the ease., But such is not the case.721 Virtually all modern studies of the distances to galaxies as gauged by optical observations of Cepheids use VV., Virtually all modern studies of the distances to galaxies as gauged by optical observations of Cepheids use $W$.722 For the sake of the following caleulation we assume that à; = 2.45 (as in Freedman et al., For the sake of the following calculation we assume that $R_{VI}$ = 2.45 (as in Freedman et al.723 2001) and that ;»—3.0 (as derived. lor example. Irom the sample of Galactic Cepheids observed by Benedict et al.," 2001) and that $\beta = 3.0$ (as derived, for example, from the sample of Galactic Cepheids observed by Benedict et al."724 2008. illustrated in Figure 3).," 2008, illustrated in Figure 3)."725 In this case the reduction factor V to Win the slope change as given above is —(2—ο)=—(3.02.45)/2.45—0.3.," In this case the reduction factor $V$ to $W$ in the slope change as given above is $-(R -726\beta)/\beta = -(3.0 - 2.45)/2.45 = -0.3$."727 That is. a change in slope seen in V-band PL relation translates into a change in slope of the mean W -logP relation.," That is, a change in slope seen in V-band $PL$ relation translates into a change in slope of the mean $W$ -logP relation."728 Had. and Ro been numerically identical then (here would have been absolutely no impact of a change in (he disposition of the instability strip on the slope of the mean HW -logP relation., Had $\beta$ and R been numerically identical then there would have been absolutely no impact of a change in the disposition of the instability strip on the slope of the mean $W$ -logP relation.729 And indeed this would be almost exactly the case if we had adopted (he value of 9 = 2.439 as advocated by Sandage Tanunann (2008) based on a study of LAIC! Cepheids., And indeed this would be almost exactly the case if we had adopted the value of $\beta$ = 2.43 as advocated by Sandage Tammann (2008) based on a study of LMC Cepheids.730 In that case the slope changes in the optical would reduce (o a less that. 6wo-tentlis of a percent change in the slope in VW., In that case the slope changes in the optical would reduce to a less that two-tenths of a percent change in the slope in $W$.731 We do not believe that either 2 or £2 are currently known to precision themselves. so the exercise must be taken cautiously. being illustrative rather (han definitive.," We do not believe that either $\beta$ or $R$ are currently known to precision themselves, so the exercise must be taken cautiously, being illustrative rather than definitive."732 The point studs however (hat the slope of M. is clearly going to be relatively impervious to possible changes in the slopes al oplical wavelengths., The point stands however that the slope of $W$ is clearly going to be relatively impervious to possible changes in the slopes at optical wavelengths.733 Not only does (he scatter intrinsic to the W-loeP relation collapse with respect to the optical PL relations. but the slope of the HW -IogP relation is also very insensitive (o changes in slope of the originating optical PL relations.," Not only does the scatter intrinsic to the $W$ -logP relation collapse with respect to the optical $PL$ relations, but the slope of the $W$ -logP relation is also very insensitive to changes in slope of the originating optical $PL$ relations."734 Changes in the tilt of the instability strip that naturally explain and will give rise to changes in slopes of the monochromatic L relations are greatlv diminished in (heir overall impact in the projection of data into the W -logP? plane., Changes in the tilt of the instability strip that naturally explain and will give rise to changes in slopes of the monochromatic $PL$ relations are greatly diminished in their overall impact in the projection of data into the $W$ -logP plane.735 The Wesenheit function is defined to be reddenine-Iree: however its slope is additionally ancl coincidently very resistant to changes in the slopes of (he originating monochromatic. optical PL velations.," The Wesenheit function is defined to be reddening-free; however its slope is additionally and coincidently very resistant to changes in the slopes of the originating monochromatic, optical $PL$ relations."736 The demonstration bv Neeow lxanbur (2005) that the Wesenheit πιο10 for LAIC Cepheids does not show anv evidence lor a in slope over the full range of, The demonstration by Ngeow Kanbur (2005) that the Wesenheit function for LMC Cepheids does not show any evidence for a in slope over the full range of737All stars with masses between «0.8 and MM. will eventually evolve up the Asymptotic Giant Branch (AGB).,All stars with masses between $\sim$ 0.8 and $_{\odot}$ will eventually evolve up the Asymptotic Giant Branch (AGB).738 The life time on the AGB. the nucleosynthesis. and the amount of dust and gas returned to the interstellar chemical cycle are all strongly affected by the mass-loss rate of the star during this phase.," The life time on the AGB, the nucleosynthesis, and the amount of dust and gas returned to the interstellar chemical cycle are all strongly affected by the mass-loss rate of the star during this phase."739 This makes the mass loss the most Important process for the final evolution of low- to intermediate-mass stars(?)., This makes the mass loss the most important process for the final evolution of low- to intermediate-mass stars.740. The processes governing the mass loss of the AGB stars are not understood., The processes governing the mass loss of the AGB stars are not understood.741 In general. the mass loss is assumed to be smooth. spherically symmetric and driven by a pulsation-enhanced dust-driven wind.," In general, the mass loss is assumed to be smooth, spherically symmetric and driven by a pulsation-enhanced dust-driven wind."742 However. recent advances have revealed what appears to be a more complicated picture.," However, recent advances have revealed what appears to be a more complicated picture."743 —nages of light scattered by the circumstellar dust have revealed ares. elongated and bipolar structures. and even spiral shapes around a number of well-known AGB stars(??).," Images of light scattered by the circumstellar dust have revealed arcs, elongated and bipolar structures, and even spiral shapes around a number of well-known AGB stars."744. Whether this is a result of how the matter is expelled from the star or later interaction in the wind is under debate?)., Whether this is a result of how the matter is expelled from the star or later interaction in the wind is under debate.745. Reports on observations indicating a clumpy circumstellar medium (both gas and dust). become more common as the resolution of the observations increase).," Reports on observations indicating a clumpy circumstellar medium (both gas and dust), become more common as the resolution of the observations increase."746. Interferometric observations of OH. SiO and H»O maser emission also indicate à clumpy gas distributior and. in some cases. what appears to be bipolar outflows or jets close to the stars(22222).," Interferometric observations of OH, SiO and $_{2}$ O maser emission also indicate a clumpy gas distribution and, in some cases, what appears to be bipolar outflows or jets close to the stars."747.. In addition. although very successful in. simulating mass loss in carbon stars. frequency-dependent hydrodynamic models are not able to reproduce the observed mass-loss rates in Μ- (C/O«1) and S-type (C/Ox1) stars(?).. unless special conditions are assumed(?).," In addition, although very successful in simulating mass loss in carbon stars, frequency-dependent hydrodynamic models are not able to reproduce the observed mass-loss rates in M- $<$ 1) and S-type $\approx$ 1) stars, unless special conditions are assumed."748. The observations of clumps and deviations from spherical symmetry. together with the difficulties to reproduce the observed mass-loss rates in M- and S-type stars. indicate that our current picture of mass loss on the AGB ts perhaps too simple or lacking crucial ingredients.," The observations of clumps and deviations from spherical symmetry, together with the difficulties to reproduce the observed mass-loss rates in M- and S-type stars, indicate that our current picture of mass loss on the AGB is perhaps too simple or lacking crucial ingredients."749 Late in the evolution on the AGB. the transition from (in most cases) a spherically symmetric CSE to an asymmetric planetary nebula (PN)(??).. where bipolar and elliptical morphologies are common(??).. continues to be a puzzle.," Late in the evolution on the AGB, the transition from (in most cases) a spherically symmetric CSE to an asymmetric planetary nebula (PN), where bipolar and elliptical morphologies are common, continues to be a puzzle."750 Several ideas on how and when these features emerge exist: binary interaction(22).. interaction with a planet or a brown dwarf2).. or magnetic. fields2).," Several ideas on how and when these features emerge exist: binary interaction, interaction with a planet or a brown dwarf, or magnetic fields."751. So far it is not clear which model (or combination of models) gives the more satisfactory explanation., So far it is not clear which model (or combination of models) gives the more satisfactory explanation.752 Observations of remarkably spherically symmetric detached shells around a handful of carbon stars add to this mystery to some degree (e.g.. Olofsson et al.," Observations of remarkably spherically symmetric detached shells around a handful of carbon stars add to this mystery to some degree (e.g., Olofsson et al."753 1996. Gonzalez-Delgado et al.," 1996, Gonzalez-Delgado et al."754 2001. 2003. Maercker el al.," 2001, 2003, Maercker el al."755 2010. Olofsson et al.," 2010, Olofsson et al."756 2010)., 2010).757 The general consensus Is that the detached shells are formed as a consequence of a substantially increased. mass-loss rate during a brief period. possibly following a thermal pulse.," The general consensus is that the detached shells are formed as a consequence of a substantially increased mass-loss rate during a brief period, possibly following a thermal pulse."758 However. the details of the formation process. why they are only seen around carbon stars. or how their formation correlates with the potential onset of asymmetries toward the end of the AGB. ts not clear.," However, the details of the formation process, why they are only seen around carbon stars, or how their formation correlates with the potential onset of asymmetries toward the end of the AGB, is not clear."759 Imaging the circumstellar envelope (CSE. gas or dust component) will give us general information on the symmetry of the mass loss. while comparing images at different wavelengths tells us something about the interaction between the two components.," Imaging the circumstellar envelope (CSE, gas or dust component) will give us general information on the symmetry of the mass loss, while comparing images at different wavelengths tells us something about the interaction between the two components."760 Both the general symmetry and the interaction are important for our understanding of how mass is expelled from the star and of the interaction further out in the CSE., Both the general symmetry and the interaction are important for our understanding of how mass is expelled from the star and of the interaction further out in the CSE.761 Detailed images of AGB CSEs are so far available only for a limited number of (in most cases) high-mass-loss-rate sources., Detailed images of AGB CSEs are so far available only for a limited number of (in most cases) high-mass-loss-rate sources.762 This makes it impossible to know whether the asymmetries sometimes observed are a general feature of the AGB evolution or only present in some objects and are created only in combination with. for instance. a binary companion or à strong magnetic field.," This makes it impossible to know whether the asymmetries sometimes observed are a general feature of the AGB evolution or only present in some objects and are created only in combination with, for instance, a binary companion or a strong magnetic field."763 Problems with imaging the CSE are (for the gas component) insufficient. spatial resolution at radio wavelengths. and (for the dust component) at shorter wavelengths. the very large star-to-CSE brightness ratio.," Problems with imaging the CSE are (for the gas component) insufficient spatial resolution at radio wavelengths, and (for the dust component) at shorter wavelengths, the very large star-to-CSE brightness ratio."764 One possible solution for the latter problem is provided by imaging polarimetry at optical and IR wavelengths., One possible solution for the latter problem is provided by imaging polarimetry at optical and IR wavelengths.765 This ts a comparatively simple technique that requires relatively little telescope time. making it ideal to study large samples to be able to draw more general conclusions.," This is a comparatively simple technique that requires relatively little telescope time, making it ideal to study large samples to be able to draw more general conclusions."766of halos containing the highest specific star formation rates (sSEIs) are thought to increase with increasing look-back ime. consistent with “top-clown” galaxy formation scenarios (Cowie et al.,"of halos containing the highest specific star formation rates (sSFRs) are thought to increase with increasing look-back time, consistent with “top-down” galaxy formation scenarios (Cowie et al.,"767 1996: Neistein et ab.," 1996; Neistein et al.,"768 2006)., 2006).769 Tracking the occurrence of ealactic winds across cosmic time. particularly in manners unbiased by Luminosity or halo mass. would ον]ο a powerful way to study such models.," Tracking the occurrence of galactic winds across cosmic time, particularly in manners unbiased by luminosity or halo mass, would provide a powerful way to study such models."770 Furthermore. outIows are believed to be required to explain a wide variety of astrophysical observations. from the shape of the galaxy uminositv function (Benson et ab.," Furthermore, outflows are believed to be required to explain a wide variety of astrophysical observations, from the shape of the galaxy luminosity function (Benson et al.,"771 2003: IXhochfar et al..," 2003; Khochfar et al.,"772 2007). to the stellar mass-metallicity relation (Iremonti. 2tWA: Erb et aL.," 2007), to the stellar mass-metallicity relation (Tremonti, 2004; Erb et al.,"773 2006: Brooks et al..," 2006; Brooks et al.,"774 2007: Finlator Dave.. 2008).10 the large extent of dust ancl metals in galactic halos and in the intergalactic medium. (Scannapieco. Ferrara. Aladau. 2002: Oppenheimer Davé.. 2006: Kobayashi οἱ abl.," 2007; Finlator Davé,, 2008), the large extent of dust and metals in galactic halos and in the intergalactic medium (Scannapieco, Ferrara, Madau, 2002; Oppenheimer Davé,, 2006; Kobayashi et al.,"775 2007). and many other related. phenomena.," 2007), and many other related phenomena."776 Despite their clear importance in the galaxy formation process. outllows have generally been overlooked. theoretically and. until recently. have proved dillieult to study observationally at redshifts z21.4. the epoch when the Universe formed most of its stars and superwinds were ubiquitous.," Despite their clear importance in the galaxy formation process, outflows have generally been overlooked theoretically and, until recently, have proved difficult to study observationally at redshifts $z \simeq 1 - 4$, the epoch when the Universe formed most of its stars and superwinds were ubiquitous."777 Surveys have identified outllowing gas from galaxies at redshift z0 through strong. bluc-shifted: resonance-line absorption in their spectra arising in low-ion gas entrained in the flows (e.g.. Pettini et al..," Surveys have identified outflowing gas from galaxies at redshift $z>0$ through strong, blue-shifted resonance-line absorption in their spectra arising in low-ion gas entrained in the flows (e.g., Pettini et al.,"778 2001: Shapley et al..," 2001; Shapley et al.,"779. 2003: ‘Tremonti. Moustakas. Diamonc-Stanic. 2007: Wiener et al.," 2003; Tremonti, Moustakas, Diamond-Stanic, 2007; Wiener et al.,"780 2009)., 2009).781 Llowever. there are two important limitations inherent in methods. which rely only on spectra of the outllow hosts.," However, there are two important limitations inherent in methods which rely only on spectra of the outflow hosts."782 First. they provide no information on the ocation of the outllowing gas: it is only presumed. that he material reaches the LGAL," First, they provide no information on the location of the outflowing gas; it is only presumed that the material reaches the IGM."783 Secondly. these surveys searched for evidence of outllows in spectra of either the wieghtest galaxies at the relevant redshift. known star-orming galaxies. or known post-starburst galaxies.," Secondly, these surveys searched for evidence of outflows in spectra of either the brightest galaxies at the relevant redshift, known star-forming galaxies, or known post-starburst galaxies."784 What is needed is the reverse experiment: a survey of the galaxies rom which known large-scale outflows originate., What is needed is the reverse experiment: a survey of the galaxies from which known large-scale outflows originate.785 “Vhis bees he question: how does one identify a galactic wind withoutpriori knowledge of the galaxy itself?, This begs the question: how does one identify a galactic wind without knowledge of the galaxy itself?786 Quasar absorption ines may oller such an opportunity. as they select. ealaxies owed. on the gas absorption cross section. with no clirect dependence on emission from the galaxy.," Quasar absorption lines may offer such an opportunity, as they select galaxies based on the gas absorption cross section, with no direct dependence on emission from the galaxy."787 The physical processes that determine the properties of intervening low-ion quasar absorption line svstems are not well understood., The physical processes that determine the properties of intervening low-ion quasar absorption line systems are not well understood.788 While it has long been known that such absorbers can in general be identified with individual galaxies (e.g. Bergeron Boissé.. 1991: Steidel. Dickinson. Persson. 1994) correlations between emission (1.6... of the galaxy) and absorption (i.o.. strength and velocity structure of the absorbing gas) properties have been elusive (Ixaeprzak et al..," While it has long been known that such absorbers can in general be identified with individual galaxies (e.g., Bergeron Boissé,, 1991; Steidel, Dickinson, Persson, 1994) correlations between emission (i.e., of the galaxy) and absorption (i.e., strength and velocity structure of the absorbing gas) properties have been elusive (Kacprzak et al.,"789. 2007) and/or inconclusive (e.g. Steidel et al..," 2007) and/or inconclusive (e.g., Steidel et al.,"790. 2002: Ixacprzak et al..," 2002; Kacprzak et al.,"791 2010)., 2010).792 Phe strongest absorbers. which have until recently. been neglected. clue to their relative scarcity. nav hold important clues.," The strongest absorbers, which have until recently been neglected due to their relative scarcity, may hold important clues."793 For example. Bond et ((2001) considered the velocity profiles of the strongest aabsorbers known at the time (rest equivalent widths s PAY) measured with high-resolution spectroscopy. and. proposed. that such svstems may. arise. in galactic superwinds.," For example, Bond et (2001) considered the velocity profiles of the strongest absorbers known at the time (rest equivalent widths $\sim 2$ ) measured with high-resolution spectroscopy, and proposed that such systems may arise in galactic superwinds."794 Detections οἱ outllows.— through. broad. low-ion absorption in the spectra of starbursting —galaxies suggest that galactic winds result in very strong aabsorption along a sightline past a galaxy., Detections of outflows through broad low-ion absorption in the spectra of starbursting galaxies suggest that galactic winds result in very strong absorption along a sightline past a galaxy.795 However.i this does not necessarily implv that all or even. any of the strongest intervening absorbers detected in quasar spectra actually arise in the winds of foreground. galaxies.," However, this does not necessarily imply that all or even any of the strongest intervening absorbers detected in quasar spectra actually arise in the winds of foreground galaxies."796 Indeed. models have been proposed. that account for the observed distribution of aabsorption strength. without. relving on outllows (e.g. linker Chen 2008).," Indeed, models have been proposed that account for the observed distribution of absorption strength without relying on outflows (e.g., Tinker Chen 2008)."797 Alternatively. the huge kincmatic spreads that define the strongest. svstems may be. due simplv to the chance intersection of the sightline with multiple “normal” aabsorbing galaxies ini a rich eroup or cluster. as first suggested by Pettini et ((1983).," Alternatively, the huge kinematic spreads that define the strongest systems may be due simply to the chance intersection of the sightline with multiple “normal” absorbing galaxies in a rich group or cluster, as first suggested by Pettini et (1983)."798 Very large aabsorber surveys (e.g. Nestor et ab.," Very large absorber surveys (e.g., Nestor et al.,"799 2005: Prochter. Prochaska. Burles. 2006: Quicer et al.," 2005; Prochter, Prochaska, Burles, 2006; Quider et al.,"800 2010). which are now becoming available. have uncovered large numbers (e.g.. -600 in Quider ct al.)," 2010), which are now becoming available, have uncovered large numbers (e.g., $>600$ in Quider et al.)"801" of ""ultra-strong"" πα svstems with BAL ", of “ultra-strong” ) systems with $\ge 3$.802Catalogs of such systems alford the opportunity to explore in depth the proposed aabsorber-galactic wind connection., Catalogs of such systems afford the opportunity to explore in depth the proposed absorber-galactic wind connection.803 Recent work has alreacly given support for a connection between the strongest ssyvstems and star forming galaxies. which is usually. considered as support of an outflow scenario.," Recent work has already given support for a connection between the strongest systems and star forming galaxies, which is usually considered as support of an outflow scenario."804 For example. by stacking thousands of rclatively-shallow Sloan Digital Sky Survey (SDSS) images of the fields of strong aabsorption systems Zibetti et ((2007) demonstrated the strongest svstenis are associated with bluer galaxies closer to the sightline to the background quasar compared to weaker systems.," For example, by stacking thousands of relatively-shallow Sloan Digital Sky Survey (SDSS) images of the fields of strong absorption systems Zibetti et (2007) demonstrated the strongest systems are associated with bluer galaxies closer to the sightline to the background quasar compared to weaker systems."805 Similarly. Bouché et ((2007) have detected strong Io emission at the absorption redshift towards strong aabsorbers and Rubin et ((2009) have identified an aabsorber in the spectrum of a background galaxy that they identify with a wind from a foreground galaxy.," Similarly, Bouché et (2007) have detected strong $\alpha$ emission at the absorption redshift towards strong absorbers and Rubin et (2009) have identified an absorber in the spectrum of a background galaxy that they identify with a wind from a foreground galaxy."806 Perhaps the most compelling evidence suggesting à connection between aabsorbers and star formation is the relation between aand cemission discussed by Ménnard et ((2009). wherein they demonstrate that the strongest aabsorbers are on average associated with the highest luminosity densities and are therefore likely to be hosted by vigorously star-forming galaxies.," Perhaps the most compelling evidence suggesting a connection between absorbers and star formation is the relation between and emission discussed by Ménnard et (2009), wherein they demonstrate that the strongest absorbers are on average associated with the highest luminosity densities and are therefore likely to be hosted by vigorously star-forming galaxies."807 Nestor ct ((2007: hereafter. NMPRQ) published the irst imagine survey aimed specifically at the strongest aabsorption systems. including images of the fields of hirteen mocderate-redshift (0.42<2« 0.84) ssvstenis.," Nestor et (2007; hereafter NTRQ) published the first imaging survey aimed specifically at the strongest absorption systems, including images of the fields of thirteen moderate-redshift $0.42 < z < 0.84$ ) systems."808 These revealed bright galaxies at relatively low impact parameter to the absorption sightline (compared to he fields of most aabsorbers)., These revealed bright galaxies at relatively low impact parameter to the absorption sightline (compared to the fields of most absorbers).809 While consistent with the outflow: model. in general and. e.g.. the results of Zibetti et al.," While consistent with the outflow model in general and, e.g., the results of Zibetti et al.,"810 in particular. detailed. study of the galaxies associated with aabsorbers is needed to test this putative connection.," in particular, detailed study of the galaxies associated with absorbers is needed to test this putative connection."811" LE the ""ultra-strong"" nature of these absorbers is indeed linked to galactic winds. we expect to find evidence of recent. high mass fraction starbursts in one or more of the low impact parameter (low-5) galaxies."," If the “ultra-strong” nature of these absorbers is indeed linked to galactic winds, we expect to find evidence of recent, high mass fraction starbursts in one or more of the low impact parameter $b$ ) galaxies."812 Ln this paper. we present the," In this paper, we present the"813ol the Constrained Trausport (CT: Evaus Hawley. 1988) maetetic field variables B’=Cjjhjp. as OB!—0)(VB—V/B')= 0. where V!=U'/U' is the trasport velocity. and C=Wa. with W the Lorentz factor.,"of the Constrained Transport (CT; Evans Hawley, 1988) magnetic field variables ${\cal B}^i = \epsilon_{i j k}\,F_{j k}$, as $\partial_t {\cal B}^i - 814\partial_j\left( V^i\,{\cal B}^j - V^j\,{\cal B}^i\right)= 0$ , where $V^i=U^i/U^t$ is the transport velocity, and $U^t=W/\alpha$, with $W$ the Lorentz factor."815 The CTalgorithiu ensures that the constraint Qj!=0 is satisfied to rouudiug error., The CTalgorithm ensures that the constraint $\partial_i {\cal B}^i = 0$ is satisfied to rounding error.816" The Ixerr metric is expressed in Boyer-Lindatistn coordinates.n lora whichn #qudi?4gooAU?-gy, dors a=(=g!"")V?> is the lapse function."," The Kerr metric is expressed in Boyer-Lindquist coordinates, for which ${ds}^2=g_{t t}\,{dt}^2+2\,g_{t \phi}\,{dt}\,{d \phi}+g_{r r}\,{dr}^2 +817g_{\theta \theta}\,{d \theta}^2 +g_{\phi \phi}\,{d \phi}^2$ ; $\alpha = {(-g^{tt})}^{-1/2}$ is the lapse function."818" The lL-velocity is subject to the constraint. OfU,=—1."," The 4-velocity is subject to the constraint $U^\mu\,U_\mu=-1$."819" Deining the l-mnomentuim as U,. we obtain the equivalent condition 5/5,=—(pWAVbl,W "," Defining the 4-momentum as $S_\mu = (\rho\,h\ + {\|b\|}^2)\,W\,U_\mu$ , we obtain the equivalent condition $S^\mu S_\mu= -{(\rho\,h\,W + {\|b\|}^2\,W)}^2$ ."820In the GRMHD code. the fundamental variables D=pM. aud E=De are usec to write phi=D+TE: the spatial components of the [-mioimnentuui are treated as fuucdaiment:il variables aid evolved usine[n] the momentum equations (equation (30) of DHO3): aud the Lorentz actor. Wo. is extracted using the uormalizatiou condition at the end of each time step (along with V). It is straightforward to slow that the normalization condition yields the following quartic expression for TV. where iy=|[.S ΓΕ. €=[bl/(D+EE). ancl [152=ojmyUp+55Goo57jnUo ," In the GRMHD code, the fundamental variables $D=\rho\,W$ and $E=D\,\epsilon$ are used to write $\rho\,h\,W=D+\Gamma\,E$; the spatial components of the 4-momentum are treated as fundamental variables and evolved using the momentum equations (equation (30) of DH03); and the Lorentz factor, $W$, is extracted using the normalization condition at the end of each time step (along with $V^i$ ).It is straightforward to show that the normalization condition yields the following quartic expression for $W$, where $\eta = {\|\tilde{S}\|}/(D+\Gamma\,E)$ , $\xi = {\|b\|}^2/(D+\Gamma\,E)$, and ${\|\tilde{S}\|}^2=S_r^2/g_{rr}+S_\theta^2/g_{\theta \theta}+S_\phi^2/821g_{\phi \phi}$."822In this. approach. the solutions for the Lorentz [actor span a two-dimensional parameter space. W(4.£). with 5g analogous to a fluid. velocity and £ analogous to an Alfvénn velocity.," In this approach, the solutions for the Lorentz factor span a two-dimensional parameter space, $W(\eta,\xi)$, with $\eta$ analogous to a fluid velocity and $\xi$ analogous to an Alfvénn velocity."823 Using the analytic expression for the plivsically allowed root of equation (1)) provides a significant improvement over the simpler (aud faster) calculation used in earlier versions of the GRMHD code., Using the analytic expression for the physically allowed root of equation \ref{wquartic}) ) provides a significant improvement over the simpler (and faster) calculation used in earlier versions of the GRMHD code.824 Though costlier [rom a uumerical point of view. this quartic solution significanty raises the maximum allowable value of the Lorentz [actor from V4;= 8 in the original cocle to 50 in the current version.," Though costlier from a numerical point of view, this quartic solution significantly raises the maximum allowable value of the Lorentz factor from $W_{\rm max}=$ 8 in the original code to 50 in the current version."825 This upper bound. which occurs in the limitof εί3» 1. is set by rounding error (in arithmetic Wa.<o 80. but the moreconservative limit of Was=250 bas been used in the siniulatious reported here).," This upper bound, which occurs in the limitof $\xi/\eta \gg 1$ , is set by rounding error (indouble-precision arithmetic $W_{\rm safe} \lesssim 80$ , but the moreconservative limit of $W_{\rm max}=50$ has been used in the simulations reported here)."826inflow is completely suppressed ( see Fig.,inflow is completely suppressed ( see Fig.827 S. middle panel corresponding to 7= 4/3), \ref{fig:mhd_corona2} middle panel corresponding to $\gamma=4/3$ ).828" The moment of the sudden decreaseof AL,/My (Fig. 1))", The moment of the sudden decreaseof $\MDOT_{\rm a}/\MDOT_{\rm B}$ (Fig. \ref{fig:accretion_evolution}) )829 corresponds to the time of the outflow formation., corresponds to the time of the outflow formation.830 Next. we describe what happens for 5 —1.01 ( run 4. bottom panels in Figs.," Next, we describe what happens for $\gamma$ =1.01 ( run 4, bottom panels in Figs."831 4. and 8))., \ref{fig:mhd_corona} and \ref{fig:mhd_corona2}) ).832 Already in the LLD simulations (runs €. IL. LJ in Ges in MPOS). one may notice that because of much lower gas pressure. the torus is ecometrically thinner compared to the cases with higher 5.," Already in the HD simulations (runs G, H, I, J in fig.8 in MP08), one may notice that because of much lower gas pressure, the torus is geometrically thinner compared to the cases with higher $\gamma$."833 Here. a strongly turbulent magnetic corona forms above the disc.," Here, a strongly turbulent magnetic corona forms above the disc."834 Phe corona is geometrically thick. but it does not expand into the polar regions as in the previous cases.," The corona is geometrically thick, but it does not expand into the polar regions as in the previous cases."835 As in run 1. initially the outllow is caused by the centrifugal ancl magnetic forces on both sides (as in Proga 2005)).," As in run 1, initially the outflow is caused by the centrifugal and magnetic forces on both sides (as in \citealt{proga:2005}) )."836 However. this collimated outflow does not. completely prevent thelow-£ matter inflow toward the DII from the polar regions.," However, this collimated outflow does not completely prevent the matter inflow toward the BH from the polar regions."837" ""Therefore. Al,Aly remains alwavs high (close the Bondi rate)."," Therefore, $\MDOT_{\rm a}/\MDOT_{\rm B}$ remains always high (close the Bondi rate)."838 In the lower panels in Figs., In the lower panels in Figs.839 4 and S.. the dotted contours in the angular momentum panels indicate that theligh-f matter is separated from the outllow by thelow-£ accreting matter marked. as the solid contours.," \ref{fig:mhd_corona}840 and \ref{fig:mhd_corona2}, the dotted contours in the angular momentum panels indicate that the matter is separated from the outflow by the accreting matter marked as the solid contours."841 The low-:7 corona is separated from the collimated outflow with he high-:? region of the accreting matter., The $\beta$ corona is separated from the $\beta$ collimated outflow with the $\beta$ region of the accreting matter.842 As we mentioned in the previous section. the moment of the outITow formation cannot be clearly identified in the mass accretion rate curve (lig. 1)).," As we mentioned in the previous section, the moment of the outflow formation cannot be clearly identified in the mass accretion rate curve (Fig. \ref{fig:accretion_evolution}) )."843 The persistenth aceretinglow-/ matter separates he polar outllow and magnetic corona for most of the simulation time., The persistently accreting matter separates the polar outflow and magnetic corona for most of the simulation time.844 In this case. the accretion [low consists of our parts (from the equator to the pole): C1) geometrically hin torus in the equatorial plane. (2) highly turbulent magnetic corona. (3)low-£ matter inflow through polar tunnels. and (4) polar outflow.," In this case, the accretion flow consists of four parts (from the equator to the pole): (1) geometrically thin torus in the equatorial plane, (2) highly turbulent magnetic corona, (3) matter inflow through polar funnels, and (4) polar outflow."845 In the intermediate case of 5 —1.2 (run 3. third row of panels in Figs.," In the intermediate case of $\gamma$ =1.2 (run 3, third row of panels in Figs."846 4— and 8)). although the magnetic corona forms. the polar outllow forms in both manners as described for runs 1 and 2.," \ref{fig:mhd_corona} and \ref{fig:mhd_corona2}) ), although the magnetic corona forms, the polar outflow forms in both manners as described for runs 1 and 2."847 In Fig. 4..," In Fig. \ref{fig:mhd_corona},"848 one notices the corona formation on the N and ο sides., one notices the corona formation on the N and S sides.849 The corona extends bevond r=10075. which is clearly seen in Fig. 4..," The corona extends beyond $r = 100 R_{\rm S}$, which is clearly seen in Fig. \ref{fig:mhd_corona}. ."850 First. on the S pole. the expanding corona causes the outflow.," First, on the S pole, the expanding corona causes the outflow."851 The outllow on the opposite pole. is caused by the magneto-centrifugal mechanism described in Proga(2005).," The outflow on the opposite pole, is caused by the magneto-centrifugal mechanism described in \citet{proga:2005}."852. Phe mass accretion rate. just as in the case of 51.01. does not experience a sudden reduction during its evolution because the outflow is weak so that the [ow-Z matter. persistently accretes and mainly contributes to the total mass accretion rate.," The mass accretion rate, just as in the case of $\gamma$ =1.01, does not experience a sudden reduction during its evolution because the outflow is weak so that the matter persistently accretes and mainly contributes to the total mass accretion rate."853 Nevertheless. the mass accretion rate for 5-—1.2 is slightlv lower than that for 5 —1.01.," Nevertheless, the mass accretion rate for $\gamma$ =1.2 is slightly lower than that for $\gamma$ =1.01."854 In our models. the collimation of the jet-like outllow depends on the 5 index and it is related to the mechanism ol its formation rather than the torus geometrical thickness.," In our models, the collimation of the jet-like outflow depends on the $\gamma$ index and it is related to the mechanism of its formation rather than the torus geometrical thickness."855 For 5=5/3.4/3 and ~=1.2 (S side). the jet-like outflow at the final time of the simulation is not. well collimated. because it is driven from the torus corona.," For $\gamma=5/3, 4/3$ and $\gamma=1.2$ (S side), the jet-like outflow at the final time of the simulation is not well collimated, because it is driven from the torus corona."856 To investigate the problem of collimation. one should perform the simulation over a longer time period to allow the Low to reach the quasistationary state at larger radii.," To investigate the problem of collimation, one should perform the simulation over a longer time period to allow the flow to reach the quasistationary state at larger radii."857 ουσ=1.01 and >=1.2 (N side) the outflow is more collimated in comparison to the coronal jet-like outflow because it is formed by theIow-£ matter and collimated by the accretinglow-£ matter., For $\gamma=1.01$ and $\gamma=1.2$ (N side) the outflow is more collimated in comparison to the coronal jet-like outflow because it is formed by the matter and collimated by the accreting matter.858" Lor 7 —1.01 (as well as for 5, —1.2). Al,Ah, remain high for most of the simulations time."," For $\gamma$ =1.01 (as well as for $\gamma$ =1.2), $\MDOT_{\rm a}/\MDOT_{\rm B}$ remain high for most of the simulations time."859 However. at the late phases of the simulations. we observe a few significant minima in the nis accretion rate curves (lower panels in Fie.1)).," However, at the late phases of the simulations, we observe a few significant minima in the mass accretion rate curves (lower panels in \ref{fig:accretion_evolution}) )."860 These minima are caused by small scale coronal outllows which temporary suppresses accretion of thelow-£ matter in the polar funel., These minima are caused by small scale coronal outflows which temporary suppresses accretion of the matter in the polar funel.861 Fie., Fig.862 9 presents the sequence of maps of the logarithmic density. angular momoentum contours. and plasma parameter 7. before. during. and after an episode of an outllow in run 4.," \ref{fig:burst} presents the sequence of maps of the logarithmic density, angular momentum contours, and plasma parameter $\beta$, before, during, and after an episode of an outflow in run 4."863 To better show the structure of the inner How. we present only a half of the computational domain above the equator within 500 As.," To better show the structure of the inner flow, we present only a half of the computational domain above the equator within 500 $R_{\rm S}$."864 Before the outLow. the magnetic torus corona extents το 100. fs (the two top rows of panels).," Before the outflow, the magnetic torus corona extents to 100 $R_{\rm S}$ (the two top rows of panels)."865 During an outflow. the corona expands up to 300. As (the third. and fourth rows of panels).," During an outflow, the corona expands up to 300 $R_{\rm S}$ (the third and fourth rows of panels)."866 Later. the matter Lows back towzud the DII.," Later, the matter flows back toward the BH."867 Before and after the outflow. the torus corona and polar outllow are separated by a stream of thelow-£ matter.," Before and after the outflow, the torus corona and polar outflow are separated by a stream of the matter."868 After the outburst. A/Mg increases back to its mean high level (the bottom row ofpanels).," After the outburst, $\MDOT_{\rm a}/\MDOT_{\rm B}$ increases back to its mean high level (the bottom row of panels)."869 The whole evcle lasts about 3500 Fu., The whole cycle lasts about 3500 $t_{\rm dyn}$.870" In this section. we return to our investigation of the time evolution of Al,Ah, for various 5."," In this section, we return to our investigation of the time evolution of $\dot{M}_{\rm a} / \dot{M}_{\rm B}$ for various $\gamma$."871 Here. we identify accretion states that correspond to various episodes of torus accretion.," Here, we identify accretion states that correspond to various episodes of torus accretion."872 Figs., Figs.873" LO shows the segments of the NLMy evolution for runs 1. 2. 3. and 4. which contain the typical ""accretion states’ that appeared for a given. model."," \ref{fig:accretion_evolution_mini} shows the segments of the $\MDOT_{\rm874a}/\MDOT_{\rm B}$ evolution for runs 1, 2, 3, and 4, which contain the typical `accretion states' that appeared for a given model."875 The characteristic times. are marked with arrows denoted as SL. 82 (in run 1 and 2). 83 (only in run 2). 84 and 55 (in run 3 and 4).," The characteristic times, are marked with arrows denoted as S1, S2 (in run 1 and 2), S3 (only in run 2), S4 and S5 (in run 3 and 4)."876 We consider the How to be unstable (MIRI) when the Following relation holds (Balbus&Llawley1998): where wy is the Alfyénn speed. © is the angular velocity. + is the distance from the BIL and is the half of the clisk thickness.," We consider the flow to be unstable (MRI) when the following relation holds \citep{balbus:1998}: where $u_A$ is the Alfvénn speed, $\Omega$ is the angular velocity, $r$ is the distance from the BH and is the half of the disk thickness."877 We define fas the height at which the density of the matter decreases by along the vertical direction in comparison to the density at the equator., We define as the height at which the density of the matter decreases by along the vertical direction in comparison to the density at the equator.878 For run 1. 2. and 3. the disk height can be approximated with its radius har in Eq. 10..," For run 1, 2, and 3, the disk height can be approximated with its radius h=r in Eq. \ref{eq:disk_thickness}."879 For run 4. we adopt the numerical value of  (h roughly corresponds to 1/3 r).," For run 4, we adopt the numerical value of $h$ $h$ roughly corresponds to 1/3 r)."880 In the vertical direction. the torus typically contains 50.42.40 ancl 24 erid points. for 5 —5/3. 4/3. 1.2. ancl 1.01. respectively.," In the vertical direction, the torus typically contains $\sim50, 42, 40$ and 24 grid points, for $\gamma$ =5/3, 4/3, 1.2, and 1.01, respectively."881 In the racial direction. there are ~60 and ~90 equaly spaced in logarithmic scale zones within first 20 fs ancl LOO 725. respectively.," In the radial direction, there are $\sim 60$ and $\sim 90$ equaly spaced in logarithmic scale zones within first 20 $R_S$ and 100 $R_S$, respectively."882 To find. whether the fastest. growing miocle of the MIU is resolved. with our computational mesh. we compute its critical wavelength Agri as defined by eq.," To find, whether the fastest growing mode of the MRI is resolved with our computational mesh, we compute its critical wavelength $\lambda_{crit}$ as defined by eq."883 113 in Balbus&Lawley(1998)., 113 in \citet{balbus:1998}.884. We checked the ratio between Avi and Ar (the eric spacing) as a function of position onthe eric., We checked the ratio between $\lambda_{crit}$ and $\Delta x$ (the grid spacing) as a function of position onthe grid.885 If the ratio is larger than one. the grid. resolves torus for MIL.," If the ratio is larger than one, the grid resolves torus for MRI."886 In regions where the ratio is smaller than one the erid does not resolve the critical wavelength Avni., In regions where the ratio is smaller than one the grid does not resolve the critical wavelength $\lambda_{crit}$ .887 We have analysed the [ow properties at cach aceretion state as PBOSb did., We have analysed the flow properties at each accretion state as PB03b did.888 For 7? 25/3. we foundthat the accretion," For $\gamma$ =5/3, we foundthat the accretion"889the spectral shape of this region.,the spectral shape of this region.890 After subtracting the contribution frou the kuot. we re-do the joiut spectral fitting of he spectra of regious 1 and 2 as well as the whole jet.," After subtracting the contribution from the knot, we re-do the joint spectral fitting of the spectra of regions 1 and 2 as well as the whole jet."891 The results are also sununarized in Table 1.., The results are also summarized in Table \ref{spec_par}.892 The photon indices iu these two regions remain to be consistent within lo uncertainties., The photon indices in these two regions remain to be consistent within $1\sigma$ uncertainties.893 Therefore. we conclude that no evidence for spectral steepeniug aloug the ταν jet can be found in this observation.," Therefore, we conclude that no evidence for spectral steepening along the X-ray jet can be found in this observation."894 Iu order to search for XN-rav pulsations frou the pulsar PSR D2221165. only the data takeu from the PN αμα window mode with a temporal resolution of 5.7 ms can be used.," In order to search for X-ray pulsations from the pulsar PSR B2224+65, only the data taken from the PN small window mode with a temporal resolution of 5.7 ms can be used."895" We extracted 1150 counts from) a circle with a radius of 20"". centere at the radio finie position.", We extracted 1450 counts from a circle with a radius of $20''$ centered at the radio timing position.896 We urther selected these eveuts within the good time intervals with the counts rate of the entire field ower than 0.02 cts/sec in order to reduce the contamination from the sky backeround., We further selected these events within the good time intervals with the counts rate of the entire field lower than 0.02 cts/sec in order to reduce the contamination from the sky background.897 After filtering. a total of 523 source counts was left iu our study.," After filtering, a total of 523 source counts was left in our study."898 The photon arrival times were corrected to he sol system. barveenter with the BARYCEN ool (version: 1.18: JPL DE200 Earth eplemeris) of NAIMISAS., The photon arrival times were corrected to the solar system barycenter with the BARYCEN tool (version: 1.18; JPL DE200 Earth ephemeris) of XMMSAS.899 We noticed that the misar has a elitch at ALJD ~51266. which is about two vears before our observation (MD 55025).," We noticed that the pulsar has a glitch at MJD $\sim$ 54266, which is about two years before our observation (MJD 55025)."900 Since there is no urther information about the relaxation time. we ien performed a detailed search for a ranee that cover both the post-elitch frequency as well as 1ο extrapolated value at the mean epoch of the NMM-Newton observation.," Since there is no further information about the relaxation time, we then performed a detailed search for a range that cover both the post-glitch frequency as well as the extrapolated value at the mean epoch of the XMM-Newton observation."901 We applied the Z2 statistics (Buecheri et al., We applied the $Z^{2}_{n}$ statistics (Buccheri et al.902" 1983) with the harionics iunber (n) from one to teu :id the IT-Test. (de Jaeger. Raubenhenuer Swanepocl 1989) with re searcliung step of 1/5 correspouding Fourier width in the range of 1.1650 to 1.1652 !,"," 1983) with the harmonics number (n) from one to ten and the H-Test (de Jager, Raubenheimer Swanepoel 1989) with the searching step of 1/5 corresponding Fourier width in the range of 1.4650 to 1.4652 $^{-1}$."903 No sienificant signal was detected., No significant signal was detected.904 We also folded i6 light curve by using the radio spin period extrapolated for the epoch of he XNMM-Newtou observation., We also folded the light curve by using the radio spin period extrapolated for the epoch of the XMM-Newton observation.905 However. no meaniugful light. curve was obtained.," However, no meaningful light curve was obtained."906 The pulsar epliemeris reported from the ATNF Catalogue (Mauchester et al., The pulsar ephemeris reported from the ATNF Catalogue (Manchester et al.907 2005). f=(Ld6511023680 ITz aud f=—2.0737«1015κος2 (at MJD = 51120.0) were used in our study.," 2005), $f = 1.46511023680$ Hz and $\dot{f} = -2.0737 \times 10^{-14}~\mbox{sec}^{-2}$ (at MJD = 54420.0) were used in our study."908" We further computed the upper Πιτ of the pulsed fraction f, by f,=JN;Na}ENS. where Vy and Ny, are the umuber of total photous and the backerouud photons respectively aud ο is the duty evele."," We further computed the upper limit of the pulsed fraction $f_{p}$ by $f_{p}=\beta\left(N_{t}-N_{b}\right)/N_{t}$, where $N_{t}$ and $N_{b}$ are the number of total photons and the background photons respectively and $\beta$ is the duty cycle."909 Asstuning ο=0.5. we placed a lo upper limit for the pulsed fraction to be ~8S.," Assuming $\beta=0.5$, we placed a $1\sigma$ upper limit for the pulsed fraction to be $\sim8\%$."910 As an X-ray jet is possibly subjected to maenetohydrodvuamic instability. variability has been ποσα in mmany PWN systems (e.g. DeLauex et al.," As an X-ray jet is possibly subjected to magnetohydrodynamic instability, variability has been seen in many PWN systems (e.g. DeLaney et al."911 2006)., 2006).912 Tn order to investigate the lone-termi variability from the jet. we analyse tlie X-rav observations of this field) in differcut epochs.," In order to investigate the long-term variability from the jet, we analyse the X-ray observations of this field in different epochs."913 We have ignored one of the Chandra observations (Obs ID., We have ignored one of the Chandra observations (Obs ID.914 6691) as its short exposure (~10 ks) does not provide sufficient photon statistic for his analysis., 6691) as its short exposure $\sim10$ ks) does not provide sufficient photon statistic for this analysis.915 The iulti-epoch spectral results are sunuuuixdiu Table 2.., The multi-epoch spectral results are summarized in Table \ref{jet_var}.916" Since the flux estimates are scusitively to the colum absorption. we fixed he vy, iu all observations at the value imferred Ton the analysis of he NAIALENewtou observation as it provides a superior photon statistic in the soft xud aud heuce put a better estimate on the nj."," Since the flux estimates are sensitively to the column absorption, we fixed the $n_{H}$ in all observations at the value inferred from the analysis of the XMM-Newton observation as it provides a superior photon statistic in the soft band and hence put a better estimate on the $n_{H}$ ."917 Also. for the sake comparison. we compute the flix in au cucreyv range of 0.5—10 keV for all cases.," Also, for the sake comparison, we compute the flux in an energy range of $0.5-10$ keV for all cases."918 We found that both observed aud absorptiou-corrected fluxes. as well as the photon iudex are consistent among the observations iu different epochs within lo uncertainties.," We found that both observed and absorption-corrected fluxes, as well as the photon index are consistent among the observations in different epochs within $1\sigma$ uncertainties."919 Therefore. we do uot find anv evidence of the long-term spectral aud flux variability.," Therefore, we do not find any evidence of the long-term spectral and flux variability."920 Apart from searching for the lone-terim variability. we have also investigated if there is anv noticeable flux variation within cach individual exposure.," Apart from searching for the long-term variability, we have also investigated if there is any noticeable flux variation within each individual exposure."921 By examining the lieht curves. we also do not fud any evidence for the variability within each observation window.," By examining the light curves, we also do not find any evidence for the variability within each observation window."922 hhas a spiu-down age of ~109 ves., has a spin-down age of $\sim10^{6}$ yrs.923 Tt has been speculated that the accelerating reeious can still be sustained iu the maguetospherces of some old pulsars (e.g. Zhang et al., It has been speculated that the accelerating regions can still be sustained in the magnetospheres of some old pulsars (e.g. Zhang et al.924 2001 Thi Becker 2007)., 2004; Hui Becker 2007).925 Tudeed. pulsed +raves with energies," Indeed, pulsed $\gamma-$rays with energies"926"The asteroils semimajor axis a is unchanged by the secular perturbations: thus. the changes in J reflect changes in the asteroid's eccentricity ο,","The asteroid's semimajor axis $a$ is unchanged by the secular perturbations; thus, the changes in $J$ reflect changes in the asteroid's eccentricity $e$."927 For asteroids with non-zero initial eccentricitv. (he phase dependence in equation (21)) means (hat secular resonance sweeping can potentially both excite and damp orbital ecceiricities.," For asteroids with non-zero initial eccentricity, the phase dependence in equation \ref{e:Jf}) ) means that secular resonance sweeping can potentially both excite and damp orbital eccentricities."928 We also note that the magnitude ol eccentricity change is inversely related to the speed of planet migration., We also note that the magnitude of eccentricity change is inversely related to the speed of planet migration.929 In linear secular theory (equation (1))). eecentricilv and inclination are decoupled. and therefore the effect of the sweeping 14 does not depend «o the inclination.," In linear secular theory (equation \ref{e:resHamiltonian}) )), eccentricity and inclination are decoupled, and therefore the effect of the sweeping $\nu_6$ does not depend on the inclination."930 However. as showed. the location of the 4; does depend on inclination. but the dependence is weak Lor (vpical inclinations of main belt objects.," However, as \cite{Williams:1981p532} showed, the location of the $\nu_6$ does depend on inclination, but the dependence is weak for typical inclinations of main belt objects."931 Nevertheless. (here are populations of main bell asteroids at high inclination (such as the Hungaria and Phocaea lamiies). and an analvsis of secular resonance sweeping (hat incorporates coupling between ecceiricióv and inclination would be valuable for understaucing the effects of planet migration o1 these populations: we leave this to a [future investigatio1.," Nevertheless, there are populations of main belt asteroids at high inclination (such as the Hungaria and Phocaea families), and an analysis of secular resonance sweeping that incorporates coupling between eccentricity and inclination would be valuable for understanding the effects of planet migration on these populations; we leave this to a future investigation."932 For small e. wecan use the ayyproximation. J7$y/ae?.," For small $e$, wecan use the approximation $J\simeq{\frac{1}{2}}\sqrt{a}e^2$."933"> Consideri.Big all possible values of cosze;€[—1.+1}. an asteroid wiLh initial eccentricity e; that is swept by the νο resonance will have a final eccentricity in the range 65,5, lo ομως. where and Equations (011) (33)) have the following implications:"," Considering all possible values of $\cos\varpi_i\in\{-1,+1\}$, an asteroid with initial eccentricity $e_i$ that is swept by the $\nu_6$ resonance will have a final eccentricity in the range $e_{min}$ to $e_{max}$ , where and Equations \ref{e:Jf}) \ref{e:deltaedef}) ) have the following implications:"934derivatives of the CALB power spectra with respect to the cosmological parameters.,derivatives of the CMB power spectra with respect to the cosmological parameters.935 Since numerical errors in these derivatives. can artificially break real parameter degeneracies. we have mace a detailed analysis of numerical errors in our computations and shown that they are small.," Since numerical errors in these derivatives can artificially break real parameter degeneracies, we have made a detailed analysis of numerical errors in our computations and shown that they are small."936 Vhe results of our. Fisher matrix. analysis are summarized in Tables 3 44 for an idealized two dimensional space of wy and wy and [or a more realistic space of six cosmological parameters., The results of our Fisher matrix analysis are summarized in Tables 3 4 for an idealized two dimensional space of $\omega_\Lambda$ and $\omega_K$ and for a more realistic space of six cosmological parameters.937 These show that gravitational lensing is detectable hy a Planck-tvpe experiment and must be taken into account when estimating the values of cosmological parameters., These show that gravitational lensing is detectable by a Planck-type experiment and must be taken into account when estimating the values of cosmological parameters.938 The effects of eravitational lensing are detectable in both the temperature ancl polarisation anisotropies., The effects of gravitational lensing are detectable in both the temperature and polarisation anisotropies.939 For some experimental parameters. the elfects of lensing are more asily detectable in the polarisation signal (because of the gaiwpness of the peaks and minima in the polarisation power spectrum) than in the temperature power spectrum. even rough the anisotropies are polarised at only the few percent level.," For some experimental parameters, the effects of lensing are more easily detectable in the polarisation signal (because of the sharpness of the peaks and minima in the polarisation power spectrum) than in the temperature power spectrum, even though the anisotropies are polarised at only the few percent level."940 Gravitational lensing of the CMD anisotropics breaks 10 geometrical degeneracy and so it should be possible to set limits on the values of wy and wy Crom observations of the CAIB anisotropies alone., Gravitational lensing of the CMB anisotropies breaks the geometrical degeneracy and so it should be possible to set limits on the values of $\omega_\Lambda$ and $\omega_K$ from observations of the CMB anisotropies alone.941 For example. from the 6 xwameter analysis in Table 4 for model la (a spatially [Lat A-clominatecl universe) it should be possible to set. Le limits of δων&0.03 and (wg8g0.003 using temperature. and xobarisation measurements and limits of δανzz0.04. and dey820.004 from observations of temperature anisotroples alone.," For example, from the 6 parameter analysis in Table 4 for model 1a (a spatially flat $\Lambda$ -dominated universe) it should be possible to set $1\sigma$ limits of $\delta \omega_\Lambda \approx 0.03$ and $\delta942\omega_K \approx 0.003$ using temperature and polarisation measurements and limits of $\delta \omega_\Lambda \approx 0.04$ and $\delta \omega_K \approx 0.004$ from observations of temperature anisotropies alone."943 This shows that for certain target models a Planck-ype experiment is capable of setting tight limits on the geometry of the Universe., This shows that for certain target models a Planck-type experiment is capable of setting tight limits on the geometry of the Universe.944 Furthermore. the possibility of detecting gravitational lensing acdcds to the scientific case for measuring CMD polarisation at high sensitivity and angular resolution.," Furthermore, the possibility of detecting gravitational lensing adds to the scientific case for measuring CMB polarisation at high sensitivity and angular resolution."945 The lensing constraints on wy and oy are sensitive to the normalisation of the present day mass IHuctuations and the growth rate of the matter Ποιαλος hence we find less stringent limits for a standard CDM model normalised to σκ({0)=0.52 (Tables 3 and 4)., The lensing constraints on $\omega_\Lambda$ and $\omega_K$ are sensitive to the normalisation of the present day mass fluctuations and the growth rate of the matter fluctuations hence we find less stringent limits for a standard CDM model normalised to $\sigma_8(t_0) = 0.52$ (Tables 3 and 4).946 Nevertheless. even in this case. a Planck-like experiment can set lo errors of wyzz0.06 and wy=0.01.," Nevertheless, even in this case, a Planck-like experiment can set $1 \sigma$ errors of $\omega_\Lambda \approx 0.06$ and $\omega_K = 0.01$."947 The ecometrical degeneracy can be broken hy applying constraints derived from more conventional astronomical techniques., The geometrical degeneracy can be broken by applying constraints derived from more conventional astronomical techniques.948 For example. accurate measurements of the," For example, accurate measurements of the"949scope of the original RIME publications. but various authors have been incorporating them into the RIME since.,"scope of the original RIME publications, but various authors have been incorporating them into the RIME since."950 ? and ? provide an in-depth review of these developments. especially as pertaining to imaging and deconvolution.," \citet{Rau:DDEs} and \citet{SB:calibration-low-freq} provide an in-depth review of these developments, especially as pertaining to imaging and deconvolution."951 The above authors have developed a description of DDEs using the 4+x4 Mueller matrix and coherency vector formalism of the first RIME paper by ?.., The above authors have developed a description of DDEs using the $4\times4$ Mueller matrix and coherency vector formalism of the first RIME paper by \citet{ME1}.952 The 4x formalism has also been included in the 2nd edition of ?.Sect.4.8.., The $4\times4$ formalism has also been included in the 2nd edition of \citet*[Sect.~4.8]{tms}.953 In the meantime. ? has recast the RIME using only 2x matrices.," In the meantime, \citet{ME4} has recast the RIME using only $2\times2$ matrices."954 The 2x form of the RIME has far more intuitive and is far better suited for describing calibration problems. yet has been somewhat unjustly ignored in the literature.," The $2\times2$ form of the RIME has far more intuitive and is far better suited for describing calibration problems, yet has been somewhat unjustly ignored in the literature."955 Addressing this perceived injustice is vet another aim of these papers. (, Addressing this perceived injustice is yet another aim of these papers. (956Section 6 describes the 4« vs. 2x formalisms in more detail.),Section \ref{sec:formulations} describes the $4\times4$ vs. $2\times2$ formalisms in more detail.)957 Last but certainly not least. Paper HI (?) shows an application of these concepts to real data.," Last but certainly not least, Paper III \citep{RRIME3} shows an application of these concepts to real data."958 It presents a record dynamie range (over 1.6 million) calibration of a WSRT observation. including calibration of DDEs.," It presents a record dynamic range (over 1.6 million) calibration of a WSRT observation, including calibration of DDEs."959 It then analyzes the results of this calibration. shows how the calibration solutions can be used to improve sky models. and demonstrates a rather important implication for the calibratability of future telescopes.," It then analyzes the results of this calibration, shows how the calibration solutions can be used to improve sky models, and demonstrates a rather important implication for the calibratability of future telescopes."960 Like many erucial insights. the RIME seems perfectly obvious and simple in hindsight.," Like many crucial insights, the RIME seems perfectly obvious and simple in hindsight."961 In fact. it can be almost trivially derived from basic considerations of signal propagation. as shown by ?.," In fact, it can be almost trivially derived from basic considerations of signal propagation, as shown by \citet{ME1}."962 In this paper. [ will essentially repeat and elaborate on this derivation.," In this paper, I will essentially repeat and elaborate on this derivation."963 This is not original work. but there are several good reasons for reiterating the full argument. as opposed to simply referring back to the original RIME papers.," This is not original work, but there are several good reasons for reiterating the full argument, as opposed to simply referring back to the original RIME papers."964 Firstly. some aspects of the basic RIME noted here are not covered by the original papers at all.," Firstly, some aspects of the basic RIME noted here are not covered by the original papers at all."965 These are the commutation considerations of Sect. 1.6..," These are the commutation considerations of Sect. \ref{sec:taxonomy},"966 the fact that Jones matrices and coherency matrices behave differently under coordinate transforms (for which reason | even propose a different typographical convention for them). as discussed i Sect. 6.3..," the fact that Jones matrices and coherency matrices behave differently under coordinate transforms (for which reason I even propose a different typographical convention for them), as discussed in Sect. \ref{sec:circular},"967 and the 1/2-vs.-] controversy of Sect. 8.1.., and the 1/2-vs.-1 controversy of Sect. \ref{sec:factor2}.968 The there’s the fact that the 2x version of the formalism proposec by ? and and employed here provides for a much clearer and more intuitive picture that the original 4+x derivation (see Sect., Then there's the fact that the $2\times2$ version of the formalism proposed by \citet{ME4} and and employed here provides for a much clearer and more intuitive picture that the original $4\times4$ derivation (see Sect.969 6.1. for a discussion). and so deserves far more exposure in the literature than the sole Hamaker paper to date.," \ref{sec:mueller} for a discussion), and so deserves far more exposure in the literature than the sole Hamaker paper to date."970 Finally. | want to establish some typographical conventions anc mathematical nomenclature. and lay the groundwork for my own extensions of the formalism. which start at Sect. 3..," Finally, I want to establish some typographical conventions and mathematical nomenclature, and lay the groundwork for my own extensions of the formalism, which start at Sect. \ref{sec:full-sky-rime}. ."971 This seemed sufficient reason to give a complete derivation of the RIME from scratch., This seemed sufficient reason to give a complete derivation of the RIME from scratch.972 In Sects., In Sects.973 2 and 3.. I extend the 2x formalism into the image-plane domain. show how the van Cittert-Zernike (VCZ) theorem naturally follows from the RIME. and sketch the problem of DDEs.," \ref{sec:me-multiple-sources} and \ref{sec:full-sky-rime}, I extend the $2\times2$ formalism into the image-plane domain, show how the van Cittert-Zernike (VCZ) theorem naturally follows from the RIME, and sketch the problem of DDEs."974 Section 4. elaborates someRIME-based closure relationships. Sect.," Section \ref{sec:closures} elaborates someRIME-based closure relationships, Sect."975 5. then examines some important limitations and boundaries of the RIME formalism. and Sect.," \ref{sec:rime-limitations} then examines some important limitations and boundaries of the RIME formalism, and Sect."976 6 looks at alternative formulations of the RIME., \ref{sec:formulations} looks at alternative formulations of the RIME.977 Finally. Sect.," Finally, Sect."978 7 attempts to clear up some errors and controversies surrounding the formalism., \ref{sec:controversies} attempts to clear up some errors and controversies surrounding the formalism.979 Consider a single source of quasi-monochromatic signal (1:89. à sky consisting of a single point source)., Consider a single source of quasi-monochromatic signal (i.e. a sky consisting of a single point source).980 The signal at a fixed point in space and time can be then be described by the complex vector e., The signal at a fixed point in space and time can be then be described by the complex vector $\vec e$.981 Let us pick an orthonormal xvz coordinate system. with z along the direction of propagation (1.9. from antenna to source).," Let us pick an orthonormal $xyz$ coordinate system, with $z$ along the direction of propagation (i.e. from antenna to source)."982 In such a system. e can be represented by a column vector of 2 complex numbers: Our fundamental assumption isJinearity: all transformations along the signal path are linear wirt.," In such a system, $\vec e$ can be represented by a column vector of 2 complex numbers: Our fundamental assumption is: all transformations along the signal path are linear w.r.t."983 e., $\vec e$ .984 Basic linear algebra tells us that all linear transformations of à 2-vector can be represented (in any given coordinate system) by à matrix multiplication: where J is a 2x complex matrix known as the matrix. (?).., Basic linear algebra tells us that all linear transformations of a 2-vector can be represented (in any given coordinate system) by a matrix multiplication: where $\jones{J}{}$ is a $2\times2$ complex matrix known as the matrix \citep{jones}.985 Obviously. multiple effects along the signal propagation path correspond to repeated matrix multiplications. forming what I call achain. We can regard multiple effects separately and write out Jones chains. or we can collapse them all into a single cumulative Jones matrix as convenient: The order of terms in a Jones chain corresponds to the physical order in which the effects occur along the signal path.," Obviously, multiple effects along the signal propagation path correspond to repeated matrix multiplications, forming what I call a. We can regard multiple effects separately and write out Jones chains, or we can collapse them all into a single cumulative Jones matrix as convenient: The order of terms in a Jones chain corresponds to the physical order in which the effects occur along the signal path."986 Since matrix multiplication does not (in general) commute. we must be careful to preserve this order in our equations.," Since matrix multiplication does not (in general) commute, we must be careful to preserve this order in our equations."987 Now. the signal hits our antenna and ts ultimately converted into complex voltages by the antenna feeds.," Now, the signal hits our antenna and is ultimately converted into complex voltages by the antenna feeds."988" Let us further assume that we have two feeds a and b (for example. two linear dipoles. or left/right circular feeds). and that the voltages v, and vp are linear w.r.t. e."," Let us further assume that we have two feeds $a$ and $b$ (for example, two linear dipoles, or left/right circular feeds), and that the voltages $v_a$ and $v_b$ are linear w.r.t. $\vec e$."989 We can formally treat the two voltages as a voltage vector v. analogous to e.," We can formally treat the two voltages as a voltage vector $\vec v$, analogous to $\vec e$."990" Their linear relationship ts yet another matrix multiplication: Equation (2)) can be thought of as representing the fundamental linear relationship between the voltage vector v as measured by the antenna feeds. and the ""original"" signal vector e at some arbitrarily distant point. with Jbeing the cumulative product of all propagation effects along the signal path (including electronic effects in the antenna/feed itself)."," Their linear relationship is yet another matrix multiplication: Equation \ref{eq:e-voltage}) ) can be thought of as representing the fundamental linear relationship between the voltage vector $\vec v$ as measured by the antenna feeds, and the “original” signal vector $\vec e$ at some arbitrarily distant point, with $\jones{J}{}$being the cumulative product of all propagation effects along the signal path (including electronic effects in the antenna/feed itself)."991 I shall call refer to this J as the matrix. as distinct from the individual Jones terms in aJones chain.," I shall call refer to this $\jones{J}{}$ as the matrix, as distinct from the individual Jones terms in aJones chain."992if we fit from 0 to 30 r2.,if we fit from $0$ to $30$ $r_{-2}$.993 Such a high degree of accuracy indicates that if the 2D distribution is indeed a projected Einasto protile. the 3D parameters can be recovered very well even from a limited radial range of observations.," Such a high degree of accuracy indicates that if the 2D distribution is indeed a projected Einasto profile, the 3D parameters can be recovered very well even from a limited radial range of observations."994 We note that. for the entire range of 0.1x(a=i)| the fits always converged for an intial guess of à<{η ἂν νο(rie ro» and p2 i= he range (0.1 to 4) p/7.," We note that, for the entire range of $0.1 \leq (\alpha=\frac{1}{n}) \leq 1$ the fits always converged for an intial guess of $\alpha < true$ $\alpha$ , $r_s > true$ $ r_{-2}$ and $\rho_{-2}$ in the range $0.1$ to $4$ ) $\rho^{true}_{-2}$."995 An inital guess of very low à0.05 and a guess for kr.»roo for the type of object (galaxy or cluster) being considered can be a reasonable starting value for the fit to converge., An inital guess of very low $\alpha \sim 0.05$ and a guess for $r_{-2} \sim r_{200}$ for the type of object (galaxy or cluster) being considered can be a reasonable starting value for the fit to converge.996 We also did not encounter any local minima., We also did not encounter any local minima.997 ie. if the fit converges. it always converged to the true set ofta.r s.p ο).," i.e. if the fit converges, it always converged to the true set of $\alpha$, $r_{-2}$, $\rho_{-2}$ )."998 Non-parameteric estimates of density profiles. in N-body simulations (NavO4.MO6). favour Einasto-like profiles. since they provide better fits than the two-parameter NFW and Moore profiles.," Non-parameteric estimates of density profiles in N-body simulations (Nav04,M06) favour Einasto-like profiles, since they provide better fits than the two-parameter NFW and Moore profiles."999 Merrittetal.(2006) have also shown that a de-projected Sersic profile tits the 3D halo mass distribution almost as well as the Einasto profile. and a Sersic profile provides good fits to non-parametric estimates of surface mass densities (MOS) of the Nav04 N-body haloes.," \cite{M06} have also shown that a de-projected Sersic profile fits the 3D halo mass distribution almost as well as the Einasto profile, and a Sersic profile provides good fits to non-parametric estimates of surface mass densities (M05) of the Nav04 N-body haloes."1000 We have observed that fits with a Sersic function (3) to a numerically projected Einasto profile (Cv ) are sensitive to whether one fits using linear density Xs (errors increasing for large R) or log density /n(YX4) (errors increasing for small R) yielding widely varying results., We have observed that fits with a Sersic function $\Sigma_S$ ) to a numerically projected Einasto profile $\Sigma_N$ ) are sensitive to whether one fits using linear density $\Sigma_S$ (errors increasing for large R) or log density $ln(\Sigma_S)$ (errors increasing for small R) yielding widely varying results.1001 Consequently. the Sersic protile does not give an adequate description of the projected Einasto profile.," Consequently, the Sersic profile does not give an adequate description of the projected Einasto profile."1002 Sersic profile fits to the surface mass density of N-body haloes (MOS). whose 3D spatial densities are well fit by Einasto profiles with 0.1200.22. have been obtained from the limited radial range Of boone to rogo.," Sersic profile fits to the surface mass density of N-body haloes (M05), whose 3D spatial densities are well fit by Einasto profiles with $0.12$$\leq$$\alpha$$\leq$$0.22$, have been obtained from the limited radial range of $r_{conv}$ to $r_{200}$."1003 For the haloes in MOS and NavOA. this range is generally less than two decades in radius.," For the haloes in M05 and Nav04, this range is generally less than two decades in radius."1004 Hence. if the 3D distribution is indeed Einasto-like. interpreting structural properties from fits with a Sersic profile. especially m in as the shape parameter. Js(0) as the central density and /?z as the half-mass radius. can be misleading.," Hence, if the 3D distribution is indeed Einasto-like, interpreting structural properties from fits with a Sersic profile, especially $m$ in as the shape parameter, $\Sigma_S(0)$ as the central density and $R_E$ as the half-mass radius, can be misleading."1005 In this paper. we have provided an analytical approximation to the projected surface mass density of Einasto-like 3D density distributions.," In this paper, we have provided an analytical approximation to the projected surface mass density of Einasto-like 3D density distributions."1006 The fit errors are well contained to <2'% for the projected radial range O@R=(1930) +» equivalent to (3Ὁους and shape parameter. 1:nx:10. or Olea.," The fit errors are well contained to $<$$2\%$ for the projected radial range $0$$\leq$$R$$\leq (10-30)$ $r_{-2}$ equivalent to $(3-5)$$r_{200}$ and shape parameter, $1$$\leq$$n$$\leq$$10$, or $0.1$$\leq$$\alpha$$\leq$$1$."1007 This model can therefore be used both as a fitting function for 2D observations and also to extract the 3D parameters of Einasto-like profiles., This model can therefore be used both as a fitting function for 2D observations and also to extract the 3D parameters of Einasto-like profiles.1008 Since Mp fits a projected Einasto profile in a wide radial range. it can be used for fitting strong and weak lensing observations in systems whose total 3D density distribution is believed to be Einasto-like.," Since $\Sigma_E$ fits a projected Einasto profile in a wide radial range, it can be used for fitting strong and weak lensing observations in systems whose total 3D density distribution is believed to be Einasto-like."1009 One can also numerically integrate to get reliable estimates of the mass enclosed., One can also numerically integrate to get reliable estimates of the mass enclosed.1010 Finally. we note that the form similarity of and(1.2). Le. fitting functions that describe the 3D mass density of dark matter haloes and the 2D light distributions of galaxies. respectively. could be largely coincidental and should be used with caution when drawing conclusions about the similarity of dynamical evolution that lead to the formation of the stellar components of ellipticals and dark matter haloes.," Finally, we note that the form similarity of and, i.e. fitting functions that describe the 3D mass density of dark matter haloes and the 2D light distributions of galaxies, respectively, could be largely coincidental and should be used with caution when drawing conclusions about the similarity of dynamical evolution that lead to the formation of the stellar components of ellipticals and dark matter haloes."1011 BKD and LLRW would like to acknowledge thesupport of NASA Astrophysics Theory Grant NNX07AGSG6G. We thank Jaan Einasto and Urmas Haud for pointing us to the original literature on the Einasto profile., BKD and LLRW would like to acknowledge thesupport of NASA Astrophysics Theory Grant NNX07AG86G. We thank Jaan Einasto and Urmas Haud for pointing us to the original literature on the Einasto profile.1012spin in Figure 4.,spin in Figure 4.1013" The X-ray [ας therefore increases with e, because O, at the ISCO increases.", The X-ray flux therefore increases with $a_*$ because $\Theta_e$ at the ISCO increases.1014 The dependence on 7;/7. is mainly due to synchirotvon sell-absorption. which is strongest al high inclination.," The dependence on $\Trat$ is mainly due to synchrotron self-absorption, which is strongest at high inclination."1015 For example. because the 7=35deg. 7/7.=10 model is optically thick al 230GIIz the emission is produced in a svuchrotron photosphere well outside rico.," For example, because the $i =101685\deg$, $\Trat = 10$ model is optically thick at $230\GHz$ the emission is produced in a synchrotron photosphere well outside $\risco$."1017" The ivpical radius of the svnchrotron photosphere ranges between 15. C/c for low spin models (a,—0.5.0.75) and 8 GAL/e? [or high spin models (e,>0.75)."," The typical radius of the synchrotron photosphere ranges between 15 $\Rg$ for low spin models $a_*=0.5,0.75$ ) and 8 $\Rg$ for high spin models $a_*> 0.75$ )."1018 The 230GlIz flix can then be produced only with large M: as M increases the optically thin flux in the NI. increases due to increasing density. and field strength., The $230\GHz$ flux can then be produced only with large $\munit$; as $\munit$ increases the optically thin flux in the NIR increases due to increasing density and field strength.1019 The scattered spectrum also depends on T;/T. since the energy boost per scattering is ~1607x1/(O3/T. ., The scattered spectrum also depends on $\Trat$ since the energy boost per scattering is $\sim 16\Theta_e^2 \propto 1/(\Trat)^2$ .1020 The inclination dependence is. interestingly. a relativistic effect.," The inclination dependence is, interestingly, a relativistic effect."1021 Mis nearly independent of £ Gt varies bv ~1056. except for T;/T;=10. which due to optical depth effects has much larger variation). so models with different inclination are nearly identical.," $\munit$ is nearly independent of $i$ (it varies by $\sim 10\%$, except for $\Trat = 10$, which due to optical depth effects has much larger variation), so models with different inclination are nearly identical."1022 Nevertheless the [αν varies dramatically with 7. increasing bv almost 2 orders of magnitude [rom 7=5deg to i— 85deg.," Nevertheless the X-ray flux varies dramatically with $i$, increasing by almost 2 orders of magnitude from $i = 5\deg$ to $i = 85\deg$ ."1023 This occurs because Compton scattered photons are beamecl forward parallel to the orbital motion of the disk gas., This occurs because Compton scattered photons are beamed forward parallel to the orbital motion of the disk gas.1024 The variation of mun flux with / is due to sell-absorption., The variation of mm flux with $i$ is due to self-absorption.1025 The mm [lux rellects the temperature and size of the svnehrotron photosphere., The mm flux reflects the temperature and size of the synchrotron photosphere.1026 At lower ; the visible svnchrotron photosphere is hotter (han at high /., At lower $i$ the visible synchrotron photosphere is hotter than at high $i$.1027 There is an additional constraint. due to Faraday. rotation. measurements. but. (his constraint is qualitativelv different because we do not directly caleulate Faraday rotation in our model.," There is an additional constraint due to Faraday rotation measurements, but this constraint is qualitatively different because we do not directly calculate Faraday rotation in our model."1028 Instead we adopt the constraints on AZ which are inferred. via a separate model. from the Faraday. rotation data (Boweretal.2005... Marroneetal. 2006)).," Instead we adopt the constraints on $\mdot$ which are inferred, via a separate model, from the Faraday rotation data \citealt{bower:2005}, \citealt{marrone:2006a}) )."1029 M increases. in a nonlinear way. will increasing Zi;/T&..," $\dot{M}$ increases, in a nonlinear way, with increasing $\Trat$."1030 For Ti/[1.=Lal>6x10MLvr.ft.," For $\Trat = 1, \dot{M} > 6 \times 10^{-10}1031\MSUNYR$."1032" For T/T.=10.Mc4x107M,vr."," For $\Trat = 10, \dot{M} < 4 \times 10^{-7} \MSUNYR$."1033| All these values are consistent with the Faraday rotation constraints. although the highest Af. T;/T;=10. models are only margmally consistent.," All these values are consistent with the Faraday rotation constraints, although the highest $\dot{M}$, $\Trat = 10$, models are only marginally consistent."1034 There are a lew other general trends worth mentioning., There are a few other general trends worth mentioning.1035 Ii all models the average optical depth drops below 1 at 0.4 to L.3mm., In all models the average optical depth drops below $1$ at $0.4$ to $1.3\mm$.1036" For />45deg and high BIL spins a,>0.75 the emission in NIR band (2 jm) is formed by the direct svnchrotron emission while the 2—8keV enission results [rom a first-order scattering.", For $i>45 \deg$ and high BH spins $a_* > 0.75$ the emission in NIR band (2 ${\rm \mu m}$ ) is formed by the direct synchrotron emission while the $2-8\keV$ emission results from a first-order scattering.1037" For low BIL spins e,<0.75 (he emission in NIB. is due to first-order Compton scatterings aud (heX-ray is second-order scattering.", For low BH spins $a_* \le 0.75$ the emission in NIR is due to first-order Compton scatterings and theX-ray is second-order scattering.1038 ForT/T.=10 and ¢=5deg independently of the DII spin the NIE. emission is formed by a first-order Compton scatterings and X-ravs- by second-order scatterings., For$\Trat=10$ and $i=5\deg$ independently of the BH spin the NIR emission is formed by a first-order Compton scatterings and X-rays- by second-order scatterings.1039compared to the uniform-Dypy case.,compared to the $\Gamma_{\rm HeII}$ case.1040 However. because he forest is seusitive to πω~1. Egi fluctuations are less of a concern for studying ircionization with the forest compared to with the LLwa forest (which is sensitive to yap<1).," However, because the forest is sensitive to $x_{\rm HeII} \sim 1$, $\Gamma_{\rm HeII}$ fluctuations are less of a concern for studying reionization with the forest compared to with the $\alpha$ forest (which is sensitive to $x_{\rm HeII} \ll 1$ )."1041 The top subpanels in Figures 1 and 2. show the value of yap that results from this algorithm. where Iubble's aw is used to relate position to velocity.," The top subpanels in Figures \ref{fig:HeIforest_z4}~ and \ref{fig:HeIforest_z3} show the value of $x_{\rm HeII}$ that results from this algorithm, where Hubble's law is used to relate position to velocity."1042 The blue curve is LsΠωί and the black curve is Ay., The blue curve is $4 \times x_{\rm HeII}$ and the black curve is $\Delta_b$.1043 The value of eia can be quite large for the weak backerouuds that are assumed., The value of $x_{\rm HeII}$ can be quite large for the weak backgrounds that are assumed.1044" For Ay,1. T=10! K. aud Τα=5«LO16 1 (1«1019 1j η equals 0.06: (0.25) at >=3."," For $\Delta_b = 1$, $T= 10^4~$ K, and $\Gamma_{\rm HeII} = 5 \times 10^{-16}~$ $^{-1}$ $1 \times 10^{-16}~$ $^{-1}$ ), $ x_{\rm HeII}$ equals $0.06$ $0.25$ ) at $z= 3$."1045 This πανο becomes 0.11 (0.39) at 2=Ι., This number becomes $0.11$ $0.39$ ) at $z=4$.1046 The bottom) subpanels in cach larger panel icere Figures d and 20 zoom in ou the residual transiissio in the Τα forest (absorption at waveleugths of 301]1|:] ÀJ.," The bottom subpanels in each larger panel in Figures \ref{fig:HeIforest_z4}~ and \ref{fig:HeIforest_z3} zoom in on the residual transmission in the $\alpha$ forest (absorption at wavelengths of $304 \, [1+z] \, $ )."1047 Note that in all of the cases there is niminial transmission in this forest because the LLwo transition saturates for πω~10! ," Note that in all of the cases there is minimal transmission in this forest because the $\alpha$ transition saturates for $x_{\rm HeII} \sim 10^{-3} \, \Delta_b^{-1}$."1048"There is only a detectable amount of transmission A,im the case with Pur2581019 1! and +=3 (aniddle panel. Fie. 2))."," There is only a detectable amount of transmission in the case with $\Gamma_{\rm HeII} = 5\times 10^{-16}~$ $^{-1}$ and $z=3$ (middle panel, Fig. \ref{fig:HeIforest_z3}) )."1049 Because irelonization was patch. regions of transmission iu the Livan forest can occur even if reijoulzation was nof complete.," Because reionization was patchy, regions of transmission in the $\alpha$ forest can occur even if reionization was not complete."1050 Iu contrast. aabsorptiou has the poteutial to reveal whether those opaque neighboring regions were in fact iregious because it is seusitive to eppo1.," In contrast, absorption has the potential to reveal whether those opaque neighboring regions were in fact regions because it is sensitive to $x_{\rm HeII} \sim 1$."1051 The middle subpanuels in Figures d. and 2. show the transiuission in the Livni forest (blue curves) aud hala fforest(blackeurces), The middle subpanels in Figures \ref{fig:HeIforest_z4}~ and \ref{fig:HeIforest_z3} show the transmission in the $\alpha$ forest (blue curves) and $584~$ forest (black curves).1052 Dhesepanelsdemonstratethatthetrais aand le fforestsishighlyeorrclated, These panels demonstrate that the transmission in the and forests is highly correlated.1053 Thelle aabsorbersthatcorrespondtothedcepest {νο forest lines are the most visible. aud the weaker ]lines (systems that are not dense enough to selfshicld) disappear in the cases in which the helium is mostly doubly ionized.," The absorbers that correspond to the deepest $\alpha$ forest lines are the most visible, and the weaker lines (systems that are not dense enough to self-shield) disappear in the cases in which the helium is mostly doubly ionized."1054 The third subpaucl down in cach larger pancl iu Figures d aud 2. zooms in on the the Balto ttransmission(solidblackeurcves)," The third subpanel down in each larger panel in Figures \ref{fig:HeIforest_z4}~ and \ref{fig:HeIforest_z3} zooms in on the the $584 \, $ transmission (solid black curves)."1055DT hesesubpanelsalsoinelude ion πμ softheobservcedspectriinatthesewavelengthsti.c.. Sala pplus foreground Ίσα absorptiou: solid blue).," These subpanels also include mock realizations of the observed spectrum at these wavelengths (i.e., $584 \, $ plus foreground $\alpha$ absorption; solid blue)."1056 Each panel uses a different skewer through the ICAL to calculate this foreground absorption., Each panel uses a different skewer through the IGM to calculate this foreground absorption.1057 The highlighted regious in these pancls represcut the locations with Typτοις2723 for absorption coeval to that of theL.," The highlighted regions in these panels represent the locations with $\tau_{\rm HI, 1216} > 3$ for absorption coeval to that of the."1058 Outside of the highlighted reeious. the amount of aabsorption is substantially different between the three cases In cach figure.," Outside of the highlighted regions, the amount of absorption is substantially different between the three cases in each figure."1059 Trace amouuts of absorption remain in essentially just the yer=1 case., Trace amounts of absorption remain in essentially just the $x_{\rm HeII} = 1$ case.1060 A detection of aabsorptiou im these regions would indicate that irelonization was occurring., A detection of absorption in these regions would indicate that reionization was occurring.1061 The next section quautifies the prospects for detecting this absorption., The next section quantifies the prospects for detecting this absorption.1062 The top paucl in Figure 3.? plots the effective optical depth (defined as z4=log7. where 7 is the average transmission).," The top panel in Figure \ref{fig:abs} plots the effective optical depth (defined as $\tau_{\rm eff} = - \log{\bar{{\cal T}}}$, where $\bar{{\cal T}}$ is the average transmission)."1063 This quantity is plotted for both the Sala forestandthe forcgroundLya forest., This quantity is plotted for both the $584~$ forest and the foreground $\alpha$ forest.1064 The Sala οσαπο τω is shown for the model with μι=1 (thick dashed black curve} aud the model with Pia= 3 (thick solid red curve}., The $584~$ value of $\tau_{\rm eff}$ is shown for the model with ${x}_{\rm HeII} = 1$ (thick dashed black curve) and the model with $\Gamma_{\rm HeII} = 10^{-16}~$ $^{-1}$ (thick solid red curve).1065 The value of τμ is conrparable in these two models aud comparable to that of the foreground. Lya absorption (thick ereen dashed curve)., The value of $\tau_{\rm eff}$ is comparable in these two models and comparable to that of the foreground $\alpha$ absorption (thick green dashed curve).1066 Yet. map ds 3 times larger at 2=3 in the supoLb omndel compared to the Τη=10ts | uodel. which could potentially allow these models to )o distinguished.," Yet, $\tau_{\rm eff}$ is $3$ times larger at $z=3$ in the ${x}_{\rm HeII} =1$ model compared to the $\Gamma_{\rm HeII} = 10^{-16}~$ $^{-1}$ model, which could potentially allow these models to be distinguished."1067 Also. thevalue of ma in the case with Ting=ον1016-2 l (not shown in Fig. 3))," Also, thevalue of $\tau_{\rm eff}$ in the case with $\Gamma_{\rm HeII} = 5\times 10^{-16}~$ $^{-1}$ (not shown in Fig. \ref{fig:abs}) )"1068 is a factor of 10 simaller at 2=3 than the πω=1 case., is a factor of $10$ smaller at $z=3$ than the ${x}_{\rm HeII} =1$ case.1069 Tf Pg fluctuates spatially such with Ty>5«1019 8? (approximately the mimi value derived frou Live analyses at z23: McQuinn20093). the signal will vc even smaller than in this case.," If $\Gamma_{\rm HeII}$ fluctuates spatially such with $\Gamma_{\rm HeII} > 5\times 10^{-16}~$ $^{-1}$ (approximately the minimum value derived from $\alpha$ analyses at $z\approx 3$; \citealt{mcquinn09b}) ), the signal will be even smaller than in this case."1070 The thin curves that represcut hala aabsorptioninthetoppanclin Figure 3arethesamecasthethick. οσομέ! an the coeval να forest (and the thin curves for the model with Pii=101068 1 are multiplied by 10).," The thin curves that represent $584~$ absorption in the top panel in Figure \ref{fig:abs} are the same as the thick, except regions are masked with $\tau_{\rm HI, 1216} >3$ in the coeval $\alpha$ forest (and the thin curves for the model with $\Gamma_{\rm HeII} = 10^{-16}~$ $^{-1}$ are multiplied by $10$ )."1071 This figure also demoustrates that the trausmission is mach different between the Πω=Land Egi=loτον 3 models if deuser regions that have Tupisió2D are masked.," This figure also demonstrates that the transmission is much different between the $x_{\rm HeII} = 1$ and $\Gamma_{\rm HeII} = 10^{-16}~$ $^{-1}$ models if denser regions that have $\tau_{\rm HI, 1216} >3$ are masked."1072 We have shown that the amount of mabsooptith Ab υπΙαν differcut between the case where the wwas ionized by a weak background aud the case l., We have shown that the amount of absorption is substantially different between the case where the was ionized by a weak background and the case $x_{\rm HeII} = 1$ .1073 There is also the exciting possibility that the wwas recombining after being ionized by an carly generation of sources (Venkatesanctal.2003) or after a rearby quasar had turned off., There is also the exciting possibility that the was recombining after being ionized by an early generation of sources \citep{venkatesan03} or after a nearby quasar had turned off.1074 Iu this case. the fraction of a gas parcel μι=Loexpt Δι). where Af is the time since the t--ionizing background urned off. free=(tann2) land olia is the Case D recombination coefficient.," In this case, the fraction of a gas parcel is $x_{\rm HeII} = 1 - \exp(-\Delta t/t_{\rm rec})$ , where $\Delta t$ is the time since the -ionizing background turned off, $t_{\rm rec} = (\alpha_{\rm HeII}^{\rm B} \, n_e)^{-1}$, and $\alpha_{\rm HeII}^{\rm B}$ is the Case B recombination coefficient."1075 ΔΙ=3 aud T=20.000 Is. fag is roughly equal to 0.8 of the IIubble time at the ," At $z = 3$ and $T = 20,000~$ K, $t_{\rm rec}$ is roughly equal to $0.8$ of the Hubble time at the mean density."1076Thos. the lielitan in uuderdeuse regions at 2—3 would iive remained doubly ionized for Af2II(:) after the vackeround turned off.," Thus, the helium in underdense regions at $z\sim 3$ would have remained doubly ionized for $\Delta t \gtrsim H(z)^{-1}$ after the background turned off."1077 The density dependence of -eypery is different in this case than im the other cases we have considered. such that there is the possibility that it also can be distinguished using aabsorptiou.," The density dependence of $x_{\rm HeII}$ is different in this case than in the other cases we have considered, such that there is the possibility that it also can be distinguished using absorption."1078 Ilowever. it takes an extremely weak backeround with Purcalapom12410lt Ass! to counteract recombinations in a region.," However, it takes an extremely weak background with $\Gamma_{\rm HeII} > \alpha_{\rm HeII}^{\rm B} \, n_e \approx 1.2 \times10^{-17}~\Delta_b~$ $^{-1}$ to counteract recombinations in a region."1079 McQuinnetal. found in simulations that such a background developed soon after ircbonization bw quasars was underway., \citet{mcquinn09} found in simulations that such a background developed soon after reionization by quasars was underway.1080 Therefore. we consider the recombining scenario to be less Likely thui the others at 3X: L but nevertheless a tantalizingpossibility.," Therefore, we consider the recombining scenario to be less likely than the others at $3 \lesssim z \lesssim 4$ , but nevertheless a tantalizingpossibility."1081binary svstenis or are they more simular to co-moving eroups. despite their age?,"binary systems or are they more similar to co-moving groups, despite their age?"1082 We need a laree study of sdB proper motions usine archival and possibly new data., We need a large study of sdB proper motions using archival and possibly new data.1083 With the release of the UCACS catalogue. which has leer sky coverage aud ieher precision proper motions (at least in some cases) sole progress is already beime made in this direction.," With the release of the UCAC3 catalogue, which has larger sky coverage and higher precision proper motions (at least in some cases) some progress is already being made in this direction."1084 The rise of survey telescopes (e.g. SkvMapper) may uake it more and amore straghttforward to obtain accurate proper motions in the comine decade., The rise of survey telescopes (e.g. SkyMapper) may make it more and more straightforward to obtain accurate proper motions in the coming decade.1085 Ou op of these surveys. the GAIA space mission will deliver precise astrometry (to ~0.3 τας) of stars down o Vzz220nunag.," On top of these surveys, the GAIA space mission will deliver precise astrometry (to $\sim$ mas) of stars down to $\approx$ mag."1086 Since space velocities are in three dimensions. it will also be iuportaut to obtain relatively xecise radial velocities. allowing the status of the candidates presented here to be confined.," Since space velocities are in three dimensions, it will also be important to obtain relatively precise radial velocities, allowing the status of the candidates presented here to be confirmed."1087 We plan to carry out a detailed spectroscopic study of the companion stars prescuted here. as well as several other caucidates found in the Sloan Digital Sky Survey database.," We plan to carry out a detailed spectroscopic study of the companion stars presented here, as well as several other candidates found in the Sloan Digital Sky Survey database."1088 We will use spectra to determine plotometric parallaxes of the late I& and AL dwarf companions by iieasurine TiO-. Call aud CaOT-hand spectral iudices using the prescription of Cruz&Reid(2002) aud metallicities using the calibration of Woolf&Waller-stein (2006).," We will use spectra to determine photometric parallaxes of the late K and M dwarf companions by measuring TiO-, CaH- and CaOH-band spectral indices using the prescription of \citet{CR2002} and metallicities using the calibration of \citet{WW2006}."1089. We also plan to observe hot subdwarfs with uo available spectroscopy. and then measure their effective. temperatures. surface eravities and helm abuudances using standard line-profile fitting (e.g.Liskeretal.2005:Stroer 2007).," We also plan to observe hot subdwarfs with no available spectroscopy, and then measure their effective temperatures, surface gravities and helium abundances using standard line-profile fitting \citep[e.g. ][]{Lisker2005, Stroeer2007}."1090. There are several late C-fearly I-tvpe companions az1none our sample (uot discussed here) and we will initally use the enipirieal relatiouships of Ivezicctal. (2008).. before eventually obtainiug high resolution spectra aud conducting amore detailed analysis of their xwanmieters.," There are several late G-/early K-type companions among our sample (not discussed here) and we will initally use the empirical relationships of \citet{Ivezic2008}, before eventually obtaining high resolution spectra and conducting a more detailed analysis of their parameters."1091 The successtul completion ofthis project will dramaticallylg increase the uunmber of hot subdwarfs with accurate nass determinationsimodels., The successful completion of this project will dramatically increase the number of hot subdwarfs with accurate mass determinations.1092. We will also eternune the first accurate lasses or ΠΠΠα Πλ. which is a class of stars hat cannot be investigated using other methods. such as stellar oscillations aud asteroseismniolosv.," We will also determine the first accurate masses for helium-rich subdwarfs, which is a class of stars that cannot be investigated using other methods, such as stellar oscillations and asteroseismology."1093 The nasses will allow the first robust tests of the proposed orlation chaunels for some of these objects (6.8. Justhiin. these proceedings).," The masses will allow the first robust tests of the proposed formation channels for some of these objects (e.g. Justham, these proceedings)."1094was too small to be reconstructed.,was too small to be reconstructed.1095 The photometric lightcurves for sets | to 3 are shown in the right-hand side of Figure |.., The photometric lightcurves for sets 1 to 3 are shown in the right-hand side of Figure \ref{set1t3}.1096 For sets 4 to 7. the fit to the photometric lighteurve and reconstructed surface brightness images are shown respectively in the centre and the right-hand side of Figure 2..," For sets 4 to 7, the fit to the photometric lightcurve and reconstructed surface brightness images are shown respectively in the centre and the right-hand side of Figure \ref{set4t7}."1097 What is distinctive about these plots are the spot features at the quadrature points (90 and 270°)., What is distinctive about these plots are the spot features at the quadrature points $^\circ$ and $^\circ$ ).1098 These spot features are not artifacts of the maximum entropy reconstruction. but occur as a consequence of the X7 minimisation technique.," These spot features are not artifacts of the maximum entropy reconstruction, but occur as a consequence of the $\chi^2$ minimisation technique."1099 If a star is peppered with small unresolvable spots. the effect on the star's lighteurve will be to reduce the depth of the primary eclipse.," If a star is peppered with small unresolvable spots, the effect on the star's lightcurve will be to reduce the depth of the primary eclipse."1100 To fit this with VE minimisation it is necessary to increase the level of the whole computed lightcurve to fit the reduced primary eclipse depth., To fit this with $\chi^2$ minimisation it is necessary to increase the level of the whole computed lightcurve to fit the reduced primary eclipse depth.1101 The difference in light at the quadrature points ean only be accounted or by placing large spurious spots at these longitudes., The difference in light at the quadrature points can only be accounted for by placing large spurious spots at these longitudes.1102 For sets 4 and 5. the spot feature at 270 longitude is fainter jin the spot feature at 90° longitude as there is a higher degree of spot coverage at the first quadrature than at the second.," For sets 4 and 5, the spot feature at $^\circ$ longitude is fainter than the spot feature at $^\circ$ longitude as there is a higher degree of spot coverage at the first quadrature than at the second."1103 In ye reconstructed surface brightness distributions. the spots at O° ongitude result from the total spot coverage between second and jird contact. ie. during primary eclipse. while the spots at 180 ongitude result from spots on the primary star visible during secondary eclipse.," In the reconstructed surface brightness distributions, the spots at $^\circ$ longitude result from the total spot coverage between second and third contact, i.e. during primary eclipse, while the spots at $^\circ$ longitude result from spots on the primary star visible during secondary eclipse."1104 Size distributions of starspots extrapolated from the case of, Size distributions of starspots extrapolated from the case of1105observations. with the High Ποιον “Transmission Crating Speetrometer (UEPGS:2?) in the focal plane.,"observations, with the High Energy Transmission Grating Spectrometer \citep[HETGS:][]{hetg} in the focal plane."1106 The first observation (obsicl 7742) was performed. on 2007. August 6th. for 115 ks. while the second one (obsid 8590) on 2007. August 9th. for 35 ks.," The first observation (obsid 7742) was performed on 2007, August 6th, for 115 ks, while the second one (obsid 8590) on 2007, August 9th, for 35 ks."1107 Data were reduced with the Chandra Interactive Analysis of Observations (CLXO:7). 4.0.1 and the Chandra. Calibration Data Base (CALDD) 3.42 software. adopting standard: procedures.," Data were reduced with the Chandra Interactive Analysis of Observations \citep[CIAO:][]{ciao} 4.0.1 and the Chandra Calibration Data Base (CALDB) 3.4.2 software, adopting standard procedures."1108 First. order Ligh Enerey Crating (LEG) and Medium Energy Grating (ALEC) spectra were extracted for the source ancl the background., First order High Energy Grating (HEG) and Medium Energy Grating (MEG) spectra were extracted for the source and the background.1109 After having verified that there is no significant. variability neither within anv single observation nor between the two. we co-added them with the toolSPECTRA.. in order to have a single LEC spectrum and. a single MIC spectrum. for a total exposure time of 115 ks cach.," After having verified that there is no significant variability neither within any single observation nor between the two, we co-added them with the tool, in order to have a single HEG spectrum and a single MEG spectrum, for a total exposure time of 148 ks each."1110 All the fits were performed. with 12.4.0 (?).. taking into account the instrumental resolution with the response matrix computed with standard. procedures.," All the fits were performed with 12.4.0 \citep{xspec}, taking into account the instrumental resolution with the response matrix computed with standard procedures."1111 Local fits were performed: around. the iron We band. with the unbinned spectra. using the ο statistic. in order to take advantage of the high spectral resolution of the gratings.," Local fits were performed around the iron $\alpha$ band with the unbinned spectra, using the \citet{cash76} statistic, in order to take advantage of the high spectral resolution of the gratings."1112 Broacl banc (04-10 keV). fits were instead. performed on the binned spectra. where the large number of counts in each bin (250) allowed the use of the v statistic.," Broad band (0.4-10 keV) fits were instead performed on the binned spectra, where the large number of counts in each bin (250) allowed the use of the $\chi^2$ statistic."1113 We cid not analyse the Oth order data in this paper. since the count-rate per frame (220.5 + in the inner 2-pixel region) is larger than the one suggested for pileup-free spectra (sec as confirmed by the resulting very (at spectrum.," We did not analyse the 0th order data in this paper, since the count-rate per frame $\simeq0.5$ $^{-1}$ in the inner 2-pixel region) is larger than the one suggested for pileup-free spectra (see ), as confirmed by the resulting very flat spectrum."1114 In order to measure the physical width of the Ho line. we asked for clirector discretionary time (LD: 279.B-5054A) to obtain a quasi-simultaneous observation of NGC 7213 at the NTT telescope (La Silla. Chile).," In order to measure the physical width of the $\alpha$ line, we asked for director discretionary time (ID: 279.B-5054A) to obtain a quasi-simultaneous observation of NGC 7213 at the NTT telescope (La Silla, Chile)."1115 The observation was carried. out in service mode on 2007. September 22th with the IEEMÁMIE spectrograph equipped: with grating #277 and a l-arcsec width slit.," The observation was carried out in service mode on 2007, September 22th with the EMMI spectrograph equipped with grating 7 and a 1-arcsec width slit."1116 Phe wavelength resolution was 2.49 (the pixel scale was 0.82 A)) in the range 5650-7140A., The wavelength resolution was 2.49 (the pixel scale was 0.82 ) in the range 5650-7140.1117. Four spectra. with 30. sec ong integrations each. were obtained with 15 aresec olfseted. positions (pattern A D Α D).," Four spectra, with 30 sec long integrations each, were obtained with 15 arcsec offsetted positions (pattern A B A B)."1118 The reduction process used standard and facilities., The reduction process used standard and facilities.1119 The raw data were bias-subtracted. corrected. for. pixel-to-pixel variations (La ficld) and eventually. skv-subtractec.," The raw data were bias-subtracted, corrected for pixel-to-pixel variations (flat field) and eventually sky-subtracted."1120 Wavelength calibrations were carried out. by comparison with exposures of Ie and Ar lamps. with an accuracy of 0.17 ((1 m).," Wavelength calibrations were carried out by comparison with exposures of He and Ar lamps, with an accuracy of 0.17 (1 $\sigma$ )."1121 Relative {ux calibration was carried out. by observations of the spectrophotometric standard. star LTT9239 (77)..," Relative flux calibration was carried out by observations of the spectrophotometric standard star LTT9239 \citep{hamuy92,hamuy94}."1122 The final S/N ratio was about 22., The final S/N ratio was about 22.1123 In the following. errors correspond to the confidence level for one interesting parameter GN?= 271). while error bars in the plots correspond to Loa.," In the following, errors correspond to the confidence level for one interesting parameter $\Delta \chi^2 =2.71$ ), while error bars in the plots correspond to 1 $\sigma$."1124 Energics and wavelengths are reported in the rest-frame of the source., Energies and wavelengths are reported in the rest-frame of the source.1125" The Galactic column density along the line of sight to NGC 7213 is included (2.04107"" 7:ο].", The Galactic column density along the line of sight to NGC 7213 is included \citep[$2.04\times10^{20}$ $^{-2}$:.1126 /pileuppabügesi)- shows the LEG spectrum in the 6.-7.5 keV band., Figure \ref{fekacomplex} shows the HEG spectrum in the 6.-7.5 keV band.1127" ""Three significant emission lines are apparent.", Three significant emission lines are apparent.1128 The strongest is the neutral Ke line at 6.397 keV. consistent with iron less ionised than Fe (1). (ya," The strongest is the neutral $\alpha$ line at $6.397^{+0.006}_{-0.011}$ keV, consistent with iron less ionised than Fe \citep{house69}."1129)Phe observed [Dux (2.91 ph 7? f) and the EW (120.25 eV) are in agreement. within errors. with those found by (7)..," The observed flux $2.9^{+0.9}_{-0.7}$ ph $^{-2}$ $^{-1}$ ) and the EW $120^{+40}_{-30}$ eV) are in agreement, within errors, with those found by \citep{bianchi03b}."1130 The iron Να line is actually composed of a doublet. Kay at 6.404 keV and Was at 6.391 keV. with a flux ratio 2:1 (?)..," The iron $\alpha$ line is actually composed of a doublet, $\alpha_1$ at 6.404 keV and $\alpha_2$ at 6.391 keV, with a flux ratio 2:1 \citep{bea67}."1131 Although the separation of this doublet cannot be resolved w the HEC. we adopted. a rigorous approach iting two Caussians. separated by 19 eV. the flux ratio ixed to the expected one ancl the width free to vary. but orced to be the same for the two lines.," Although the separation of this doublet cannot be resolved by the HEG, we adopted a rigorous approach fitting two Gaussians, separated by 13 eV, the flux ratio fixed to the expected one and the width free to vary, but forced to be the same for the two lines."1132" The width of the ines is resolved: σ=22""i eV. Forcing the lines to be narrow (o= 0) leaves large residuals and a significantly worse fit. CAC=| 15).", The width of the lines is resolved: $\sigma=22^{+10}_{-6}$ eV. Forcing the lines to be narrow $\sigma=0$ ) leaves large residuals and a significantly worse fit $\Delta\mathrm{C}=+15$ ).1133 We note here that the measure of he width is completely unallectecl by this modelling with respect to a single €raussian. as already observed by 2? for other sources.," We note here that the measure of the width is completely unaffected by this modelling with respect to a single Gaussian, as already observed by \citet{yaq01} for other sources."1134 Let us investiga ethe origin of the observed broadening., Let us investigate the origin of the observed broadening.1135 A possible origin for the observed width may be the presence of a Compton Shouder (CS)., A possible origin for the observed width may be the presence of a Compton Shoulder (CS).1136 I£ the CS is modelled with a Gaussian line with centroid οποιον at 6.3 keV and 0=40 eV (?).. while the iron line width is fixed to 0. the fit is significantly worse (AC=| 14) and only an upper Limit on the CS flux is Kkια.," If the CS is modelled with a Gaussian line with centroid energy at 6.3 keV and $\sigma=40$ eV \citep{matt02}, while the iron line width is fixed to 0, the fit is significantly worse $\Delta\mathrm{C}=+14$ ) and only an upper limit on the CS flux is found."1137 “Phis is not surprising. given the absence of a Compon rellection component. associated. to the CS.," This is not surprising, given the absence of a Compton reflection component associated to the CS."1138 Another exxeanation for the width of the iron line can be blending with iron lines from higher ionisation states. but this would imply a Larger value for the centroid energy of the resulting line and a clear asvmimetrie profile.," Another explanation for the width of the iron line can be blending with iron lines from higher ionisation states, but this would imply a larger value for the centroid energy of the resulting line and a clear asymmetric profile."1139 Pherefore. Doppler broadening is left as the most. likely explanation [or the width of the iron line. which would correspond to a EFWIIM-2400OOO1275 karst (sce Fig. 2)).," Therefore, Doppler broadening is left as the most likely explanation for the width of the iron line, which would correspond to a $2\,400^{+1\,100}_{-600}$ km $^{-1}$ (see Fig. \ref{fekacontours}) )."1140The fIux calibration of the narrow-band images can be achieved using spectrophotonmetric standard stars. by obtaining synthetic magnitudes using the known SED of the spectrophotometric slars.,"The flux calibration of the narrow-band images can be achieved using spectrophotometric standard stars, by obtaining synthetic magnitudes using the known SED of the spectrophotometric stars."1141 There are different. choices for the election of the zero point of the narrow-band filter magnitude., There are different choices for the election of the zero point of the narrow-band filter magnitude.1142 The particular election does not affect the selection of objects or the measured [Iuxes., The particular election does not affect the selection of objects or the measured fluxes.1143 Different zero points in the bands only introduce an offset in the broad-navrrow color., Different zero points in the bands only introduce an offset in the broad-narrow color.1144 One approach is to use AB magnitudes (?) or ST magnitudes (J. Walsh that provide a fixed physical magnitude scale., One approach is to use AB magnitudes \citep{1974ApJS...27...21O} or ST magnitudes (J. Walsh that provide a fixed physical magnitude scale.1145 In. other approximations. a broad-band filler is chosen as reference and the zero point of the narrow band is obtained by fixing a zero color for a particular SED.," In other approximations, a broad-band filter is chosen as reference and the zero point of the narrow band is obtained by fixing a zero color for a particular SED."1146 We adopt. unless noted otherwise. the normalization of color zero for the flat fy spectrum.," We adopt, unless noted otherwise, the normalization of color zero for the flat $f_\lambda$ spectrum."1147 This is equivalent to make equal the zero points of both bands., This is equivalent to make equal the zero points of both bands.1148 The redshift of each source entering (he narrow-band filter is unknownpriori., The redshift of each source entering the narrow-band filter is unknown.1149 Sources with strong emission lines (particularly. but not only.Ho...[Orit]AMO959.5007... and Lyo)) produce a narrow-band flix excess.," Sources with strong emission lines (particularly, but not only, and ) produce a narrow-band flux excess."1150 Different emission lines at different recshilts cannot be distinguished using only the narrow-band excess emission., Different emission lines at different redshifts cannot be distinguished using only the narrow-band excess emission.1151 Additionally. other sources (eilher galactic or extragalactic) without enission lines can exhibit a narrow-band [Iux excess when their SEDs passes through the filler set used for ELG selection.," Additionally, other sources (either galactic or extragalactic) without emission lines can exhibit a narrow-band flux excess when their SEDs passes through the filter set used for ELG selection."1152 Galaxies ancl stars wilh abundant absorption features in (he atmospheric windows studied can potentially appear in narrow-band surveys as emitting objects., Galaxies and stars with abundant absorption features in the atmospheric windows studied can potentially appear in narrow-band surveys as emitting objects.1153 This aspect has to be studied for each filler sel particularly. Gn Section 6.. examples with different filters are shown).," This aspect has to be studied for each filter set particularly (in Section \ref{sec:examples}, examples with different filters are shown)."1154 In general. stars show colors similar to those of the black body of their effective temperature.," In general, stars show colors similar to those of the black body of their effective temperature."1155 For the late spectral twpes. the presence of molecular bands change the trend. ancl large colors can be observed.," For the late spectral types, the presence of molecular bands change the trend and large colors can be observed."1156 In the specilic wavelength range of the (wo atmospheric windows. the absorption produced by some molecular species present in (he atmosphere of cold stars (TiO. VO) dominates.," In the specific wavelength range of the two atmospheric windows, the absorption produced by some molecular species present in the atmosphere of cold stars (TiO, VO) dominates."1157 For late Ix stus. broad-narrow colors diverge [rom the black body.," For late K stars, broad-narrow colors diverge from the black body."1158 White dwarls with broad Hydrogen absorption lines would produce also a narrow-band Πας depression., White dwarfs with broad Hydrogen absorption lines would produce also a narrow-band flux depression.1159 It is important (ο note that depending on the filters used. particularly on the relative position of their Ap. molecular bands of cold stars could produce an increase of the color.," It is important to note that depending on the filters used, particularly on the relative position of their $\lambda_0$, molecular bands of cold stars could produce an increase of the color."1160 Those stus with a laree color excess produced by absorption lines ean be nmisclassified, Those stars with a large color excess produced by absorption lines can be misclassified1161uncertainty in the line strength is at the level (Tashkunetal.. 2003).,uncertainty in the line strength is at the level \citep{Tashkun03}.1162". The strongest CH, lines shown in Fig.", The strongest $_4$ lines shown in Fig.1163" 6. have an average uncertainty in their positions of ~107 cem""! or ~60 m/s and uncertainties in their line strengths of up to (Rothmanetal..2005:Brown2003)."," \ref{fig:2336} have an average uncertainty in their positions of $\sim10^{-3}$ $^{-1}$ or $\sim60$ m/s and uncertainties in their line strengths of up to \citep{HITRAN2004,Brown2003}."1164. This level of positional uncertainties influences the wavelength solution and the line fitting., This level of positional uncertainties influences the wavelength solution and the line fitting.1165 As expected. even the strongest water vapour lines shown in Fig.," As expected, even the strongest water vapour lines shown in Fig."1166 10. have positional uncertainties of up to cem! or ~2.6 km/s and their line strength can be uncertain to more than (Rothmanetal.. 2005).., \ref{fig:1134} have positional uncertainties of up to $^{-1}$ or $\sim2.6$ km/s and their line strength can be uncertain to more than \citep{HITRAN2004}. .1167 This explains the bad fit to the data shown in Fig. 10.., This explains the bad fit to the data shown in Fig. \ref{fig:1134}.1168 Other limitations arise from the limited treatment of line mixing (aka line coupling) effects and from the assumed line profile., Other limitations arise from the limited treatment of line mixing (aka line coupling) effects and from the assumed line profile.1169 Line mixing in LBLRTM ts modeled using a first order perturbation approach., Line mixing in LBLRTM is modeled using a first order perturbation approach.1170 For CO». line mixing is treated according to Niroetal.(2005).," For $_2$, line mixing is treated according to \citet{Niro05}."1171. LBLRTM employs a Voigt line shape at all atmospheric levels with an algorithm based on a linear combination of approximating functions (Cloughetal..2005)., LBLRTM employs a Voigt line shape at all atmospheric levels with an algorithm based on a linear combination of approximating functions \citep{Clough05}.1172. A Rautian. Galatry or speed-dependent Voigt profile would be needed to account more precisely for speed-dependent broadening effects and line mixing effects (e.g..Braultetal..2003.Fig.1)..," A Rautian, Galatry or speed-dependent Voigt profile would be needed to account more precisely for speed-dependent broadening effects and line mixing effects \citep[e.g.,][Fig.1]{Brault03}."1173 The errors induced by this simplification are. however. comparatively small against the uncertainties in other line parameters entries of the HITRAN database.," The errors induced by this simplification are, however, comparatively small against the uncertainties in other line parameters entries of the HITRAN database."1174 As long as the total column densities. of the different molecular species can be varied. the uncertainties in the model atmosphere have only a minor impact on the model spectrum.," As long as the total column densities of the different molecular species can be varied, the uncertainties in the model atmosphere have only a minor impact on the model spectrum."1175 Exceptions are CO and Os. where changes in the vertical abundance profiles lead to notably different line widths. because either the abundance maximum or minimum of the species is close to the temperature inversion of the Earths atmosphere (see Fig.," Exceptions are CO and $_3$, where changes in the vertical abundance profiles lead to notably different line widths, because either the abundance maximum or minimum of the species is close to the temperature inversion of the Earths atmosphere (see Fig."1176 | and 2)), \ref{fig:equ_profile} and \ref{fig:atmos}) ).1177 The model for our mid- case presented in Sec., The model for our mid-infrared case presented in Sec.1178 ??. does show a dependence on the type of model atmosphere. 1.e. whether an equatorial or night-time MIPAS model is used.," \ref{sec:4760} does show a dependence on the type of model atmosphere, i.e. whether an equatorial or night-time MIPAS model is used."1179 The intrinsic line width is. however. degenerate with the instrumental profile and while the formal resolution measured as the width of the instrumental profile varies. the residuals give no hint which of the two model atmospheres is more representative of the actual conditions.," The intrinsic line width is, however, degenerate with the instrumental profile and while the formal resolution measured as the width of the instrumental profile varies, the residuals give no hint which of the two model atmospheres is more representative of the actual conditions."1180 For the water vapour. we did not find a significant improvement in the fit quality when using the MM5 atmospheric models instead of the GDAS models.," For the water vapour, we did not find a significant improvement in the fit quality when using the MM5 atmospheric models instead of the GDAS models."1181 The fitting delivered the same PWV for both models and the different vertical distribution of the water vapour had no noticeable influence on our test cases., The fitting delivered the same PWV for both models and the different vertical distribution of the water vapour had no noticeable influence on our test cases.1182 Re-fitting of the vertical distribution of the water vapour will thus lead only to minor improvements. if at all. and seems only feasible when enough lines are present. preferably from different vibrational transitions.," Re-fitting of the vertical distribution of the water vapour will thus lead only to minor improvements, if at all, and seems only feasible when enough lines are present, preferably from different vibrational transitions."1183 The fitting of a telluric model to an observed spectrum will be more complicated in the presence of blends between telluric and stellar lines., The fitting of a telluric model to an observed spectrum will be more complicated in the presence of blends between telluric and stellar lines.1184 Various strategies could be used to allow for the same fitting quality as compared to the featureless early type stars used in this study. (, Various strategies could be used to allow for the same fitting quality as compared to the featureless early type stars used in this study. (1185I) The usage of a stellar model spectrum in the fitting process would significantly improve the telluric model. (,I) The usage of a stellar model spectrum in the fitting process would significantly improve the telluric model. (1186ID In the thermal infrared. the telluric emission lines could be used to further constrain the fit in terms of wavelength solution and molecular abundances. (,"II) In the thermal infrared, the telluric emission lines could be used to further constrain the fit in terms of wavelength solution and molecular abundances. ("1187III) In the worst case. an observation of a telluric standard star in the same spectral setting but not necessarily at the same time and airmass can be used to constrain the model fit for the target (e.g...lanuevaetal..2008).,"III) In the worst case, an observation of a telluric standard star in the same spectral setting but not necessarily at the same time and airmass can be used to constrain the model fit for the target \citep[e.g.,][]{Villanueva}."1188. We have shown that with the use of LBLRTM. a line- radiative transfer code. and an appropriate model atmosphere. synthetic telluric transmission spectra can be constructed that match the observed telluric spectrum to or better (see. e.g.. Fig.5)). even close to saturated lines.," We have shown that with the use of LBLRTM, a line-by-line radiative transfer code, and an appropriate model atmosphere, synthetic telluric transmission spectra can be constructed that match the observed telluric spectrum to or better (see, e.g., \ref{fig:2076}) ), even close to saturated lines."1189 These results were achieved with only a modest effort in back-fitting of atmospheric properties., These results were achieved with only a modest effort in back-fitting of atmospheric properties.1190 Compilation of LBLRTM ts straight forward and when using the described IDL fitting routines for v minimisation. the time needed for a model fit to a single CRIRES chip ts less than 2 minutes on standard desktop PC.," Compilation of LBLRTM is straight forward and when using the described IDL fitting routines for $\chi^2$ minimisation, the time needed for a model fit to a single CRIRES chip is less than 2 minutes on standard desktop PC."1191 User interaction is only required to download the appropriate GDAS model from the NOAA website. to set up an initial wavelength scale. and to choose the species to be fitted.," User interaction is only required to download the appropriate GDAS model from the NOAA website, to set up an initial wavelength scale, and to choose the species to be fitted."1192 Although full photon noise limited performance is never achieved. the usage of the synthetic transmission spectra offers an alternative to the usage of standard star observations.," Although full photon noise limited performance is never achieved, the usage of the synthetic transmission spectra offers an alternative to the usage of standard star observations."1193 The tight constraints in matching airmass and instrumental profile of the science target imposed on tellurie standard stars are hard to meet in reality without downgrading the achievable SNR or the spectral resolution., The tight constraints in matching airmass and instrumental profile of the science target imposed on telluric standard stars are hard to meet in reality without downgrading the achievable SNR or the spectral resolution.1194 We demonstrate this problem by using the data shown in Sect. ??..," We demonstrate this problem by using the data shown in Sect. \ref{CO2},"1195 this time showing in Fig.1l the spectrum from nodding position A divided by the one in nodding position B. taken mmin later.," this time showing in \ref{fig:ab} the spectrum from nodding position A divided by the one in nodding position B, taken min later."1196 The difference in airmass is only 0.005., The difference in airmass is only 0.005.1197 The spectrum of the B position had to be mapped onto the wavelength scale of the A position due to the slit curvature which changes the wavelength zero point and the dispersion between both positions., The spectrum of the B position had to be mapped onto the wavelength scale of the A position due to the slit curvature which changes the wavelength zero point and the dispersion between both positions.1198 We note that at this step the wavelength solution provided by the telluric model for both nodding positions had to be used to achieve this result., We note that at this step the wavelength solution provided by the telluric model for both nodding positions had to be used to achieve this result.1199 Despite the fact that both spectra are of the same star and taken close in time and airmass. a slight change in the AO performance over time and in the instrumental profile between both nodding positions led to the apparent residuals in the division.," Despite the fact that both spectra are of the same star and taken close in time and airmass, a slight change in the AO performance over time and in the instrumental profile between both nodding positions led to the apparent residuals in the division."1200 The detector response at the twonodding positions is uniform to better than after correcting for non-linearity and applying a flatfield correction as outlined in, The detector response at the twonodding positions is uniform to better than after correcting for non-linearity and applying a flatfield correction as outlined in

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