ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 7 has a auch lower intensity but a much longer duration than pulse A. so that the total radiated cnerev is approximately the same.," \ref{FigObs} has a much lower intensity but a much longer duration than pulse A, so that the total radiated energy is approximately the same."3 If we assmme that these pulses are produced in the same source then the variations of the pulse iuteusitv and duration can be caused by the radiation scattering during propagation. which is different for the different source orientations.," If we assume that these pulses are produced in the same source then the variations of the pulse intensity and duration can be caused by the radiation scattering during propagation, which is different for the different source orientations."4 Aw alternative explanation is that the active sector width AX can vary significantly over timescales of about one hour. while the total number of the energetic clectrous in this sector remains nearly constant.," An alternative explanation is that the active sector width $\Delta\lambda$ can vary significantly over timescales of about one hour, while the total number of the energetic electrons in this sector remains nearly constant."5 We have simulated the dynamic spectra of radio cluission from ultracool dwarts., We have simulated the dynamic spectra of radio emission from ultracool dwarfs.6 The stellar maguetic field was modeled by a tilted dipole., The stellar magnetic field was modeled by a tilted dipole.7 Two source models were considered: the model in which the cussion was xoduced. as a result of the star-satellite interaction. aud the model with ciuission from a narrow sector of nagnetic longitudes.," Two source models were considered: the model in which the emission was produced as a result of the star-satellite interaction, and the model with emission from a narrow sector of magnetic longitudes."8 The cussion was assumed to be eenerated due to the electron-cvclotron maser instability: wo unstable electron distributions (the loss cone and the shell distribution) were considered., The emission was assumed to be generated due to the electron-cyclotron maser instability; two unstable electron distributions (the loss cone and the shell distribution) were considered.9 We have compared he simulation results with the observations of the ultracool cawarf TVLM 513., We have compared the simulation results with the observations of the ultracool dwarf TVLM 513.10 We have fouud that: The experimental and theoretical studies of radio cluission frou ultracool cdwwarfs are only at their beeiuuins., We have found that: The experimental and theoretical studies of radio emission from ultracool dwarfs are only at their beginning.11 Dynamic spectra of the cussion (with lieh spectral aud temporal resolution) covering wide frequency range aud loug time intervals are necessary to make more definite conclusious about the magnetic field topology. particle acceleration mechanisni and other parameters of the stellar maguctospheres.," Dynamic spectra of the emission (with high spectral and temporal resolution) covering wide frequency range and long time intervals are necessary to make more definite conclusions about the magnetic field topology, particle acceleration mechanism, and other parameters of the stellar magnetospheres."12 ALA. Kuzuetsov. J.C. Dovle. aud S. Yu thauk the Leverhuhnue Trust for financial support.," A.A. Kuznetsov, J.G. Doyle, and S. Yu thank the Leverhulme Trust for financial support."13 C. IHalliuan is a Jausky Fellow of the National Radio ÀÁstrononiv Observatory., G. Hallinan is a Jansky Fellow of the National Radio Astronomy Observatory.14 A. Autonova gratefully acknowledges the support of the Bulgarian National Science. Fund. (eraut No., A. Antonova gratefully acknowledges the support of the Bulgarian National Science Fund (grant No.15 DDVU02/10-2010)., DDVU02/40-2010).16almost equal despite the very different amount of low-level clouds.,almost equal despite the very different amount of low-level clouds.17 Noticeable changes can be found in the 9.6um O3 and the 15um CO» bands., Noticeable changes can be found in the $9.6 \ \mathrm{\mu m}$ $\mathrm{O_3}$ and the $15 \ \mathrm{\mu m}$ $\mathrm{CO_2}$ bands.18" These differences however are not the results of the different cloud covers, but of the different temperature profiles as already discussed in Sect. 4.1.."," These differences however are not the results of the different cloud covers, but of the different temperature profiles as already discussed in Sect. \ref{sub_basic_effects}."19 From the direct comparison of the two scenarios shown in Fig., From the direct comparison of the two scenarios shown in Fig.20 8 it is obvious that the high-level ice clouds have the strongest impact on the thermal emission spectra for planets with the same surface temperature., \ref{all_288} it is obvious that the high-level ice clouds have the strongest impact on the thermal emission spectra for planets with the same surface temperature.21 This can be understood by the fact that the low-level clouds emit thermal radiation at almost the same temperature as the surface (previously discussed in Sect. 4.1))., This can be understood by the fact that the low-level clouds emit thermal radiation at almost the same temperature as the surface (previously discussed in Sect. \ref{sub_basic_effects}) ).22 This limits their influence on the spectra in these particular cases because the surface temperature is the same for all considered scenarios., This limits their influence on the spectra in these particular cases because the surface temperature is the same for all considered scenarios.23 The high-level clouds on the other hand are located higher up in the atmosphere and emit at temperatures generally much colder than the surface., The high-level clouds on the other hand are located higher up in the atmosphere and emit at temperatures generally much colder than the surface.24 Their influence on the spectra therefore directly depends on their respective coverage (see also Sect. 4.1))., Their influence on the spectra therefore directly depends on their respective coverage (see also Sect. \ref{sub_basic_effects}) ).25 Thermal emission spectra can in principle be used to obtain information about atmospheric or surface temperatures of planets., Thermal emission spectra can in principle be used to obtain information about atmospheric or surface temperatures of planets.26 Usually black-body radiation curves are fitted to the spectral shape of observed thermal emission spectra., Usually black-body radiation curves are fitted to the spectral shape of observed thermal emission spectra.27" Clouds conceal the surface below them as a function of their optical depth, but also act as emitters of thermal radiation."," Clouds conceal the surface below them as a function of their optical depth, but also act as emitters of thermal radiation."28" Since clouds emit at their own radiative equilibrium temperature, the temperatures derived by fitting of black-body curves are in general not directly connected to the planetary surface temperature if high-level clouds are present in the atmosphere."," Since clouds emit at their own radiative equilibrium temperature, the temperatures derived by fitting of black-body curves are in general not directly connected to the planetary surface temperature if high-level clouds are present in the atmosphere."29 Fig., Fig.30" 9 shows two spectra, namely for a small and a large cloud cover, for each of the central star scenarios."," \ref{blackbody_all} shows two spectra, namely for a small and a large cloud cover, for each of the central star scenarios."31 In, In32can combine (he images using iDrizzle.,can combine the images using iDrizzle.33 This will allow the user to check how many iterations it will take to obtain a reasonable result., This will allow the user to check how many iterations it will take to obtain a reasonable result.34 As the amplification of the noise tends to grow with the number of iterations. greatly exceeding (he number of required iterations is nol advised.," As the amplification of the noise tends to grow with the number of iterations, greatly exceeding the number of required iterations is not advised."35 Usually a few to a dozen interations will do., Usually a few to a dozen interations will do.36 Indeed. in the case of the real UDF data. convergence stopped alter only a few iterations.," Indeed, in the case of the real UDF data, convergence stopped after only a few iterations."37 As mentioned earlier. this is because the technique was limited by the variability of the HST DSF.," As mentioned earlier, this is because the technique was limited by the variability of the HST PSF."38 In this paper. a new method for the combination of dithered astronomical images has been introduced.," In this paper, a new method for the combination of dithered astronomical images has been introduced."39 The method. iDrizzle. has the ability to handle shifts. distortions and missing data. and converges rapidly to an accurate representation of the underlving image.," The method, iDrizzle, has the ability to handle shifts, distortions and missing data, and converges rapidly to an accurate representation of the underlying image."40 It provides a dramatic improvement in fidelity over Drizzle. particularly on resolved objects. al the cost of a small increase in statistical noise.," It provides a dramatic improvement in fidelity over Drizzle, particularly on resolved objects, at the cost of a small increase in statistical noise."41 It requires. however. (hat the combined images come close to Nvquist sampling across the combined image.," It requires, however, that the combined images come close to Nyquist sampling across the combined image."42 The algoritlim upon which this worked is in part based. Drizzle. bv itself creates excellent images ofresolved objects (such as galaxies in a deep LST image). and will produce images of slightly higher signal-to-noise images (than iDrizzle. in the case (hat statistical noise is arger (han the small artifacts of using Drizzle.," The algorithm upon which this worked is in part based, Drizzle, by itself creates excellent images of objects (such as galaxies in a deep HST image), and will produce images of slightly higher signal-to-noise images than iDrizzle, in the case that statistical noise is larger than the small artifacts of using Drizzle."43 Similarly. observers attempting precise stellar photonmetry. may use Drizzle aud/or iDrizzle to locate their stars aud remove image defects. and can do photometry on each individual image and combine results (o avoid the small increase in slalislical noise produced by iDrizzle.," Similarly, observers attempting precise stellar photometry, may use Drizzle and/or iDrizzle to locate their stars and remove image defects, and can do photometry on each individual image and combine results to avoid the small increase in statistical noise produced by iDrizzle."44 However. this approach would require a substantial amount of elfort to avoid the inherent photometric biases of working with undersanipled data — something that iDrizzle does directly.," However, this approach would require a substantial amount of effort to avoid the inherent photometric biases of working with undersampled data – something that iDrizzle does directly."45 Where iDrizzle truly stands out is in creating accurate images of objects wilh unresolved or nearlv-unresolved. components., Where iDrizzle truly stands out is in creating accurate images of objects with unresolved or nearly-unresolved components.46 As the test with the UDF data showed. iDrizzle allows far more accurate image subtraction. and thus may be of great use to observers irving (to remove powerful point sources underlving extended objects. such as AGN from their host galaxies.," As the test with the UDF data showed, iDrizzle allows far more accurate image subtraction, and thus may be of great use to observers trying to remove powerful point sources underlying extended objects, such as AGN from their host galaxies."47 In the long-run though. an important use of iDrizzle may be the most direct application. (he creation of point-source Dunctions.," In the long-run though, an important use of iDrizzle may be the most direct application, the creation of point-source functions."48 Future space-based wice-fieldl imagers are likely to be undersampled., Future space-based wide-field imagers are likely to be undersampled.49 Nonetheless they will be used (and some will be expressly intended) lor applications such as lensing which require excellent knowledge of the PSF., Nonetheless they will be used (and some will be expressly intended) for applications such as lensing which require excellent knowledge of the PSF.50 As shown here. with a moderate number of dithers. even with random sampling. iDrizzle can produce high-fidelity PSFs.," As shown here, with a moderate number of dithers, even with random sampling, iDrizzle can produce high-fidelity PSFs."51 The desire to cover a large area of sky. however. may mean (hat some projects will prefer to keep the munber of dithers in a given filler to a bare minimum — four exposures may be a common preference.," The desire to cover a large area of sky, however, may mean that some projects will prefer to keep the number of dithers in a given filter to a bare minimum – four exposures may be a common preference."52 While four dithers is too few for iDrizzle to estimate the image in the absence of near regular, While four dithers is too few for iDrizzle to estimate the image in the absence of near regular53The Roche tomograms show an asvmumetric irradiation pattern on all 4 CVs.,The Roche tomograms show an asymmetric irradiation pattern on all 4 CVs.54 This can be explained if the accretion column/stream shields the leading hemisphere in AM Ler. QQ Vul and LIU ar.," This can be explained if the accretion column/stream shields the leading hemisphere in AM Her, QQ Vul and HU Aqr."55 Phere is also evidence for a fainter shadow. present on the trailing hemisphere of HU qr., There is also evidence for a fainter shadow present on the trailing hemisphere of HU Aqr.56 We propose that the stream itself contributes significantIy to the irradiation. and that the shadow on the trailing hemisphere occurs as these regions on the secondary star have no direct view of the majority of the stream.," We propose that the stream itself contributes significantly to the irradiation, and that the shadow on the trailing hemisphere occurs as these regions on the secondary star have no direct view of the majority of the stream."57 Further observations using absorption lines originating [rom the secondary. star are needed to confirm this., Further observations using absorption lines originating from the secondary star are needed to confirm this.58 A different scenario occurs in LP Pee. where irradiation alfects the leading hemisphere only.," A different scenario occurs in IP Peg, where irradiation affects the leading hemisphere only."59 We suggest that. the bright spot. which is on the correct side of the secondary star to cause such an irradiation pattern. may be the principal illuminating source in this system.," We suggest that the bright spot, which is on the correct side of the secondary star to cause such an irradiation pattern, may be the principal illuminating source in this system."60 Although we still expect irracliation of the trailing hemisphere by the white dwarf (as seen in the magnetic CVs). there is no evidence for this in the tomogram.," Although we still expect irradiation of the trailing hemisphere by the white dwarf (as seen in the magnetic CVs), there is no evidence for this in the tomogram."61 Lt may be the case that the accretion disc in LP Pee ts shielding the secondary star from irradiation by the white dwarl, It may be the case that the accretion disc in IP Peg is shielding the secondary star from irradiation by the white dwarf.62 Unlike 7.. we find no evidence for irradiation extending onto the back hall of the star. and hence cannot support their idea that circulation. currents operate in IP leg.," Unlike \citet{davey92}, we find no evidence for irradiation extending onto the back half of the star, and hence cannot support their idea that circulation currents operate in IP Peg."63 We have used the entropy. landscape technique to derive the system parameters., We have used the entropy landscape technique to derive the system parameters.64 Although we cannot reliably constrain the inclination. and therefore the masses. in the non-eclipsing CVs. the technique does provide a consistent result. for the mass ratio that is independent of the inclination.," Although we cannot reliably constrain the inclination, and therefore the masses, in the non-eclipsing CVs, the technique does provide a consistent result for the mass ratio that is independent of the inclination."65 For the two eclipsing CVs (LP oo and LLU αν]. we believe that the masses derived in this work are the most accurate to date.," For the two eclipsing CVs (IP Peg and HU Aqr), we believe that the masses derived in this work are the most accurate to date."66 In adcdition. it is found tia nmnieasturenments of the systemic velocity using circular orbi fits to the raclial-velocity. variations are unreliable. anc arc! dependent. upon the intensity clistribution across the sec“ondary star.," In addition, it is found that measurements of the systemic velocity using circular orbit fits to the radial-velocity variations are unreliable, and are dependent upon the intensity distribution across the secondary star."67 We might therefore expect such measuremen sto be both line and time-dependent., We might therefore expect such measurements to be both line and time-dependent.68 Since the intensity cistribution across the secondary star is known in Roche tomography. systemic velocity measurements using this technique should prove far more accurate.," Since the intensity distribution across the secondary star is known in Roche tomography, systemic velocity measurements using this technique should prove far more accurate."69 We thank Stuart Littlefair for many useful conversations., We thank Stuart Littlefair for many useful conversations.70 CAN is supported by a PPARC studentship., CAW is supported by a PPARC studentship.71 This project was supported in part by the Bunelesministerium [tir Jildune und Forschung through the Deutsches Zentrum fürr Luft- und Haumfahrt eV. (DLR) under grant. number 50 OR 9706 S., This project was supported in part by the Bundesministerium fürr Bildung und Forschung through the Deutsches Zentrum fürr Luft- und Raumfahrt e.V. (DLR) under grant number 50 OR 9706 8.72 We would also like to thank the referee. Andrew Cameron. for his comments. which substantially improved the clarity of the paper.," We would also like to thank the referee, Andrew Cameron, for his comments, which substantially improved the clarity of the paper."73 differrent sets of photo-Z's is better for the subsample with secure spectroscopic redshifts than for the whole catalogue., rent sets of$z$ 's is better for the subsample with secure spectroscopic redshifts than for the whole catalogue.74 Outher rates in the latter are typically larger by at least a factor of two., Outlier rates in the latter are typically larger by at least a factor of two.75"that one or more of a. ji and g, had smaller values at z=0.247 than at the present epoch.","that one or more of $\alpha$ , $\mu$ and $g_p$ had smaller values at $z = 0.247$ than at the present epoch."76" The limiting cases. assuming that only one of o. jr. and g, changes. are [nn]=(-3.1+ (for [Ann]m»MNDj[Ayi]. [Agον). [Ayη=(76.2x2.4)«10 (for p|>>[Aa/a]. VNep/eph and [Ag,/2,]271.18+0.436)«107 (for [An n]. [An )."," The limiting cases, assuming that only one of $\alpha$ , $\mu$ , and $g_p$ changes, are $\dal = (-3.1 \pm 1.2) \times 10^{-6}$ (for $\dal >> \dmu$, $[\Delta g_p/g_p]$ ), $\dmu = (-6.2 \pm 2.4) \times 10^{-6}$ (for $\dmu >> \dal$, $[\Delta g_p/g_p]$ ), and $[\Delta g_p/g_p] = (-1.18 \pm 0.46) \times 10^{-5}$ (for $[\Delta g_p/g_p] >> \dal$ , $\dmu$ )."77" Changes in g, ηare expected to be far smaller than those in µ and o (Langackeretal.2002).", Changes in $g_p$ are expected to be far smaller than those in $\mu$ and $\alpha$ \citep{langacker02}.78. Further. a stringent constraint on changes in ji from a higher redshift absorber has recently been obtained from comparisons between NH inversion and HCN/HCO* rotational lines: Murphyetal.(20088). find [App]<1.6«10 (20) from a gravitational lens at z~ 0.685.," Further, a stringent constraint on changes in $\mu$ from a higher redshift absorber has recently been obtained from comparisons between $_3$ inversion and $^+$ rotational lines: \citet{murphy08} find $\dmu < 1.6 \times 10^{-6}$ $2\sigma$ ) from a gravitational lens at $z \sim 0.685$ ."79" This suggests that changes in G=g,[pa]? at zo0.25 may be dominated by changes in a. Le. the first limiting case above. yielding [Aan]=(-3.141.2)«10°."," This suggests that changes in $G \equiv g_p [\mu \alpha^2]^{1.85}$ at $z \sim 0.25$ may be dominated by changes in $\alpha$, i.e. the first limiting case above, yielding $\dal = (-3.1 \pm 1.2) \times 10^{-6}$."80 It is interesting that this result for [Ann] is similar in both amplitude and sign to the value of [na] obtained by Murphyetal.(2004). using the many-multiplet method at a higher redshift. |Na/n]2075.71.1)«I0 at (2)=1.75.," It is interesting that this result for $\dal$ is similar in both amplitude and sign to the value of $\dal$ obtained by \citet{murphy04} using the many-multiplet method at a higher redshift, $\dal = (-5.7 \pm 1.1) \times 10^{-6}$ at $\langle z \rangle = 1.75$."81 Other sensitive astronomicalE techniques to probe fundamental constant evolution include those based on the many-multiplet method (Murphyetal.2004).. H» lines (Kingetal.2008).. 21cm and OH lines 2005).. inversion and rotational lines (Flambaum 2007... 21em and ultraviolet carbon lines (Kanekaretal. 2010). ete.," Other sensitive astronomical techniques to probe fundamental constant evolution include those based on the many-multiplet method \citep{murphy04}, $_2$ lines \citep{king08}, 21cm and OH lines \citep{kanekar05}, inversion and rotational lines \citep{flambaum07b}, 21cm and ultraviolet carbon lines \citep{kanekar10}, etc."82 All of these are affected by systematic effects of different types (e.g. Kanekar 2008))., All of these are affected by systematic effects of different types (e.g. \citealp{kanekar08b}) ).83 For example. Griestetal.(2010) have recently shown that Keck-HIRES spectra are affected by wavelength calibration errors of unknown origin: the effect of these systematic errors on the many-multiplet result of Murphyetal.(2004) is not known. although it seems clear that the error budget will increase.," For example, \citet{griest10} have recently shown that Keck-HIRES spectra are affected by wavelength calibration errors of unknown origin; the effect of these systematic errors on the many-multiplet result of \citet{murphy04} is not known, although it seems clear that the error budget will increase."84 Similar problems have been found with VLT-UVES spectra (e.g. Centurionetal.2009:Whitmore 2010)). which would affect the H» results of Kingetal.(2008).," Similar problems have been found with VLT-UVES spectra (e.g. \citealp{centurion09,whitmore10}) ), which would affect the $_2$ results of \citet{king08}."85 The importance of the conjugate satellite OH technique stems from the fact that it has fewer systematic effects than other approaches and allows a test of its own applicability. in the prediction that the shapes of the satellite OH lines must be the same.," The importance of the conjugate satellite OH technique stems from the fact that it has fewer systematic effects than other approaches and allows a test of its own applicability, in the prediction that the shapes of the satellite OH lines must be the same."86 We have also demonstrated that the expected null result is obtained on applying the technique to a local conjugate satellite system. Cen.," We have also demonstrated that the expected null result is obtained on applying the technique to a local conjugate satellite system, Cen."87A. Equally important. and again unlike most other techniques. the conjugate satellite lines allow an estimate of changes in the fundamental constants from alocation. without any averaging over multiple absorbers (which. for example. is essential in the many-multiplet method to average out local systematics).,"A. Equally important, and again unlike most other techniques, the conjugate satellite lines allow an estimate of changes in the fundamental constants from a, without any averaging over multiple absorbers (which, for example, is essential in the many-multiplet method to average out local systematics)."88 The only apparent drawback to the technique is the possibility of RFI at the line frequencies: this can be ameliorated by using multiple telescopes. as done here. or multiple observing epochs. taking advantage of the shift in the line frequency in the terrestrial frame due to the motion of the Earth around the Sun.," The only apparent drawback to the technique is the possibility of RFI at the line frequencies; this can be ameliorated by using multiple telescopes, as done here, or multiple observing epochs, taking advantage of the shift in the line frequency in the terrestrial frame due to the motion of the Earth around the Sun."89 In summary. we have obtained deep WSRT and Arecibo Telescope spectra in the redshifted satellite OH 18em lines from at z—0.247.," In summary, we have obtained deep WSRT and Arecibo Telescope spectra in the redshifted satellite OH 18cm lines from, at $z \sim 0.247$."90 The lines are conjugate at our sensitivity. with the sum of the optical depths consistent with noise.," The lines are conjugate at our sensitivity, with the sum of the optical depths consistent with noise."91 We find that the peak of the cross-correlation of the satellite OH 18cm lines ts offset from zero velocity (at ~2.66 significance). tentative evidence for a redshift offset between them.," We find that the peak of the cross-correlation of the satellite OH 18cm lines is offset from zero velocity (at $\sim 2.6 \sigma$ significance), tentative evidence for a redshift offset between them."92 We have examined the data for systematic effects and find no evidence that such effects might give rise to the observed velocity offset., We have examined the data for systematic effects and find no evidence that such effects might give rise to the observed velocity offset.93 We have also verified that the cross-correlation of the satellite OH 18em lines in the local conjugate satellite system in Cen., We have also verified that the cross-correlation of the satellite OH 18cm lines in the local conjugate satellite system in Cen.94A peaks at zero velocity. within the errors.,"A peaks at zero velocity, within the errors."95" The observed offset in satellite line redshifts in iimplies AG/G=(-1.18+0.46)«107. where e|]. suggesting that one or more of o. jr. and g, had smaller values at z0.247 than at the present epoch,"," The observed offset in satellite line redshifts in implies $\Delta G/G = 96(-1.18 \pm 0.46) \times 10^{-5}$, where $G \equiv g_p [\mu \alpha^2]^{1.85}$ , suggesting that one or more of $\alpha$, $\mu$, and $g_p$ had smaller values at $z \sim 0.247$ than at the present epoch."97 We thank Huib van Langevelde for providing us the conjugate satellite spectra towards Cen., We thank Huib van Langevelde for providing us the conjugate satellite spectra towards Cen.98A. Carlos Martins for stimulating discussions. and Rene Vermeulen and Chris Salter for much help with the WSRT and AOobservations.,"A, Carlos Martins for stimulating discussions, and Rene Vermeulen and Chris Salter for much help with the WSRT and AOobservations."99 The WSRT is operated by theASTRON (Netherlands Foundation for Research in Astronomy) with support from the Netherlands Foundation for Scientific Research NWO., The WSRT is operated by theASTRON (Netherlands Foundation for Research in Astronomy) with support from the Netherlands Foundation for Scientific Research NWO.100 The Arecibo Observatory is a part of the NAIC. operated by Cornell University under a cooperative agreement with the NSF.," The Arecibo Observatory is a part of the NAIC, operated by Cornell University under a cooperative agreement with the NSF."101 NK acknowledges supportfrom an NRAO Jansky Fellowship and a Ramanujan Fellowship. and from the Max Planck Society.," NK acknowledges supportfrom an NRAO Jansky Fellowship and a Ramanujan Fellowship, and from the Max Planck Society."102and IGN(Spain).,and IGN (Spain).103thin.,thin.104 It is therefore likely that we are secing a iuild level of uuresolved saturation., It is therefore likely that we are seeing a mild level of unresolved saturation.105 Since the profile fitting is more robust to saturation iu the line core. it is a more reliable measure of the column deusitv in the svsteiu.," Since the profile fitting is more robust to saturation in the line core, it is a more reliable measure of the column density in the system."106 Moreover. the profile fits do not formally reach zero fiux (sce Figure 2)). nor do the data show strong evidence of saturation. which leads us to believe that the uuresolved saturation is muld. aud we can confidently proceed by adopting the fitting results as our final ccolun deusitics.," Moreover, the profile fits do not formally reach zero flux (see Figure \ref{fig: stack-plot}) ), nor do the data show strong evidence of saturation, which leads us to believe that the unresolved saturation is mild, and we can confidently proceed by adopting the fitting results as our final column densities."107" The ccoluun density in the ccloud was also ~O.tdex higher than predicted by the optically thin case. but the fitting errors were very large (0.6 τους),"," The column density in the cloud was also $\sim 0.4\dex$ higher than predicted by the optically thin case, but the fitting errors were very large $0.6-0.7\dex$ )."108 Thus the ccoluun density in the ccloud is poorly constrained by the profile fitting. because the line is at best marginallv resolved.," Thus the column density in the cloud is poorly constrained by the profile fitting, because the line is at best marginally resolved."109" This is shown clearly by the low doppler ναπιο, and correspondiuelv large errors in both JN an "," This is shown clearly by the low doppler $b$ -value, and correspondingly large errors in both $N$ and $b$."110This uncertainty in the ccoluun deusitv is the dominant source of uncertainty iu our analysis of the ccloud below., This uncertainty in the column density is the dominant source of uncertainty in our analysis of the cloud below.111 We also note that there is au offset iu the centroids ofthe aand lliues in the ecloud as a result of errors in the COS waveleneth calibration., We also note that there is an offset in the centroids of the and lines in the cloud as a result of errors in the COS wavelength calibration.112 We determined the galaxy redshifts by fitting template spectra to the LRIS spectra., We determined the galaxy redshifts by fitting template spectra to the LRIS spectra.113 This template fitting is a modified version of the SDSSzfind code. which operates by fitting a linear combination of SDSS QSO cigenspectra to the ealaxy spectrum (see7.fordetails). Galaxy," This template fitting is a modified version of the SDSS code, which operates by fitting a linear combination of SDSS QSO eigenspectra to the galaxy spectrum \citep[see][for114details]{werk-etal-11-galaxies}."115 27_19.. at gal=0.3529+0.0001. is the only galaxy within wwhich is spectroscopically confirmed to be at the same redshift as the absorbers.," Galaxy , at $\zgal = 0.3529 \pm 0.0001$, is the only galaxy within which is spectroscopically confirmed to be at the same redshift as the absorbers."116 Ta all cases. we use the redshift of the ealaxy to set the systemic redshift. aud measure velocity offsets from this redshift.," In all cases, we use the redshift of the galaxy to set the systemic redshift, and measure velocity offsets from this redshift."117 The formal fitting error on the redshift is much less than the quoted redshift uncertainty. but svstematic effects (ee. in the wavelength calibration due to spectrograph flexure) limit the accuracy to ~25knis which we adopt as our redshift uncertainty.," The formal fitting error on the redshift is much less than the quoted redshift uncertainty, but systematic effects (e.g. in the wavelength calibration due to spectrograph flexure) limit the accuracy to $\sim 25\kms$, which we adopt as our redshift uncertainty."118 We recall. for comparison. that the COS resolution ix 1520)aus.," We recall, for comparison, that the COS resolution is $15-20\kms$."119 The ealaxy spectrum shows a few. verv weak cussion les aud the S/N is not sufficient to detect anv absorption.," The galaxy spectrum shows a few, very weak emission lines and the S/N is not sufficient to detect any absorption."120 Despite the relative weakness of the cussion lines. the redshift determination is confirmed by the detection of I1]. LI) audIL.," Despite the relative weakness of the emission lines, the redshift determination is confirmed by the detection of ], ] and."121.. The spectrum of Hs shown in Fieure 1.., The spectrum of is shown in Figure \ref{fig: gal_spec}.122 Since any star-formation rate (SER) aud metallicity indicators we derive depoeud seusitivelv ou the measured line streneth. care is needed when fiux-calibratiug the ealaxv spectra.," Since any star-formation rate (SFR) and metallicity indicators we derive depend sensitively on the measured line strength, care is needed when flux-calibrating the galaxy spectra."123 We attempt to eusure consistent flix calibration of both blue aud red sides of the LRIS spectra., We attempt to ensure consistent flux calibration of both blue and red sides of the LRIS spectra.124 The secius durius the LRIS observations was uot exceptional. so light losses from a sslit were corrected by comparing our spectra with SDSS photometry.," The seeing during the LRIS observations was not exceptional, so light losses from a slit were corrected by comparing our spectra with SDSS photometry."125" We accomplish this absolute flux correction by convolving the LRIS spectra with SDSS «gri: filter response curves (soe2.foradescriptionoftheIDLcode""spec2iiag ).. aud comparing the observed spectral apparent magnitudes with the SDSS catalog apparent nagnitudes (see?.fordetails)..."," We accomplish this absolute flux correction by convolving the LRIS spectra with SDSS $ugriz$ filter response curves \citep[see][for a description126of the IDL code ``spec2mag'']{da-silva-etal-11}, , and comparing the observed spectral apparent magnitudes with the SDSS catalog apparent magnitudes \citep[see][for127details]{werk-etal-11-galaxies}."128 This process vields au independent multiplicative correction for both blue aud red spectra., This process yields an independent multiplicative correction for both blue and red spectra.129 We derive flux correction factors of 2.2 for he blue ας in g-band) anc 2.0 for the red side sideπας in ας}., We derive flux correction factors of 2.2 for the blue side mag in -band) and 2.0 for the red side mag in -band).130 Note that this correspouds slit losses of some 50°55%. and ciuplasizes the inportauce and dithculty of absolute flux calibration.," Note that this corresponds to slit losses of some $50-55\%$, and emphasizes the importance and difficulty of absolute flux calibration."131 We took deveddened iagnuitudoes aud colors for οι SDSS. and computed the distance modulus. aud absolute magnitude with the software (7) using the measured redshift. allof which are listed iu TabletionL.," We took de-reddened magnitudes and colors for from SDSS, and computed the distance modulus and absolute magnitude with the software \citep{blanton-roweis-07-kcorrect} using the measured redshift, allof which are listed in Table \ref{tab: galaxy_properties}."132 For conrparisoj we used the SDSS luminosity func paralucters frou ?..," For comparison, we used the SDSS luminosity function parameters from \citet{blanton-etal-03-SDSS-LF}. ."133 These parametersare strictly appropriate oulv for comparisons at 2=0.1 κο for the calculation of the Iuninositv in Table we correct to ;= O.1: in all other cases wecorrect to+= 0.," These parametersare strictly appropriate only for comparisons at $z = 0.1$ so for the calculation of the luminosity in Table \ref{tab: galaxy_properties} we correct to $z = 0.1$ ; in all other cases wecorrect to$z =1340$ ."135 We also, We also136"molecular clouds have studied the morphologies of clumps and cores with magnetic fields (??),, and found they were also filamentary and irregular.","molecular clouds have studied the morphologies of clumps and cores with magnetic fields \citep{Li04,Tilley07}, and found they were also filamentary and irregular."137 This suggests that the addition of molecular fields would not substantially alter our results., This suggests that the addition of molecular fields would not substantially alter our results.138" MHD codes are grid based, and require adaptive mesh refinement in order to match the dynamical range of SPH, which enables us to resolve scales of 10 pc down to a few hundred AU."," MHD codes are grid based, and require adaptive mesh refinement in order to match the dynamical range of SPH, which enables us to resolve scales of $10$ pc down to a few hundred AU."139" It is this property which has allowed us to both generate a large dataset of cores, and to probe their structure on the smallest scales."," It is this property which has allowed us to both generate a large dataset of cores, and to probe their structure on the smallest scales."140" There have been valiant attempts to introduce magnetic fields into SPH (??),, but as yet there are no large scale simulations of an entire molecular cloud, as would be needed to robustly assemble enough cores for a statistical analysis."," There have been valiant attempts to introduce magnetic fields into SPH \citep{Price08,Price10}, but as yet there are no large scale simulations of an entire molecular cloud, as would be needed to robustly assemble enough cores for a statistical analysis."141" Our simulation also lacks full radiative transfer, and instead uses a crude heating prescription."," Our simulation also lacks full radiative transfer, and instead uses a crude heating prescription."142" This is almost certainly wrong, particularly as it assumes spherical symmetry, which we have just shown to be a poor assumption."," This is almost certainly wrong, particularly as it assumes spherical symmetry, which we have just shown to be a poor assumption."143" However, this heating prescription, if anything, overestimates the heating from the protostars, and therefore is likely to support the core and smooth its structure."," However, this heating prescription, if anything, overestimates the heating from the protostars, and therefore is likely to support the core and smooth its structure."144" Without this prescription, our cores would be even more filamentary."," Without this prescription, our cores would be even more filamentary."145" We include it in this analysis as there will be a supporting force from the radiative transfer, and it is better to overestimate it than underestimate it."," We include it in this analysis as there will be a supporting force from the radiative transfer, and it is better to overestimate it than underestimate it."146 We have classified the structures of Class 0 cores in a large SPH simulation of a giant molecular cloud., We have classified the structures of Class 0 cores in a large SPH simulation of a giant molecular cloud.147 We define the cores as the material within r—0.01 pc of the sink when it first forms., We define the cores as the material within $r=0.01$ pc of the sink when it first forms.148 Our main conclusions are as follows., Our main conclusions are as follows.149" Due to the non-axisymetric nature of the cores, the line profiles of collapsing cores are likely to be more complex than spherical models suggest."," Due to the non-axisymetric nature of the cores, the line profiles of collapsing cores are likely to be more complex than spherical models suggest."150" It will be harder to slow down, or prevent core accretion through feedback, as most of the surface of the cores is at low column densities, allowing radiation to escape (?),,"," It will be harder to slow down, or prevent core accretion through feedback, as most of the surface of the cores is at low column densities, allowing radiation to escape \citep{Dale08},"151Understanding the nature and origin of spiral structure in galaxies is still a fundamental problem in astrophysics.,Understanding the nature and origin of spiral structure in galaxies is still a fundamental problem in astrophysics.152 lt is evident that in many galaxies spiral structure is driven by tical effects. either externally by interaction with a Companion. or companions. or internally by a central rotating bar.," It is evident that in many galaxies spiral structure is driven by tidal effects, either externally by interaction with a companion, or companions, or internally by a central rotating bar."153 It is worth noting than the possibility. of tidal excitation is not. precluded by the apparent absence of a visible perturber.. because orbiting clumps of dark matter might be responsible (ον.," It is worth noting than the possibility of tidal excitation is not precluded by the apparent absence of a visible perturber, because orbiting clumps of dark matter might be responsible \citep{Tutukov2006,Dubinski2008}."154 Indeed. some authors have argued that all spiral structure is driven in this manner (e.g. ?22)).," Indeed, some authors have argued that all spiral structure is driven in this manner (e.g. \citealt{Kormendy1979,Bottema2003}) )."155 However determining whetheraff spiral structure is tically induced is not a simple observational problem., However determining whether spiral structure is tidally induced is not a simple observational problem.156 There is also the possibility. at least from. theoretical considerations. that some spirals can be self-excited.," There is also the possibility, at least from theoretical considerations, that some spirals can be self-excited."157 Lere wo distinct possible mechanisms for the excitation of spiral structure have been proposed., Here two distinct possible mechanisms for the excitation of spiral structure have been proposed.158 First. there is the argument hat spiral structure is the result. of quasi-steady.. global mocles in the stellar cise (??)..," First, there is the argument that spiral structure is the result of quasi-steady, global modes in the stellar disc \citep{Lin1964,Bertin1989}."159" This is commonly. referred ο as ""density wave theory’.", This is commonly referred to as `density wave theory'.160 Second there is the suggestion hat spiral structure is the result. of local. transient. eravitational instabilities (7). which shear to form short-ived spiral armis (27)...," Second there is the suggestion that spiral structure is the result of local, transient self-gravitational instabilities \citep{Toomre1964} which shear to form short-lived spiral arms \citep{Toomre1990,Sellwood1991}."161 Early. numerical simulations of this oocess (?) indicated. that such activity. might be short ived. in the absence of some other phenomenon. such as gas accretion. which could act to reduce the stellar dispersion velocity. and so maintain the disc close to the borderline for sel-eravitational instability.," Early numerical simulations of this process \citep{Sellwood1984} indicated that such activity might be short lived, in the absence of some other phenomenon, such as gas accretion, which could act to reduce the stellar dispersion velocity, and so maintain the disc close to the borderline for self-gravitational instability."162 However. more recent. higher resolution simulations suggest that the activity can last for a substantial fraction of a Hubble time (?)..," However, more recent, higher resolution simulations suggest that the activity can last for a substantial fraction of a Hubble time \citep{Fujii2010}."163 One problem. highlighted. in a recent review (ο). is hat it is οΠο to find observational tests to distinguish tween the various theoretical models.," One problem, highlighted in a recent review \citep{Sellwood2010}, is that it is difficult to find observational tests to distinguish between the various theoretical models."164 In fact. the usual observational approach seems to be to assume one model (usually the assumption is that there is a well-defined global xdtern speed). and to then interpret. the observations in erms of that particular model (e.g. 277)).," In fact the usual observational approach seems to be to assume one model (usually the assumption is that there is a well-defined global pattern speed), and to then interpret the observations in terms of that particular model (e.g. \citealt{Elmegreen1989c, Kendall2008,165Mart2009}) )."166 Several authors jwe tried to infer pattern speeds by use of colour gradients o observe a transition in stellar ages across the spiral armis (??2?777)..," Several authors have tried to infer pattern speeds by use of colour gradients to observe a transition in stellar ages across the spiral arms \citep{Efremov1982,Regan1993,Beckman1990,Gonzalez1996,Mart2009}."167 Llowever with the exception of one or two cases. here is rarely an identifiable trend in the colour gradients.," However with the exception of one or two cases, there is rarely an identifiable trend in the colour gradients."168 For nearby. galaxies. it is also possible to study. the ages of individual clusters (22?777)..," For nearby galaxies, it is also possible to study the ages of individual clusters \citep{Anders2004,Fall2005,Scheepmaker2007,Fall2009, Bastian2009}."169 This technique involves itting the Lea magnitudes to those predicted. by stellar population and starburst models. and then estimating an age for each star cluster.," This technique involves fitting the $\alpha$ magnitudes to those predicted by stellar population and starburst models, and then estimating an age for each star cluster."170 Estimates of ages are thought o be accurate to within [actors of around two. and ages can xf derived from. around. 1. Myr to around. LOO Myr.," Estimates of ages are thought to be accurate to within factors of around two, and ages can be derived from around 1 Myr to around 100 Myr."171 This method. has been applied. to the LAIC ancl SMC. (777).. and interacting galaxies. the Antennae (7). and M51 (77).," This method has been applied to the LMC and SMC \citep{Hunter2003,deGrijs2006,Chandar2010}, and interacting galaxies, the Antennae \citep{Fall2009} and M51 \citep{Bik2003,Kaleida2010}."172 So far. the age-dating of clusters has been largely used o examine intrinsic properties of clusters. e.g. the cluster IME. age mass relation. size age relation.," So far, the age-dating of clusters has been largely used to examine intrinsic properties of clusters, e.g. the cluster IMF, age mass relation, size age relation."173 However if one can assume that in spiral galaxies such stellar clusters form wedominantly in regions of high gas density. for example edominantly. within the spiral arms. then the distribution of agc-dated clusters throughout the spiral galaxy can be used. as a means of obtaining some idea of the nature and imine of the gas flow relative to the spiral arms.," However if one can assume that in spiral galaxies such stellar clusters form predominantly in regions of high gas density, for example predominantly within the spiral arms, then the distribution of age-dated clusters throughout the spiral galaxy can be used as a means of obtaining some idea of the nature and timing of the gas flow relative to the spiral arms."174 In this wav it might be possible to distinguish between the various heoretical models for spiral arm formation., In this way it might be possible to distinguish between the various theoretical models for spiral arm formation.175 7. also mace predictions about stellar clusters in the context of density wave theory., \citet{Bash1977} also made predictions about stellar clusters in the context of density wave theory.176 However their. analysis, However their analysis177Although the present results provide important new insights into the FU Ori svstem new questions arose as well.,Although the present results provide important new insights into the FU Ori system new questions arose as well.178 Future investigations will include a more thorough and detailed modeling of (he observations with numerical radiative transfer disk models., Future investigations will include a more thorough and detailed modeling of the observations with numerical radiative transfer disk models.179 These models will not only need to consider the high accretion rates but also such effects as sell-irradiation of the disk., These models will not only need to consider the high accretion rates but also such effects as self-irradiation of the disk.180 It will be interesting to see whether these models are able to confirm the apparent rotation of the disks position angle with wavelength ancl whether they. can reproduce the increasing visibility curve for the. UT3-UT4 baseline., It will be interesting to see whether these models are able to confirm the apparent rotation of the disk's position angle with wavelength and whether they can reproduce the increasing visibility curve for the UT3-UT4 baseline.181 Also. these disk models will have to reproduce the observed NIB. ancl MIB. visibiliGes simultaneously with hieher accuracy (han (he current simple models are able to do.," Also, these disk models will have to reproduce the observed NIR and MIR visibilities simultaneously with higher accuracy than the current simple models are able to do."182 From the observational side re-measuring the baseline might be eligible aud anv other new baseline configuration will certainly help to constrain the disk geometry (especially the position angle) even better., From the observational side re-measuring the UT3-UT4 baseline might be eligible and any other new baseline configuration will certainly help to constrain the disk geometry (especially the position angle) even better.183 Concerning the dust structure the lack of ervstalline silicates needs to be analvzed in greater detail., Concerning the dust structure the lack of crystalline silicates needs to be analyzed in greater detail.184 Is it still just a contrast effect that we do not see any ervstalline features in (he spectra or are {μον simply not there?, Is it still just a contrast effect that we do not see any crystalline features in the spectra or are they simply not there?185 Eventually we will have to face the problem that currently all FUORs that have been observed with hieh spatial resolution techiiques draw a rather inhomogeneous picture ol the group., Eventually we will have to face the problem that currently all FUORs that have been observed with high spatial resolution techniques draw a rather inhomogeneous picture of the group.186 Apparently. some are still surrounded by nearby dense envelopes while for others the cireumstellar disks sullice to explain the observations.," Apparently, some are still surrounded by nearby dense envelopes while for others the circumstellar disks suffice to explain the observations."187 However. even those (i.e.. FU Ori and V1647 Ori) seem to be different in terms of physical properties as different temperature and surface density. profiles are derived.," However, even those disk-systems (i.e., FU Ori and V1647 Ori) seem to be different in terms of physical properties as different temperature and surface density profiles are derived."188 Without anv doubt interferometric observations of cireumstellar disks in the NIR aud AUR provide an unprecedented means for deriving geometrical disk properties ancl put new constraints on (he physical (and also chemical) processes (aking place within protoplanetary disks., Without any doubt interferometric observations of circumstellar disks in the NIR and MIR provide an unprecedented means for deriving geometrical disk properties and put new constraints on the physical (and also chemical) processes taking place within protoplanetary disks.189 Ancl as more and more interferometric data of cireumstellar disks are published our view on the cradle of planetary svstems will be once more relined., And as more and more interferometric data of circumstellar disks are published our view on the cradle of planetary systems will be once more refined.190 5. P. Quanz kindly acknowledges financial support bv the GermanStiftung., S. P. Quanz kindly acknowledges financial support by the German.191.. Th., Th.192 Henning and J. Bouwman acknowledge financial support bv the EC-RTN on “The Formation and Evolution of Young Stellar Clusters” (. IIDN-CTT-2000-00155).," Henning and J. Bouwman acknowledge financial support by the EC-RTN on ""The Formation and Evolution of Young Stellar Clusters"" ( HPRN-CT-2000-00155)."193 We are most grateful to R. Wobbler aud F. Laliuis for their support during the data reduction and to B. Lachaunme zd E. Malbet for providing MIR. data derived from their disk models (secon 7.2.)., We are most grateful to R. Köhhler and F. Lahuis for their support during the data reduction and to R. Lachaume and F. Malbet for providing MIR data derived from their disk models (section 7.2.).194 We thank our anonvmous releree for a detailed and (thorough review that improved the manuscript., We thank our anonymous referee for a detailed and thorough review that improved the manuscript.195 This researeh has made use of the SIMDAD database. operated al CDS. Strasbourg. France. and was partly based on observations made with the," This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France, and was partly based on observations made with the"196which would lead to a softening of the spectrum and a decrease of the cut-off energy. has to be included in the model with a= |.,"which would lead to a softening of the spectrum and a decrease of the cut-off energy, has to be included in the model with $a\simeq 1$ ."197 Namely. an etheient nonthermal synchrotron emission from relativistic e*. coming from the decay of charged pions copiously produced through proton-proton collisions in a flow around. a rapidly rotating black hole. where 7;7I0 K. would provide a strong seed photon input in addition to the thermal synchrotron emission.," Namely, an efficient nonthermal synchrotron emission from relativistic $^\pm$, coming from the decay of charged pions copiously produced through proton-proton collisions in a flow around a rapidly rotating black hole, where $T_{\rm i} \ga 10^{13}$ K, would provide a strong seed photon input in addition to the thermal synchrotron emission."198 However. we leave a more detailed comparison of the spectrum observed from Cen A with the hot flow model spectra to a future work. in which we will take into account the relevant hadronie processes.," However, we leave a more detailed comparison of the spectrum observed from Cen A with the hot flow model spectra to a future work, in which we will take into account the relevant hadronic processes."199 Black-hole binaries in the hard spectral state have typical X-ray joheton spectra (measured typically in the 3-10 keV range) of D= L5-2 (e.g. Zdziarski Gierlifisski 2004: McClintock Remillard 2006).," Black-hole binaries in the hard spectral state have typical X-ray photon spectra (measured typically in the 3–10 keV range) of $\Gamma\simeq 1.5$ –2 (e.g., Zdziarski Gierlińsski 2004; McClintock Remillard 2006)."200 In luminous spectral states. £70.01Lp or so. the ugh energy cut-offs in those spectra occur at energies = 50—200 keV (e.g.. Grove et 11998: Wardzinsski et 22002: Zdziarski Gierlifisski 2004). as measured by the position of the spectral urnover in EF; spectra.," In luminous spectral states, $L\ga 0.01\ledd$ or so, the high energy cut-offs in those spectra occur at energies $\simeq 50$ –200 keV (e.g., Grove et 1998; Wardzińsski et 2002; Zdziarski Gierlińsski 2004), as measured by the position of the spectral turnover in $EF_E$ spectra."201 Thus. the X-ray slope of our model spectra. Γ5 1.5-1.7. is in the range of the observed values.," Thus, the X-ray slope of our model spectra, $\Gamma\simeq 1.5$ –1.7, is in the range of the observed values."202 On the other hand. the ligh-energy turnovers in our spectra are at =SOO keV. which is üigher than the values observed.," On the other hand, the high-energy turnovers in our spectra are at $\simeq 500$ keV, which is higher than the values observed."203" However. our models have L/ (0.448)x107. which is lower than L/L, at which most of the spectral cut-offs have been measured."," However, our models have $L/\ledd \simeq (0.4$ $8)\times 10^{-3}$, which is lower than $L/\ledd$ at which most of the spectral cut-offs have been measured."204 When measured. the cut-off energy has been found to increase with the decreasing luminosity (Wardzinsski et 22002: Yamaoka et 22006: Miyakawa et 22008). and thus it is possible that the cut-off energy is at ~500 keV in some low-Z hard states.," When measured, the cut-off energy has been found to increase with the decreasing luminosity (Wardzińsski et 2002; Yamaoka et 2006; Miyakawa et 2008), and thus it is possible that the cut-off energy is at $\sim$ 500 keV in some $L$ hard states."205 The value of the X-rayphoton index shows a negutive correlation with the luminosity in luminous hard states of black-hole binaries. at £L70.01£4: or so. i.e. the spectra soften with the increasing £L.," The value of the X-rayphoton index shows a negative correlation with the luminosity in luminous hard states of black-hole binaries, at $L\ga 0.01\ledd$ or so, i.e., the spectra soften with the increasing $L$."206 However. the correlation changes its sign at low £. where the spectra soften with the decreasing L (e.g.. Corbel et 22004: Zdziarski et 22004: Yuan et 22007: Wu Gu 2008: Sobolewska et 22011).," However, the correlation changes its sign at low $L$, where the spectra soften with the decreasing $L$ (e.g., Corbel et 2004; Zdziarski et 2004; Yuan et 2007; Wu Gu 2008; Sobolewska et 2011)."207 As pointed out by Sobolewska et (2011). this indicates a change in the physical nature of the X-ray source at a luminosity of a fraction of a per cent.," As pointed out by Sobolewska et (2011), this indicates a change in the physical nature of the X-ray source at a luminosity of a fraction of a per cent."208 Those authors discuss two scenarios explaining this change., Those authors discuss two scenarios explaining this change.209 One is that the emission is dominated by an accretion flow at high £L. and by a nonthermal jet radiation (mostlikely synchrotron) at low £L.," One is that the emission is dominated by an accretion flow at high $L$, and by a nonthermal jet radiation (mostlikely synchrotron) at low $L$."210 This scenario for the black-hole binary XTE J1550—564 is discussed by Russell et (2010). who found the near-infrared/optical (~107. Hz) emission is tightly correlated with X-rays at low £. but not at high £.," This scenario for the black-hole binary XTE J1550–564 is discussed by Russell et (2010), who found the near-infrared/optical $\sim 10^{14.5}$ Hz) emission is tightly correlated with X-rays at low $L$, but not at high $L$."211" A potential problem for this model is presented by the fact that basically the same L-I correlation. negative at low L/L, and positive at high L/Ly is observed in AGNs."," A potential problem for this model is presented by the fact that basically the same $L$ $\Gamma$ correlation, negative at low $L/\ledd$ and positive at high $L/\ledd$ is observed in AGNs."212 The transition is at L/L.~0.01 or so. about the same as in black-hole binaries (e.g... Gu Cao 2009: Constantin et 22009: Younes et 22011: Veledina et 22011).," The transition is at $L/\ledd\sim 0.01$ or so, about the same as in black-hole binaries (e.g., Gu Cao 2009; Constantin et 2009; Younes et 2011; Veledina et 2011)."213 The magnetic field in jets in black-hole sources is expected to scale as BoxM7 (eg. Heinz Sunyaev 2003). which (since the cyclotron frequency is « B) very strongly atfects the jet emission. leading. in particular. to the strong mass dependence of the relative strength of the jet emission at a given frequency (Merloni. Heinz Di Matteo 2003).," The magnetic field in jets in black-hole sources is expected to scale as $B\propto M^{-1/2}$ (e.g., Heinz Sunyaev 2003), which (since the cyclotron frequency is $\propto B$ ) very strongly affects the jet emission, leading, in particular, to the strong mass dependence of the relative strength of the jet emission at a given frequency (Merloni, Heinz Di Matteo 2003)."214 Thus. it appears highly unlikely that the X-ray jet emission would start to dominate the accretion-flow emission below about the same Eddington ratio in both black-hole binaries and AGNs (see also Yuan Cui 2005: Yuan. Yu Ho 2009).," Thus, it appears highly unlikely that the X-ray jet emission would start to dominate the accretion-flow emission below about the same Eddington ratio in both black-hole binaries and AGNs (see also Yuan Cui 2005; Yuan, Yu Ho 2009)."215 The second possibility explaining the form of the L- T correlation discussed by Sobolewska et (2011). and independently by Veledina et (20113. 1s that it is duetoa change of the character of the dominant seed photons for Comptonization.," The second possibility explaining the form of the $L$ $\Gamma$ correlation discussed by Sobolewska et (2011), and independently by Veledina et (2011), is that it is dueto a change of the character of the dominant seed photons for Comptonization."216 The overall idea follows the model for spectral changes of black-hole binaries developed by Esin et ((1997. 1998). whose model did predict the changing £-T correlation. see. e.g. |] in Esin et (1998).," The overall idea follows the model for spectral changes of black-hole binaries developed by Esin et (1997, 1998), whose model did predict the changing $L$ $\Gamma$ correlation, see, e.g, 1 in Esin et (1998)."217 At high £L. above the transition L/Li. the seed photons are likely to be from an optically-thick dise overlapping with the hot flow.," At high $L$, above the transition $L/\ledd$, the seed photons are likely to be from an optically-thick disc overlapping with the hot flow."218 There is a lot of observational evidence for the presence of an outer cold dise in luminous hard states (as summarized by Done. Gierlifisski Kubota 2007). e.g.. a strong correlation of EL with qe relative strength of Compton reflection (Zdziarski. Lubifisski Smith 1999).," There is a lot of observational evidence for the presence of an outer cold disc in luminous hard states (as summarized by Done, Gierlińsski Kubota 2007), e.g., a strong correlation of $\Gamma$ with the relative strength of Compton reflection (Zdziarski, Lubińsski Smith 1999)."219 Also. the inner disc radius decreases with the increasing L (e.g.. Done et 22007).," Also, the inner disc radius decreases with the increasing $L$ (e.g., Done et 2007)."220 This naturally explains ae positive L-T correlation. since the resulting increasing overlap between the cold dise and the hot flow leads to both an increase of the strength of Compton reflection and increased cooling of the Comptonizing plasma. resulting in softening of the X-ray spectra.," This naturally explains the positive $L$ $\Gamma$ correlation, since the resulting increasing overlap between the cold disc and the hot flow leads to both an increase of the strength of Compton reflection and increased cooling of the Comptonizing plasma, resulting in softening of the X-ray spectra."221" However. at low L/L,. the outer dise may be truncated far away. and the dominant source of seed photons for Comptonization becomes synchrotron emission. as in the models studied in this work as well as in the ADAF model in general (Narayan Yi 1995)."," However, at low $L/\ledd$, the outer disc may be truncated far away, and the dominant source of seed photons for Comptonization becomes synchrotron emission, as in the models studied in this work as well as in the ADAF model in general (Narayan Yi 1995)."222 This model can also explain the correlation of the X-rays with the near-infrared/optical emission. which. in this scenario. would be from the ADAF flow. see reffig:spectra sel.," This model can also explain the correlation of the X-rays with the near-infrared/optical emission, which, in this scenario, would be from the ADAF flow, see \\ref{fig:spectra_stel}."223 As shown in Section 3.2.. our models spectra do harden with he increasing £. with AT~—0.1 for £ increasing by a factor of several.," As shown in Section \ref{final}, our models spectra do harden with the increasing $L$ , with $\Delta\Gamma\sim -0.1$ for $L$ increasing by a factor of several."224" This strongly supports the suggestion of Sobolewska et (201D that the negative £-P correlation seen at L/L,50.01 is due o the dominance of synchrotron seed photons in that regime.", This strongly supports the suggestion of Sobolewska et (2011) that the negative $L$ $\Gamma$ correlation seen at $L/\ledd\la 0.01$ is due to the dominance of synchrotron seed photons in that regime.225 A wrdening of the ADAF spectra with increasing L. below a few vr cent of Li. was studied previously by Esin et (1997): their model seems to predict a much stronger effect. with the increase of i by a factor of 10 corresponding to ΔΓ=—0.7.," A hardening of the ADAF spectra with increasing $L$, below a few per cent of $\ledd$, was studied previously by Esin et (1997); their model seems to predict a much stronger effect, with the increase of $\dot m$ by a factor of 10 corresponding to $\Delta\Gamma\approx -0.7$."226 In this work. we ive considered only two values of the accretion rate. and have not ully tested this model against observational data.," In this work, we have considered only two values of the accretion rate, and have not fully tested this model against observational data."227 We will consider his issue in detail in a paper in preparation., We will consider this issue in detail in a paper in preparation.228 We note that Oda et (2010) propose another possible explanation for the difference between the low and high luminosity wird states., We note that Oda et (2010) propose another possible explanation for the difference between the low and high luminosity hard states.229 It is a transition between two equilibrium states of an optically thin. two temperature flow with a weak and a strong magnetic field. respectively.," It is a transition between two equilibrium states of an optically thin, two temperature flow with a weak and a strong magnetic field, respectively."230 Such a change of magnetic field is outside the scope of our model., Such a change of magnetic field is outside the scope of our model.231 We have developed a fully GR. model with global Compton seattering of hot. tenuous accretion flows.," We have developed a fully GR model with global Compton scattering of hot, tenuous accretion flows."232 The dominant source of seed photons in our model is the synchrotron process., The dominant source of seed photons in our model is the synchrotron process.233 We assume that an outer. optically-thick. accretion dise is truncated at large radii. so irradiation of the hot flow by it is negligible.," We assume that an outer, optically-thick, accretion disc is truncated at large radii, so irradiation of the hot flow by it is negligible."234 We have also neglected direct viscous electron heating and outflows., We have also neglected direct viscous electron heating and outflows.235" We have considered the accretion rates of fi=0.1 and 0.5. for which our model gives the bolometric luminosities of L/L,~ (04-8)x10 7."," We have considered the accretion rates of $\dot m = 0.1$ and 0.5, for which our model gives the bolometric luminosities of $L/\ledd \simeq (0.4$ $8)\times 10^{-3}$ ."236 In this range of L/L;. we find our models predict X-ray spectra hardening with increasing L. which is in agreement with the correlation observed at L/L.“0.01 in both black-hole binaries in thehard state and AGNs.," In this range of $L/\ledd$ , we find our models predict X-ray spectra hardening with increasing $L$ , which is in agreement with the correlation observed at $L/\ledd\la 0.01$ in both black-hole binaries in thehard state and AGNs."237 This is also in agreement with the suggestion of Sobolewska et (2011) that synchrotron seed, This is also in agreement with the suggestion of Sobolewska et (2011) that synchrotron seed238Flexiou has recently been introduced as a iuecaus of casting ΜΗ scale variations iu weak eravitational leus fields (Goldberg Bacon. 2005: Bacon. Goldberg. Rowe Tavlor. 2006. lereatter DGRT).,"Flexion has recently been introduced as a means of measuring small scale variations in weak gravitational lens fields (Goldberg Bacon, 2005; Bacon, Goldberg, Rowe Taylor, 2006, hereafter BGRT)."239 Rather than simply measting the ellipticities of arclets. this techuique aims to measure the “arciness” and “skewness” (collectively referred to as “flexion”) of a lensed nuage.," Rather than simply measuring the ellipticities of arclets, this technique aims to measure the “arciness” and “skewness” (collectively referred to as “flexion”) of a lensed image."240 Flexion is a complementary approach to shear analysis iu that it uses the odd moments (3rd imultipole moments. for exanrple) to compute local gradients in a shear field.," Flexion is a complementary approach to shear analysis in that it uses the odd moments (3rd multipole moments, for example) to compute local gradients in a shear field."241" DGRT have discussed how flexion παν be used to identify substructure in clusters. to normalize the matter power Προςπα on sub-arcniünute scales via ""cosmic flexion (as an analog to cosmic shear). and to estimate the ellipticitv of ealaxy-galaxy lenses."," BGRT have discussed how flexion may be used to identify substructure in clusters, to normalize the matter power spectrum on sub-arcminute scales via “cosmic flexion” (as an analog to cosmic shear), and to estimate the ellipticity of galaxy-galaxy lenses."242 As a practical application. flexion has already been used to measure ealaxy-galaxy lensing (Goldberg Bacon. 2005). and is presently being used iu cluster reconstruction (Leonard et al.," As a practical application, flexion has already been used to measure galaxy-galaxy lensing (Goldberg Bacon, 2005), and is presently being used in cluster reconstruction (Leonard et al.,"243 in preparation)., in preparation).244 However. there have beeu several difficultics iu the estihuation of flexion on real objects.," However, there have been several difficulties in the estimation of flexion on real objects."245 First. the flexion Inversion is difficult to describe. contaius an enormous uunber of terms. and thus. is rather daunting to code.," First, the flexion inversion is difficult to describe, contains an enormous number of terms, and thus, is rather daunting to code."246 Secondly. there has been little discussion of the explicit effects of PSF couvolution or deconvolution.," Secondly, there has been little discussion of the explicit effects of PSF convolution or deconvolution."247 Finally. uulike shear. there has; until recently. been no simple form to even approximate what the “flexion” is.," Finally, unlike shear, there has, until recently, been no simple form to even approximate what the “flexion” is."248 The remainder of this paper will thus be a practical euide to 1icasuriue flexion in real images., The remainder of this paper will thus be a practical guide to measuring flexion in real images.249 We begin. below. * renüudiug the reader of the basic terius involved iu Hexion analysis.," We begin, below, by reminding the reader of the basic terms involved in flexion analysis."250 Iu 2.. we review shapelet decomposition. and discuss some of the issues involved in using shapelets ο nieasiure fexion.," In \ref{sec:shapelets}, we review shapelet decomposition, and discuss some of the issues involved in using shapelets to measure flexion."251" Iu δν, we discuss a new. conceptually simpler. form of flexion analysis developed by Okura et al. ("," In \ref{sec:holics}, we discuss a new, conceptually simpler, form of flexion analysis developed by Okura et al. ("2522006). which uses moments. rather than basis fuuctions olncasure flexion.,"2006), which uses moments, rather than basis functions to measure flexion."253 They call their technique Ποπο Order Lensing huage*s Characteristics. or HOLICs.," They call their technique Higher Order Lensing Image's Characteristics, or HOLICs."254 We refine he IIOLICs approach somewhat. aud develop a KSB (Ixaiser. Squires. Broadhurst. 1995)-type approach using a Gaussian filter to perform an inversion. as well as describe a technique for PSF deconvolution.," We refine the HOLICs approach somewhat, and develop a KSB (Kaiser, Squires, Broadhurst, 1995)-type approach using a Gaussian filter to perform an inversion, as well as describe a technique for PSF deconvolution."255 Iu L.. we discuss Comparisons of the two techniques using simulated lenses and simulated PSEsS.," In \ref{sec:simulate}, we discuss comparisons of the two techniques using simulated lenses and simulated PSFs."256 Tn 5. we compare shapelets and HOLICS inversious on UST images.," In \ref{sec:measurement}, we compare shapelets and HOLICs inversions on HST images."257" Finally. in 6,, we discuss the implications of this study."," Finally, in \ref{sec:discuss}, we discuss the implications of this study."258 Iu Appendix A. we also preseut the explicit HIOLIC'S Inversion niatrix. so the reader can write his/her own code.," In Appendix A, we also present the explicit HOLICs inversion matrix, so the reader can write his/her own code."259 Ie/she need not do so. however. as all codes discussed herein are available from the flexion What is flexion?," He/she need not do so, however, as all codes discussed herein are available from the flexion What is flexion?"260 Conceptually. flexion represeuts local variability in the shear field which expresses itself as second-order distortions in the coordinate transformation between unleused. and lensed ininages: with where 0; is shorthaud for 0/00.," Conceptually, flexion represents local variability in the shear field which expresses itself as second-order distortions in the coordinate transformation between unlensed and lensed images: with where $\partial_k$ is shorthand for $\partial/\partial x_k$."261 Hore. A 15 the normal deprojection operator: and thus. the second terii on right im equation (1)) represents the flexion signal.," Here, ${\bf A}$ is the normal deprojection operator: and thus, the second term on right in equation \ref{eq:transform}) ) represents the flexion signal."262 D max be written as: These distortions create asviunetries in a lensed image a skewness and a bendiug. depending on the values of individual cocticicuts.," ${\bf D}$ may be written as: These distortions create asymmetries in a lensed image – a skewness and a bending, depending on the values of individual coefficients."263 πα Shlinalova (2005:2006) describe a simula leusine analysis technique im which, Irwin Shmakova (2005;2006) describe a similar lensing analysis technique in which264the lack of alignment.,the lack of alignment.265" Weak but significant X-ray emission associated with the south-eastern extension of the northern coincident with a bend in the radio counter-jet (N-C-jet-bend""), can be explained by iC/CMB emission with a field of 32-1 "," Weak but significant X-ray emission associated with the south-eastern extension of the northern radio-lobe, coincident with a bend in the radio counter-jet (“N-C-jet-bend”), can be explained by iC/CMB emission with a field of $\pm1$ "266where an overdot denotes derivative with respect to the cosmic time. a prime denotes derivative with respect to the redshift. and f is the fraction of haloes with mass greater than m7 (Press&Schechter 1974)...,"where an overdot denotes derivative with respect to the cosmic time, a prime denotes derivative with respect to the redshift, and $F$ is the fraction of haloes with mass greater than $m$ \citep{1974ApJ...187..425P}."267 The critical density for spherical collapse is symbolized by 5.. and σ(ni) is the variance in the initial density fluctuation field when smoothed with a top-hat filter of a scale corresponding to mass ni.," The critical density for spherical collapse is symbolized by $\delta_\mathrm{c}$, and $\sigma^2(m)$ is the variance in the initial density fluctuation field when smoothed with a top-hat filter of a scale corresponding to mass $m$."268 The rate of growth for perturbations in ye linear theory is denoted by d.(2)., The rate of growth for perturbations in the linear theory is denoted by $d_+(z)$.269 The total amount of baryons added to haloes of mass greater jin 107 M... is taken to be the amount of gas available for star ormation., The total amount of baryons added to haloes of mass greater than $10^8$ $_\odot$ is taken to be the amount of gas available for star formation.270 Gas already present in haloes is not considered for star ormation., Gas already present in haloes is not considered for star formation.271 We do not consider the contribution of minihaloes as jese. do not contribute significantly to the total star formation due to radiative feedback (Trenti&Stiavelli2009).., We do not consider the contribution of minihaloes as these do not contribute significantly to the total star formation due to radiative feedback \citep{2009arXiv0901.0711T}.272" We detine the efficiency of star formation. f, as the fraction of this gas thatis converted into stars."," We define the efficiency of star formation, $f_*$ as the fraction of this gas that is converted into stars."273" The rate of change of stellar mass can now be written as where p. is the critical density and Q), is the density parameter for baryons.", The rate of change of stellar mass can now be written as where $\rho_\mathrm{c}$ is the critical density and $\Omega_\mathrm{b}$ is the density parameter for baryons.274 Here we have ignored mass lost by stars through winds. outflows. and supernovae.," Here we have ignored mass lost by stars through winds, outflows, and supernovae."275 This can be taken into account using. for example. population synthesismodels?.," This can be taken into account using, for example, population synthesis."276. Equation (2)) illustrates the small number of parameters and approximations that go into estimating p. in our formulation., Equation \ref{rhodot}) ) illustrates the small number of parameters and approximations that go into estimating $\dot\rho_*$ in our formulation.277 Observations of absorption systems in quasar spectra have been used to put constraints on the average ete of the IGM (Cowieetal.1995:Songaila1997:Ellison2000:Simcoe.Sar- 2009).. ," Observations of absorption systems in quasar spectra have been used to put constraints on the average metallicity of the IGM \citep{1995AJ....109.1522C, 1997ApJ...490L...1S, 2000AJ....120.1175E,278 2004ApJ...606...92S,2008arXiv0812.2856B,2009arXiv0902.1991R}. ."279These observationsindicate that the amount of C IV in the IGM not evolve significantly between 2<=2.«X5.5 (Songaila2001:weBecker.Rauch.&Sargent2008: 2009)..," These observations indicate that the amount of C IV in the IGM does not evolve significantly between $2 \leq z \leq 5.5$ \citep{2001ApJ...561L.153S,2008arXiv0812.2856B,2009arXiv0902.1991R}."280 Itis not vet clear whether the IGM has been contaminated by metals throughout. or if the enriched regions of the IGM are restricted to the neighborhood of galaxies and filaments.," It is not yet clear whether the IGM has been contaminated by metals throughout, or if the enriched regions of the IGM are restricted to the neighborhood of galaxies and filaments."281 There are also issues related with understanding the ionization state to map from absorption by a particular species to metallicity (Schayeetal. 2003).., There are also issues related with understanding the ionization state to map from absorption by a particular species to metallicity \citep{2003ApJ...596..768S}.282 Observations also support a correlation between density and metallicity of the IGM. indicating that regions in proximity of galaxies are enriched to higher level than regions of IGM far away from galaxies (Schayeetal.2003:Pieri.Schaye.&Aguirre2006Seannapiecoetal. 2006)..," Observations also support a correlation between density and metallicity of the IGM, indicating that regions in proximity of galaxies are enriched to higher level than regions of IGM far away from galaxies \citep{2003ApJ...596..768S, 2006ApJ...638...45P, 2006MNRAS.365..615S}."283 We assume that the IGM is uniformly enriched at the level indicated by Songaila(2001) at 2~5.5., We assume that the IGM is uniformly enriched at the level indicated by \citet{2001ApJ...561L.153S} at $z \sim 5.5$.284 Winds and outflows are expected to be the dominant processes that lead to ejection of metals from the inter-stellar medium (ISM) of galaxies., Winds and outflows are expected to be the dominant processes that lead to ejection of metals from the inter-stellar medium (ISM) of galaxies.285 There is considerable evidence in favor of this mechanism as observations have detected outflows around almost all galaxies at high κ (Pettinietal.2001:Frye.Broad-hurst.&Benítez2002).. “h," There is considerable evidence in favor of this mechanism as observations have detected outflows around almost all galaxies at high redshifts \citep{2001ApJ...554..981P,2002ApJ...568..558F}."286eThe fraction of processed metals that can be depositec from ISM to the IGM without disturbing the IGM in an opservable manner is no known., The fraction of processed metals that can be deposited from the ISM to the IGM without disturbing the IGM in an observable manner is not known.287 Several authors often assume tha around 1% of metals oroduced in galaxies ean be ejected and deposited in the IGM., Several authors often assume that around $1\%$ of metals produced in galaxies can be ejected and deposited in the IGM.288 This may also be computed from first. princisles in detailed modeς etal.2004.2006:Samui.Subramanian.&Srianand2008).. enih," This may also be computed from first principles in detailed models \citep{2004ApJ...617..693D,2006ApJ...647..773D,2008MNRAS.385..783S}."289eIn these models supernova-driven outflows are responsible for IGM enrichment., In these models supernova-driven outflows are responsible for the IGM enrichment.290 The efficiency of these outflows depends on the star formation efficiency. the IMF and the efficiency of winds (Macau.Ferrara.2005:Furlanetto&Loeb2003).. NIAF," The efficiency of these outflows depends on the star formation efficiency, the IMF and the efficiency of winds \citep{2001ApJ...555...92M, 2002ApJ...574..590S, 2005ApJ...624L...1S,291 2003ApJ...588...18F}."292or a star formation efficiency of the volume filling factor the ejecta can be and at 2~3 the IGM metallicity could be around [-3] as detected by Songaila(2001).., For a star formation efficiency of the volume filling factor of the ejecta can be and at $z\sim 3$ the IGM metallicity could be around [-3] as detected by \citet{2001ApJ...561L.153S}.293 The amount of metals produced per baryon in stars can be computed once we fix the initial mass function IMF) of stars. and metallicity of the star-forming gas (Leitherer&Leitherer 2005)..," The amount of metals produced per baryon in stars can be computed once we fix the initial mass function (IMF) of stars, and metallicity of the star-forming gas \citep{1999ApJS..123....3L,2005ApJ...621..695V}."294 We can write for the number density of metals that reaches the IGM., We can write for the number density of metals that reaches the IGM.295 Here foseg is the fraction of total metals produced that is deposited in the IGM and p is the metal yield of the stars per baryon.," Here $f_\mathrm{esc, Z}$ is the fraction of total metals produced that is deposited in the IGM and $p$ is the metal yield of the stars per baryon."296 Note that we assume the same escape fraction for metals from galaxies of different masses. whereas it is far more likely that low mass galaxies lose nearly all the metals from the ISM and more massive galaxies lose very little (Dekel&Silk1986)..," Note that we assume the same escape fraction for metals from galaxies of different masses, whereas it is far more likely that low mass galaxies lose nearly all the metals from the ISM and more massive galaxies lose very little \citep{1986ApJ...303...39D}."297 Finally. observations of the temperature and. polarization anisotropies in the CMB provide a constraint on the EoR. Free electrons produced during reionization scatter the CMB photons and suppress temperature anisotropies on scales smaller than the Hubble radius at that time.," Finally, observations of the temperature and polarization anisotropies in the CMB provide a constraint on the EoR. Free electrons produced during reionization scatter the CMB photons and suppress temperature anisotropies on scales smaller than the Hubble radius at that time."298 The suppression is of the form e where is the Thomson scattering optical depth., The suppression is of the form $\mathcal{C}_l^{T^\prime}\!=e^{-2\tau}\mathcal{C}_l^T$ where is the Thomson scattering optical depth.299" Here »,(/) is the number density of free electrons and oy is the Thomson scattering cross-section.", Here $n_e(t)$ is the number density of free electrons and $\sigma_T$ is the Thomson scattering cross-section.300 This damping is degenerate with the amplitude of the primordial power spectrum., This damping is degenerate with the amplitude of the primordial power spectrum.301 The degeneracy is broken by detection of a polarization anisotropy for scales greater thanthe Hubble radius at the reionization redshift. an effect that dominates at scale," The degeneracy is broken by detection of a polarization anisotropy for scales greater thanthe Hubble radius at the reionization redshift, an effect that dominates at scale"3022010).,.303. Phe tapering can then have an influcnee on a substantial portion of the circumplanctary disc., The tapering can then have an influence on a substantial portion of the circumplanetary disc.304 estimated the disc outer radius based on where the angular momentum per unit disc mass ceparts from Ixeplerian and begins to decline in radius., \cite{ayliffe09} estimated the disc outer radius based on where the angular momentum per unit disc mass departs from Keplerian and begins to decline in radius.305 Phev obtained a disc outer radius of 20.35rg. (see the upper right panel of their Fig.," They obtained a disc outer radius of $\simeq 0.35306r_{\rm H}$ (see the upper right panel of their Fig."307 2)., 2).308 This radius is somewhat inside the orbit crossing radius of 20.41rg., This radius is somewhat inside the orbit crossing radius of $\simeq 0.41 r_{\rm H}$.309 The effect of the dise tapering on the distribution of disc angular momentum in our SPII simulations can be seen in Pig. 11.., The effect of the disc tapering on the distribution of disc angular momentum in our SPH simulations can be seen in Fig. \ref{vphi}.310 lt leads to sublxeplerian. velocities inside the orbit Crossing radius. similar to the results of Avlilfe&Bate(2009).," It leads to subKeplerian velocities inside the orbit crossing radius, similar to the results of \cite{ayliffe09}."311. The results of these two studies can be further reconciled by considering the dillerences in the models., The results of these two studies can be further reconciled by considering the differences in the models.312 In their simulations. the disc is hotter than in our simulations.," In their simulations, the disc is hotter than in our simulations."313 Consequently the oessure forces and their effects on departures from Ixeplerian rotation in the outer parts of the disc should be stronger than in Fig. 11..," Consequently the pressure forces and their effects on departures from Keplerian rotation in the outer parts of the disc should be stronger than in Fig. \ref{vphi},"314 as is consistent with their results., as is consistent with their results.315 Also the work of AXvlilfe&Bate(2000). includes the inllowing eas from larger radii that is omitted in our simulations., Also the work of \cite{ayliffe09} includes the inflowing gas from larger radii that is omitted in our simulations.316 This inllowing sublxeplerian gas and its interaction with the disc outer edge as it »ecomes entrained could farther modify the results plotted in Fig. 11.., This inflowing subKeplerian gas and its interaction with the disc outer edge as it becomes entrained could further modify the results plotted in Fig. \ref{vphi}.317 Lt is also possible that the cise radius is alfected by he location of wave damping. as discussed below.," It is also possible that the disc radius is affected by the location of wave damping, as discussed below."318 Such etfects should be explored. further., Such effects should be explored further.319 Another implication of the high values of {1ἐν is that a small fraction of the disc mass can reside at larger disc radii than he orbit-crossing radius and so be subject to the ellects of resonances that [ie outside this radius. as discussed in Section (sce Fig. 10)).," Another implication of the high values of $H/r$ is that a small fraction of the disc mass can reside at larger disc radii than the orbit-crossing radius and so be subject to the effects of resonances that lie outside this radius, as discussed in Section \ref{res} (see Fig. \ref{phase}) )."320 In addition. olf-resonant tidal forcing of the outer parts of the dise that lie inside the orbit crossing radius can play an important role.," In addition, off-resonant tidal forcing of the outer parts of the disc that lie inside the orbit crossing radius can play an important role."321 Lhe resonance width depends on (44/70)? and is not small., The resonance width depends on $(H/r)^{2/3}$ and is not small.322 Phe substantial width can allow he resonant region to overlap with the denser parts of disc., The substantial width can allow the resonant region to overlap with the denser parts of disc.323 As a result of these two effects. two-armecl spiral waves can be aunched in such disces. even though exact resonances do not lie within the main body of the disces.," As a result of these two effects, two-armed spiral waves can be launched in such discs, even though exact resonances do not lie within the main body of the discs."324 We have found evidence of such waves in our SPL simulations (see Fig. 9))., We have found evidence of such waves in our SPH simulations (see Fig. \ref{final}) ).325 For these waves to play a role in extracting angular momentum from the disc. they must. damp in order to introduce irreversibility.," For these waves to play a role in extracting angular momentum from the disc, they must damp in order to introduce irreversibility."326 Otherwise. a standing wave is produced that results in little or no orque on the disc.," Otherwise, a standing wave is produced that results in little or no torque on the disc."327 Some damping can be produced by the dise turbulent. viscosity in the fractional amount that is roughly he ratio of the viscous wave damping rate to the wave eroup propagation rate. about a(rfff).," Some damping can be produced by the disc turbulent viscosity in the fractional amount that is roughly the ratio of the viscous wave damping rate to the wave group propagation rate, about $\alpha (r/H)$."328 This ratio can be quite small or à«Ir and the torque is reduced to a similarly small fraction of its potentially maximum value., This ratio can be quite small for $\alpha \ll H/r$ and the torque is reduced to a similarly small fraction of its potentially maximum value.329 For a thin disc. this damping could occur as launched waves propagate. steepen and shock. since their wavelengths are short compared to the disc racius.," For a thin disc, this damping could occur as launched waves propagate, steepen and shock, since their wavelengths are short compared to the disc radius."330 But for warm circumplanctary clises. this process is less important because the wavelengths are not short compared to he disc radius.," But for warm circumplanetary discs, this process is less important because the wavelengths are not short compared to the disc radius."331 In the SPIEL simulations of Section 7. the damping seems to occur from the strongly nonlinear forcing in the outer disc. similar to the case of mildly warm dises (44/7=0.1) previously investigated for binary star systems 1994).," In the SPH simulations of Section 7, the damping seems to occur from the strongly nonlinear forcing in the outer disc, similar to the case of mildly warm discs $H/r=0.1)$ previously investigated for binary star systems \citep{savonije94}."332. Phe SPLL simulations suggest that the negative torque is produced in the outer parts of the disc. somewhat inside and bevond the radius where nested. particle orbits cross or become unstable.," The SPH simulations suggest that the negative torque is produced in the outer parts of the disc, somewhat inside and beyond the radius where nested particle orbits cross or become unstable."333 Phis torque involves a relatively small amount of disc mass (see Fig. 10))., This torque involves a relatively small amount of disc mass (see Fig. \ref{phase}) ).334 However. the disces in our SPLE simulations were two-dimensional and not as warm as could occur. where £r~0.3.," However, the discs in our SPH simulations were two-dimensional and not as warm as could occur, where $H/r \sim 0.3$."335 Phe wave damping issue should be explored in future work., The wave damping issue should be explored in future work.336 The aceretion dise model does not provide an obvious explanation for the locations of the regular satellites of Jupiter anc Saturn that occur within 0.06rg of the planet., The accretion disc model does not provide an obvious explanation for the locations of the regular satellites of Jupiter and Saturn that occur within $0.06 r_{\rm H}$ of the planet.337 As discussed above. the dise structure is insensitive to the angular momentum of the inllowing gas and satellites lic well inside the tidal truncation radius of the disc.," As discussed above, the disc structure is insensitive to the angular momentum of the inflowing gas and satellites lie well inside the tidal truncation radius of the disc."338 This conclusion is consistent with the results of recent threec-dimensional simulations of Estradaetal.(2008) and Avlille&Bate(2009)., This conclusion is consistent with the results of recent three-dimensional simulations of \cite{estrada08} and \cite{ayliffe09}.339. We have considere circumplanetary clises with a smoothly varving turbulent viscosity with radius., We have considered circumplanetary discs with a smoothly varying turbulent viscosity with radius.340 But such cises could also harbor dead. zones. as discussed in Section 2..," But such discs could also harbor dead zones, as discussed in Section \ref{properties}."341 Such situations could result in rapid disc density variations at their boundaries., Such situations could result in rapid disc density variations at their boundaries.342 Phe existence of satellites requires survival against the effects of migration., The existence of satellites requires survival against the effects of migration.343 Such density variations could alfect satellite migration and possibly trapping satellites. since migration rates depend on density. gradients (c.g..Matsumura.Pudritz&Thommes2007).," Such density variations could affect satellite migration and possibly trapping satellites, since migration rates depend on density gradients \citep[e.g.,][]{matsumura07}."344. But. if the inner dead zone boundary is due to thermal tonisation at a temperature of. 107Ix. then the disc temperatures there woul be too hot for the survival of an icy. satellite.," But, if the inner dead zone boundary is due to thermal ionisation at a temperature of $~10^3\,\rm K$, then the disc temperatures there would be too hot for the survival of an icy satellite."345 Of course. other sources of ionisation could change the locations ofdead zone edges.," Of course, other sources of ionisation could change the locations of dead zone edges."346 In addition. the nonlinear feedback [rom waves in à low viscosity dise could slow migration 2009).," In addition, the nonlinear feedback from waves in a low viscosity disc could slow migration \citep{ward97,rafikov03,li09}."347. However. this slowing is less effective for the warmer cireumplanetary disces.," However, this slowing is less effective for the warmer circumplanetary discs."348 Lf the satellite formation occurs after partial disc depletion. as suggested by Canup Ward (2002). then the ionisation through the vertical extent of the disc becomes easier and the dead zones are less likely to occur at that stage.," If the satellite formation occurs after partial disc depletion, as suggested by Canup Ward (2002), then the ionisation through the vertical extent of the disc becomes easier and the dead zones are less likely to occur at that stage."349 Circumplanetary discs are not very bright as we see in equation (8))., Circumplanetary discs are not very bright as we see in equation \ref{lum}) ).350 Time dependent aceretion and outbursts could occur in dead zones. as has been suggested to explain FU Orionis outbursts in voung stellar systems 2001).," Time dependent accretion and outbursts could occur in dead zones, as has been suggested to explain FU Orionis outbursts in young stellar systems \citep*{armitage01}."351. During a cireumplanetary dise outburst. the ratio of the circumplanctary to circumstellar luminosities could be much higher.," During a circumplanetary disc outburst, the ratio of the circumplanetary to circumstellar luminosities could be much higher."352 We thank Matthew Bate. Gennaro. DAngelo. and. Jim Prinele for helpful discussions.," We thank Matthew Bate, Gennaro D'Angelo, and Jim Pringle for helpful discussions."353 ROM thanks the Space Telescope Science Institute for a Giacconi Fellowship., RGM thanks the Space Telescope Science Institute for a Giacconi Fellowship.354 SUL acknowledges support from NASA grant. NNNOTAT?2Ci., SHL acknowledges support from NASA grant NNX07AI72G.355the only term which most halomodels use.,the only term which most halo–models use.356 The remaining terms are due to the substructure., The remaining terms are due to the substructure.357 Before we compute then. it will prove convenient to rewrite this first term as llere A«usosn(r) denotes the correlation function if the total mass were smoothly. distributed around the center of the parent halo(i.e. i£ there were no subeclumps).," Before we compute them, it will prove convenient to rewrite this first term as Here $\lambda_{\rm smooth}({\bm r})$ denotes the correlation function if the total mass were smoothly distributed around the center of the parent halo (i.e, if there were no subclumps)."358" Thus. the factor of(AL,ΑΙ1 simply denotes the fact that now only a fraction of the mass is in the smooth component."," Thus, the factor of $(M_{s}/M)^2$ simply denotes the fact that now only a fraction of the mass is in the smooth component."359 Let Air) denote the result. of wens each of the second terms in equation (5)) over ptr;)., Let $\lambda_{ii}({\bm r})$ denote the result of averaging each of the second terms in equation \ref{lambdar}) ) over $p({\bm r}_i)$.360 Then where we have set a=8sr;., Then where we have set ${\bm x}={\bm s}-{\bm r}_i$.361 Vhis term is the convolution of each subclump profile f; with itself., This term is the convolution of each subclump profile $f_i$ with itself.362 Averaging the third. termi in. equation (5)) is more complicated so we will do it last., Averaging the third term in equation \ref{lambdar}) ) is more complicated so we will do it last.363 Phe result. of averaging the fourth term is where Ase denotes the convolution of P with pifp. (, The result of averaging the fourth term is where $\lambda_{sc}$ denotes the convolution of $F$ with $\rho_c/\bar\rho$. (364Lf the subclumps were distributed around the halo center similarly to the dark matter. Le. p.pxPF. then Asex Ass.),"If the subclumps were distributed around the halo center similarly to the dark matter, i.e., $\rho_c/\bar\rho\propto F$, then $\lambda_{sc}\propto\lambda_{ss}$ .)"365 ὃν symmetry. the average of the fifth term is the samo.," By symmetry, the average of the fifth term is the same."366 And finally. the average of the third term is where the integral over s is the convolution of the two subclump profiles.," And finally, the average of the third term is where the integral over ${\bm s}$ is the convolution of the two subclump profiles."367 Written this way. À;; Is the weighted sum of this convolution over all pairs of subclump positions.," Written this way, $\lambda_{ij}$ is the weighted sum of this convolution over all pairs of subclump positions."368 Lt is interesting to re-arrange the order of the integrals above: where Αι denotes the convolution of pofp with itself., It is interesting to re-arrange the order of the integrals above: where $\lambda_{cc}$ denotes the convolution of $\rho_c/\bar\rho$ with itself.369 The second line follows from setting 7;;=»;το the third. line from setting a=sr; anc the final expression from setting y=zx|vrr;j.," The second line follows from setting ${\bm r}_{ij} = {\bm r}_i - {\bm r}_j$ , the third line from setting ${\bm x}={\bm s}-{\bm r}_i$ and the final expression from setting ${\bm y}={\bm x} +{\bm r} + {\bm r}_{ij}$."370" When written in this way. Aj; appears very similar to the two-halo term when substructure is absent: A, plavs the vole of the csubclump.subclump correlation function (compare equation 2 in Sheth ct al."," When written in this way, $\lambda_{ij}$ appears very similar to the two-halo term when substructure is absent; $\lambda_{cc}$ plays the role of the `subclump–subclump correlation function' (compare equation 2 in Sheth et al."371 2001)., 2001).372 Using the above results. the correlation function £(r) defined in equation (6)) can be expressed as Note that all the A terms on the right-hand. side have dimensions of volume. so that £ is dimensionless.," Using the above results, the correlation function $\xi(r)$ defined in equation \ref{xir}) ) can be expressed as Note that all the $\lambda$ terms on the right-hand side have dimensions of volume, so that $\xi$ is dimensionless."373 Now consider some simple limiting cases., Now consider some simple limiting cases.374 LE the subelumps are much smaller than the parent halo. then we can treat them as point masses when performing the integrals which define As; and δει ," If the subclumps are much smaller than the parent halo, then we can treat them as point masses when performing the integrals which define $\lambda_{si}$ and $\lambda_{ij}$ ."375The associated delta function. profiles simplify the integrals. so that [fin addition. the distribution of subelumps around the halo center is similar to the dark matter. p.x£. then we can set AgXAss and AcxAsus," The associated delta function profiles simplify the integrals, so that If in addition, the distribution of subclumps around the halo center is similar to the dark matter, $\rho_c\propto F$, then we can set $\lambda_{sc}\propto \lambda_{ss}$ and $\lambda_{cc}\propto \lambda_{ss}$."376 dn this case. the previous expression becomes (Reeall that Aguesth denotes the correlation function if all the mass was smoothly distributed. around. the halo center.)," In this case, the previous expression becomes (Recall that $\lambda_{\rm smooth}$ denotes the correlation function if all the mass was smoothly distributed around the halo center.)"377 Lf small.the fraction of the total mass which is in subelumpsis then €(7)zzΠλ)|» nAÀ;;tv).," If the fraction of the total mass which is in subclumps is small, then $\xi({\bm r})\approx \bar n \lambda_{\rm smooth}({\bm r}) 378 + \sum_i \bar n \lambda_{ii}({\bm r})$."3791n this limit. the total correlation function is well approxiniated by taking what one would have got if the mass was smoothly distributed. and then adding the contribution from the individual subclumyp components.," In this limit, the total correlation function is well approximated by taking what one would have got if the mass was smoothly distributed, and then adding the contribution from the individual subclump components."380 In the small mass ancl size limit. the contribution from the subclumps can only be important on scales smaller than the typical subcelump. so that this additional contribution is only important. on very small scales.," In the small mass and size limit, the contribution from the subclumps can only be important on scales smaller than the typical subclump, so that this additional contribution is only important on very small scales."381 On scales larger than the diameter of a tvpical subelump. thecorrelation function looksjust. as though themass within halos is smoothly distributed.," On scales larger than the diameter of a typical subclump, thecorrelation function looks just as though themass within halos is smoothly distributed."382 ‘This, This383Studying the effect. of merging according to curren structure formation models in . XC'DM-simulations. we find a qualitatively similar behaviour.,"Studying the effect of merging according to current structure formation models in $\Lambda$ CDM-simulations, we find a qualitatively similar behaviour."384 Phe scatter decreases with the number of mergers (α= 0.3). and as a consequence i also decreases with cosmic time.," The scatter decreases with the number of mergers $a = 0.3$ ), and as a consequence it also decreases with cosmic time."385 This is also quantitatively consistent with the best-matching random: merging mocle (refill-ratio 1/3 and low mass refill:pool) at. least for the limit of the low merger number range (e= 0.34). since in ACDALmereing the most massive galaxies experience only ~5008 merger events.," This is also quantitatively consistent with the best-matching random merging model (refill-ratio $1/3$ and low mass refill-pool) at least for the limit of the low merger number range $a = 0.34$ ), since in $\Lambda$ CDM-merging the most massive galaxies experience only $\sim 50-60$ merger events."386 Fherefore. the scatter evolution in ACDALmergine can be well approximated by a simple model assuming random mereing of galaxies.," Therefore, the scatter evolution in $\Lambda$ CDM-merging can be well approximated by a simple model assuming random merging of galaxies."387 From the above results we can draw some implications about recent observations of high redshift black holes:, From the above results we can draw some implications about recent observations of high redshift black holes:388in the material ejected from LIMS.,in the material ejected from LIMS.389. 10 has. often. been suggested that the progenitors of the PNe which are observed. to have carbon isotopic ratios below the values expected [rom standard AGB models must have undergone some non-standard mixing process. perhaps induced by rotation. during their red. giant phase and/or ACG:B phase (Bachiller ct al.," It has often been suggested that the progenitors of the PNe which are observed to have carbon isotopic ratios below the values expected from standard AGB models must have undergone some non-standard mixing process, perhaps induced by rotation, during their red giant phase and/or AGB phase (Bachiller et al."390 1997: Palla et al., 1997; Palla et al.391 2000: Balser. MeMullin Wilson 2002).," 2000; Balser, McMullin Wilson 2002)."392 The existence of this non-stanclare nmüxing mechanism is also invoked in order to reconcile predictions from. standard. Galactic: evolutionary models with observations of Le (c.g. Galli et al.," The existence of this non-standard mixing mechanism is also invoked in order to reconcile predictions from standard Galactic evolutionary models with observations of $^3$ He (e.g., Galli et al."393 1997: Charbonnel do Nascimento 1998: Chiappini. Renda Matteucci 2002).," 1997; Charbonnel do Nascimento 1998; Chiappini, Renda Matteucci 2002)."394 However. the extent of the LC enhancement. as a function of mass with varving metallicity is. to date. rather uncertain.," However, the extent of the $^{13}$ C enhancement as a function of mass with varying metallicity is, to date, rather uncertain."395 In fact. the requirement of sampling low-mass objects has often led. to concentrating the observational ellorts. on metal-poor clusters.," In fact, the requirement of sampling low-mass objects has often led to concentrating the observational efforts on metal-poor clusters."396 Charbonnel. Brown Wallerstein (1998) found that Ποια giants belonging to the old. Galactic dise. population {οΗ ~ — 0.6) can reach Heese 2 TS ," Charbonnel, Brown Wallerstein (1998) found that field giants belonging to the old Galactic disc population ([Fe/H] $\sim$ $-$ 0.6) can reach $^{12}$ $^{13}$ C $\sim$ 7."397por more metal-rich stars. a reasonable estimate might be ~ 115 (from observations of the carbon isotopic ratio in stars ascending the RGB in the open cluster 667: Gilroy Brown 1991).," For more metal-rich stars, a reasonable estimate might be $\sim$ 15 (from observations of the carbon isotopic ratio in stars ascending the RGB in the open cluster 67; Gilroy Brown 1991)."398 Measurements of FC and LC abundanees in eleven. bright giant menibers of the globular cluster « Centauri spanning the metallicity range LS « FejM)-« O.S do not reveal any real tren of the cllicacy of the first giant branch mixing with metallicity (Smith. Ferndrup Suntzelt 2002).," Measurements of $^{12}$ C and $^{13}$ C abundances in eleven bright giant members of the globular cluster $\omega$ Centauri spanning the metallicity range $-$ 1.8 $<$ [Fe/H] $<$ $-$ 0.8 do not reveal any real trend of the efficacy of the first giant branch mixing with metallicity (Smith, Terndrup Suntzeff 2002)."399 The mean value for this sumple is (070/70) =43404. with nine stars sharing. within the errors. the equilibrium ratio of 3.5.," The mean value for this sample is $\langle ^{12}$ $^{13}$ $\rangle = 4.3 \pm 0.4$, with nine stars sharing, within the errors, the equilibrium ratio of 3.5."400 Standard stellar evolution theory predicts a decrease of “CIC from  90 to ~ 25 during the first. credgc-up on the RGB for LIMS (Lhen 1964: Lben Renzini 1984)., Standard stellar evolution theory predicts a decrease of $^{12}$ $^{13}$ C from $\sim$ 90 to $\sim$ 25 during the first dredge-up on the RGB for LIMS (Iben 1964; Iben Renzini 1984).401 Pherefore. an extra-mixing which further processes material during the RGB seers to be at work.," Therefore, an extra-mixing which further processes material during the RGB seems to be at work."402 The C/C patio in Galactic carbon stars has been observed by Lambert ct al. (, The $^{12}$ $^{13}$ C ratio in Galactic carbon stars has been observed by Lambert et al. (4031986). Onhaka Tsuji (1996. 1999). Abia Isern (1997) and Schóier Olofsson (2000).,"1986), Onhaka Tsuji (1996, 1999), Abia Isern (1997) and Schöiier Olofsson (2000)."404 In particular. Onhaka Εκ (1996. 1999) found ο” - ratios about a [actor of 2 to 32 smaller than those of Lambert et al. (," In particular, Onhaka Tsuji (1996, 1999) found $^{12}$ $^{13}$ C ratios about a factor of 2 to 3 smaller than those of Lambert et al. ("4051986) for the samestars*.. whereas Abia Iscrn (1997) found something falling in between the results obtained by Lambert ct al. (,"1986) for the same, whereas Abia Isern (1997) found something falling in between the results obtained by Lambert et al. ("4061986) and. Onhaka Psuji (1996).,1986) and Onhaka Tsuji (1996).407 To solve the controversy. Schóier Olofsson (2000) »erformed independent estimates of the 12€ 1C ratio. using CO radio line emission from the cireumstellar envelopes. for a sample of carbon stars showing large discrepancies between he sets of photospheric estimates.," To solve the controversy, Schöiier Olofsson (2000) performed independent estimates of the $^{12}$ $^{13}$ C ratio, using CO radio line emission from the circumstellar envelopes, for a sample of carbon stars showing large discrepancies between the sets of photospheric estimates."408 They. used a non-ETIE M ⋅ . ⋅ ⋅ ↓⋅⋯⊔⋜⊔↓∖⇁∢⊾↓⋅⋜, They used a non-LTE radiative transfer code.409⋯⊳∖⇂⋖⊾↓⋅≼⇍⋯⇂∢⊾⊳∐↥⋖⋅≺⋟≺↓⋅⋜∐↓⇜↓⋅⋜⋯⋏∙≟⋖⊾⇂↓⋅∪⊔↓−≽⊳⋅↱≻ ο 90 and agree with those estimated in the photospheres by Lambert et al. (, The $^{12}$ $^{13}$ C ratios range from 2.5 to 90 and agree with those estimated in the photospheres by Lambert et al. (4101986).,1986).411 Finally. in a recent. paper. Abia et al.," Finally, in a recent paper, Abia et al."412with This eives an augular rotation rate profile with with where coefficient A iucludes the Carrington rotation rate.,with This gives an angular rotation rate profile with with where coefficient $A$ includes the Carrington rotation rate.413 This auguluo rotation rate is nearly identical to that fouud by Wometal.(L993A) Or the time interval 1975-1991 usiug simular data and methods., This angular rotation rate is nearly identical to that found by \cite{Komm_etal93A} for the time interval 1975-1991 using similar data and methods.414 We do fiud a sheht morth-south asvnuuetry as seen in Fie., We do find a slight north-south asymmetry as seen in Fig.415 2 bv the deviation of the measured profile frou: the svunuetric profile even by the dashed line., 2 by the deviation of the measured profile from the symmetric profile given by the dashed line.416 The differeutial rotation was sheltly weaker iu the south than in the north., The differential rotation was slightly weaker in the south than in the north.417 We also note the flatteniug of the profile at the equator with a slight (~Lins 1!) but significant dip fro c5? to the equator., We also note the flattening of the profile at the equator with a slight $\sim 1 \rm{\ m\ s}^{-1}$ ) but significant dip from $\pm 5\degr$ to the equator.418 A similar “dimple” at the equator was seen previously in direct Doppler data by Towardctal.(1980). and in magnetic clement motions by Snoderass(1983)., A similar “dimple” at the equator was seen previously in direct Doppler data by \cite{Howard_etal80} and in magnetic element motions by \cite{Snodgrass83}.419 The average meridional flow profile for the eutire dataset is shown iu Fig., The average meridional flow profile for the entire dataset is shown in Fig.420 3., 3.421 Although the average meridional flow profile does display substantial north-south asvunuetiy. the profile is well represcuted with just the two auti-sviinicetric ternis with This gives a peak poleward iueridioual flow velocity of 12.2us tata latitude of 35.2°.," Although the average meridional flow profile does display substantial north-south asymmetry, the profile is well represented with just the two anti-symmetric terms – with This gives a peak poleward meridional flow velocity of $11.2 \rm{\ m\ s}^{-1}$ at a latitude of $35.2\degr$."422 This is somewhat slower than the meridional flow found w οιetal.(1993D) for the time interval 1975 to 1991 but with a peak at nearly the same atitude., This is somewhat slower than the meridional flow found by \cite{Komm_etal93B} for the time interval 1975 to 1991 but with a peak at nearly the same latitude.423 Our average meridional flow profile shows substantially cüffereut flows in the north aud in the south., Our average meridional flow profile shows substantially different flows in the north and in the south.424 The flow velocity is faster in the south aud oeaks at a higher latitude than in the north., The flow velocity is faster in the south and peaks at a higher latitude than in the north.425 The How in the north appears to nearly vanish at the extreme northern linut (757) of our measurements while the flow in the south is still poleward with a speed of about 5iis:| at the southern limit., The flow in the north appears to nearly vanish at the extreme northern limit $75\degr$ ) of our measurements while the flow in the south is still poleward with a speed of about $5\rm{\ m\ s}^{-1}$ at the southern limit.426 Variations in the amplitudes of the axisviumetric flow components were examined by plotting the rotatiou-by-rotation histories of the Legeudre polvuouial cocficicuts., Variations in the amplitudes of the axisymmetric flow components were examined by plotting the rotation-by-rotation histories of the Legendre polynomial coefficients.427 The Legendre polvuouials were normalized so that their maxima values were either 1.0 or -1.0., The Legendre polynomials were normalized so that their maximum values were either 1.0 or -1.0.428 The coefficients that multiply them then eive the peak velocity for that commponueut., The coefficients that multiply them then give the peak velocity for that component.429 The normalized polvnomials we used are, The normalized polynomials we used are430It is remarkable. that to first order in stellar rotation. an initially uniformly rotating shell continues to rotate uniforiulv as it ex]xuxds or contracts;,"It is remarkable, that to first order in stellar rotation, an initially uniformly rotating shell continues to rotate uniformly as it expands or contracts."431 Our formula shows that near r=M the shift in frequency AQ should be sunaller than that predicted by Newtouian theory., Our formula shows that near $r = 3 M$ the shift in frequency $\Delta \Omega$ should be smaller than that predicted by Newtonian theory.432 This has correctly been noted by Weyl (2000). aud it reflects the fact. known previously (Abramowicz Prasanna 1990). that iu tle| gravitational Ποια of abody. matter which moves ou nearly circular orbits with σουΤα angular moment experiences no shear (in the seuse that dQdr= 0) exactly at the location of the circular photon orbit (0= 23M). be. at the location where the ceutrifueal force reverses.," This has correctly been noted by Heyl (2000), and it reflects the fact, known previously (Abramowicz Prasanna 1990), that in the gravitational field of a, matter which moves on nearly circular orbits with constant angular momentum experiences no shear (in the sense that $d\Omega/dr = 0$ ) exactly at the location of the circular photon orbit $r = 3M$ ), i.e., at the location where the centrifugal force reverses."433 Eq. (8)), Eq. \ref{heyl}) )434 shows that for matter moving on nearly circular orbits with coustaut aneular momentum in the gravitational field of a (slowly) rotating body. zex yshear occurs at some radius ry<3M. contrary to Tevls result. but iu accordance. e... with the well known fact th:u the ereater the angular momentum of the black hole. the smaller the radius of the (corotating) circular photon orbit rp). (," shows that for matter moving on nearly circular orbits with constant angular momentum in the gravitational field of a (slowly) rotating body, zero shear occurs at some radius $r_0 < 3M$, contrary to Heyl's result, but in accordance, e.g., with the well known fact that the greater the angular momentum of the black hole, the smaller the radius of the (corotating) circular photon orbit $r_{ph}$. ("435Note. however. that ouly for nou-rotating boclic org=Fyn dn general this is not true. because for rotatiiig bodies rp depends only ou AL aud J. while ry depends. in addition. ou O.),"Note, however, that only for non-rotating bodies $r_0 = r_{ph}$, in general this is not true, because for rotating bodies $r_{ph}$ depends only on $M$ and $J$, while $r_0$ depends, in addition, on $\Omega$ .)"436" Iu anv case, the derivative of O in eq. ("," In any case, the derivative of $\Omega$ in eq. ("4378) is positive oulv for r«2.6AL|[5£/(2R2)aDE1].,8) is positive only for $r< 2.6 M + [5I/(2R_*^2)-1]$.438 For realistic-H neutron star models. the τιjouent of inertia is lower than that of a uniformilp Newtoniaun-. sphere. £<κ2M2 BRZ/5. so the zero shear radius is less than the causality lit for neutrou star radi. Π.2.84 Ulacusel. Lasota Zdunik 1999).," For realistic neutron star models, the moment of inertia is lower than that of a uniform Newtonian sphere, $I<2 MR_*^2 /5$ , so the zero shear radius is less than the causality limit for neutron star radii, $R_*>2.8 M$ (Haensel, Lasota Zdunik 1999)."439 We may ask if the formmila (8)) is relevant to the problem of frequency shifts observed in QPOs during type I X-rav bursts and te| the coustraits on the imassracdius relation for neutron stars., We may ask if the formula \ref{heyl}) ) is relevant to the problem of frequency shifts observed in QPOs during type I X-ray bursts and to the constraints on the mass-radius relation for neutron stars.440 For this. the Strobuuaver et al. (," For this, the Strohmayer et al. ("4411997b) model relatine the QPO frequeucy to the neutro- stars spin and the frequency shift to movements of the ATMOS]phere must be correct.end duriug the expausio- and coutraction the specific angular momentum / of the ΟΡΟ source should be conserved.,"1997b) model relating the QPO frequency to the neutron star's spin and the frequency shift to movements of the atmosphere must be correct, during the expansion and contraction the specific angular momentum $\l$ of the QPO source should be conserved."442 We are skeptical ou bot[um counts., We are skeptical on both counts.443 Aino et al (, Muno et al. (4442001). find that the presence of a ~ Tz quasiperkxlic oscillation im the N-rayv ciission is correlated witli radius expansion iu X-ray bursts. but that the presence of a -ο Tz QPO is not correlated.,"2001), find that the presence of a $\sim600$ Hz quasiperiodic oscillation in the X-ray emission is correlated with radius expansion in X-ray bursts, but that the presence of a $\sim445300$ Hz QPO is not correlated."446 This 1 itself raises doubt as to the general validity of the rotational-modulation model of these QPOs., This in itself raises doubt as to the general validity of the rotational-modulation model of these QPOs.447 Further. we note that an independent confirmation of the rotational iod of the neutrou stars is needed before the frequencv observed can be identified with the spin rate.," Further, we note that an independent confirmation of the rotational period of the neutron stars is needed before the frequency observed can be identified with the spin rate."448 Second. uo long-lastiug mhomogencitics lave as vet been demostrated im computations of the burst evolution.," Second, no long-lasting inhomogeneities have as yet been demonstrated in computations of the burst evolution."449 Third. even if the model is correct. there secu to be so nuuiv ulwcertainties involved in the motion of a hot spot in ascllar afmosphnere. that we do not sec how any frequency chauge cau be reliably identified with the properties of the space-time metric.," Third, even if the model is correct, there seem to be so many uncertainties involved in the motion of a hot spot in a stellar atmosphere, that we do not see how any frequency change can be reliably identified with the properties of the space-time metric."450 Suppose that no frequency change is observed., Suppose that no frequency change is observed.451 Would we claim that this is because the radius of the star. r=R coiucides with the zero-shear radius ry. or should we rather suppose that the hot spot is stationary at the surface of the rotating star?," Would we claim that this is because the radius of the star, $r=R$ coincides with the zero-shear radius $r_0$, or should we rather suppose that the hot spot is stationary at the surface of the rotating star?"452 Is the frequency decrease observed in 1U 1636-53 Strolunaver 1999). due to R<ry or is some other effect oewolved (perhaps the hot spot is rising like a balloon)?," Is the frequency decrease observed in 4U 1636-53 (Strohmayer 1999), due to $R<r_0$ or is some other effect involved (perhaps the hot spot is rising like a balloon)?"453 Finally. we know of no atimospheric phenomenon on Earth which would resemble the proposed modelcastellanus clouds do not show a systematic westerly bend with altitude. and large scale motions which cau be ascribed to Coriolis forces. such as the jet stream or trade winds. are related to latitudinal motious of air masses. not vertical.," Finally, we know of no atmospheric phenomenon on Earth which would resemble the proposed model—castellanus clouds do not show a systematic westerly bend with altitude, and large scale motions which can be ascribed to Coriolis forces, such as the jet stream or trade winds, are related to latitudinal motions of air masses, not vertical."454 I1 asa; conserved when the ΟΡΟ is observed?, Is $l=-u_\phi/u_t$ conserved when the QPO is observed?455" Tn the case of axially svuuuetric. stationary motion of a perfect finid. both —«P|p)ín aud «(P|p)/n. where P. p aud à are respectively the pressure. euergy and particle densities, are conserved (see. e.c. Bardeen 1973) and because 7 is simply their ratio. it is conserved as well."," In the case of axially symmetric, stationary motion of a perfect fluid, both $-u_t (P+\rho)/n$ and $u_{\varphi}(P+\rho)/n$, where $P$, $\rho$ and $n$ are respectively the pressure, energy and particle densities, are conserved (see, e.g., Bardeen 1973) and because $\l$ is simply their ratio, it is conserved as well."456 It is not clear what relevance this has to the frequency observed iu N-rav bursts, It is not clear what relevance this has to the frequency observed in X-ray bursts.457 After all. if the frequency is related to the stellar rotation it mist be related to non-axisviunietry. breaking the basic assiunption under which fis conserved for perfect fics.," After all, if the frequency is related to the stellar rotation it must be related to non-axisymmetry, breaking the basic assumption under which $\l$ is conserved for perfect fluids."458 A naive reading of the sugeestion that the X-ray burst yequency may be caused by a dark or bright fluid clement conserving aneular momentum as it changes altitude. sugeests the motion of a hovercraft.," A naive reading of the suggestion that the X-ray burst frequency may be caused by a dark or bright fluid element conserving angular momentum as it changes altitude, suggests the motion of a hovercraft."459 This would be a article free of azimuthal forces but supported vertically. and the relevant question would be the change of its azimuthal velocity or simply angular frequency. as seen wea distant observer. when the particle changes its radial vosition.," This would be a particle free of azimuthal forces but supported vertically, and the relevant question would be the change of its azimuthal velocity or simply angular frequency, as seen by a distant observer, when the particle changes its radial position."460 The euergy per unit rest mass —4; of the particle would not be conserved. but its angular momentum per muit rest mass 4.=(1BALryt?? would. aud heuce. in his case. could be a better model for frequency shift thau (8)).," The energy per unit rest mass $-u_t$ of the particle would not be conserved, but its angular momentum per unit rest mass $u_{\varphi} = \l (1 -4612M/r)^{1/2}$ would, and hence, in this case, could be a better model for frequency shift than \ref{heyl}) )."462 Iu conclusion. it seems uulikelv that HIevI's idea can ever be used to constrain the mass-radius relationship of a neutron star.," In conclusion, it seems unlikely that Heyl's idea can ever be used to constrain the mass-radius relationship of a neutron star."463 Uutortunately. it secs that the effect two ofus discovered 27 years ago has vet to be observed.," Unfortunately, it seems that the effect two ofus discovered 27 years ago has yet to be observed."464 One of us (ALA.A.) would like to thauk Jeremy Hevl for an interesting discussion., One of us (M.A.A.) would like to thank Jeremy Heyl for an interesting discussion.465Sa-5ab galaxies with high levels of emission. HLameed&Young(2003) [id unambiguous siens οἱ recent interactions in 6 of these galaxies.,"Sa-Sab galaxies with high levels of emission, \citet{HY2003} find unambiguous signs of recent interactions in 6 of these galaxies."466 Interaction signatures include HI tidal tails (NGC 972. NGC 3885. NGC. 7213) and neutral hydrogen bridges connecting neighboring ealaxies (NGC 3471. NGC 5915. NGC 7582).," Interaction signatures include HI tidal tails (NGC 972, NGC 3885, NGC 7213) and neutral hydrogen bridges connecting neighboring galaxies (NGC 3471, NGC 5915, NGC 7582)."467 some of the dispersion seen in the equivalent width vs (B-V) plot of Figure 8 max also be attributed to interactions., Some of the dispersion seen in the equivalent width vs (B-V) plot of Figure 8 may also be attributed to interactions.468 Kennicuttοἱaf(1957). find a similar dispersion in (heir sample of interacting galaxies (hal can be explained by superimposing a burst of star formation on an evolved stellar population.," \citet{Kennicutt1987}469 find a similar dispersion in their sample of interacting galaxies that can be explained by superimposing a burst of star formation on an evolved stellar population."470 The strength of the burst and (he location of a ealaxv on the plot. of course. depends on a number of parameters including (he extinction. the gas content. and the orbital parameters of the interaction.," The strength of the burst and the location of a galaxy on the plot, of course, depends on a number of parameters including the extinction, the gas content, and the orbital parameters of the interaction."471 Nevertheless. the dispersion of colors and equivalent widths seen among early-(wpe spirals is reminiscent of that seen among the interacting galaxies. providing further support for the idea Chat elevated star formation max ouly be a temporary. pliase for these nearby early-(wpe spirals.," Nevertheless, the dispersion of colors and equivalent widths seen among early-type spirals is reminiscent of that seen among the interacting galaxies, providing further support for the idea that elevated star formation may only be a temporary phase for these nearby early-type spirals."472 It should be noted. however. that not all interacting early-tvpe spirals exhibit unusually hieh FIR or emissions.," It should be noted, however, that not all interacting early-type spirals exhibit unusually high FIR or emissions."473 For example. IHE maps of M81 (Yun.Ho.&Lo 1994).. NGC 3368 (Schneider 1939).. and NGC 4725 (Weverse£al...1984). reveal unambiguous interaction signabures and vet imaging reveals relatively little evidence for enhanced star formation.," For example, HI maps of M81 \citep{Yun1994}, , NGC 3368 \citep{Schneider1989}, , and NGC 4725 \citep{Wevers1984} reveal unambiguous interaction signatures and yet imaging reveals relatively little evidence for enhanced star formation."474 On the other hand. it is to be expected that the HII signature of an interaction will last [ar longer (han (he associated episode of massive star formation that the interaction causes.," On the other hand, it is to be expected that the HI signature of an interaction will last far longer than the associated episode of massive star formation that the interaction causes."475 It is now well documented that the presence of a bar in a galaxy can induce star ormation either at the ends of the bar or in the nuclear and cireium-nuclear regions., It is now well documented that the presence of a bar in a galaxy can induce star formation either at the ends of the bar or in the nuclear and circum-nuclear regions.476 The influence of bars on global star formation rates has been the subject of many studies over the past few decades and has led to the concensus that there are no significant differences inglobal nassive star formation rates between barred. anc unbarred galaxies (e.g. Ryder&Dopila (1994): Tomita.Tomita&Saito (1996)))., The influence of bars on global star formation rates has been the subject of many studies over the past few decades and has led to the concensus that there are no significant differences in massive star formation rates between barred and unbarred galaxies (e.g. \citet{RD1994}; \citet{Tomita1996}) ).477 However. there is some evidence that nuclear star omnnation appears to be enhanced in earl-type barred spirals compared to their unbarred counterparts (Devereux1937:Huangefαἰ.1996:Ho.Filippenko.&Sargent1997).," However, there is some evidence that nuclear star formation appears to be enhanced in early-type barred spirals compared to their unbarred counterparts \citep{Devereux1987, Huang1996, HFS1997}."478. Such an effect is not seen in lale-twpe spiral galaxies and may be related {ο the location of the inner Lindblad resonance (ILI). which is dependent on (he central mass distribution.," Such an effect is not seen in late-type spiral galaxies and may be related to the location of the inner Lindblad resonance (ILR), which is dependent on the central mass distribution."479 The ]ILR in an earlv-tvpe spiral is expected to be located inside the bar and closer to the nucleus (han in a Iate-tvpe spiral (Elmeereen&Elmeereen1985). and (hus can transfer gas more elliciently to the central region of the galaxy. triggering star formation.," The ILR in an early-type spiral is expected to be located inside the bar and closer to the nucleus than in a late-type spiral \citep{EE1985} and thus can transfer gas more efficiently to the central region of the galaxy, triggering star formation."480 It should be noted. however. that not all barred earlv-tvpe spiralshaveenhanced nuclear star formation: (hus," It should be noted, however, that not all barred early-type spiralshaveenhanced nuclear star formation; thus"481Eclipse observations of dwarf novae during quiescence show that the X-ray emitting region is centred on the white chwarl. within a size that is comparable to that of the white dwarf (e.g. IE Cas. Mukaial... 1997).,"Eclipse observations of dwarf novae during quiescence show that the X-ray emitting region is centred on the white dwarf, within a size that is comparable to that of the white dwarf (e.g. HT Cas, Mukai, 1997)."482 The emission is believed to originate [rom material in à boundary laver slowing from a Ixeplerian. velocity in the disk. to settle onto the white chvarl surface.," The emission is believed to originate from material in a boundary layer slowing from a Keplerian velocity in the disk, to settle onto the white dwarf surface."483 Observations of some systems have shown hard. X-ray emission. dominating during quiescence and an extreme-ultraviolet component dominating during outburst. when the hard. X-ray component. is. suppressed. (Patterson ltavmond. 1985a 1985b. SS Cye by Cordova 1984. U Gem by Cordova 1980 and Mason LOSS. VAV Livi by Pringle 987).," Observations of some systems have shown hard X-ray emission dominating during quiescence and an extreme-ultraviolet component dominating during outburst, when the hard X-ray component is suppressed (Patterson Raymond, 1985a 1985b, SS Cyg by Cordova 1984, U Gem by Cordova 1980 and Mason 1988, VW Hyi by Pringle 1987)."484 The X-rav [lux recovers only at the very end of the optical outburst (Wheatleyal... 1996a).," The X-ray flux recovers only at the very end of the optical outburst (Wheatley, 1996a)."485 During quiescence both the accretion. rate and. the boundary [laver density are low. cooling occurs incllicicntly. and so the temperature remains high (Pringle Savonije. 1979).," During quiescence both the accretion rate and the boundary layer density are low, cooling occurs inefficiently, and so the temperature remains high (Pringle Savonije, 1979)."486 During outburst the mass accretion rate increases. 16 boundary laver becomes optically thick ancl ellicient at cooling. thus the emission of hard X-rays is reduced (Pringle 1977).," During outburst the mass accretion rate increases, the boundary layer becomes optically thick and efficient at cooling, thus the emission of hard X-rays is reduced (Pringle 1977)."487 Such an optically thick boundary laver cools to an elective. blackbody temperature of ]1OIx. (10ceV) in the xtreme ultra-violet (Patterson Itavmond. 1985b).," Such an optically thick boundary layer cools to an effective blackbody temperature of $^5$ K eV) in the extreme ultra-violet (Patterson Raymond, 1985b)."488 X-ray observations with the satellite confirm wt this picture also applies to Z Can during outburst Wheatleyal... 1996b).," X-ray observations with the satellite confirm that this picture also applies to Z Cam during outburst (Wheatley, 1996b)."489. However. these data suller from the low exposure of the all-sky survey. as well as 1¢ intrinsic limitations of a soft X-ray proportional counter in the study of hard spectra.," However, these data suffer from the low exposure of the all-sky survey, as well as the intrinsic limitations of a soft X-ray proportional counter in the study of hard spectra."490 Done Osborne (1997) have mace a detailed: analysis of the X-ray spectrum. of the dwarf nova SS (νο using the and satellites., Done Osborne (1997) have made a detailed analysis of the X-ray spectrum of the dwarf nova SS Cyg using the and satellites.491 Phey find that physically plausible spectral fits require moclels for gas cooling onto the white dwarf surface. with absorption by a photo-ionised mecium.," They find that physically plausible spectral fits require models for gas cooling onto the white dwarf surface, with absorption by a photo-ionised medium."492 Phev find that a greater proportion of cool gas anc, They find that a greater proportion of cool gas and493 Phev find that a greater proportion of cool gas ancl, They find that a greater proportion of cool gas and494about 8«10AZ sec which is shorter than the overall time-scale of iaguetie coufiematiou.,about $8\times 10^3 M_{7}$ sec which is shorter than the overall time-scale of magnetic configuration.495 Therefore. we welect the tine delay. due to the propagation of photons from the fare to the disk. aud consider ouly the effects of the bulk motion of flares on the time-averaged line properties.," Therefore, we neglect the time delay due to the propagation of photons from the flare to the disk, and consider only the effects of the bulk motion of flares on the time-averaged line properties."496 At the reverberation mapping nuc-scale. the N-vav spectrmu of a flare tends to vary in a complicated way because the fare detaches from he uuderlviug accretion disk (Poutanen&Fabian1999).," At the reverberation mapping time-scale, the X-ray spectrum of a flare tends to vary in a complicated way because the flare detaches from the underlying accretion disk \citep[]{pf99}."497. This is in contrast to the instantaneous flare with fixeck spectral slope adopted im previous work (Revuoldsetal.1999)., This is in contrast to the instantaneous flare with fixed spectral slope adopted in previous work \citep[]{rey99}.498. Thus the reverberation properties will be significantly affected: however. the reverberation study of an evolving flare is bevoud the scope of the xeseut paper.," Thus the reverberation properties will be significantly affected; however, the reverberation study of an evolving flare is beyond the scope of the present paper."499 We consider three typical bulk iiotious for flares: 1) on-axis flares with bulk motion along the kerr lack hole axis: 2) off-axis flares with bulk motion upward or downward normal to the accretion disk plane: 3) off-axis fares with bulk motion outward or inward alone the radial direction., We consider three typical bulk motions for flares: 1) on-axis flares with bulk motion along the Kerr black hole axis; 2) off-axis flares with bulk motion upward or downward normal to the accretion disk plane; 3) off-axis flares with bulk motion outward or inward along the radial direction.500 If a primary X-ray flare moves outward with muldly relativistic bulk velocity. the relativistic beaming effect obviously compoetes with the eravitational lensing effect ou both the profile and EW of the line.," If a primary X-ray flare moves outward with mildly relativistic bulk velocity, the relativistic beaming effect obviously competes with the gravitational lensing effect on both the profile and EW of the line."501 On the oue hand. if the flare is verv close to the black hole (sav. r<ολ a significant fraction of the X-ray photons from the flare are bent into the disk plaue by the stroug eravitation Ποια 1996).," On the one hand, if the flare is very close to the black hole (say, $r<15M$ ), a significant fraction of the X-ray photons from the flare are bent into the disk plane by the strong gravitation field \citep[]{mm96}."502. The ilhuuinatiou flux onto the iuuer accretion disk is then enhanced whereas the direct continuum fli is reduced., The illumination flux onto the inner accretion disk is then enhanced whereas the direct continuum flux is reduced.503 Due to the strong leusine effect. the red wine of the line profile extends downward toward lower energies aud the EW increases (\lartocchia.Ikaras&Matt.2000:DabrowskiLascuby2001).," Due to the strong lensing effect, the red wing of the line profile extends downward toward lower energies and the EW increases \citep[]{mkm00,dl01}."504. Ou the other hand. if the flare moves with an outward bulk velocity along the axis. direct fix will increase. and iluminatiou flux impinging outo the disk surface will decrease as a result of relativistic beaming effect (Reynolds&Fabian1997).," On the other hand, if the flare moves with an outward bulk velocity along the axis, direct flux will increase, and illumination flux impinging onto the disk surface will decrease as a result of relativistic beaming effect \citep[]{rf97}."505. As a result. both the red wing aud EW are reduced.," As a result, both the red wing and EW are reduced."506 We calculate line profiles for various cases using Moute-Carlo simulation., We calculate line profiles for various cases using Monte-Carlo simulation.507 The predicted line shapes aud EWs are plotted in Figures P. and 2. for a maxima herr black hole with spin paramcter e/AM=0.998., The predicted line shapes and EWs are plotted in Figures \ref{fig:onaxisprof} and \ref{fig:onaxisew} for a maximum Kerr black hole with spin parameter $a/M=0.998$.508" Both the line profile and EW are detected by an observer at a distance of 100037 with inclination augles 0,—5. 157. 30° and 607.. respectively."," Both the line profile and EW are detected by an observer at a distance of $1000M$ with inclination angles $\theta_{\rm o}=5$, $15$, $30$ and $60$, respectively."509 As discussed by Alartocchia&Matt(1996). aud (2001).. the exteusion of the red wine. which is controlled by the streneth of the gravitational redshift. increases as the fluorescent emission is enliauced in the region close to the black hole.," As discussed by \citet[]{mm96} and \citet[]{dl01}, the extension of the red wing, which is controlled by the strength of the gravitational redshift, increases as the fluorescent emission is enhanced in the region close to the black hole."510 As the flare eots close to the black hole. it iluuimates the iuuer disk more intensively aud the red wing becomes larger (sce Fig. 1)).," As the flare gets close to the black hole, it illuminates the inner disk more intensively and the red wing becomes larger (see Fig. \ref{fig:onaxisprof}) )."511 The παν (outward) bulk motion of the fare enhances (weakens) the illunination fiux in the inner disk region aud thus results in strone (weal) dux of highly redshitted line emission. which is clearly illustrated in Figure 1..," The inward (outward) bulk motion of the flare enhances (weakens) the illumination flux in the inner disk region and thus results in strong (weak) flux of highly redshifted line emission, which is clearly illustrated in Figure \ref{fig:onaxisprof}."512 Indeed. the extension of the red wing sliatks as the outward bulk velocity of the flare increases.," Indeed, the extension of the red wing shrinks as the outward bulk velocity of the flare increases."513 Conversely. the red wing extends down to lower energies as the inward bulk velocity of the fare increases (sce Fie. 1)).," Conversely, the red wing extends down to lower energies as the inward bulk velocity of the flare increases (see Fig. \ref{fig:onaxisprof}) )."514" For distant observers at low inclination angles (6,Z 30°) :id for flares close to the black hole (cZ 15M). the red wing of the line profiles vary substantially with bulk velocity."," For distant observers at low inclination angles $\theta_{\rm o}\simlt 30\arcdeg$ ) and for flares close to the black hole $r\simlt 15M$ ), the red wing of the line profiles vary substantially with bulk velocity."515" Iu contrast. the location of the line blue ""edge. which is determined by the inclination angle. is 1useusitive to the bulk motion of flares."," In contrast, the location of the line blue `edge', which is determined by the inclination angle, is insensitive to the bulk motion of flares."516 For distaut, For distant517If both species have the same properties (redshift distribution. photometric quality). we have Wy=AVS and Ny=AX. where κ stands for the population ratio.,"If both species have the same properties (redshift distribution, photometric quality), we have $W_1 = k W_2$ and $X_1 = k X_2$, where k stands for the population ratio."518 So. This expression describes as well all events belonging to a suele species. which completes the proof.," So, This expression describes as well all events belonging to a single species, which completes the proof."519 As expected. the argument breaks down if there are nof enough eveuts to constrain gi or go. ie. if Wy or We is siugular.," As expected, the argument breaks down if there are not enough events to constrain $g_1$ or $g_2$ , i.e. if $W_1$ or $W_2$ is singular."520 One may also note that the arewmment applies as well to anv umber of event species., One may also note that the argument applies as well to any number of event species.521density inferred. [or the absorber by Crenshaw et aare not terribly different than those inferred for the narrow-line region (e.g.. Kraemer et 11994).,"density inferred for the absorber by Crenshaw et are not terribly different than those inferred for the narrow-line region (e.g., Kraemer et 1994)."522 The high-£ warm absorber may be coincident with the low-£ warm absorber., The $\xi$ warm absorber may be coincident with the $\xi$ warm absorber.523 If so. a lower density by 2 orders of magnitude would be inferred.," If so, a lower density by 2 orders of magnitude would be inferred."524 Circiumstantial evidence for this scenario is the [act the velocity offsets of the UV and X-ray absorbers are consistent with one another. as [ar as we can tell.," Circumstantial evidence for this scenario is the fact the velocity offsets of the UV and X-ray absorbers are consistent with one another, as far as we can tell."525 It should be noted that the outflow velocity of LOG197 km s! revealed by (the [AST STIS echelle (Crenshawetal.2002) is difficult to be detected by the HETCS because of the relatively poorer data equality of compared withLST., It should be noted that the outflow velocity of 106–197 km $^{-1}$ revealed by the STIS echelle \citep{cre02} is difficult to be detected by the HETGS because of the relatively poorer data quality of compared with.526 llowever. it is not necessary lor the high-£ warm absorber to be coincident with the € one.," However, it is not necessary for the $\xi$ warm absorber to be coincident with the $\xi$ one."527 Close examination of (he regions of the spectrum right around the absorption lines reveals suggestions of emission line wings tailing toward higher and lower energies (e.g.. the hieher and lower energy sice of (he ο Ίνα aud Ne Lyo lines. respectively). although most of these features are not statistically significant.," Close examination of the regions of the spectrum right around the absorption lines reveals suggestions of emission line wings tailing toward higher and lower energies (e.g., the higher and lower energy side of the O $\alpha$ and Ne $\alpha$ lines, respectively), although most of these features are not statistically significant."528 These structures resemble those in the UV in which the center of the emission lines has been removed by the nearly saturated broad absorption lines such that only the high and low energy wings of the line remains (Crenshaw et 22002)., These structures resemble those in the UV in which the center of the emission lines has been removed by the nearly saturated broad absorption lines such that only the high and low energy wings of the line remains (Crenshaw et 2002).529 The warm absorber shows us ionized gas along our line of sight ancl the same photoionization may also power eniission lines in (he gas predominately oul of our line to the central source if the covering fraction is large enough., The warm absorber shows us ionized gas along our line of sight and the same photoionization may also power emission lines in the gas predominately out of our line to the central source if the covering fraction is large enough.530 eraling observations have been reported [rom three NLS1s., grating observations have been reported from three NLS1s.531 In NGC 4051. lound many absorption lines Irom highly ionized ions such as oxveen. neon. silicon and sulphur.," In NGC 4051, \citet{collinge01} found many absorption lines from highly ionized ions such as oxygen, neon, silicon and sulphur."532 They resolved (wo distinct absorption svstems with hieh outflow velocity kms !) and low outflow velocity (6004130 km +)., They resolved two distinct absorption systems with high outflow velocity $2340\pm130$ km $^{-1}$ ) and low outflow velocity $600\pm130$ km $^{-1}$ ).533 On the other hand. no absorptioΕν lines were detected in the spectrum of Ton S180 (Turneretal.2001) and Mrk 478 2003).," On the other hand, no absorption lines were detected in the spectrum of Ton S180 \citep{tur01} and Mrk 478 \citep{mar03}."534. The properties of the absorber in Ark 564 are different from both of them., The properties of the absorber in Ark 564 are different from both of them.535 Although it is properly classified as a Seyfert 1 galaxy and has relatively narrow optical lines. the features reported four —6-30-15 by Leeetal.(2001) ave similar to what we found in Ark 564.," Although it is properly classified as a Seyfert 1 galaxy and has relatively narrow optical lines, the features reported from $-$ 6-30-15 by \citet {lee01}536 are similar to what we found in Ark 564."537 Specilicallv. they also detected narrow absorption lines from He-like and lI-like oxvgen without detectable velocity shifts.," Specifically, they also detected narrow absorption lines from He-like and H-like oxygen without detectable velocity shifts."538 Moreover. in the ο) Ix-edge range. the deficit starts al an energy lower by about 30 eV than the energv of O Ix-edge.," Moreover, in the O K-edge range, the deficit starts at an energy lower by about 30 eV than the energy of O K-edge."539 Absorption lines possibly from ionized iron are also detected., Absorption lines possibly from ionized iron are also detected.540 All of these featuresare common between AICG—6-30-15 and Ark 564., All of these featuresare common between $-$ 6-30-15 and Ark 564.541"We now consider correlations between the X-ray and radio fluxes. reff:X,adio((",We now consider correlations between the X-ray and radio fluxes. \\ref{f:X_radio}( (542f-| —j)showstherelationshipsbetweentheX rayf luxinselectedAS MandBAT bandsandthe15G Hzradiof lux.,f–j) shows the relationships between the X-ray flux in selected ASM and BAT bands and the 15 GHz radio flux.543T| Ithepácponidentee Glte, The colours identify the spectral state.544"hüren cay rpeintatirdhe BAT range(i— jisbecauseeachrequiressimultaneousBAT, 15GHzradioandAS McoverXga(yhBlastintéeetednexbbsgdrthletdiey."," The reason that there are fewer points in the BAT range (i--j) is because each requires simultaneous BAT, 15 GHz radio and ASM coverage (the last to determine the spectral state)."545" It can be seen that the hard-state fluxes (shown in red) approximately follow a power-law relationship, F(15GHz)«Εκ, but the power-law index is a strong function of the X-ray energy band."," It can be seen that the hard-state fluxes (shown in red) approximately follow a power-law relationship, $F({\rm 15\,GHz})\propto F_{\rm X}^{p}$, but the power-law index is a strong function of the X-ray energy band."546 The fitted parameters (see Appendix 3 for the fitting method) are given in Table 1.., The fitted parameters (see Appendix \ref{fits} for the fitting method) are given in Table \ref{t:fit}.547" The high significance of the correlations is confirmed by the values of the Spearman's correlation coefficient, rs, and the null hypothesis probability, Ρε, also given in Table 1.."," The high significance of the correlations is confirmed by the values of the Spearman's correlation coefficient, $r_{\rm s}$, and the null hypothesis probability, $P_{\rm s}$ , also given in Table \ref{t:fit}."548" The index, p, changes from ~0.9 at 1.5-3 keV to ~ 1.7-1.8 in the 14—150 keV range."," The index, $p$, changes from $\simeq 0.9$ at 1.5–3 keV to $\simeq 1.7$ –1.8 in the 14–150 keV range."549 The variation of p with energy is summarised in reff:index.., The variation of $p$ with energy is summarised in \\ref{f:index}.550 The low value of the index in the 150-195 keV band index is apparently due the fact that this energy range corresponds to where the high-energy cut-off of the spectra starts to have a major effect., The low value of the index in the 150–195 keV band index is apparently due the fact that this energy range corresponds to where the high-energy cut-off of the spectra starts to have a major effect.551" Thus much of the variability is associated with a different physical process — changes in the cut-off energy, apparently due to a variable electron temperature."," Thus much of the variability is associated with a different physical process – changes in the cut-off energy, apparently due to a variable electron temperature."552" The relationship between the radio flux, F(15 GHz), and the X-ray hardness is illustrated in reff:gamma((b)."," The relationship between the radio flux, $F(\rm 15\, GHz)$ , and the X-ray hardness is illustrated in \\ref{f:gamma}( (b)."553" There is a strong correlation in the hard state, 0.22, P,=2x 107, which continues up to I~2.1."," There is a strong correlation in the hard state, $r_{\rm s} = 0.22$ , $P_{\rm s} = 2\times 10^{-19}$ , which continues up to $\Gamma\sim 2.1$."554" When the spectra are soft, there is a strong decrease in the radio emission; for T>2.3 the (anti-)correlation has r,=—0.57, P,=2x1077. reff:bol,adiol5(("," When the X-ray spectra are soft, there is a strong decrease in the radio emission; for $\Gamma>2.3$ the (anti-)correlation has $r_{\rm s} = -0.57$, $P_{\rm s} = 2\times 10^{-37}$. \\ref{f:bol_radio15}( ("555a— —b)showstherelationshipbetweenthel5 GHzfluxandthebolometric flux.,a–b) shows the relationship between the 15-GHz flux and the bolometric flux.556T heapproximatepower lawrelationshipinthehardstatenowextend stomostof. theintermediaiate faddbsarptiony ff VO}," The approximate power-law relationship in the hard state now extends to most of the intermediate state, though it breaks down in the soft state."557 ittzstdanfobsRaholsitetearegiveninthethire t, The fit results for the hard state are givenin the third part of Table \ref{t:fit}.558"he correlationis much steeper (py,=1.68+ 0.11) than at E€5 keV, where the power law index was p~ 0.9-1.3."," Although the low energy data are included in $F_{\rm bol}$, the correlation is much steeper $p_{\rm bol}=1.68\pm 0.11$ ) than at $E\leq 5$ keV, where the power law index was $p\simeq 0.9$ –1.3."559" AS peu= dlnF(I5GHz)/dlnFyg, while p= and p= dlnFyy/din (where the differential coefficients are those of the fitted Fxfunctional dependencies), in the absence of hidden systematic variability patterns one might expect peo=p/p’, and indeed it can be seen from Table 1 that this is very close to being the case, especially at EZS5keV. We note that reff:X,adio((f —j) showthattheradio f luxinthestateswithastrongX — rayblackbodycontributions, i.e., intermediateandso ft,de pendsasapowerlawontheem keV. This indicates that the level of the radio emission is associated with the high-energy electrons in the X-ray emitting region, presumably a corona in the intermediate and soft states (e.g., Gierlifiskietal. 1999))."," As $p_{\rm bol} = {\rm d} \ln F({\rm 15\,GHz}) / {\rm d} \ln F_{\rm bol}$, while $p = {\rm d} \ln F({\rm 15\, GHz}) / {\rm d} \ln F_{\rm X}$ and $p' = {\rm d} \ln F_{\rm bol} / {\rm d} \ln F_{\rm X}$ (where the differential coefficients are those of the fitted functional dependencies), in the absence of hidden systematic variability patterns one might expect $p_{\rm bol}\simeq p/p'$, and indeed it can be seen from Table \ref{t:fit} that this is very close to being the case, especially at $E\ga 5$ keV. We note that \\ref{f:X_radio}( (f–j) show that the radio flux in the states with a strong X-ray blackbody contributions, i.e., intermediate and soft, depends as a power law on the emission at high energies, $\ga 5$ keV. This indicates that the level of the radio emission is associated with the high-energy electrons in the X-ray emitting region, presumably a corona in the intermediate and soft states (e.g., \citealt{gierlinski99}) )."560" To test this hypothesis, we have hecolouceikidtiext TOfetlee sch twee blackbody contribution, i.e., For calculated in Section 3.2.. reff:bol.adiolS(("," To test this hypothesis, we have considered the dependence of the 15 GHz flux on the integrated X-ray flux integrated excluding the disc blackbody contribution, i.e., $F_{\rm hot}$ calculated in Section \ref{xray}. \\ref{f:bol_radio15}( ("561c)showstheresultingrelationship.,c) shows the resulting relationship.562"Incontrastto reff:bol,adio15((a——b), weseethatnowthereisanapproximatesinglepower— lawdependenceencompassingallthestateso f CygX withp=1.73+0.07."," In contrast to \\ref{f:bol_radio15}( (a–b), we see that now there is an approximate single power-law dependence encompassing the states of Cyg X-1, with $p=1.73\pm 0.07$."563 The GBI data provide information at frequencies below 15 GHz and were simultaneous with part of the ASM and BATSE data., The GBI data provide information at frequencies below 15 GHz and were simultaneous with part of the ASM and BATSE data.564 We find correlations at 2.25 and 8.3 GHz in the hard state similar to that found at 15 GHz - see reff:radio28 and the first and last sections of Table 1.., We find correlations at 2.25 and 8.3 GHz in the hard state similar to that found at 15 GHz – see \\ref{f:radio28} and the first and last sections of Table \ref{t:fit}.565" Despite the relatively low quality of those data, the correlations are highly significant, as seen from the low values of P;."," Despite the relatively low quality of those data, the correlations are highly significant, as seen from the low values of $P_{\rm s}$."566" The fitted indices are, however, subject to some systematic errors associated with the choice of the minimum radio flux, Fgmin, considered."," The fitted indices are, however, subject to some systematic errors associated with the choice of the minimum radio flux, $F_{\rm R,min}$, considered."567 Using Frmin=15 mJy at 2.25 GHz and 8.3 GHz would lead to somewhat lower values of p than with the limit of 10 mJy adopted here.," Using $F_{\rm R,min}= 15$ mJy at 2.25 GHz and 8.3 GHz would lead to somewhat lower values of $p$ than with the limit of 10 mJy adopted here."568" In any case, p decreases with the decreasing frequency."," In any case, $p$ decreases with the decreasing frequency."569 reff:sprx shows the broad-band spectra of Cyg X-1 from radio to X-rays., \\ref{f:sprx} shows the broad-band spectra of Cyg X-1 from radio to X-rays.570 The black circles and vertical error bars show the average hard-state radio fluxes from Fenderetal.(2000)., The black circles and vertical error bars show the average hard-state radio fluxes from \citet{fender00}.571". The dotted line shows ana=0 (Fg«E, a=Y— 1) dependence, which approximately fits the hard-state radio data."," The dotted line shows an $\alpha=0$ $F_E\propto E^{-\alpha}$, $\alpha=\Gamma-1$ ) dependence, which approximately fits the hard-state radio data."572" We show the line extending to 0.1 eV, which approximately correspond to the turnover frequency (at which the jetbecomes optically thin to statesyhohgdhiténesdl 2AexT (2011).."," We show the line extending to 0.1 eV, which approximately correspond to the turnover frequency (at which the jetbecomes optically thin tosynchrotron self-absorption) of$2.9\times 10^{13}$ Hz found by \citet{rahoui11}. ."573" The red, green and blue crosses show the (geometric) average fluxes in the hard, intermediate and soft state, respectively, in the radio and X-ray ranges."," The red, green and blue crosses show the (geometric) average fluxes in the hard, intermediate and soft state, respectively, in the radio and X-ray ranges."574 Only the ASM and BAT data simultaneous with the 15 GHz monitoring were included., Only the ASM and BAT data simultaneous with the 15 GHz monitoring were included.575 The 2.25 GHz and 8.3 GHz data are the averages over all the data for which there were simultaneous ASM data for determining the spectral, The 2.25 GHz and 8.3 GHz data are the averages over all the data for which there were simultaneous ASM data for determining the spectral576The probability. density. function. (PDIP) of the density field. in molecular clouds is a key ingredient in most analvtic models of star formation (Pacdoan Nordlund 2002: Ixrumholz Melxee 2005: Elmeercen 2008: Llennebelle Chabrier 2008: Padoan Nordlund 2009: Lennebeclle Chabrier 2009).,The probability density function (PDF) of the density field in molecular clouds is a key ingredient in most analytic models of star formation (Padoan Nordlund 2002; Krumholz McKee 2005; Elmegreen 2008; Hennebelle Chabrier 2008; Padoan Nordlund 2009; Hennebelle Chabrier 2009).577 Ixnowledge of the density. PDI is required to determine the overall star formation rate or efficiency., Knowledge of the density PDF is required to determine the overall star formation rate or efficiency.578 In some models. the density. PDE is of central importance in determining the emergent stellar initial mass function.," In some models, the density PDF is of central importance in determining the emergent stellar initial mass function."579 The majority of models assume a lognormal density. PDE (Vazzquez-Semadeni 1994). with the width of the PDI increasing with the Mach number of the turbulence (Pacoan. Nordlund. Jones 1997: Passot Vázzquez-Semacdeni 1998: Federrath. IxIessen. Schmidt 2JOS).," The majority of models assume a lognormal density PDF (Vázzquez-Semadeni 1994), with the width of the PDF increasing with the Mach number of the turbulence (Padoan, Nordlund, Jones 1997; Passot Vázzquez-Semadeni 1998; Federrath, Klessen, Schmidt 2008)."580 Observational knowledge of density. fields in molecular clouds (et alone the PDE) is very limited., Observational knowledge of density fields in molecular clouds (let alone the PDF) is very limited.581 We do not have access to the density field. in twee dimensions (3D) but instead can only view the projeced column density [ielc in two dimensions (2D)., We do not have access to the density field in three dimensions (3D) but instead can only view the projected column density field in two dimensions (2D).582" Use of molecular tracers of cülferent critical density can in principle vield some information. but even the most sophisticated excitation analyses provide only a single ""densitv per line-of-sight whereas the transverse variations in “density” so measured must imply comparable. or perhaps greater. Huctuations in density along the A route to the PDE could involve (for example) the measurement of mass exceeding a range of critical densities from a suite of tracers."," Use of molecular tracers of different critical density can in principle yield some information, but even the most sophisticated excitation analyses provide only a single “density” per line-of-sight whereas the transverse variations in “density” so measured must imply comparable, or perhaps greater, fluctuations in density along the A route to the PDF could involve (for example) the measurement of mass exceeding a range of critical densities from a suite of tracers."583" While the amount of data involved here would likely be prohibitive for nearby clouds of large angular extent. it can be usefully applied in an extragalactic context (oe. Ixrumholz ""Thompson 2007)."," While the amount of data involved here would likely be prohibitive for nearby clouds of large angular extent, it can be usefully applied in an extragalactic context (e.g. Krumholz Thompson 2007)."584 Column density fields traced by extinction of background. stars are perhaps the most. robust. way of acquiring constraining data on the density PDF in nearby clouds., Column density fields traced by extinction of background stars are perhaps the most robust way of acquiring constraining data on the density PDF in nearby clouds.585 Column density PDEs can be constructed (e.g. Cambresy 1999: Lombardi 2009: Ixainulainen et al 2009) but the relation between these ancl the 3D. density. PDE is currently unknown., Column density PDFs can be constructed (e.g. Cambresy 1999; Lombardi 2009; Kainulainen et al 2009) but the relation between these and the 3D density PDF is currently unknown.586 Compression of the PDE due to linc-of-sight averaging is expected. and there are some indications that a lognormal density PDI will project into a (less broad) lognormal column density PDE (Ostriker. Stone. CGammie. 2001: Vázzquez-Semadeni: Carefaa 2001. Fecderrath et al 2009).," Compression of the PDF due to line-of-sight averaging is expected, and there are some indications that a lognormal density PDF will project into a (less broad) lognormal column density PDF (Ostriker, Stone, Gammie 2001; Vázzquez-Semadeni Garcíaa 2001, Federrath et al 2009)."587 Phe degree of compression is presently unknown. but recent work bv Brunt. Federrath. Price (2010: hereafter BEP) demonstrated how to calcula the normalised density variance in 3D [rom information contained solely in the column density. field.," The degree of compression is presently unknown, but recent work by Brunt, Federrath, Price (2010; hereafter BFP) demonstrated how to calculate the normalised density variance in 3D from information contained solely in the column density field."588 Comparison of the measured. normalised. column density variance with the inferred. normatisecl density variance can provide some information on the degree of compression., Comparison of the measured normalised column density variance with the inferred normalised density variance can provide some information on the degree of compression.589 In this paper. we introduce a method. by which the 3D density PDE can be constructed. from measurements mace on the column density Ποιά alone.," In this paper, we introduce a method by which the 3D density PDF can be constructed from measurements made on the column density field alone."590 Measurements of, Measurements of591 , 592Iuid ancl gets confined in the pancake plane.,fluid and gets confined in the pancake plane.593 This qualitative result is consistent with the pattern of the magnetic fields observed in spiral and disc ealaxies., This qualitative result is consistent with the pattern of the magnetic fields observed in spiral and disc galaxies.594 To obtain a more quantitative result we need to solve the magnetic evolution equations (17))-(19))., To obtain a more quantitative result we need to solve the magnetic evolution equations \ref{B'1*}) \ref{B'3*}) ).595" Using expressions (8)) and (9)) we arrive at where eo. D, are initial values."," Using expressions \ref{expZ}) ) and \ref{shearZ}) ) we arrive at where $a_0$, $B_{i_0}$ are initial values."596 In l-climensional planar collapse along the 3rd. eigen-direction (Àj=0A» and Ax« 0). the pancake singularity is reached as ao»1/Às.," In 1-dimensional planar collapse along the 3rd eigen-direction $\lambda_1=0=\lambda_2$ and $\lambda_3<0$ ), the pancake singularity is reached as $a\rightarrow-1/\lambda_3$."597 In that case Da decavs. whereas 2). Ds increase without bound (neglecting backreaction).," In that case $B_3$ decays, whereas $B_1$, $B_2$ increase without bound (neglecting backreaction)."598 We now compare with spherical collapse. limiting to the Zeldovich. case which is given by three equal eigenvalues.," We now compare with spherical collapse, limiting to the Zel'dovich case which is given by three equal eigenvalues."599 Phen. any one of (21))-(23)) reduces to and all the magnetic components diverge as we approach the point singularity. (e1/A.," Then, any one of \ref{B1}) \ref{B3}) ) reduces to and all the magnetic components diverge as we approach the point singularity, $a\rightarrow-1/\lambda$."600" For comparison. we assume equal initial values D;,=Do. which leads to the patio with an analogous relation for D»FU "," For comparison, we assume equal initial values $B_{i_0}=B_0$, which leads to the ratio with an analogous relation for $B_2/B^{\rm sph}$."601This result shows that the relative growth of the field depends on the eigenvalues. corresponding to the two alternative patterns of collapse., This result shows that the relative growth of the field depends on the eigenvalues corresponding to the two alternative patterns of collapse.602 When A;<A«0. or equivalently when 0*1As1/A. the anisotropy dominates the collapse.," When $\lambda_3<\lambda<0$, or equivalently when $0<-1/\lambda_3<-1/\lambda$, the anisotropy dominates the collapse."603" ‘Thus eLid, before αT/A. and therefore By.Bo“> LP."," Thus $a\rightarrow-1/\lambda_3$ before $a\rightarrow-1/\lambda$, and therefore $B_1,\,B_2\gg B^{\rm604sph}$ ."605 in other words. anisotropy can lead to a considerable increase in the streneth of the magnetic field.," In other words, anisotropy can lead to a considerable increase in the strength of the magnetic field."606" Conditions such as A,«A arise naturally whenever we compare pancake to spherical collapse.", Conditions such as $\lambda_3<\lambda$ arise naturally whenever we compare pancake to spherical collapse.607" Indeed. consider pure pancake collapse along the 3rd shear eigen-direction (A,=O= As)."," Indeed, consider pure pancake collapse along the 3rd shear eigen-direction $\lambda_1=0=\lambda_2$ )."608 Then. from (8)) we have For spherical collapse on the other hand. Ίσα. (8))," Then, from \ref{expZ}) ) we have For spherical collapse on the other hand, Eq. \ref{expZ}) )"609 gives so that Ay< A., gives so that $\lambda_3<\lambda$ .610 Accordingly. one should expect stronger amplification for magnetic fields frozen into anisotropic. rather than isotropic. collapse.," Accordingly, one should expect stronger amplification for magnetic fields frozen into anisotropic, rather than isotropic, collapse."611 Note that we have implicitLy assumed that. initially. the value of Ο is the same both for the pancake and for the spherical collapse.," Note that we have implicitly assumed that, initially, the value of $\tilde{\Theta}$ is the same both for the pancake and for the spherical collapse."612 An alternative wav olf estimating the relative amplification is via the initial density contrast., An alternative way of estimating the relative amplification is via the initial density contrast.613 For Ap0—Ax. Eq. (25))," For $\lambda_1=0=\lambda_2$, Eq. \ref{Anis-Sph1}) )"614" leads to with the same relation for Ds/Ber"".", leads to with the same relation for $B_2/B^{\rm sph}$.615 Substituting for A. Ax from (26)) and (27)) we arrive at the expression where the equality on the right hand. side holds at a=ay.," Substituting for $\lambda$, $\lambda_3$ from \ref{r1}) ) and \ref{r2}) ) we arrive at the expression where the equality on the right hand side holds at $a=a_0$."616 The above directly relates the ratio Bs/l to the overdensity oy at the onset of the nonlinear regime.," The above directly relates the ratio $B_{1,2}/B^{\rm sph}$ to the overdensity $\delta_0$ at the onset of the nonlinear regime."617 In deriving Eq. (29)), In deriving Eq. \ref{pan-Sph}) )618 we have also used the relation dy=yOu. which arises cirecthy from the Zelclovich ansatz. Eq. (7)).," we have also used the relation $\delta_0=-a_0\tilde{\Theta}_0$ , which arises directly from the Zeldovich ansatz, Eq. \ref{ansatz}) )."619" Aecording to (29)). the ratio DjD keeps increasing as the collapse proceeds towards the pancake singularity. namely as aαι.|8,1)."," According to \ref{pan-Sph}) ), the ratio $B_1/B^{\rm sph}$ keeps increasing as the collapse proceeds towards the pancake singularity, namely as $a\rightarrow a_0(1+\delta_0^{-1})$."620 At that) point πλfpr diverges.," At that point $B_{1,2}/B^{\rm621sph}$ diverges."622" Note that. for the same initial O. the isotropic. collapse reaches the singularity. at e=ag(3ao|à,px7). that is later than the pancake collapse."," Note that, for the same initial $\tilde{\Theta}$, the isotropic collapse reaches the singularity at $a=a_0(3+\delta_0^{-1})$, that is later than the pancake collapse."623 On using σα. (29)), On using Eq. \ref{pan-Sph}) )624 we can caleulate the relative amplification of the magnetic field. for a given dy. at any time prior to the pancake singularity.," we can calculate the relative amplification of the magnetic field, for a given $\delta_0$, at any time prior to the pancake singularity."625 To obtain a numerical estimate consider the following example., To obtain a numerical estimate consider the following example.626 Assume that y=1 at the onset of the nonlinear regime., Assume that $\delta_0=1$ at the onset of the nonlinear regime.627 This means that the pancake singularity is reached at e=2eay. whereas the point singularity at e=tay.," This means that the pancake singularity is reached at $a=2a_0$, whereas the point singularity at $a=4a_0$."628 Then. the anisotropically collapsing magnetic field. is one order of magnitude stronger than an isotropically collapsing one (Le. Byec 104713) bv the time e=L.95ay (i.e. when we have undergone of the total pancake collapse).," Then, the anisotropically collapsing magnetic field is one order of magnitude stronger than an isotropically collapsing one (i.e. $B_{1,2}\simeq10B^{\rm sph}$ ) by the time $a=1.95a_0$ (i.e. when we have undergone of the total pancake collapse)."629 This means that the elfect of the anisotropy on the amplification. though weak early. on. increases Last as we approach the final stages of the collapse (see Fig. 2)).," This means that the effect of the anisotropy on the amplification, though weak early on, increases fast as we approach the final stages of the collapse (see Fig. \ref{fig:2}) )."630 Phen. the presence of shear can strengthen the magnetic field. well bevond the limits of simple isotropic compression.," Then, the presence of shear can strengthen the magnetic field well beyond the limits of simple isotropic compression."631 In other words. as the field is dragged. deep into the potential wells of the CDM. one should expect an appreciable increase in the magnetic strength due to shearing effects alone.," In other words, as the field is dragged deep into the potential wells of the CDM, one should expect an appreciable increase in the magnetic strength due to shearing effects alone."632 Although Eq. (29)), Although Eq. \ref{pan-Sph}) )633 has been derived in the idealized case of a l-dimensional pancake. with the spherical case treated via the Zelclovich approximation. we expect it to be approximately true in more realistic situations as well.," has been derived in the idealized case of a 1-dimensional pancake, with the spherical case treated via the Zel'dovich approximation, we expect it to be approximately true in more realistic situations as well."634 This reasonable expectation is further strengthened by the [act that our analytical estimates are in good agreement with those obtained by numerical simulations see (Dolag 1999)]]., This reasonable expectation is further strengthened by the fact that our analytical estimates are in good agreement with those obtained by numerical simulations [see \cite{DBL1}] ].635 These simulations also argue for an extra order of magnitude increase in the strength of the magnetic seed feld. during the final stages of the collapse. because of shearing effects.," These simulations also argue for an extra order of magnitude increase in the strength of the magnetic seed field, during the final stages of the collapse, because of shearing effects."636 Finally. we can gain further insightinto the relative amplification of anistropicallv versus isotropically collapsing magnetic fields by rewriting (28)) as where we have also usec Eqs. (15)). (260). (27)).," Finally, we can gain further insightinto the relative amplification of anistropically versus isotropically collapsing magnetic fields by rewriting \ref{purePan-Sph}) ) as where we have also used Eqs. \ref{ell}) ), \ref{r1}) ), \ref{r2}) ),"637 and linear. initial conditions for two initially spherical [uid elements., and linear initial conditions for two initially spherical fluid elements.638" This relation shows that the ratio D,/7""*ph erows", This relation shows that the ratio ${B_1}/{B^{\rm sph}}$ grows639skv north of 6=2.57 and blue magnitude ranee 5 to 12.,sky north of $\delta \ = \ -2.5^{\circ}$ and blue magnitude range 5 to 12.640 Oulv a partial set of the ACTN2 data was available for UCAC2., Only a partial set of the AGK2 data was available for UCAC2.641" Over 1.2 million stars (see Table 1) could be measured this time. while ""oulv about 156.000 stars were measured. reduced aud published in the original ACGK2/AÀGIN3 project from a several decade lone effort. when “computers” were lias."," Over 1.2 million stars (see Table 1) could be measured this time, while “only"" about 186,000 stars were measured, reduced and published in the original AGK2/AGK3 project from a several decade long effort, when “computers"" were humans."642ps Tn addition. a total of about 2000 Tambure Zone Astroeraph (ZA). 900 USNO Black Birch Astrograph (vellow lens. BY}. aud 2300 Lick Astrograph (LA) plates were scanned ou StarScan and reduced with Iüpparcos reference stars to provide accurate earlv epoch positious for stars down to V = Ll (ZA. BY) and V = 16 (LA).," In addition, a total of about 2000 Hamburg Zone Astrograph (ZA), 900 USNO Black Birch Astrograph (yellow lens, BY), and 300 Lick Astrograph (LA) plates were scanned on StarScan and reduced with Hipparcos reference stars to provide accurate early epoch positions for stars down to V = 14 (ZA, BY) and V = 16 (LA)."643 However. all those plates together cover ouly about 1/3 of the sky. tarecting fields around ICRF extragalactic sources aud special fields observed for other programs.," However, all those plates together cover only about 1/3 of the sky, targeting fields around ICRF extragalactic sources and special fields observed for other programs."644 A complete new reduction of the SPAT data was performed applying the modified StarScau (Zachariasetal.2008) pipeline reduction code to the Precision Measuring Machine (PAID (Monet&Levine2001) pixel data.," A complete new reduction of the SPM data was performed applying the modified StarScan \citep{starscan} pipeline reduction code to the Precision Measuring Machine (PMM) \citep{pmm}645 pixel data."646 The resulting elobal-plate c.y center coordinates were processed by the Yale University reduction pipeline to correct for systematic errors as function of magnitude. utilizing all erating images of those data (Cürard et al. in preparation).," The resulting global-plate $x,y$ center coordinates were processed by the Yale University reduction pipeline to correct for systematic errors as function of magnitude, utilizing all grating images of those data (Girard et al, in preparation)."647 The new processing of these data inroved the proper motions of UCACS stars fainter than about 11th magnitude aud covered by the SPM2 by about a factor of2 wart., The new processing of these data improved the proper motions of UCAC3 stars fainter than about 14th magnitude and covered by the SPM2 by about a factor of 2 w.r.t.648 the UCAC2 release., the UCAC2 release.649 Unufortunatelv. the correspondius Nortlern Proper Motion (NPM) reductions did not progress ‘ast enough for the UCACS3 schedule aud will 0 utilized at a later time for UCACL," Unfortunately, the corresponding Northern Proper Motion (NPM) reductions did not progress fast enough for the UCAC3 schedule and will be utilized at a later time for UCAC4."650 The SuperCOSAIOS data (Ibuublyetal.2001a) based ou Schunüdt πιάνο plates provided carly epoch positions to derive proper motions of faint UCACS stars all-sky., The SuperCOSMOS data \citep{superc1} based on Schmidt survey plates provided early epoch positions to derive proper motions of faint UCAC3 stars all-sky.651 For cach catalog used in the proper notion calculation an estimated systematic error floor was added to the iuternal errors (Table 2)., For each catalog used in the proper motion calculation an estimated systematic error floor was added to the internal errors (Table 2).652 Individual CCD 120622 position errors (siuall iuuber statistics from scatter of a few observations oer star) were already. clipped to a mimi of 10 nas prior to this step., Individual CCD mean position errors (small number statistics from scatter of a few observations per star) were already clipped to a minimum of 10 mas prior to this step.653 SuperCOSAIOS data were rot excluded im areas covered by SPM: however. he SPM data with their significantly: lower errors dominate the proper motion solution. if available.," SuperCOSMOS data were not excluded in areas covered by SPM; however, the SPM data with their significantly lower errors dominate the proper motion solution, if available."654 Au effort has been made to tag previously known Wiel Proper Motion (IIPM) stars in the UCACS catalog utilizing published proper motion catalogs aud surveys., An effort has been made to tag previously known High Proper Motion (HPM) stars in the UCAC3 catalog utilizing published proper motion catalogs and surveys.655 While we have made an effort to ideutifv most previously known IIPM stars with p> 0715 d. the list is not complete.," While we have made an effort to identify most previously known HPM stars with $\mu \ge$ $\farcs$ 15 $^{-1}$, the list is not complete."656 Iu all but a few cases data for these known proper motion stars were retrieved using the VizieR ou-line data tool at the Strashoure Astronomical Data Center (CDS)., In all but a few cases data for these known proper motion stars were retrieved using the VizieR on-line data tool at the Strasbourg Astronomical Data Center (CDS).657 For the few cases where data were not available through CDS. the data were retrieved through the correspouding published literature.," For the few cases where data were not available through CDS, the data were retrieved through the corresponding published literature."658 The proper motion data eiven in the UCACS catalog for these previously known IIPM stars come from the catalogs theniselves and are uot computed as other proper notions are in the UCAC?23 catalog., The proper motion data given in the UCAC3 catalog for these previously known HPM stars come from the catalogs themselves and are not computed as other proper motions are in the UCAC3 catalog.659 A list of TPAD stars was compiled aud cach UCAC CCD frame searched for possible images of those stars., A list of HPM stars was compiled and each UCAC CCD frame searched for possible images of those stars.660 Those images were extracted from the regular pipeline processing of UCACS to avoid confusion and iiis-matches with other catalogs., Those images were extracted from the regular pipeline processing of UCAC3 to avoid confusion and mis-matches with other catalogs.661 A total of 51.297 HIIPM stars could. be identified iu UCACS data: they are identified bv theALPOS munbers lavecr than 110 1aillion.," A total of 51,297 HPM stars could be identified in UCAC3 data; they are identified by the numbers larger than 140 million."662 The mean positions of the IIPM stars are based on UCAC CCD observations: however. no attempt was inade to identify these stars m carly epoch catalogs to derive new proper motions.," The mean positions of the HPM stars are based on UCAC CCD observations; however, no attempt was made to identify these stars in early epoch catalogs to derive new proper motions."663 More details and a list of references can be found iu the readiue file of UCACS3 and the upcoming paper about new IIPM stars and common proper motion pairs found in UCACS data (Finch et al)., More details and a list of references can be found in the readme file of UCAC3 and the upcoming paper about new HPM stars and common proper motion pairs found in UCAC3 data (Finch et al).664 A veeion of the skv around 6—|20° was observed at CTIO and then repeated frou: NOFS within about 3 mouths (see UCAC2 paper)., A region of the sky around $\delta = +20^{\circ}$ was observed at CTIO and then repeated from NOFS within about 3 months (see UCAC2 paper).665 Based ou these 10 CCD frames separate mean positions were generated frou the data of cach site. utiliziug the final version of the svstematic οπου COIT‘tions. which are cifereut for location aud telesco2ο orientation.," Based on these 1410 CCD frames separate mean positions were generated from the data of each site, utilizing the final version of the systematic error corrections, which are different for location and telescope orientation."666 For the C'TIO observing the telescoye Was on the West side of the pier. while at NOFS it was ou he East.," For the CTIO observing the telescope was on the West side of the pier, while at NOFS it was on the East."667 Figure & shows the yosition differences between the CTIO and NOFS based data as fiction of magnitude., Figure 8 shows the position differences between the CTIO and NOFS based data as function of magnitude.668 Large liftvenees are foe oulv for bright.," Large differences are found only for bright,"669and are streaming towards higher transverse velocities.,and are streaming towards higher transverse velocities.670" At later times in the low mass-ratio simulation one can see that both electrons and protons are getting accelerated simultaneously, as illustrated in the next two images in the upper rows of Figs."," At later times in the low mass-ratio simulation one can see that both electrons and protons are getting accelerated simultaneously, as illustrated in the next two images in the upper rows of Figs."671 4. and 5.., \ref{2Dhist_elec_pos} and \ref{2Dhist_prot}.672" As emphasized before there is no clear disunction between a low and high mass instability in this case, thus the simultaneous acceleration is clearly in agreement with the energy evolution (see Fig. 15)."," As emphasized before there is no clear distinction between a low and high mass instability in this case, thus the simultaneous acceleration is clearly in agreement with the energy evolution (see Fig. \ref{B_vergleich}) )."673" When going to higher mass-ratios and early umes (lower leftmost image of both figures) only the electrons are visible, as the protons sull remain at their initial momentum."," When going to higher mass-ratios and early times (lower leftmost image of both figures) only the electrons are visible, as the protons still remain at their initial momentum."674 When the initial phase of the instability is over (/x700.) the electrons are no longer significantly accelerated., When the initial phase of the instability is over $t \approx 70 \omega_p^{-1}$ ) the electrons are no longer significantly accelerated.675 The protons are sull gaining more energy until about /=|ἴθωρ.. which is roughly at the maximum of the proton instability (see Fig.," The protons are still gaining more energy until about $t = 110 \omega_p^{-1}$, which is roughly at the maximum of the proton instability (see Fig."676 1 for comparison)., \ref{B_vergleich} for comparison).677 This supports the idea of two almost separated instabilities., This supports the idea of two almost separated instabilities.678 In both cases the particle distributions show a diffusion-like behaviour: The initial distribution in parallel direction is stretched [rom y«5 to y=15., In both cases the particle distributions show a diffusion-like behaviour: The initial distribution in parallel direction is stretched from $\gamma \approx 5$ to $\gamma \approx 15$.679 The parücle energy is converted into perpendicular field energy which in turn accelerates the particles., The particle energy is converted into perpendicular field energy which in turn accelerates the particles.680 We want to stress an interesüng feature of the different particle distributions in the diverse simulations: Both simulations have a proton distribution which is strongly elongated in the perpendicular direction and an electron distribution whose center is below the initial y=10 and extends more or less equal in the parallel and perpendicular direction., We want to stress an interesting feature of the different particle distributions in the diverse simulations: Both simulations have a proton distribution which is strongly elongated in the perpendicular direction and an electron distribution whose center is below the initial $\gamma=10$ and extends more or less equal in the parallel and perpendicular direction.681 In the high mass case it is obvious that the electrons are partially decelerated to lower energies., In the high mass case it is obvious that the electrons are partially decelerated to lower energies.682 In Fig., In Fig.683 6 we show a one-dimensional plot of the temporal evolution of the total momentum distribution of all the parücles (from both proton and pair-proton stream) in the lab frame., \ref{ohneboost} we show a one-dimensional plot of the temporal evolution of the total momentum distribution of all the particles (from both proton and pair-proton stream) in the lab frame.684" Particles moving in negative (positive) z-direcuion are plotted with a negative (positive) total momentum and the narrow peak lor each lime shows the protons, the broad ones represent the electrons/positrons."," Particles moving in negative (positive) z-direction are plotted with a negative (positive) total momentum and the narrow peak for each time shows the protons, the broad ones represent the electrons/positrons."685 One can see that most of the acceleration of the electrons and positrons is happening between 20; and 700;. the protons still eain more energy until about 1ἵθωρ..," One can see that most of the acceleration of the electrons and positrons is happening between $20 \omega_p^{-1}$ and $70 \omega_p^{-1}$, the protons still gain more energy until about $110 \omega_p^{-1}$."686 This corresponds with the behaviour of the parücles seen in Fig., This corresponds with the behaviour of the particles seen in Fig.687 4. and in Fig. 5.., \ref{2Dhist_elec_pos} and in Fig. \ref{2Dhist_prot}.688 We have conducted several simulations of counterstreaming plasmas with different mass-ratios «100.0 in order to invesügate the influence of the mass-ratio on the development of twostream instabilities., We have conducted several simulations of counterstreaming plasmas with different mass-ratios $1.0 < m_p/m_e < 100.0$ in order to investigate the influence of the mass-ratio on the development of twostream instabilities.689 We can draw two major conclusions [rom our simulations: (1) the physics of acceleration in mixed counterstreaming plasmas can be understood by using particle-in-cell simulations and (2) we are able to show that there is indeed a strong implication of the mass-ratio on the results but in order to extrapolate the behaviour to the physical mass-ratio one still needs to perform some simulations with higher mass-ratio of 200 or 500., We can draw two major conclusions from our simulations: (1) the physics of acceleration in mixed counterstreaming plasmas can be understood by using particle-in-cell simulations and (2) we are able to show that there is indeed a strong implication of the mass-ratio on the results but in order to extrapolate the behaviour to the physical mass-ratio one still needs to perform some simulations with higher mass-ratio of 200 or 500.690 We are able to demonstrate that the mass-ratio has a qualitative and not only quantütatve effect on the simulated physics., We are able to demonstrate that the mass-ratio has a qualitative and not only quantitative effect on the simulated physics.691 For very low mass-ratios only one instability develops which changes for mass-ratios around 50., For very low mass-ratios only one instability develops which changes for mass-ratios around 50.692 Taking these findings as a starting point we conclude that further simulations of counterstreaming plasma have to be conducted with mass-ratios of 100 and above to find the correct physical behaviour., Taking these findings as a starting point we conclude that further simulations of counterstreaming plasma have to be conducted with mass-ratios of 100 and above to find the correct physical behaviour.693 A, A694((530.6 keV).,(530.6 keV).695 In contrast to the complex photospheric absorption line formation problem. the formation of the X-ray [Inorescent. O Ίνα line is relatively simple. depending only on the geometry of the overlviug coronal source of irradiation and the heliocentric angle of the photospheric region in question).," In contrast to the complex photospheric absorption line formation problem, the formation of the X-ray fluorescent O $\alpha$ line is relatively simple, depending only on the geometry of the overlying coronal source of irradiation and the heliocentric angle of the photospheric region in question."696. We present Monte Carlo calculations of the [Inorescent O Ka line in 822. ancl address its potential as an abundance diagnostic in 833 and 844.," We present Monte Carlo calculations of the fluorescent O $\alpha$ line in 2, and address its potential as an abundance diagnostic in 3 and 4."697 We adopt the same computational methods described in earlier work on Fe and Ne [Inorescence lines. ancl (he reader is relerred to and for details.," We adopt the same computational methods described in earlier work on Fe and Ne fluorescence lines, and the reader is referred to and for details."698 A brief summary is provided below., A brief summary is provided below.699" Nerav Ceharacteristic"" (fluorescence) Ka lines correspond to the 2p—1s decay of the excited state resulting [rom ejection of an inner-shell 15 electron in the neutral (or atom by either electron impact or photoionisation.", X-ray “characteristic” (fluorescence) $\alpha$ lines correspond to the $2p-1s$ decay of the excited state resulting from ejection of an inner-shell $1s$ electron in the neutral (or near-neutral) atom by either electron impact or photoionisation.700 In the case of solar ancl stellar photospheric [Inorescent lines. the former is expected (ο dominate1984).," In the case of solar and stellar photospheric fluorescent lines, the former is expected to dominate."701. For a given coronal X-ray. source spectrum. F(A). the observed flux of Ixa photons from the photosphere then depends on the photospheric abundance A of the [Inorescing species relative to that of other elements of significance for the photoabsorption opacitv in the vicinity of the 15 ionisation edge: the height  of the emitting source: and the heliocentric angle 9 between (he emitting source and the observer1979).," For a given coronal X-ray source spectrum, $F(\lambda)$, the observed flux of $\alpha$ photons from the photosphere then depends on the photospheric abundance $A$ of the fluorescing species relative to that of other elements of significance for the photoabsorption opacity in the vicinity of the $1s$ ionisation edge; the height $h$ of the emitting source; and the heliocentric angle $\theta$ between the emitting source and the observer."702. Fluorescent lines are formed in the region of the atmosphere corresponding to optical depth of approximately unitv lor the primary WK-shell ionising photons., Fluorescent lines are formed in the region of the atmosphere corresponding to optical depth of approximately unity for the primary K-shell ionising photons.703 In the case of O. for normal incidence the solar atmospheric Model C (VALC) of reaches the Ix-shell photoabsorption 7=1 depth slightly above the temperature minimun. al a gas temperature of about. 5600 Ix and about 800 km above the point where the continuum optical depth at 5000À.. 7509). is unity.," In the case of O, for normal incidence the solar atmospheric Model C (VALC) of reaches the K-shell photoabsorption $\tau=1$ depth slightly above the temperature minimum, at a gas temperature of about 5600 K and about 800 km above the point where the continuum optical depth at 5000, $\tau_{5000}$, is unity."704 The expected intensity of the emergent O Ka line was computed using a mocilied version of the 3D Monte Carlo radiative transfer code MOC'ASSINcaleulations)., The expected intensity of the emergent O $\alpha$ line was computed using a modified version of the 3D Monte Carlo radiative transfer code MOCASSIN.705. This eode follows enerev packels representing incident A-ray photons as thev interact. with the photospheric eas through photoelectric absorption or scattering events until the packets escape., This code follows energy packets representing incident X-ray photons as they interact with the photospheric gas through photoelectric absorption or scattering events until the packets escape.706 O Ίνα packets are produced following Ix-shell X-ray absorption wilh a probability dictated by the Ka fluorescent. vield [ον oxygen: these packets are followed in (he same fashion., O $\alpha$ packets are produced following K-shell X-ray absorption with a probability dictated by the $\alpha$ fluorescent yield for oxygen: these packets are followed in the same fashion.707 We adopted a value of 8.3x107 for the fInorescence vield of neutral oxveen, We adopted a value of $8.3\times 10^{-3}$ for the fluorescence yield of neutral oxygen708Ihne during eveuts confirmed with simultaneous optical photometry.,line during events confirmed with simultaneous optical photometry.709" Several solar flares have also been detected in the continuum region near 1.5652 in the IR. near the opacity παπα, inplviug formation deep within the solar atinosphere (Xuetal.2006:Cheng2010)."," Several solar flares have also been detected in the continuum region near $\mu$ m in the IR, near the $^{-}$ opacity minimum, implying formation deep within the solar atmosphere \citep{xu06,che10}."710. Some types of stellar activity have already been observed to “contaminate” exoplanet detection ad characterization studies., Some types of stellar activity have already been observed to “contaminate” exoplanet detection and characterization studies.711 Variations in the appearance aud depth of trauxit light curves have been observed for FORM host stars (Beutleyetal.2009:Dittinaun2009:Aeolctal.2010:INuudurthvet2011) aud iu transmission spectra of the M dwarf GI 136 (I&nutsonetal. 2011).," Variations in the appearance and depth of transit light curves have been observed for FGKM host stars \citep{ben09,dit09,ago10,kun11} and in transmission spectra of the M dwarf Gl 436 \citep{knu11}."712. Moreover. Kkuutsouetal.(2010). suggest that UV fux from chromosplerically active stars may destrov the atmospheric compounds responsible for producing temperature inversions observed in the atinospheres of exoplauets orbiting less active stars.," Moreover, \citet{knu10} suggest that UV flux from chromospherically active stars may destroy the atmospheric compounds responsible for producing temperature inversions observed in the atmospheres of exoplanets orbiting less active stars."713" Although AL dwarfs are known to exhibit a range of activity. the magnitude of such variability in IR contimuni bandpasses relevant to the detection (via primary transits) aud characterization (wia secoudary transits and phase mapping) of exoplaucts remains poorly ""understood."," Although M dwarfs are known to exhibit a range of activity, the magnitude of such variability in IR continuum bandpasses relevant to the detection (via primary transits) and characterization (via secondary transits and phase mapping) of exoplanets remains poorly understood."714 Marginal variability that may be due to flares was seen dun oa statistical investigation of single-epoch 2MÁASS calibration data (Davenportctal.2011)., Marginal variability that may be due to flares was seen in a statistical investigation of single-epoch 2MASS calibration data \citep{dav11}.715. That study is complementary to the simultaneous monitoring observations reported here. which provide flare rates for individual stars.," That study is complementary to the simultaneous monitoring observations reported here, which provide flare rates for individual stars."716 The few previous simultaneous optical-IR observations of AL chwart flares report anomalous IR flux decrements during optical flares (Rodono&Cutispoto1988) or uull detections (Panagi&Andrews1995)., The few previous simultaneous optical-IR observations of M dwarf flares report anomalous IR flux decrements during optical flares \citep{rod88} or null detections \citep{pan95}.717 We caution however that the observational techniques aud analyses of these simultaneous photometric studies were dubious aud not optimized for precision IR photometry., We caution however that the observational techniques and analyses of these simultaneous photometric studies were dubious and not optimized for precision IR photometry.718 Could the 5 milliaunag transit signal of a super-Earth residing in the habitable zone around a M5V. star Carwinetal.2000) be routinely masked by stellar activity and flares when observed in the IR?, Could the 5 milli-mag transit signal of a super-Earth residing in the habitable zone around a M5V star \citep{irw09} be routinely masked by stellar activity and flares when observed in the IR?719 In this paper. we preseut sinultaueouslv obtained. high time cadence optical aud IR photometric monitoring of well kuown active M dwarts at wulli-imag precision to address this question.," In this paper, we present simultaneously obtained, high time cadence optical and IR photometric monitoring of well known active M dwarfs at milli-mag precision to address this question."720 We used a suite of 3 optical photometric facilities aud L IR photometric facility to obtain simüiultaucous broad-baud optical and IR photometry of three active AL dwarts known to exhibit frequent flares. between 2009 October 2 - F and 2011 February 11 - 16.," We used a suite of 3 optical photometric facilities and 1 IR photometric facility to obtain simultaneous broad-band optical and IR photometry of three active M dwarfs known to exhibit frequent flares, between 2009 October 2 - 7 and 2011 February 11 - 16."721 The blue optical photometric data were obtained to identify the onset aud characterize the energv of flare eveuts whereas the red optical photometry was used to help characterize the color of flares.," The blue optical photometric data were obtained to identify the onset and characterize the energy of flare events, whereas the red optical photometry was used to help characterize the color of flares."722" A basic summary of the targets observed at cach observational facility. along with exposure times. filters used. and observing cadences is prescuted in Table Ἐν,"," A basic summary of the targets observed at each observational facility, along with exposure times, filters used, and observing cadences is presented in Table \ref{obssum}."723 Most of our 2009 observing run was lost due to a tropical storm hittine[um IKPNO. while poor weather aud instrument failures oulv affected ~2 niehts of our 2011 observing run.," Most of our 2009 observing run was lost due to a tropical storm hitting KPNO, while poor weather and instrument failures only affected $\sim$ 2 nights of our 2011 observing run."724 The Astrophysical Research Cousortiuui Sail Aperture Telescope (ARCSAT) 0.511. at. the Apache Poiut Observatory (APO) was one of three facilities we used to obtain high caucdence optical photometry., The Astrophysical Research Consortium Small Aperture Telescope (ARCSAT) 0.5m at the Apache Point Observatory (APO) was one of three facilities we used to obtain high candence optical photometry.725 Observations were nude with the University of Washineton (Milton2011:Tiltonetal.2011) through Sloan filters. and were recorded using a thermo-clectic cooled (TEC) 1021 x 1021 pixel APOGEE CCD.," Observations were made with the University of Washington \citep{hi11a,hil11} through Sloan filters, and were recorded using a thermo-electic cooled (TEC) 1024 x 1024 pixel APOGEE CCD."726 The full frame readout of the δὲ x δ FOV was —1 second., The full frame readout of the $\farcm$ x $\farcm$ FOV was $\sim$ 1 second.727 Twilight sky flats and dark frames were obtained every nieht to aid reduction of the data., Twilight sky flats and dark frames were obtained every night to aid reduction of the data.728 The data were reduced using standard techniques. aud differential aperture photometry was extracted. using a Pythou-based script which called the IRAF package.," The data were reduced using standard techniques, and differential aperture photometry was extracted using a Python-based script which called the IRAF package."729 The New Mexico State University (NMSU) automated lin telescope at APO also provided high cadeuce Joliusou baud observations., The New Mexico State University (NMSU) automated 1m telescope at APO also provided high cadence Johnson band observations.730 Further details about the NMSU din ancl its operations are described by Holtziiuetal.(2010)., Further details about the NMSU 1m and its operations are described by \citet{hol10}.731 The data were reduced using an automatic photometrv pipeline. vieldiug differential photometry for our science targets.," The data were reduced using an automatic photometry pipeline, yielding differential photometry for our science targets."732 Diving our 2009 observiug run. we also obtained siuultauneous optical monitoriug of our science targets with the Wisconsim Tndiana Yale NOAO (WIYN) 0.910 telescope., During our 2009 observing run we also obtained simultaneous optical monitoring of our science targets with the Wisconsin Indiana Yale NOAO (WIYN) 0.9m telescope.733 We used the ο] CCD. a 2018 x 2018 pixel camera with a pixel scale of 0760 t.," We used the S2KB CCD, a 2048 x 2048 pixel camera with a pixel scale of $\farcs$ 60 $^{-1}$."734 We curploved 2 x 2 binning of the S2$D. chip. aud a 260 x 260 pixel sub-array of the full frame. to reduce read out time aud obtain higher cadence photometry.," We employed 2 x 2 binning of the S2KB chip, and a 260 x 260 pixel sub-array of the full frame, to reduce read out time and obtain higher cadence photometry."735 The data we prescut were obtained in the Warris baud filter., The data we present were obtained in the Harris band filter.736 Nightly bias and dome flat field frames were obtained. aud the data were reduced using standard IRAF techniques.," Nightly bias and dome flat field frames were obtained, and the data were reduced using standard IRAF techniques."737 Differeutial photometry was extracted using the same Pythou-based software implemented for our ARCSAT data., Differential photometry was extracted using the same Python-based software implemented for our ARCSAT data.738 Our IR photometry was obtained at the NPNO 2.1 telescope using the Simultaneous Quad DIufrared Imagine Device (SQIID)., Our IR photometry was obtained at the KPNO 2.1m telescope using the Simultaneous Quad Infrared Imaging Device (SQIID).739 SQUD obtains simultaneous (A4; = 1.267 yan). (Agente = 1.672 pan). aud (Aou = 2.22 Lynn) bandimagery im 3 of the I quadrauts of its array.," SQIID obtains simultaneous $\lambda_{center}$ = 1.267 $\mu$ m), $\lambda_{center}$ = 1.672 $\mu$ m), and $\lambda_{center}$ = 2.224 $\mu$ m) band imagery in 3 of the 4 quadrants of its array."740 At the f/15 focus. cach 512 x 512 quadrant of SOIID'« ALADDIN array spaus a field of view of 5/07 x 5/28 with a pixel scale of 0.69 aresce 1.," At the f/15 focus, each 512 x 512 quadrant of SQIID's ALADDIN array spans a field of view of $\farcm$ 07 x $\farcm$ 28 with a pixel scale of 0.69 arcsec $^{-1}$."741 Our science exposures were ecuerally obtained at or near the arrays mininimuu exposure time of 0.871 seconds. and we doefocussed the telescope until stars took the appearauce of 207 - 28 - counts. to keep the couuts below the axrav's linearity luit.," Our science exposures were generally obtained at or near the array's minimum exposure time of 0.874 seconds, and we defocussed the telescope until stars took the appearance of $\sim$ $\farcs$ - $\sim$ $\farcs$ -wide donuts, to keep the counts below the array's linearity limit."742 Because of large overheads in the transiission of data frou the array. our net observing cadence was 60 seconds (Table 13).," Because of large overheads in the transmission of data from the array, our net observing cadence was $\sim$ 60 seconds (Table \ref{obssum}) )."743 NMielt-time. deep blauk-sky ages were obtained every clear night to serve as sky flats: dark frames were also obtained every day corresponding to the iutegration times of our skv flats.," Night-time, deep blank-sky images were obtained every clear night to serve as sky flats; dark frames were also obtained every day corresponding to the integration times of our sky flats."744 We used a 1 dither poiut pattern iu order to mitigate ehosts produced from observing bright sources., We used a 3-4 dither point pattern in order to mitigate ghosts produced from observing bright sources.745 Since we were interested in performing differeutial photometry. the specific nuuber aud pattern of dither points we adopted varied by source. to ensure cach frame contained our science target and at least 1 comparisou star.," Since we were interested in performing differential photometry, the specific number and pattern of dither points we adopted varied by source, to ensure each frame contained our science target and at least 1 comparison star."746 We periodically adjusted the position of the science target ou the array to cusure that small amplitude. long time-scale telescope tracking imiperfectious did uot cause the target to fall ou differcut pixels. thus making it more susceptible to inpoerfectious in the flat fielding process.," We periodically adjusted the position of the science target on the array to ensure that small amplitude, long time-scale telescope tracking imperfections did not cause the target to fall on different pixels, thus making it more susceptible to imperfections in the flat fielding process."747"Riessal (2004) discovered 16 Type Ia supernovas at high redshifts and compiled a 157 source ""gold"" data set held to be of the highest reliability.",Riess (2004) discovered 16 Type Ia supernovas at high redshifts and compiled a 157 source “gold” data set held to be of the highest reliability.748" Extinetions are listecl in Riessal (2004) for all except 24 sources among this ""gokl set.", Extinctions are listed in Riess (2004) for all except 24 sources among this “gold” set.749 Riessal focus on the dillerences of magnitudes Ay relative to the traditional Hubble plot., Riess focus on the differences of magnitudes $\Delta \mu$ relative to the traditional Hubble plot.750 In Fig., In Fig.751 1. we show the residuals jc versus the extinction coefficients Ay. for all the sources for which extinctions are known.," \ref{fig:residuals1} we show the residuals $\Delta \mu$ versus the extinction coefficients $A_V$, for all the sources for which extinctions are known."752 There is a clear correlation., There is a clear correlation.753 The sense of correlation is (hat. points with Ay>0. Iving above the straight line Hubble plot. tend to have small or even negative exlinclion. and points lving below the straight line tend (o have large extinction.," The sense of correlation is that points with $\Delta \mu >0$, lying above the straight line Hubble plot, tend to have small or even negative extinction, and points lying below the straight line tend to have large extinction."754 A precedent for examining correlations of residuals is given in WilliamsaL. (2003).," A precedent for examining correlations of residuals is given in Williams, (2003)."755 Residuals depend on the baseline model [rom which they are measured., Residuals depend on the baseline model from which they are measured.756" Fig.l uses the FRWmodel ancl “concordance” parameters Qa,=0.27. with Q4=0.73 under the constraint 2,=0."," \ref{fig:residuals1} uses the FRWmodel and “concordance” parameters $\Omega_M=0.27$, with $\Omega_\Lambda= 0.73$ under the constraint $\Omega_k=0$."757 This is one of the baselines cited by Riessaf (2004)., This is one of the baselines cited by Riess (2004).758" Here O3; is Che matter density. dy, (he vacuum energy density and 0;=1—Qa, O4."," Here $\Omega_M$ is the matter density, $\Omega_\Lambda$ the vacuum energy density and $\Omega_k = 1-\Omega_M-\Omega_\Lambda$ ."759" The class of FRW models predicts the| luminosity clistance as llere sinn denotes sinh for O,z0. sin for Q2,<O and is equal to unity for ο=0."," The class of FRW models predicts the luminosity distance as Here ${\rm sinn}$ denotes $\sinh$ for $\Omega_k>0$, $\sin$ for $\Omega_k<0$ and is equal to unity for $\Omega_k=0$."760" Parameters ave fitH by minimizingB >V. definedH by where n and yi, are the theoretical and observed distance moduli respectively and 0/7, are (he reported errors."," Parameters are fit by minimizing $\chi^{2}$, defined by where $\mu_p^i$ and $\mu_0^i$ are the theoretical and observed distance moduli respectively and $\delta\mu_0^i$ are the reported errors."761 Our notation includes the intercept parameter τρ (not always explicit in the literature)., Our notation includes the intercept parameter $\mu_{p0}$ (not always explicit in the literature).762 The IIubble constant fy and lit parameters such as the zero point are nol reported in Riessaf (2004). which states (hat they are irrelevant. ancl arbitrarily set for the sample presented here.," The Hubble constant $H_0$ and fit parameters such as the zero point are not reported in Riess (2004), which states that they are irrelevant and arbitrarily set for the sample presented here."763" We verily (Riess al. 2004) 4?=178 for the concordanceparameters cited above. along with the other 4? values for several other studies. presented below,"," We verify (Riess , 2004) $\chi^2=178$ for the concordanceparameters cited above, along with the other $\chi^2$ values for several other studies, presented below."764yw wind outllow interior to 30445.,the wind outflow interior to $\sim 30R_0$.765 However. it is to be remembered that the current model is merely a steady-state treatment of an infinitely more complicated: picture.," However, it is to be remembered that the current model is merely a steady-state treatment of an infinitely more complicated picture."766 All that can be said at this stage is that the current theory seems to point towards the simplest. case: Scenario la. as the most likely candidate.," All that can be said at this stage is that the current theory seems to point towards the simplest case; Scenario 1a, as the most likely candidate."767" Ht is to be mentioned that the ""urrent. model may play a complementary role alongside 1e altogether different and complex mechanisms for stellar outflow involving MID or acoustic waves.", It is to be mentioned that the current model may play a complementary role alongside the altogether different and complex mechanisms for stellar outflow involving MHD or acoustic waves.768 Future work will extend the modelling. towards a more realistic Lull two- or three-dimensional picture. concomitantly including a poloidal magnetic field and allowing the entire svstem to be described dvnamically with time varving magnetic and velocity fields with convection.," Future work will extend the modelling towards a more realistic full two- or three-dimensional picture, concomitantly including a poloidal magnetic field and allowing the entire system to be described dynamically with time varying magnetic and velocity fields with convection."769 The final and. indeed ultimate picture would of course. be to then include the stochastic elfects of dust formation anc dynamics. alongside calculation of the radiative properties of the dust. as is done in some recent work (seo??)..," The final and indeed ultimate picture would of course, be to then include the stochastic effects of dust formation and dynamics, alongside calculation of the radiative properties of the dust, as is done in some recent work \citep[see][]{Woitke2005, Lobel2008}."770 Realisation of this task will ultimately explore. the true nature of the outllow from Betelgcuse ane other. red supergiants. which is now bevond doubt. understood to be more complicated than at first imagined and vet. presenting a hurdle surmountable in steps.," Realisation of this task will ultimately explore the true nature of the outflow from Betelgeuse and other red supergiants, which is now beyond doubt, understood to be more complicated than at first imagined and yet, presenting a hurdle surmountable in steps."771 Perhaps the very. first. of those steps. is the steady-state model described. in. the current stucly.," Perhaps the very first of those steps, is the steady-state model described in the current study."772":headings: exavitational lensing If we consider a 2-sphere. the geodesics (""straight lines”) are the great circles ancl any two great circles intersect in (wo places that are known as antipodal points in geography.",": gravitational lensing If we consider a 2-sphere, the geodesics (“straight lines"") are the great circles and any two great circles intersect in two places that are known as antipodal points in geography."773 There are no parallel geodesics on (he sphere. aud that is the well-known break-down of the filth axiom (or postulate: see refsecA xioms)) of plane geometry (or Euclidean geometry).," There are no parallel geodesics on the sphere, and that is the well-known break-down of the fifth axiom (or postulate; see \\ref{secAxioms}) ) of plane geometry (or Euclidean geometry)."774 Given a pair of antipodal points such as north pole ancl south pole. there are infinitely many geodesics that diverge from one antipodal point and converge to the other.," Given a pair of antipodal points such as north pole and south pole, there are infinitely many geodesics that diverge from one antipodal point and converge to the other."775 The antipodal points are the foci of (he geodesics., The antipodal points are the foci of the geodesics.776Ubineworth (1990)..,Illingworth \nocite{1990ApJ...359L..41F}.777 Phe addition of extra mass at larger radii bv the dark halo deepens the potential well. which means that even particles in the centre of the galaxy will need a [larger tto climb out of this well. causing a shift in aat all radii.," The addition of extra mass at larger radii by the dark halo deepens the potential well, which means that even particles in the centre of the galaxy will need a larger to climb out of this well, causing a shift in at all radii."778 However. particles in the outskirts of the galaxy are relatively more allected by the addition of the dark halo than particles in the more central regions: if the halo had not been present. escaping from the potential well at large racii would have been relatively easy.," However, particles in the outskirts of the galaxy are relatively more affected by the addition of the dark halo than particles in the more central regions: if the halo had not been present, escaping from the potential well at large radii would have been relatively easy."779 Pherefore. the shift in iis larger at larger radii. something that is also illustrated by Figure 16..," Therefore, the shift in is larger at larger radii, something that is also illustrated by Figure \ref{fig:vesc}."780 The net result is a change in slope., The net result is a change in slope.781 We find that the slope of the -- rrelation in NGC 3379 changes in logscale from 0.31 to 0.46. when taking the dark halo into account.," We find that the slope of the - relation in NGC 3379 changes in logscale from 0.31 to 0.46, when taking the dark halo into account."782 Lf instead of considering the infinite halo mass of the NEW. profile we only take the contribution of the halo within recy into account when calculating the gravitational potential. the slope becomes 0.43 in logscale.," If instead of considering the infinite halo mass of the NFW profile we only take the contribution of the halo within $r_{200}$ into account when calculating the gravitational potential, the slope becomes 0.43 in logscale."783 We note that in both the models with and without halo. there is àfocal relation between aandVise.," We note that in both the models with and without halo, there is a relation between and."784 Llowever. when looking at a larger sample of galaxies and studying thegfobat -- rrelation the contribution of the halo to the potential should be taken into account to interpret the slopes. since the relative contribution of the dark matter to the potential compared to the luminous one may. vary [rom galaxy to ealaxy. e.g. depending on galaxy mass or environment.," However, when looking at a larger sample of galaxies and studying the - relation the contribution of the halo to the potential should be taken into account to interpret the slopes, since the relative contribution of the dark matter to the potential compared to the luminous one may vary from galaxy to galaxy, e.g. depending on galaxy mass or environment."785 We used the SAURON LIEU as a “photon collector” to obtain stellar absorption line kincmaties and line strengths out to four elfective radii in the early-type galaxies NGC 3379 and NGC S21., We used the SAURON IFU as a “photon collector” to obtain stellar absorption line kinematics and line strengths out to four effective radii in the early-type galaxies NGC 3379 and NGC 821.786 By co-adding the individual spectra. of each lenslet into. one spectrum. for cach observed. field. we were able to obtain sullicient signal-to-noise in the outskirts of these galaxies. which are too faint to observe with traditional long-slit spectroscopy.," By co-adding the individual spectra of each lenslet into one spectrum for each observed field, we were able to obtain sufficient signal-to-noise in the outskirts of these galaxies, which are too faint to observe with traditional long-slit spectroscopy."787 The stellar velocity profiles are measured. up to the fourth Causs-Llermite moment (4). which allows us to break the mass-anisotropy degeneracy when constructing dynamical models of our ealaxies.," The stellar velocity profiles are measured up to the fourth Gauss-Hermite moment $h_4$ ), which allows us to break the mass-anisotropy degeneracy when constructing dynamical models of our galaxies."788 Phe kinematics show a smooth continuation of the profiles measured within 1-2 2. with SAURON ancl long-slit spectroscopy. and are consistent with planctary nebulac kinematics.," The kinematics show a smooth continuation of the profiles measured within 1-2 $R_e$ with SAURON and long-slit spectroscopy, and are consistent with planetary nebulae kinematics."789 The line strengths. also show a continuation of the gradients. observed within 1 A. although our 105015 measurements probably suller from. variations in the continuum shape.," The line strengths also show a continuation of the gradients observed within 1 $R_e$, although our Fe5015 measurements probably suffer from variations in the continuum shape."790 The stellar halo population is old. and metal-poor., The stellar halo population is old and metal-poor.791 The continuation of the line strength &radients and the, The continuation of the line strength gradients and the792 VBlvaV = , ^2]}_0&=& = .793Here. N is neutral velocity (not vorticity): E=(vxb)aBy—ονBy is the electromotive force. which contains a ancl . effects.," Here, ${\bf N}$ is neutral velocity (not vorticity); ${\bf E}=\langle {\bf v} \times {\bf b}\rangle = \alpha {\bf B}_0 - 794\beta \nabla \times795{\bf B}_0$ is the electromotive force, which contains $\alpha$ and $\beta$ effects."796" To compute E. we again consider (wo paris the kinematic part Ei; and the part coming trom the back reaction of the magnetic Ποιά onto the fluids Ej: dlO + dlO,, αμα ος XB, doy = Ey +E,.. where a)=—£(v:Vxv) and djτσ) are the kinematic values Ridler 1980)."," To compute ${\bf E}$, we again consider two parts – the kinematic part ${\bf E}_0$ and the part coming from the back reaction of the magnetic field onto the fluids ${\bf E}_1$: dt _t + dt _t = _0 - _0 _0 + dt _t = _0 +, where $\alpha_0 = - \frac{\tau}{3}\langle {\bf v}\cdot {\bf \nabla} 797\times {\bf798v}\rangle $ and $\beta_0 = \frac{\tau}{3}\langle v^2\rangle$ are the kinematic values \citep[c.F.,][]{Krause80}."799. These (wo coefficients can againbe expressed in terms of N as:," These two coefficients can againbe expressed in terms of ${\bf N}$ as: _0 = , _0 = ."800]t is impossible to forecast the scientific truths that will be uuraveled by future geueratious of astrophysicists looking at the sky. since the Universe is often more subtle than our imagination.,"It is impossible to forecast the scientific truths that will be unraveled by future generations of astrophysicists looking at the sky, since the Universe is often more subtle than our imagination."801 Attempts to establish a dogmatic view about the sky have ofteu failed: notable examples include, Attempts to establish a dogmatic view about the sky have often failed; notable examples include802observations of the (J.K)=(1.1) and (2.2) inversion lines have been reported by Menten&Alcolea(1995).,"observations of the $(J,K) = (1,1)$ and $(2,2)$ inversion lines have been reported by \citet{MentenAlcolea1995}."803. Moreover. the emission in these lines has subsequently been imaged with the NRAO Very Large Array (VLA) with a resolution of a few areseconds (Menten et al..," Moreover, the emission in these lines has subsequently been imaged with the NRAO Very Large Array (VLA) with a resolution of a few arcseconds (Menten et al.,"804 in prep.;, in prep.;805 see Sect. 2.3))., see Sect. \ref{inv}) ).806 The critical density of the em-wavelength inversion lines is on the order of 107 em™. while that of the sub-mm 1o—0o transition has a value ~4 orders of magnitude higher.," The critical density of the cm-wavelength inversion lines is on the order of $10^{4}$ $^{-3}$ , while that of the sub-mm $1_{0} - 0_{0}$ transition has a value $\sim4$ orders of magnitude higher."807 Thus. both types of lines should provide complementary information on different regions of the envelope.," Thus, both types of lines should provide complementary information on different regions of the envelope."808 In Sect. 9...," In Sect. \ref{results},"809 we give a general description of the sub-mm spectra we obtained with HIFI aboard (Pilbrattetal.2010.in.this volume).., we give a general description of the sub-mm spectra we obtained with HIFI aboard \citep[][in this volume]{Pilbratt2010}.810 Thereafter. in Sect. 3.2..," Thereafter, in Sect. \ref{modeling},"811 we present radiative transfer caleulations conducted to model the observed line profiles. taking advantage of the constraints from the VLA imaging.," we present radiative transfer calculations conducted to model the observed line profiles, taking advantage of the constraints from the VLA imaging."812 These lead to aabundance determinations., These lead to abundance determinations.813 The observations. were made with the two orthogonal HIFI receivers available for each band. which in all cases work in double side-band (DSB) mode (seedeGraauwetal.2010.inthis volume)..," The observations were made with the two orthogonal HIFI receivers available for each band, which in all cases work in double side-band (DSB) mode \citep[see][in this volume]{deGraauw2010}."814 This effectively doubles the instantaneous intermediate frequency (IF) coverage., This effectively doubles the instantaneous intermediate frequency (IF) coverage.815" We observed the four stars described above with à tuning that. in the upper sideband. covers the frequency of the J,=1o—0o ground state transition of ortho-NH: at 572.4981 GHz."," We observed the four stars described above with a tuning that, in the upper sideband, covers the frequency of the $J_K 816= 1_0 - 0_0$ ground state transition of $_3$ at 572.4981 GHz."817 The tuning was chosen to also cover the frequency of the JkXlio—loj ground state line of ortho-H:O at 556.9360 GHz in HIFIs lower sideband.," The tuning was chosen to also cover the frequency of the $J_{K_a,K_c} = 1_{1,0} - 8181_{0,1}$ ground state line of $_2$ O at 556.9360 GHz in HIFI's lower sideband."819 The observations were obtained using the dual-beam-switching (DBS) mode., The observations were obtained using the dual-beam-switching (DBS) mode.820 In this mode. the HIFI internal steering mirror chops between the source position and a position believed to be free of emission. which was certainly the case for our observations.," In this mode, the HIFI internal steering mirror chops between the source position and a position believed to be free of emission, which was certainly the case for our observations."821 The telescope then alternately locates the source in either of the chopped beams. providing a double-difference calibration scheme. which allows a more efficient cancellation of the residual standing waves in the spectra.," The telescope then alternately locates the source in either of the chopped beams, providing a double-difference calibration scheme, which allows a more efficient cancellation of the residual standing waves in the spectra."822 Additional details on this observing mode can be found in Helmichetal.(2010.inthis volume).., Additional details on this observing mode can be found in \citet[][in this volume]{Helmich2010}.823 The double sideband system temperature was =100 K. and the calibration uncertainty is estimated to be10%.," The double sideband system temperature was $\approx 100$ K, and the calibration uncertainty is estimated to be."824. Spectral baselines were excellent., Spectral baselines were excellent.825" ""s beam had asize of 37” FWHM at the observing frequeney. which is much larger than the NH;--emitting regions of all our sources."," 's beam had a size of $37''$ FWHM at the observing frequency, which is much larger than the -emitting regions of all our sources."826 The HIFI data shown here were obtained using the wide-band spectrometer (WBS). which is an acousto-optical spectrometer. providing à simultaneous coverage of the full instantaneous IF band in the two available orthogonal receivers. with a (oversampled) channel spacing of 0.5 MHz (0.27 s). about half the effective resolution.," The HIFI data shown here were obtained using the wide-band spectrometer (WBS), which is an acousto-optical spectrometer, providing a simultaneous coverage of the full instantaneous IF band in the two available orthogonal receivers, with a (oversampled) channel spacing of 0.5 MHz (0.27 ), about half the effective resolution."827 Spectra in the figures have been resampled and smoothed to à channel spacing of =L1κ..., Spectra in the figures have been resampled and smoothed to a channel spacing of $\approx 1.1$.828 The data were processed with the standard HIFI pipeline using. HIPE. and nonstitched Level-2 data were exported using the HiClass tool available in HIPE.," The data were processed with the standard HIFI pipeline using HIPE, and nonstitched Level-2 data were exported using the HiClass tool available in HIPE."829 Further processitΓια ie. blanking spurious signals. first order polynomial baseline removal. stitching of the spectrometer subbands and averaging. was performed in CLASS.," Further processing, i.e. blanking spurious signals, first order polynomial baseline removal, stitching of the spectrometer subbands and averaging, was performed in CLASS."830 Since the quality of the spectra measured in both horizontal and vertical polarization was good. these were averaged to lower the final noise in the spectrum.," Since the quality of the spectra measured in both horizontal and vertical polarization was good, these were averaged to lower the final noise in the spectrum."831 This approach is justified since polarization is not a concern for the presented molecular-line analysis., This approach is justified since polarization is not a concern for the presented molecular-line analysis.832 All HIFI data were originally calibrated in units of antenna temperature (71) and were converted to the main-beam temperature (Typ) scale according to Tyg=Ενην. with the main-beam efficiency Wap=0.68.," All HIFI data were originally calibrated in units of antenna temperature $T_{A}^*$ ) and were converted to the main-beam temperature $T_{\rm{MB}}$ ) scale according to $T_{\rm{MB}}=T_{A}^*/\eta_{\rm{MB}}$, with the main-beam efficiency $\eta_{\rm{MB}}=0.68$."833 In all cases we have assumed a side-band gain ratio of one., In all cases we have assumed a side-band gain ratio of one.834 The main focus of this letter is on the 7j=1o—00 line of NHs., The main focus of this letter is on the $J_K = 1_0 - 0_0$ line of $_3$ .835 Ammonia microwave spectroscopy has a long history (see.e.g...Townes&Schawlow1955.Kukolich 1967)..," Ammonia microwave spectroscopy has a long history \citep[see, e.g., ][]{TownesSchawlow1955, Kukolich1967}. ."836 Very briefly. because of the possible orientations of the hydrogen spins. two different species of eexist that do not interconvert. ortho-NH: and. para-NHs.," Very briefly, because of the possible orientations of the hydrogen spins, two different species of exist that do not interconvert, $_3$ and $_3$."837 aassumes states. Jy. with K=0 or 3j. where # is an integer (all H spins parallel). whereas Κz3 for (not all H spins parallel).," assumes states, $J_K$, with $K = 0$ or $3n$, where $n$ is an integer (all H spins parallel), whereas $K \ne 3$ for (not all H spins parallel)."838 The principal quantum numbers J and K correspond to the total angular momentum and its projection on the symmetry axis of the pyramidal molecule., The principal quantum numbers $J$ and $K$ correspond to the total angular momentum and its projection on the symmetry axis of the pyramidal molecule.839" The temperature corresponding to the energy of the lowest para level (J,= 1j) is 22 K above that of the lowest ortho level (Jy= Oo).", The temperature corresponding to the energy of the lowest para level $J_K = 1_1$ ) is 22 K above that of the lowest ortho level $J_K = 0_0$ ).840 Therefore. for formation in the interstellar gas phase. which involves reactions with high exothermicities. the ortho- to para-NHg ratio is expected to attain its equilibrium value of unity (Umemotoetal.1999).," Therefore, for formation in the interstellar gas phase, which involves reactions with high exothermicities, the ortho- to $_3$ ratio is expected to attain its equilibrium value of unity \citep{Umemoto1999}."841. This situation is also expected to hold for CSEs. given that the IR studies cited above place the tthey observe in the hot medium close to the star.," This situation is also expected to hold for CSEs, given that the IR studies cited above place the they observe in the hot medium close to the star."842 A high-resolution study of the lo—Oo transition has very recently been presented by Cazzolietal. (2009).. (, A high-resolution study of the $1_0 - 0_0$ transition has very recently been presented by \citet{Cazzoli2009}. (843Only) its upper state is split into. several hyperfine structure (hfs) components with the ~ 1-2 MHz splitting resulting from the coupling of the quadrupole moment of the N nucleus with the electric field of the electrons.,Only) its upper state is split into several hyperfine structure (hfs) components with the $\sim 1$ –2 MHz splitting resulting from the coupling of the quadrupole moment of the N nucleus with the electric field of the electrons.844 Two of these components are further split by magnetic interactions., Two of these components are further split by magnetic interactions.845 The mean frequency is 572498.] MHz and the centroid frequencies of the three main hfs groups are all within 2 MHz. corresponding to =1s!.. much less than the line widths observed for the targets of this study (see Fig. 1).," The mean frequency is 572498.1 MHz and the centroid frequencies of the three main hfs groups are all within 2 MHz, corresponding to $\approx 1$, much less than the line widths observed for the targets of this study (see Fig.\ref{nh3plot}) )."846 In Sect., In Sect.847 3.2 we use data of the (J.K)=(1.I) and (2.2) inversion linesto constrain our. models. forIK Tau and IRC+10420.," \ref{modeling} we use data of the $(J,K) = (1,1)$ and $(2,2)$ inversion linesto constrain our models forIK Tau and IRC+10420."848 For these stars. single-dish observations of those lines made with the Effelsberg 100 meter telescope were reported by Menten&Alcolea (1995)..," For these stars, single-dish observations of those lines made with the Effelsberg 100 meter telescope were reported by \citet{MentenAlcolea1995}. ."849 In addition. to place," In addition, to place"850"typically in regions that have a very low density ISM. or that they typically are active for periods smaller than the recombination time (typically ~10° years). with long gaps between ""on"" times (Chiang Rappaport 1996).","typically in regions that have a very low density ISM, or that they typically are active for periods smaller than the recombination time (typically $\sim 10^5$ years), with long gaps between “on” times (Chiang Rappaport 1996)."851 But. since it is not clear that either of these possible explanations should or does apply. it would be helpful to push the completeness limit for SSSs to lower X-ray luminosities.," But, since it is not clear that either of these possible explanations should or does apply, it would be helpful to push the completeness limit for SSSs to lower X-ray luminosities."852 If the link between nebulae and SSSs can be established and if. as predicted (Rappaport et al.," If the link between nebulae and SSSs can be established and if, as predicted (Rappaport et al."853 1994. eet al 1995). SSS nebulae can be distinguished from PNe by a careful examination of the full spectrum of excitation lines. then the nebulae may provide an independent guide to the size of SSS populations in external galaxies.," 1994, et al 1995), SSS nebulae can be distinguished from PNe by a careful examination of the full spectrum of excitation lines, then the nebulae may provide an independent guide to the size of SSS populations in external galaxies."854 The very soft X-ray emission of SSSs can resemble X-ray supernova remnants (SNRs)., The very soft X-ray emission of SSSs can resemble X-ray supernova remnants (SNRs).855 There are. e.g.. two SSSs in ΜΑΙ that were subsequently identified as SNRs based on extended morphology and multi-wavelength observations eet al.," There are, e.g., two SSSs in M31 that were subsequently identified as SNRs based on extended morphology and multi-wavelength observations et al."856 2003. Kong et al.," 2003, Kong et al."857 2002b. 2003b).," 2002b, 2003b)."858 These two SNRs appear to be constant X-ray sources. which is consistent with the expected picture of SNRs.," These two SNRs appear to be constant X-ray sources, which is consistent with the expected picture of SNRs."859 On the other hand. most of the SSSs in external galaxies are X-ray variables SStefano Kong 2003a; Kong SStefano 2003).," On the other hand, most of the SSSs in external galaxies are X-ray variables Stefano Kong 2003a; Kong Stefano 2003)."860 Although it ts extremely difficult to study the morphology of X-ray sources at the distance of M104. and high resolution narrow-band optical imaging is not available. we can study the time variability of these X-ray sources to investigate their nature.. Galactic GCs house approximately 100. times as many X-ray sources as would be expected based on their mass. suggesting that the efficiency of forming X-ray sources must be higher in GCs than elsewhere in the Galaxy (Clack 1975).," Although it is extremely difficult to study the morphology of X-ray sources at the distance of M104, and high resolution narrow-band optical imaging is not available, we can study the time variability of these X-ray sources to investigate their nature.. Galactic GCs house approximately $100$ times as many X-ray sources as would be expected based on their mass, suggesting that the efficiency of forming X-ray sources must be higher in GCs than elsewhere in the Galaxy (Clack 1975)."861 A possible explanation is that the high stellar density near the cluster centers (as large as 10° stars pe). can lead to stellar interactions in which close binaries containing white dwarfs (WDs) and neutron stars (NSs) can be formed.," A possible explanation is that the high stellar density near the cluster centers (as large as $10^6$ stars $^{-3}$ ), can lead to stellar interactions in which close binaries containing white dwarfs (WDs) and neutron stars (NSs) can be formed."862 Eventually. either because dissipative processes (gravitational radiation or magnetic braking) bring the companion stars close enough for contact to be established. or else because the non-compact star begins to evolve and comes to fill its Roche lobe. mass transfer begins.," Eventually, either because dissipative processes (gravitational radiation or magnetic braking) bring the companion stars close enough for contact to be established, or else because the non-compact star begins to evolve and comes to fill its Roche lobe, mass transfer begins."863 Because the mass of the donor is generally limited by the turn off mass ( 0.87...) these systems are classified as low-mass X-ray binaries (LMXBs).," Because the mass of the donor is generally limited by the turn off mass $\sim 0.8\, M_\odot,$ ) these systems are classified as low-mass X-ray binaries (LMXBs)."864" Detailed calculations of interactions that form close binaries. follow the subsequent binary evolution. and include interactions which may occur after the close binaries are formed. show that a combination of 2--, 3—. and 4—body interactions can create X-ray binaries and lead them to be ejected to the outer parts of the cluster. ("," Detailed calculations of interactions that form close binaries, follow the subsequent binary evolution, and include interactions which may occur after the close binaries are formed, show that a combination of $2-,$ $3-,$ and $4-$ body interactions can create X-ray binaries and lead them to be ejected to the outer parts of the cluster. ("865See. e.g.. Phinney Sigurdsson 1991.),"See, e.g., Phinney Sigurdsson 1991.)"866 It is considered likely that close binaries can be ejected from GCs. since the amount of energy needed to escape the cluster is a small fraction of the binary’s binding energy.," It is considered likely that close binaries can be ejected from GCs, since the amount of energy needed to escape the cluster is a small fraction of the binary's binding energy."867 LMXBs can also be formed in the field. because a subset of all primordial binaries are expected to evolve into close binaries In which a neutron star accretes mass from a low-mass companion.," LMXBs can also be formed in the field, because a subset of all primordial binaries are expected to evolve into close binaries in which a neutron star accretes mass from a low-mass companion."868 Before a primordial binary can turn on as an X-ray binary. several processes must occur.," Before a primordial binary can turn on as an X-ray binary, several processes must occur."869 The formation of the neutron star occurs quickly. but the spiral in of the companion. or the companion’s stellar evolution. can require several billion years.," The formation of the neutron star occurs quickly, but the spiral in of the companion, or the companion's stellar evolution, can require several billion years."870 Because there are many uncertainties in the evolution of these systems and in the evolution of galaxy populations. it is difficult to accurately predict the numbers of LMXBs expected per unit mass. due to a single burst of early star formation.," Because there are many uncertainties in the evolution of these systems and in the evolution of galaxy populations, it is difficult to accurately predict the numbers of LMXBs expected per unit mass, due to a single burst of early star formation."871 It has been suggested. however. that such systems may not be able to produce enough LMXBs to explain the numbers currently being discovered in early-type galaxies White. Sarazin. Kulkarni(2002). (," It has been suggested, however, that such systems may not be able to produce enough LMXBs to explain the numbers currently being discovered in early-type galaxies White, Sarazin, Kulkarni(2002). ("872It is important to note that some of the early-type galaxies we observe may have had more complicated histories. with multiple epochs of star formation.),"It is important to note that some of the early-type galaxies we observe may have had more complicated histories, with multiple epochs of star formation.)"873 If not. then it is possible that the LMXBs we do see are systems that have been ejected from GCs.," If not, then it is possible that the LMXBs we do see are systems that have been ejected from GCs."874 Indeed. testing this hypothesis has been an important motivator for study of the GC/LMXB connection.," Indeed, testing this hypothesis has been an important motivator for study of the GC/LMXB connection."875 Meaningful tests must include the study of a set of galaxies. including spirals. to search for evidence of differences in the LMXB/GC connection as exhibited by early- and late-type galaxies.," Meaningful tests must include the study of a set of galaxies, including spirals, to search for evidence of differences in the LMXB/GC connection as exhibited by early- and late-type galaxies."876 Until now. M31 was the only spiral with bright enough GC X-ray sources to enable a comparison with the X-ray source population in distant ellipticals.," Until now, M31 was the only spiral with bright enough GC X-ray sources to enable a comparison with the X-ray source population in distant ellipticals."877 M104 15 therefore an important addition to the set of galaxies in which we can hope to study the LMXB/GC connection., M104 is therefore an important addition to the set of galaxies in which we can hope to study the LMXB/GC connection.878 Below we focus our discussion on the GCs studied from the ground which have been matched with X-ray sources., Below we focus our discussion on the GCs studied from the ground which have been matched with X-ray sources.879 Deep. wide-field images of M104 have been acquired with the CFHTI2K mosaic. camera at the Canada-France-Hawan Telescope (CFHT) in order to investigate. the optical characteristics of its large globular cluster system (GCS).," Deep, wide-field images of M104 have been acquired with the CFHT12K mosaic camera at the Canada-France-Hawaii Telescope (CFHT) in order to investigate the optical characteristics of its large globular cluster system (GCS)."880 A complete description of this photometry will appear in. VanDalfsen et al. (, A complete description of this photometry will appear in VanDalfsen et al. (8812003).,2003).882" In summary. the GCS exhibits a classically bimodal color distribution. with ""blue? (metal-poor) and ""red"" (metal-rich) subpopulations centered at corresponding metallicities of [Fe/H|(blue) 2—1.1. and [Fe/H](red) 2—0.1."," In summary, the GCS exhibits a classically bimodal color distribution, with “blue” (metal-poor) and “red” (metal-rich) subpopulations centered at corresponding metallicities of [Fe/H](blue) $= -1.1$ and [Fe/H](red) $= -0.1$."883 The redder population — which makes up about one-third of the total GCS - is more centrally concentrated in spatial distribution than the bluer clusters., The redder population – which makes up about one-third of the total GCS – is more centrally concentrated in spatial distribution than the bluer clusters.884" In terms of the luminosity limit of our optical survey. our data reach nearly two magnitudes fainter than the normal ""turnover? point (peak frequency) of the globular cluster luminosity function (GCLF)."," In terms of the luminosity limit of our optical survey, our data reach nearly two magnitudes fainter than the normal “turnover” point (peak frequency) of the globular cluster luminosity function (GCLF)."885 The GCLF turnover is at an absolute visual magnitude My2—7.6. corresponding to a cluster mass of M~1.3.10°M... with little difference between the blue and red clusters.," The GCLF turnover is at an absolute visual magnitude $M_V = -7.6$, corresponding to a cluster mass of $M \simeq 1.3 \times 10^5 M_{\odot}$, with little difference between the blue and red clusters."886 In short. the characteristics of the GCS strongly resemble those of the “standard” Milky Way GCS. simply scaled up to a total cluster population 7 or 8 times larger.," In short, the characteristics of the GCS strongly resemble those of the “standard” Milky Way GCS, simply scaled up to a total cluster population 7 or 8 times larger."887 The procedure we have used to match GCs with X-ray sources is described in $3., The procedure we have used to match GCs with X-ray sources is described in 3.888 We find 25 matches., We find $25$ matches.889 Of these. 19 objects Ite in the metal-rich side. while 6 objects lie in the metal-poor side. giving a 1:3 ratio of blue:red objects.," Of these, 19 objects lie in the metal-rich side, while 6 objects lie in the metal-poor side, giving a 1:3 ratio of blue:red objects."890 However. a random sampling of globulars would globally yield a 2:1 ratio of blue:red objects. and approaching a 1:1 ratio of blue:red very close to M104.," However, a random sampling of globulars would globally yield a 2:1 ratio of blue:red objects, and approaching a 1:1 ratio of blue:red very close to M104."891 There also seems to be a lack of matches which are both bright and blue., There also seems to be a lack of matches which are both bright and blue.892 We therefore find a result similar to others reported for NGC 4472 (Maccarone et al 2003. Kundu et al.," We therefore find a result similar to others reported for NGC 4472 (Maccarone et al 2003, Kundu et al."893 2002) and for the Milky Way and M31 (Bellazzini et al., 2002) and for the Milky Way and M31 (Bellazzini et al.894 1995. but see also eet al.," 1995, but see also et al."895 2002). that X-ray sources are preferentially found in GCs that are metal rich. (," 2002), that X-ray sources are preferentially found in GCs that are metal rich. ("896See Figure 6),See Figure 6)897"or alternatively, the models do not describe all details.","or alternatively, the models do not describe all details."898" The statistical uncertainties in each structure function, see Eq. ("," The statistical uncertainties in each structure function, see Eq. ("899"1), are computed as the standard deviations of the means (averaged sums) for the different time lag bins.","1), are computed as the standard deviations of the means (averaged sums) for the different time lag bins."900" Although we use a very popular estimator of uncertainties, Collier&Peterson(2001) noted that not all pairs of data in a given bin are independent."," Although we use a very popular estimator of uncertainties, \citet{Col01a} noted that not all pairs of data in a given bin are independent."901" To address this problem, they multiplied their errors by 21/3."," To address this problem, they multiplied their errors by $^{1/2}$."902 We adopt the Collier Peterson’s perspective and fit again the observed structure functions., We adopt the Collier Peterson's perspective and fit again the observed structure functions.903" After slightly enlarging the error bars, we concentrate on level-2 models consisting of STF/SBF and anything else."," After slightly enlarging the error bars, we concentrate on level-2 models consisting of STF/SBF and anything else."904" Among these 7 models of f, we select those giving (7?< 2 for the three observed structure functions (main Poissonian models)."," Among these 7 models of $f$, we select those giving $\hat{\chi}^2 <$ 2 for the three observed structure functions (main Poissonian models)."905 The set of solutions is presented in Table 1.., The set of solutions is presented in Table \ref{fits}.906" With regard to the spectral behaviour, four out of the 5 models in Table 1 are able to accurately and simultaneously describe fio.12100 AA)) and ftQLM1(2600 AA)), i.e., they fit both LOLM I shapes acceptably well (0.6 <$? 14)."," With regard to the spectral behaviour, four out of the 5 models in Table \ref{fits} are able to accurately and simultaneously describe $f_{LQLM\ I}$ ) and $f_{LQLM\ I}$ ), i.e., they fit both LQLM I shapes acceptably well (0.6 $\leq \hat{\chi}^2 907\leq$ 1.4)."908 The solutions for the first model (SQF+STF) indicate that symmetric triangular flares at ~ 2100 hhave a lifetime longer than the duration of STF at ~ 2600À., The solutions for the first model (SQF+STF) indicate that symmetric triangular flares at $\sim$ 2100 have a lifetime longer than the duration of STF at $\sim$ 2600.909". However, this is puzzling with the accretion disc paradigm."," However, this is puzzling with the accretion disc paradigm."910 Similar lifetimes are expected in a reverberation scenario., Similar lifetimes are expected in a reverberation scenario.911" Moreover, τ(2100 A)) < 1(2600 A)) in a disc local- scenario, e.g., the thermal timescale is proportional to (R?/GM)!?, where M is the mass of the central black hole and Rc4*? is the emission radius (e.g.,Goicoecheaetal.2008,andreferences therein)."," Moreover, $\tau$ (2100 ) $<$ $\tau$ (2600 ) in a disc local-instability scenario, e.g., the thermal timescale is proportional to $(R^3/GM)^{1/2}$, where $M$ is the mass of the central black hole and $R \propto \lambda^{4/3}$ is the emission radius \citep[e.g.,][and 912references therein]{Goi08}."913" The solutions for the second model (SQF--SBF) incorporate supernova explosions with 1,,(2100 A)) « 1,,(2600 À)).", The solutions for the second model (SQF+SBF) incorporate supernova explosions with $t_{sg}$ (2100 ) $<$ $t_{sg}$ (2600 ).914" However, the timescale t;, is exlusively related to the circumstellar density and the total energy released in each explosion (e.g.,Aretxagaetal.1997), so a chromatic timescale is not the expected result."," However, the timescale $t_{sg}$ is exlusively related to the circumstellar density and the total energy released in each explosion \citep[e.g.,][]{Are97}, so a chromatic timescale is not the expected result."915 The solutions for the EDF+STF and STF+SBF models are the most interesting ones (LQLM I data)., The solutions for the EDF+STF and STF+SBF models are the most interesting ones (LQLM I data).916" There is a clear degeneracy between EDF and SBF, which seem to work in a similar way."," There is a clear degeneracy between EDF and SBF, which seem to work in a similar way."917" Hence, the solutions for the third and fifth models are interpreted as evidence in favour of the coexistence of ~ 100-d time-symmetric flares and longer time-asymmetric shots (see Table 1))."," Hence, the solutions for the third and fifth models are interpreted as evidence in favour of the coexistence of $\sim$ 100-d time-symmetric flares and longer time-asymmetric shots (see Table \ref{fits}) )."918" Both kinds of flares at both wavelengths can be mostly due to reverberation, i.e., two types of EUV/X-ray variation in the vicinity of the accretion disc axis that are reprocessed by two annuli of the disc gas."," Both kinds of flares at both wavelengths can be mostly due to reverberation, i.e., two types of EUV/X-ray variation in the vicinity of the accretion disc axis that are reprocessed by two annuli of the disc gas."919" Measurements of time delays (Kundi¢etal.1997;Collier2001;etal. 2008),, and the existence of an EUV jet (Hutchings2003) and a bright X-ray source (Chartas2000),, support this physical scenario."," Measurements of time delays \citep{Kun97,Col01b,Sha08}, and the existence of an EUV jet \citep{Hut03} and a bright X-ray source \citep{Cha00}, support this physical scenario."920" From Table 1,, Tasym = 168 d and Τον = 105 d is a good compromise between the results at the two wavelengths and for the two flare asymmetric profiles (exponentially decaying and starburst profile)."," From Table \ref{fits}, $\tau_{asym}$ = 168 d and $\tau_{sym}$ = 105 d is a good compromise between the results at the two wavelengths and for the two flare asymmetric profiles (exponentially decaying and starburst profile)."921" Although the relative variances depend on wavelength, there is no need to invoke some mechanism other than reverberation."," Although the relative variances depend on wavelength, there is no need to invoke some mechanism other than reverberation."922" While the ~ 2100 vvariability is consistent with the asymmetric flares producing most of the variance at this wavelength (Wasym = 72%)), the variance at ~ 2600 wwould be mainly due to the symmetric flares (Wasym = 40%))."," While the $\sim$ 2100 variability is consistent with the asymmetric flares producing most of the variance at this wavelength $w_{asym}$ = ), the variance at $\sim$ 2600 would be mainly due to the symmetric flares $w_{asym}$ = )."923" This chromaticity in the relative variances is associated with the difference between time coverages, gaps and artifacts in the g ( 2100 À) and r (~ 2600 À) bands (see middle and bottom panels in Fig. 1))."," This chromaticity in the relative variances is associated with the difference between time coverages, gaps and artifacts in the $g$ $\sim$ 2100 ) and $r$ $\sim$ 2600 ) bands (see middle and bottom panels in Fig. \ref{combi}) )."924" The LOLM I g-band combined record lasts longer than the LOLM I combined curve in the r band, so it contains a prominent decline that is not present in the shorter record."," The LQLM I $g$ -band combined record lasts longer than the LQLM I combined curve in the $r$ band, so it contains a prominent decline that is not present in the shorter record."925" Besides the longer time coverage, the g-band curve fills a gap corresponding to the peak of an important event."," Besides the longer time coverage, the $g$ -band curve fills a gap corresponding to the peak of an important event."926 The presence of a few artifacts could also play a role., The presence of a few artifacts could also play a role.927" In Fig. 4,,"," In Fig. \ref{sffits},"928" the LQLM I shapes are compared with the adopted solutions: Wasym = 9.72, Tasym = 168 d, and Tsym = 105 d for fror(2100 AA)), and Wasym = 0.40, Tasym = 168 d, and Τον = 105 d for fLoLu1(2600 AA))."," the LQLM I shapes are compared with the adopted solutions: $w_{asym}$ = 0.72, $\tau_{asym}$ = 168 d, and $\tau_{sym}$ = 105 d for $f_{LQLM\ I}$ ), and $w_{asym}$ = 0.40, $\tau_{asym}$ = 168 d, and $\tau_{sym}$ = 105 d for $f_{LQLM\ I}$ )."929" In spite of the enlargement of error bars and the use of relatively sophisticated modelling, no model leads to an acceptable global solution at both wavelengths and both epochs."," In spite of the enlargement of error bars and the use of relatively sophisticated modelling, no model leads to an acceptable global solution at both wavelengths and both epochs."930" The APO data are only consistent, in terms of £2, with the STF+STF model."," The APO data are only consistent, in terms of $\hat{\chi}^2$, with the STF+STF model."931 The corresponding solution includes ~ 100-d time-symmetric flares and other family of very short-lifetime (r~ 10 d) symmetric flares., The corresponding solution includes $\sim$ 100-d time-symmetric flares and other family of very short-lifetime $\tau \sim$ 10 d) symmetric flares.932 This last kind of fluctuations is responsible for about 1/4 of the total variance., This last kind of fluctuations is responsible for about 1/4 of the total variance.933" The dominant ~ 100-d shots are also detected in the LOLM I experiment, so the main source of these flares do not evolve over decades (in the observer's frame)."," The dominant $\sim$ 100-d shots are also detected in the LQLM I experiment, so the main source of these flares do not evolve over decades (in the observer's frame)."934" Nevertheless, the absence of longer asymmetric flares (APO data) is a mystery."," Nevertheless, the absence of longer asymmetric flares (APO data) is a mystery."935" This could be due to unfortunate gaps in the light curves, time coverage of the monitoring, etc, or simply reflects the evolution of the central engine."," This could be due to unfortunate gaps in the light curves, time coverage of the monitoring, etc, or simply reflects the evolution of the central engine."936 Assuming that UV asymmetric flares are triggered by EUV/X-ray fluctuations (reverberation, Assuming that UV asymmetric flares are triggered by EUV/X-ray fluctuations (reverberation937the small uuuber of BSS does not allow to assess the statistical sienificance of this result.,the small number of BSS does not allow to assess the statistical significance of this result.938 Tn the region 0.60<V—7055 and 18<V19.5 of the immer CMD a uuuber of stars are preseut just above the TO., In the region $0.60<V-I<0.85$ and $18<V<19.8$ of the inner CMD a number of stars are present just above the TO.939 We lave compared these stars with the corresponding objects in the S89 plotometry., We have compared these stars with the corresponding objects in the S89 photometry.940" From this analysis we ford that of our objects are blends of 2 SSO stars, are bleuds of 3 S89 stars and of them are suele stars iu the S89 photometry Gvhere the pixel size is just 0722, Le. half of ours)."," From this analysis we found that of our objects are blends of $2$ S89 stars, are blends of $3$ S89 stars and of them are single stars in the S89 photometry (where the pixel size is just $0\farcs94122$, i.e. half of ours)."942 Notice that almost no such stars are preseut in the outer. less crowded. region.," Notice that almost no such stars are present in the outer, less crowded, region."943 It is likely that all stars with V.«20 in Fie., It is likely that all stars with $V<20$ in Fig.944 2 beiue seuificautlv brighter in our photometry are photometric bleuds., \ref{comparison} being significantly brighter in our photometry are photometric blends.945 The horzoutal brauch (IB) is formed bv 5 stars (already ideuti&Bed i the literature). aud it is located In a very small region around the point (V|LF.)=(0.97. 17.18). on the red side of the instability strip. as expected on the basis of the cluster metallicity.," The horizontal branch (HB) is formed by 5 stars (already identified in the literature), and it is located in a very small region around the point $(V-I,V)= (0.97, 17.18)$ , on the red side of the instability strip, as expected on the basis of the cluster metallicity."946 A dashed horizoutal Hue marks the level of the IIB in Fig. 3.., A dashed horizontal line marks the level of the HB in Fig. \ref{cmds}.947 The TO can be ideutified at (V...7)=0.69+0.01 aud V220.50x0.1., The TO can be identified at $(V-I)=0.69\pm0.01$ and $V=20.50\pm0.1$.948 The foreground/backeround star contamination is low. as expected from the high ealactic latitude of the cluster (bz le’).," The foreground/background star contamination is low, as expected from the high galactic latitude of the cluster $b\simeq-48^\circ$ )."949 This is clearly seeu by comparing the right and left panels of Fie. 3:, This is clearly seen by comparing the right and left panels of Fig. \ref{cmds};950 the right paucl shows the typical pattern of the halo background. superposed to the cluster CMD.," the right panel shows the typical pattern of the halo background, superposed to the cluster CMD."951 The field contamination is redder than the Pal 12, The field contamination is redder than the Pal 12952negligible.,negligible.953 The very red galaxies also show little sub-mm emission. mostly consistent with zero. although with large error bars.," The very red galaxies also show little sub-mm emission, mostly consistent with zero, although with large error bars."954 The inferred SFR is therefore also very low., The inferred SFR is therefore also very low.955 This suggests that this »opulation is overall depleted of cold dust., This suggests that this population is overall depleted of cold dust.956 Additional information about the very red. galaxies can be inferred from the comparison of their optical and near-IR oroperties., Additional information about the very red galaxies can be inferred from the comparison of their optical and near-IR properties.957 We find that the (/-/vs}) colour of these galaxies is largely consistent with the colour of the RS in the (/-/Vs)) vs. plane. contirming these galaxies to have an old stellar »opulation typical of RS galaxies.," We find that the $J$ ) colour of these galaxies is largely consistent with the colour of the RS in the $J$ ) vs. plane, confirming these galaxies to have an old stellar population typical of RS galaxies."958 Moreover. most of them are ‘ound in the central regions of the cluster. where very few young dusty galaxies are expected on average for a non-merging. relaxed cluster like A3112.," Moreover, most of them are found in the central regions of the cluster, where very few young dusty galaxies are expected on average for a non-merging, relaxed cluster like A3112."959 This suggests that the observed red optical colour could arise from other factors than isotropic dust reddening., This suggests that the observed red optical colour could arise from other factors than isotropic dust reddening.960 Several authors in the recent past have shown. using both radiative transfer models (2:: 2)) and observational data (e.g. 23). that depending on galaxy geometry and orientation. more or less severe reddening can arise.," Several authors in the recent past have shown, using both radiative transfer models \citealt{Pierini03}; \citealt{Pierini04}) ) and observational data (e.g. \citealt{Driver07}) ), that depending on galaxy geometry and orientation, more or less severe reddening can arise."961 Both ? and 2? show that attenuation is largely dependent on observed wavebands. with stronger effects in the bluer bands.," Both \citet{Pierini04} and \citet{Driver07} show that attenuation is largely dependent on observed wavebands, with stronger effects in the bluer bands."962 A strong contribution is also due to galaxy morphology. the bulge-to-dise ratio plaving an important role in determining the overall effect on the observed colours.," A strong contribution is also due to galaxy morphology, the bulge-to-disc ratio playing an important role in determining the overall effect on the observed colours."963 For intermediate inclination angles (4.« 60). the ratio of the colour terms (DΕαν) is higher for dises than for bulges.," For intermediate inclination angles $i < 60$ ), the ratio of the colour terms $E(B-V)/E(J-K)$ is higher for discs than for bulges."964 BD in a 3-d orbit around an F7V star.,-mass BD in a 3-d orbit around an F7V star.965" Due to the Mjup--massfaintness of the host star (V~ 16), the BD radius (1.12*039 R5,,)) is not yet well determined."," Due to the faintness of the host star $V \sim 16$ ), the BD radius $1.12^{+0.30}_{-0.15}$ ) is not yet well determined."966" To test and refine models of BD formation and evolution, a population of well-characterised objects is required."," To test and refine models of BD formation and evolution, a population of well-characterised objects is required."967" In this letter, we present the discovery ofWASP-30b,, a brown dwarf that transits its moderately-bright host star."," In this letter, we present the discovery of, a brown dwarf that transits its moderately-bright host star."968" is a V=11.9, F8V star located in Aquarius, on the border with Cetus."," is a $V = 11.9$, F8V star located in Aquarius, on the border with Cetus."969" A transit search (CollierCameronetal.2006) of WASP-South data from 2008 July to November found strong, 4.16-d periodicity."," A transit search \citep{2006MNRAS.373..799C} of WASP-South data from 2008 July to November found a strong, 4.16-d periodicity."970 Further observationsin a2009 with both WASP instruments (Pollaccoetal.2006) led to a total of 176612 usable photometric measurements (Figure 1))., Further observationsin 2009 with both WASP instruments \citep{2006PASP..118.1407P} led to a total of 612 usable photometric measurements (Figure \ref{fig:phot-rv}) ).971" Using the CORALIE spectrograph mounted on the 1.2- Euler-Swiss telescope (Baranneetal.1996;Quelozal. 2000),, we obtained 16 spectra of WASP-30 in 2009."," Using the CORALIE spectrograph mounted on the 1.2-m Euler-Swiss telescope \citep{1996A&AS..119..373B,2000A&A...354...99Q}, we obtained 16 spectra of WASP-30 in 2009."972 Radial velocity (RV) measurements were computed by weighted cross-correlation (Baranneetal.1996;Pepeetal. with a numerical G2-spectral template.," Radial velocity (RV) measurements were computed by weighted cross-correlation \citep{1996A&AS..119..373B,2005Msngr.120...22P} with a numerical G2-spectral template."973" RV variations 2005)were detected with the same period found from the WASP photometry and with a semi-amplitude of 6.6 km s-!, consistent with a sub-stellar-mass companion."," RV variations were detected with the same period found from the WASP photometry and with a semi-amplitude of 6.6 km $^{-1}$, consistent with a sub-stellar-mass companion."974 The RV measurements are listed in Table 1 and are plotted in Figure 1.., The RV measurements are listed in Table \ref{tab:rv} and are plotted in Figure \ref{fig:phot-rv}.975" To test the hypothesis that the RV variations are due to spectral line distortions caused by a blended eclipsing binary or starspots, we performed line-bisector analysis (Quelozetal.2001) of the CORALIEa cross-correlation functions."," To test the hypothesis that the RV variations are due to spectral line distortions caused by a blended eclipsing binary or starspots, we performed a line-bisector analysis \citep{2001A&A...379..279Q} of the CORALIE cross-correlation functions."976" The lack of correlation between bisector span and RV 1)) supports our conclusion that the periodic dimming(Figure of WASP-30 and its RV variations are due to the sub-stellar orbiting body, WASP-30b."," The lack of correlation between bisector span and RV (Figure \ref{fig:phot-rv}) ) supports our conclusion that the periodic dimming of WASP-30 and its RV variations are due to the sub-stellar orbiting body, WASP-30b."977" To refine the system parameters, we obtained high signal-to-noise transit photometry through a Gunn r filter with the Euler-Swiss telescope on 2010 Aug 01 (Figure 1; Table 2))."," To refine the system parameters, we obtained high signal-to-noise transit photometry through a Gunn $r$ filter with the Euler-Swiss telescope on 2010 Aug 01 (Figure \ref{fig:phot-rv}; ; Table \ref{tab:euler}) )."978 The data were affected by light, The data were affected by light979The ISOGAL programme (Omont ct al.,The ISOGAL programme (Omont et al.980 1999. 2001) has made use of the ISO satellite to obtain cletailed surveys of sample areas of the inner Bulge anc the Galactic Plane at two mid-infrared. wavelengths. Tym anc μα. with he intention of investigating the longitude and. latitude variations of stellar properties and their bearing on galactic structure.," 1999, 2001) has made use of the ISO satellite to obtain detailed surveys of sample areas of the inner Bulge and the Galactic Plane at two mid-infrared wavelengths, $\mu$ m and $\mu$ m, with the intention of investigating the longitude and latitude variations of stellar properties and their bearing on galactic structure."981 Because many of the fields are highly obscured. xwts of the relatively clear Baacle’s Windows were included or comparison purposes (Class et al.," Because many of the fields are highly obscured, parts of the relatively clear Baade's Windows were included for comparison purposes (Glass et al."982 1999)., 1999).983 By studying the contents of the latter at infrared and visible wavelengths one obtains a picture of the basic stellar population in the Bulge. o which more heavily obseured. fields. observable. only in he infrared.+B can be compared.," By studying the contents of the latter at infrared and visible wavelengths one obtains a picture of the basic stellar population in the Bulge, to which more heavily obscured fields, observable only in the infrared, can be compared."984 Fieldsae of 15 15 arcnun*D rom cach of Ser E and 66522 were thus included. in he ISOGAL work., Fields of 15 $\times$ 15 $^2$ from each of Sgr I and 6522 were thus included in the ISOGAL work.985" These were centred at (= 1.377. b = 2.637 and (= 1.087. 6 = 3.83"" respectively."," These were centred at $\ell$ = $^{\circ}$ , $b$ = $^{\circ}$ and $\ell$ = $^{\circ}$, $b$ = $^{\circ}$ respectively."986 Near-infrared data at Z(0.79 yam). 7(1.22 m). and As(2.14 pim). where the subscript ο denotes ‘short’. for o» windows are now available from the DENIS survey (Ipehtein. 1998) and for the Serll window only at J(—1.22 um). H(1.65 yam) and. As(2.16 jii) from 2MASS (Skrutskie. 1998).," Near-infrared data at $I$ $\mu$ m), $J$ $\mu$ m) and $K_S$ $\mu$ m), where the subscript $S$ denotes `short', for both windows are now available from the DENIS survey (Epchtein, 1998) and for the I window only at $J$ $\sim$ $\mu$ m), $H$ $\mu$ m) and $K_S$ $\mu$ m) from 2MASS (Skrutskie, 1998)."987 In addition. photometry on the Caltech-C'PIO svstem by Frogel anc Whitford (LOST. hereafter PW) was obtained for many of the AL stars in. the. objective ism survey of the 66522 field by Blanco. MieCarthy ancl Blanco (1984) ancl Blanco (1986).," In addition, photometry on the Caltech-CTIO system by Frogel and Whitford (1987, hereafter FW) was obtained for many of the M stars in the objective prism survey of the 6522 field by Blanco, McCarthy and Blanco (1984) and Blanco (1986)."988 comparison of stars detected by ISOGAL with the latter survey indicates hat. except for a few probable foreground. stars. none with spectral type earlier than M2. were seen.," A comparison of stars detected by ISOGAL with the latter survey indicates that, except for a few probable foreground stars, none with spectral type earlier than M2 were seen."989 The rate of detection increased with sub-tvpe. reaching at MG.," The rate of detection increased with sub-type, reaching at M6."990 Several previous surveys of these fields for variable stars have been mace., Several previous surveys of these fields for variable stars have been made.991 {ρα photography by Lloyd Evans (1976) yielded identifications ancl periods of many Miras., $I$ -band photography by Lloyd Evans (1976) yielded identifications and periods of many Miras.992 A search for the near-infrared counterparts of LRAS sources (Class 1986) revealed some additional long-period. Iarge-amplitude variables that were not found in the Z-band survey.," A search for the near-infrared counterparts of IRAS sources (Glass 1986) revealed some additional long-period, large-amplitude variables that were not found in the $I$ -band survey."993 Infraredobservations of nearly all the long-period. Iarge-amplitude variables in Ser LP were obtained by Class et al. (," Infraredobservations of nearly all the long-period, large-amplitude variables in Sgr I were obtained by Glass et al. ("9941995).,"1995),"995parameters.,parameters.996 So this method is fully model independent., So this method is fully model independent.997 We use the 192 SNe la and 69 GRBs and find the best fit parameters are go=—0.85+ 0.19. jo=1.5040.80 and so=3.49+4.50.," We use the 192 SNe Ia and 69 GRBs and find the best fit parameters are $q_0=-0.85 \pm 0.19$ , $j_0=1.50\pm 0.80$ and $s_0=3.49\pm 4.50$."998 The results are consistent with the flat ACDM model., The results are consistent with the flat $\Lambda$ CDM model.999 In Table | we summarize the constraints on cosmographic parameters., In Table 1 we summarize the constraints on cosmographic parameters.1000 The deceleration and jerk parameters in the w= wo. GCG. Cardassian expansion and f(R) models are almost the same in the Lc confidence level.," The deceleration and jerk parameters in the $w=w_0$ , GCG, Cardassian expansion and f(R) models are almost the same in the $1\sigma$ confidence level."1001 These values are consistent with the deceleration and jerk parameters of the ACDM model in the Ic confidence level., These values are consistent with the deceleration and jerk parameters of the $\Lambda$ CDM model in the $1\sigma$ confidence level.1002 So these models can not be discriminated using the present value of the statefinder pair., So these models can not be discriminated using the present value of the statefinder pair.1003 However the snap parameter in all the models is different and thus can be used to diserimminate the cosmological models., However the snap parameter in all the models is different and thus can be used to discriminate the cosmological models.1004 In the future. more data will give à precise snap parameter in different models.," In the future, more data will give a precise snap parameter in different models."1005 The cosmic acceleration could be due to a mysterious dark energy. or a modification of general relativity (modified gravity).," The cosmic acceleration could be due to a mysterious dark energy, or a modification of general relativity (modified gravity)."1006 In this paper we investigate the deceleration. jerk and snap parameters in modified gravity models and dark energy models.," In this paper we investigate the deceleration, jerk and snap parameters in modified gravity models and dark energy models."1007 We calibrate the GRB luminosity. relations without assuming any cosmological models using Se la. Because gamma-raybursts can be detected in high redshifts.," We calibrate the GRB luminosity relations without assuming any cosmological models using SNe Ia. Because gamma-raybursts can be detected in high redshifts,"1008GIUDe 1915|105 was discovered. in. 1992 with. the WATCIIequus telescope on board. the GRANAT satellite (C'astro-Tirado et al.,GRS 1915+105 was discovered in 1992 with the WATCH telescope on board the GRANAT satellite (Castro-Tirado et al.1009 1992)., 1992).1010 A radio counterpart was. subsequently identified ancl bipolar outflows with apparent superluminal motions were observed: the standard interpretation of this . ↓≻↓↥⋖⊾⊔∪⊔↓∢⊾⊔∪⊔↓⊔↿⋖⋅↓⋅⊔↓⊳∖∪⇂↓⋅⋖⋅↓⋜∐↓∖⇁↓⊳∖↿⊓∙≯⇃∢⋅↿≱∖∪↘⋖⋅∢⋅≱∖↓≤⋈≻↭↓≻↓⋯∙⋖⋅≱∖ MAR ; ⋅⋅ the source at a distance 2—12.5 kpe at an angle ¢=10. to the line of sight (Mirabel Rodriguez 1994)., A radio counterpart was subsequently identified and bipolar outflows with apparent superluminal motions were observed; the standard interpretation of this phenomenon in terms of relativistic jets (Rees 1966) places the source at a distance $D$ =12.5 kpc at an angle $i=70^\circ$ to the line of sight (Mirabel Rodriguez 1994).1011 The source cannot be observed in the optical band. due to the heavy extinction in the Galactic plane. but the X-ray luminosity often well above the Edclington luminosity for a neutron star suggests the presence of a 10 solar mass black hole.," The source cannot be observed in the optical band, due to the heavy extinction in the Galactic plane, but the X-ray luminosity often well above the Eddington luminosity for a neutron star suggests the presence of a $\sim$ 10 solar mass black hole."1012 Other circumstantial evidence comes with the similarities with the other galactic superluminal source GRO J165540. which has been shown unambiguously to harbor a compac object of =TAL. (Orosz Bailyn 1997).," Other circumstantial evidence comes with the similarities with the other galactic superluminal source GRO J1655–40, which has been shown unambiguously to harbor a compact object of $\simeq 7 M_{\odot}$ (Orosz Bailyn 1997)."1013 Since is discovery. GRS 1915|105 has displavecl an extraordinary. richness in variability in the X-ray band (Greiner. Morgan Remillare 1996. Chen. Swank “Taam 1997. 3elloni οἱ al.," Since its discovery, GRS 1915+105 has displayed an extraordinary richness in variability in the X-ray band (Greiner, Morgan Remillard 1996, Chen, Swank Taam 1997, Belloni et al."1014 1997). in the LR and radio bands (Fender et al.," 1997), in the IR and radio bands (Fender et al."1015 1997. Poolev Lender 1997).," 1997, Pooley Fender 1997)."1016 Recent (Eikenberry. et al., Recent (Eikenberry et al.1017 L997. Mirabel e al.," 1997, Mirabel et al."1018 1997) simultaneous multiwavelength observations of this superluminal source show a strict link between activity in the inner aceretion disk ancl plasma ejections., 1997) simultaneous multiwavelength observations of this superluminal source show a strict link between activity in the inner accretion disk and plasma ejections.1019 In this paper we estimate the minimum kinetic power associated with the ejections and. investigate the possible energv transport mechanism from the compact source to distances where the radio blobs are resolved. showing that 10 more suitable solution implies the presence of a strong magnetic field at the footpoint of the jet.," In this paper we estimate the minimum kinetic power associated with the ejections and investigate the possible energy transport mechanism from the compact source to distances where the radio blobs are resolved, showing that the more suitable solution implies the presence of a strong magnetic field at the footpoint of the jet."1020 1n section 2 we summarize the existing radio anc LH ala of the ejection events., In section 2 we summarize the existing radio and IR data of the ejection events.1021 In section 3 we directly caleulate 10 minimum kinetic power during the ejection., In section 3 we directly calculate the minimum kinetic power during the ejection.1022 In. section 4 we investigate the possible origin of the kinetic power., In section 4 we investigate the possible origin of the kinetic power.1023 In - ≻∢⊾≼↛⇂↕⋖≱↓↥⋅≻∖∖⊽∢⊾⊳∖⊔⊔↓⊔↓⋜⊔⋰↓∠∢⋅⇂↓↕∢⊾⊔↓⋜↧⊲↓⊔↓⋅⋖⋅⊳∖⊔↓↿⊳∖∪⇂⋅↿↓⊔⋅↓≻⋜↧↓≻⋖⊾↓⋅⋜⋯∠⇂ iscuss their consequences., In section 5 we summarize the main results of the paper and discuss their consequences.1024" Radio observations show that GRS 1915|105 in its active state is characterized by the increase of the Dux level from Ss<10 mJy to S,~100 mJ. he so called. state. on the top of which radios are superimposed. with cdurations from clays to a month and fluxes up to a few Jv (Foster et al."," Radio observations show that GRS 1915+105 in its active state is characterized by the increase of the flux level from $S_{\n}\le 10$ mJy to $S_{\n}\sim 100$ mJy, the so called state, on the top of which radio are superimposed, with durations from days to a month and fluxes up to a few Jy (Foster et al."1025 1996)., 1996).1026" The spectra ¢uring the plateau state are eencrally Hat or inverted. a< 0fwith S,‘ x“). probably indicating svnchrotron. scll-absorption."," The spectra during the plateau state are generally flat or inverted, $\a\le 0$ (with $S_{\n}\propto\n^{-\a}$ ), probably indicating synchrotron self-absorption."1027 On the other hand the spectra of radio [ares reveal a transition from optically thick to thin (a Q0) emissio] during the rise stage. with spectra harder (a~ 1.5) when the Dluxes reach the maximun: and softer (a~ ) during the subsequent. decay. generally interpreted as indicator of svncehrotron radiation of an expanding radio cloud.," On the other hand the spectra of radio flares reveal a transition from optically thick to thin $\a> 0$ ) emission during the rise stage, with spectra harder $\a\sim 0.5$ ) when the fluxes reach the maximum and softer $\a\sim 1$ ) during the subsequent decay, generally interpreted as indicator of synchrotron radiation of an expanding radio cloud."1028 Observations with the Very Laree Arrav ancl multiwavelength campaigns (with VLA and πο... simultaneously) pointed: ou that some strong racio Lares, Observations with the Very Large Array and multiwavelength campaigns (with VLA and UKIRT simultaneously) pointed out that some strong radio flares1029appropriate steps for pursuing stroug eravitational casing without leus planes.,appropriate steps for pursuing strong gravitational lensing without lens planes.1030 Iu particular. we rave demonstrated eravitational leuxiug by weak eravitational poteutials iu the appropriate cosmological vackerounds bv udumerical iuteeration of the null eeodesic equations of general relativity to be a ccasible task.," In particular, we have demonstrated gravitational lensing by weak gravitational potentials in the appropriate cosmological backgrounds by numerical integration of the null geodesic equations of general relativity to be a feasible task."1031 A loung-standiug for the use of the lin-lens approximation aud against inteeratineg he null geodesic equations has always been the Hel computational cost of numerical iuteeration compared with the low cost of the (esseutiallv algebraic] thiu-leus approach., A long-standing argument for the use of the thin-lens approximation and against integrating the null geodesic equations has always been the high computational cost of numerical integration compared with the low cost of the (essentially algebraic) thin-lens approach.1032 Teu wears ago this was essentially true., Ten years ago this was essentially true.1033 However. the current speed and memory capacity of even siall workstations removes this arguneut against usine the general relativistic equations instead of the thiu-leus method or other higher order approximations such as those proposed by Prue&Birkenshaw(1993) or Ikliugetal(2000).," However, the current speed and memory capacity of even small workstations removes this argument against using the general relativistic equations instead of the thin-lens method or other higher order approximations such as those proposed by \citet{pyne} or \citet{knp1}."1034 This material is based upou work supported by the National Scicuce Foundation wider Grant Nos., This material is based upon work supported by the National Science Foundation under Grant Nos.1035 PIITY-0211752. and) PITY-055521s. and a Bridgewater State College Faculty aud Librarian Research Crant.," PHY-0244752 and PHY-0555218, and a Bridgewater State College Faculty and Librarian Research Grant."1036 We eratefully acknowledec the hospitality aud support of the American Institute of Mathematics during the progress of the workshop “Caravitational Leusiug in the Ierr CGeometiy.” AIM. Palo Alto. July 5-10. 2005.," We gratefully acknowledge the hospitality and support of the American Institute of Mathematics during the progress of the workshop “Gravitational Lensing in the Kerr Geometry,” AIM, Palo Alto, July 5-10, 2005."1037]t is. now more than a decade since. the first.. blank field. surveys with.. the SCUBAPEN instrument. (Holland. et al.,"It is now more than a decade since the first blank field surveys with the SCUBA instrument (Holland et al.,"1038" 1999) on the James Clerk. Maxwell sTelescope revealed. the existence: of. large numbers of ⋅⊀hiehly luminous. sources lor. which. a significant∢⊀⋅ fraction⋅⊀ of the total bolometric. output is ..in the far-infrarecl⋅⊲⋅ and submillimetree SSmail""RN οἱ αἱ."," 1999) on the James Clerk Maxwell Telescope revealed the existence of large numbers of highly luminous sources for which a significant fraction of the total bolometric output is in the far-infrared and submillimetre Smail et al.,"1039 1997: Bareer οἱ al. 1998: Hughes et al.," 1997; Barger et al, 1998; Hughes et al.,"1040 1998)., 1998).1041" These objects were quickly found to be at high redshifts and to be heavily obseured. bv. dust. (for⋅ a review. see. Blain""n ct al.."," These objects were quickly found to be at high redshifts and to be heavily obscured by dust (for a review see Blain et al.,"1042. 2002)., 2002).1043 ..Phere is ⋠⋅now evidence. that they host considerable. star formation. as well as concurrent AGNe activity2. (Alexander et al..," There is now evidence that they host considerable star formation as well as concurrent AGN activity (Alexander et al.,"1044 2005)., 2005).1045" Although many authors have concluded that the ⋅⋅⋅⋅ : "" ⇂∪↓⊔↓∢⊾↓↓≻↓∪⊓⋅⊳∖⊳∖∠⇂∪⊔∐⊔⋜⋯⋅≱∖↿⇂↥⋖⋅∣⋡∪↓∪⊔↓⋖⋅↿↓⊔∼↓⊔⊔⊔⊔∪⊳∖↓↿∙∖∪⇂⊳∖⊔∣⋡−⊲⊲⇁⋅ mm galaxies. the contribution of CIN nevertheless remains unclear."," Although many authors have concluded that the former process dominates the bolometric luminosity of sub-mm galaxies, the contribution of AGN nevertheless remains unclear."1046" Obscured quasars ave the primary candidates to explain the missing"" hard X-ray background (e.g. Worsley et al.."," Obscured quasars are the primary candidates to explain the “missing” hard X-ray background (e.g. Worsley et al.,"1047 2005)., 2005).1048 Since these highly. absorbed. sources are likely o be clust-rich objects. they would be expected. to jwe substantial. luminosities ⊀↔⊀in the infrared.uM where the reprocessed light. is. emitted.," Since these highly absorbed sources are likely to be dust-rich objects, they would be expected to have substantial luminosities in the infrared where the reprocessed light is emitted."1049. qsThe wavelength regime. in: which. this. emissionDo. peaks will. depend. upon the typical. empoerature of⋅ the obscuring. dust., The wavelength regime in which this emission peaks will depend upon the typical temperature of the obscuring dust.1050 Lit ⋅⊀⊀is cool enough. sub-mm galaxies. are viable. candidates. for⋅ this⊀ long-sought obscured. quasar population.," If it is cool enough, sub-mm galaxies are viable candidates for this long-sought obscured quasar population."1051 Obseured ACGN. models have en shown to give a reasonable [it to the bright. end of the sub-nin source counts (Cunn Shanks. 1999). while. star-forming⋅⊀ galaxies. are expected make the dominant. contributionqoa: at faintere. Duxes (Busswell) Shanks.. .2001).," Obscured AGN models have been shown to give a reasonable fit to the bright end of the sub-mm source counts (Gunn Shanks, 1999), while star-forming galaxies are expected make the dominant contribution at fainter fluxes (Busswell Shanks, 2001)."1052 ↳∖↓⋜⋯∙∖⇁⋯∐↓↥∪↓⋅⊳∖↓↕⋜↧∖⇁∢⊾↓≻↓⋅∢⋅≱∖⋖⋅⊔⊓⋅∠⇂⊳∖⊔∣⋡−⊔↓⊔↓⋜⋯∠⇂⊔∐∐↓⊔↓∢⊾↿↓⋅⋖⋅ u . ∙⋠ ↴ ∪∣⋡≱∖⋖⋅↓⋅∖⇁⋜⊔↓∪⊔≱∖∪⇂↓⊔," Many authors have presented sub-mm and millimetre observations of $z$ QSOs (e.g. Andreani et al.,"1053⋏∙≟↓↕−∶≺≥⊾↔↻⊳∖↿∖⋖⋅⊳⋏∙≟⊳⇀∖↓∐⊔⋅∢⋅⋜⋯↓∢⊾⇂⋜↧↓↦↓≤⋗≤⋗⇀⊰∶ ∙ ∙ ≺⊲↓↕," 1993; Chini Krüggel, 1994; McMahon et al.,"1054⊲↓⊔⊲↓⊾∖↽↓∖⋡↓⋅∏⋏∙≟⋏∙≟," 1994; Omont et al.,"1055∢⋅⇂⋡↓≤⋗≤⊔∶↳∖↓≼∙↳∖↓⋜↧↓↥∪⊔∢⋅⇂⋜↧↓↦↓≤," 1996, 2001, 2003; Hughes et al.,"1056⋗≤⊔∶↻⊔↓∪⊔↿⋖⊾↿⋜↧↥↣ ↓≼⋗≤," 1997; Priddey et al.,"1057⋗∪⊳⇉∪∪↓⊳⇉∪∪∶∫≻∶∐⊔⋏∙≟↓," 2003; Petric et al.,"1058↥⋖⋅⊳∖∢⊾↿⋜↧↓↦↓≼⋗≤⋗⊤∶↓↴," 2006; Coppin et al.,"1059↓⋰⊓⇂∠⇂⋖⊾∙∖⇁⋖⋅↿⋜↧↓↦⇉∪∪∶⊰∶ ↓↴∢⊾∣↓⋰⊔∼∢⋅↿⋜↧↓↦⇉∪∪∩∶≺⊲∪↓≻↓≻⊲↓⊔⋖⊾↿⋜↧↓↦⇉∪∪↖∖⋜↧∃⊳↓↕∪∖∖⋎⋖⋅∖⇁⋖⋅↓⋅↿↓↥⋖⋅↕≻≻⇂⇂∢⊾⋖≱⇂⋅ whether the active. nucleus is. ultimately- responsible. for: the high luminosities at long wavelengths remains a largely open question.," 2008a), however the issue of whether the active nucleus is ultimately responsible for the high luminosities at long wavelengths remains a largely open question."1060 Observational analyses are often unable to exclude, Observational analyses are often unable to exclude1061Iu comparing this new suite of simulations to that of Paper L the key differences are the higher metallicity cooling functions. the erosion rates for cuhanced metal abundances for all eleinents up to iron. the exploration of higher shock velocities {ρα—105 kn 1). and the suppressed cooling in the ambient medium surrounding the cloud.,"In comparing this new suite of simulations to that of Paper I, the key differences are the higher metallicity cooling functions, the erosion rates for enhanced metal abundances for all elements up to iron, the exploration of higher shock velocities $v\subscript{shock} = 10^{4}$ km $^{-1}$ ), and the suppressed cooling in the ambient medium surrounding the cloud."1062" As a consistency check. we find that the simulations with Z=Z.. for shock velocities of lau ο, 3000 kin +. and 5000 lian + produce very snuilar dust mass survival fractions. imdicating that these changes do not invalidate our previous results."," As a consistency check, we find that the simulations with $Z = Z\subscript{\odot}$ for shock velocities of $v\subscript{shock} = 1000$ km $^{-1}$, 3000 km $^{-1}$, and 5000 km $^{-1}$ produce very similar dust mass survival fractions, indicating that these changes do not invalidate our previous results."1063 Iu fact. the degree of dust survival docs not beein to deviate significantly from Paper 1 uutil the metallicity is increased to Z=100.. as expected.," In fact, the degree of dust survival does not begin to deviate significantly from Paper 1 until the metallicity is increased to $Z = 100~Z\subscript{\odot}$, as expected."1064 We also find that our dust survival fractious remain 1 agrectuent with observations of IR cussion in SNRs., We also find that our dust survival fractions remain in agreement with observations of IR emission in SNRs.1065" ympecifically, the coutimued survival of Si grains matches the hieh abundancees found in Cas À bv ?.. while colmplete destruction of Ál;O; erains and survival of amorphous carbon graius match observatious of SNR 1E0102-7219 by ?.."," Specifically, the continued survival of Si grains matches the high abundances found in Cas A by \cite{Rho:2008qf}, while complete destruction of $_2$ $_3$ grains and survival of amorphous carbon grains match observations of SNR 1E0102-7219 by \cite{Sandstrom:2009fk}."1066 Ideally. we would have liked to explore a metallicitv reeinue in which the gas in the ejecta cloud is saturate with metals. effectively minickiug clouds of pure oxvecn. silicon. sulfur. argou. or calcium.," Ideally, we would have liked to explore a metallicity regime in which the gas in the ejecta cloud is saturated with metals, effectively mimicking clouds of pure oxygen, silicon, sulfur, argon, or calcium."1067 Using oxvecu as an example. an abundance ratio of order one woule require a metallicitv of Z~1000Z. since the solar abundance ratio is ΡΟΗ~5«LO! ," Using oxygen as an example, an abundance ratio of order one would require a metallicity of $Z \sim 1000~Z\subscript{\odot}$ since the solar abundance ratio is $n\subscript{O}/n\subscript{H} \sim 5\times 10^{-4}$."1068Unfortunately. due to the extremely short cooling times. this provec computationally prolibitive.," Unfortunately, due to the extremely short cooling times, this proved computationally prohibitive."1069 The simiplest solution is to luit the simulation time-step by the cooling time aac allow the simulation to run for a longer physical time. but it is also the most computationally expensive.," The simplest solution is to limit the simulation time-step by the cooling time and allow the simulation to run for a longer physical time, but it is also the most computationally expensive."1070 Iu order to probe the highest metallicity regimes. a more resource-cficient iiethod would need to be implemented without sacrificing the validity of the simulation.," In order to probe the highest metallicity regimes, a more resource-efficient method would need to be implemented without sacrificing the validity of the simulation."1071 Such a solution is left to future work., Such a solution is left to future work.1072 Ciuvenuthe. we still operate in the limit of strictly thermal sputteriue. since our dust erains are directly coupled to the flow of the eas.," Currently, we still operate in the limit of strictly thermal sputtering, since our dust grains are directly coupled to the flow of the gas."1073 Because large graius would require a ereater transfer of momentum frou the eas before become completely eutrained in the flow. it is possible that the dominant mode of sputtering for such evains would be in the nou-thermal limit. as high velocity eas washes over them.," Because large grains would require a greater transfer of momentum from the gas before becoming completely entrained in the flow, it is possible that the dominant mode of sputtering for such grains would be in the non-thermal limit, as high velocity gas washes over them."1074 In order to decouple the dust particles frou the motions of the eas. we would wave to track separated erain populations of varviug radii.," In order to decouple the dust particles from the motions of the gas, we would have to track separated grain populations of varying radii."1075 The number of racius bius required to accurately rack the cutive dust mass for all niue erai species is nucertain. but it could be computationally significant.," The number of radius bins required to accurately track the entire dust mass for all nine grain species is uncertain, but it could be computationally significant."1076 As incutioned in Paper L it may not be unreasonable or the dust particles to be coupled to the flow if he eraimms are charged and maguetic fields permeate he ejecta material.," As mentioned in Paper I, it may not be unreasonable for the dust particles to be coupled to the flow if the grains are charged and magnetic fields permeate the ejecta material."1077" However. magnetized ejecta clouds would require au investigation of the effects of betatron acceleration on charged eraius (2?}., "," However, magnetized ejecta clouds would require an investigation of the effects of betatron acceleration on charged grains \citep{Shull:1977lr, Shull:1978fk}."1078Finally. we investigated the possibility of transitioning from) post-processing of our dust particle histories to colmpute erosiou to an “ou-the-fly” method that would sputter the eraius as the simulation ran.," Finally, we investigated the possibility of transitioning from post-processing of our dust particle histories to compute erosion to an “on-the-fly"" method that would sputter the grains as the simulation ran."1079 This would allow metals that are sputtered off the eraius to feed back iuto the ambient medium and increase the metallicity., This would allow metals that are sputtered off the grains to feed back into the ambient medium and increase the metallicity.1080 Ilowever. if we asstme that the eas within the ejecta cloud is already heavily iuetal-euriched. the amount of motals released iuto the eas in this wav would not alter the metallicity enough to make a substantial difference.," However, if we assume that the gas within the ejecta cloud is already heavily metal-enriched, the amount of metals released into the gas in this way would not alter the metallicity enough to make a substantial difference."1081 As we have shown. it takes a large change in the metal abundance to create an siguificaut clifference im the zünount of dust that survives the shiock-cloud iuteractiou.," As we have shown, it takes a large change in the metal abundance to create an significant difference in the amount of dust that survives the shock-cloud interaction."1082 We thank the anouvimous referee for conunueuts that helped to clarify and strenethen this work., We thank the anonymous referee for comments that helped to clarify and strengthen this work.1083 We also thank Robert Fesen for useful discussion aud couuucuts., We also thank Robert Fesen for useful discussion and comments.1084 The computing resources needed for this work were provided by NASA IIEC Allocation SMD-10-2612. ou the supercomputer.Plerades. at tlhe NASA Advanced Supercomputing Facility.," The computing resources needed for this work were provided by NASA HEC Allocation SMD-10-2612 on the supercomputer, at the NASA Advanced Supercomputing Facility."1085 This project was fuuded by NSF Theory Grant ASTO7-07171. STScI Archive Theory Crant AR L177LOI-A. aud the NSF Caaduate Research Fellowship Program (D.W.S.).," This project was funded by NSF Theory Grant AST07-07474, STScI Archive Theory Grant AR 11774.01-A, and the NSF Graduate Research Fellowship Program (D.W.S.)."1086The inereased moment anc cherey input by streaming velocities also affects the thermal and turbulent evolution of the eas.,The increased momentum and energy input by streaming velocities also affects the thermal and turbulent evolution of the gas.1087 In Figure lL. we compare the temperature aud velocity dispersion within all three nünibhalos.," In Figure 4, we compare the temperature and velocity dispersion within all three minihalos."1088 Ta cases with a streamine velocity. the eas temperature near the virial radius is systematically lugher.," In cases with a streaming velocity, the gas temperature near the virial radius is systematically higher."1089 This is not suprising. since the virial temperature scales with virial mass and redshift as A factor of ~3 increase in the virial mass and a coluparatively small decrease in redshift therefore result in a factor of ~2 higher virial temperature.," This is not suprising, since the virial temperature scales with virial mass and redshift as A factor of $\simeq 3$ increase in the virial mass and a comparatively small decrease in redshift therefore result in a factor of $\sim 2$ higher virial temperature."1090 Ouce the gas begius to cool efficieutly. this difference is quickly reduced. however. and we find no clear difference reaming below r&10pc.," Once the gas begins to cool efficiently, this difference is quickly reduced, however, and we find no clear difference remaining below $r\simeq 10\,{\rm pc}$."1091 Iu the bottom paucl of Figure 1d. we also show the velocity dispersion of the eas in radial bius after subtracting the bulk velocity of the halo aud a spherically averaged radial iufall aud. rotation velocity.," In the bottom panel of Figure 4, we also show the velocity dispersion of the gas in radial bins after subtracting the bulk velocity of the halo and a spherically averaged radial infall and rotation velocity."1092 Unlike the teiiperature. the velocity dispersion reniaius systematically higher by a factor of a few even at very high densitics.," Unlike the temperature, the velocity dispersion remains systematically higher by a factor of a few even at very high densities."1093 Evidently. the gas becomes more turbulent iu the presence of streamline velocities.," Evidently, the gas becomes more turbulent in the presence of streaming velocities."1094 This could affect the mass function of the first stars. since a ligher ratio of the velocity dispersion to the sound speed usually results in increased fraginentation at later stages iu the collapse (Clarketal.2011).," This could affect the mass function of the first stars, since a higher ratio of the velocity dispersion to the sound speed usually results in increased fragmentation at later stages in the collapse \citep{clark11}."1095. As a result. the typical mass of a Pop III star may be reduced.," As a result, the typical mass of a Pop III star may be reduced."1096 Tow conunon is the above delay considering the nunihalo population as a whole?, How common is the above delay considering the minihalo population as a whole?1097 Since cach component of the large-scale streaming velocity is distributed according toa Gaussian. the maeuitude of the velocity vector obeys a Maxwell distribution (Tschakhovichetal.2010):: where oq is the dispersion of cach individual velocity component.," Since each component of the large-scale streaming velocity is distributed according to a Gaussian, the magnitude of the velocity vector obeys a Maxwell distribution \citep{tbh10}: where $\sigma_{1{\rm d}}$ is the dispersion of each individual velocity component."1098 The fraction of the universe with streaming velocities ereater than σαν+ at 2=99. which we consider a lower lait for the above delay to be sjeuificautf. inav be found by inteerating the above function from 0/2=oygV¥3/2 to infinity. which vields approximately 0.586.," The fraction of the universe with streaming velocities greater than $1.5\,{\rm km\,s^{-1}}$ at $z=99$, which we consider a lower limit for the above delay to be significant, may be found by integrating the above function from $\sigma/2=\sigma_{1{\rm d}}\sqrt{3}/2$ to infinity, which yields approximately $0.86$."1099 This shows that our results may be considered represeutative for most of the volui., This shows that our results may be considered representative for most of the volume.1100 The cosinological umuber deusity of niuihalos hostius Pop III stars may then be estimated using the Shethli-Tormen (Shethctal.2001).mass function: where we set Ma1.5«10NL. for the case of no streaming velocities and Au;=5«10M. for the case of a universal Lo streaming velocity. represcuting the factor of 23 merease m mnüunmaiun halo mass.," The cosmological number density of minihalos hosting Pop III stars may then be estimated using the Sheth-Tormen \citep{smt01} mass function: where we set $M_{\rm min}=1.5\times 10^5\,{\rm M}_{\odot}$ for the case of no streaming velocities and $M_{\rm min}=5\times 10^5\,{\rm M}_{\odot}$ for the case of a universal $1\sigma$ streaming velocity, representing the factor of $\simeq 3$ increase in minimum halo mass."1101 The resulting number densities should be considered upper Duis. since not everv halo at the low-mass end forms a Pop III star.," The resulting number densities should be considered upper limits, since not every halo at the low-mass end forms a Pop III star."1102 We set Maas=o10MS. but note that our results are not seusititive to this paramcter. since nmassve halos are rare.," We set $M_{\rm max}=10^8\,{\rm M}_{\odot}$, but note that our results are not sensititive to this parameter, since massive halos are rare."1103 As shown in Figure 5. the wmuber of mnüuibhalos that cool aud form stars is reduced by up to au order of magnitude iu the presence of streaming velocities.," As shown in Figure 5, the number of minihalos that cool and form stars is reduced by up to an order of magnitude in the presence of streaming velocities."1104 Such a large effect nuplies that strowunins velocities should be taken iuto account when the influence of the first stars on observables is investigated., Such a large effect implies that streaming velocities should be taken into account when the influence of the first stars on observables is investigated.1105 We lave found that supersonic streamine velocities vetween the DAL aud gas substantially delay the ouset of eravitational collapse im iminihalos., We have found that supersonic streaming velocities between the DM and gas substantially delay the onset of gravitational collapse in minihalos.1106 The virial mass required for efficient cooling is increased by a factor of ~3. which results im an average delay of Pop LI star ‘orlnation bv A:=L," The virial mass required for efficient cooling is increased by a factor of $\simeq 3$, which results in an average delay of Pop III star formation by $\Delta z=4$."1107 Streaming velocities also cuhauce he build-up of turbulence curving runawav collapse. which could affect the fragimeutation of the eas and heuce he mass function of the first stars.," Streaming velocities also enhance the build-up of turbulence during runaway collapse, which could affect the fragmentation of the gas and hence the mass function of the first stars."1108 Our results agree well with the simulations preseuted in Stacyetal.(2010). concerning the delay of collapse., Our results agree well with the simulations presented in \citet{sbl11} concerning the delay of collapse.1109 Tn addition. and iu contrast to their result. we fud a sjenificaut iucrease in the Πτα halo mass required for the gas to cool.," In addition, and in contrast to their result, we find a significant increase in the minimum halo mass required for the gas to cool."1110 This might be due to the ~10 times higher resolution eniploved in the preseut study. Cliving that the DM softening leugth is comparable to the size of the Jeans-unustable eas cloud.," This might be due to the $\simeq 10$ times higher resolution employed in the present study, ensuring that the DM softening length is comparable to the size of the Jeans-unstable gas cloud."1111 If this criterion is not fulfilled. the collapse of the eas nuelt be artificially delaved (e.g...Yoshidaetal. 2003).," If this criterion is not fulfilled, the collapse of the gas might be artificially delayed \citep[e.g.,][]{yoshida03a}. ."1112. We have investigated this for the case MIT1., We have investigated this for the case MH–1.1113 We increased the initial DM aud eas particle masses by factors of 8 and 61 to 28.2 and 225NL... for the DM. and 5.8 and 16.0M... for the eas.," We increased the initial DM and gas particle masses by factors of $8$ and $64$ to $28.2$ and $225\,{\rm M}_{\odot}$ for the DM and $5.8$ and $46.4\,{\rm M}_{\odot}$ for the gas."1114 Tn these simulations we also decreased the unuuber of cells enforced per Jeans length from 128 to 6L aud 32 (fordetails.seeCweifetal.2011).," In these simulations we also decreased the number of cells enforced per Jeans length from $128$ to $64$ and $32$ \citep[for details, see][]{greif11}."1115. When decreasing the resolution. the virial mass of the munihalo at the poiut of collapse is increased from 3.0 to 3.3 aud L7<10*ML... and the redshift of collapse is shifted from 19.6 to 19.2 and 18.1.," When decreasing the resolution, the virial mass of the minihalo at the point of collapse is increased from $3.0$ to $3.3$ and $4.7\times 10^5\,{\rm M}_{\odot}$, and the redshift of collapse is shifted from $19.6$ to $19.2$ and $18.1$."1116 On the other haud. iu inercase of the initial resolutiou bv a factor of eight results only in a marginal decrease of the virial mass to 2.9«10°MLi and shifts the redshift of collapse to 19.5.," On the other hand, an increase of the initial resolution by a factor of eight results only in a marginal decrease of the virial mass to $2.9\times 10^5\,{\rm M}_{\odot}$, and shifts the redshift of collapse to $19.8$."1117 This shows that iusufficieut resolution can artificially delay. the collapse of the halo. which might be one ofthe reasous why find significantly hieher halo masses.," This shows that insufficient resolution can artificially delay the collapse of the halo, which might be one of the reasons why \citet{sbl11} find significantly higher halo masses."1118 Due to the large shift iu mass in the presence of streaming velocities. the number density of nminibalos expected to foin Pop III stars is reduced by up to au order of magnitude. and is further modulated with a spatial coherence length correspoucding to many Mpe in the preseut universe.," Due to the large shift in mass in the presence of streaming velocities, the number density of minihalos expected to form Pop III stars is reduced by up to an order of magnitude, and is further modulated with a spatial coherence length corresponding to many Mpc in the present universe."1119 This could leave a distinct imprint ou the 21 cu background aud the reionization of the universe (Furlanetto2006:Barkana&Loeh2001).. as well as affect the observabilitv of Pop III supernovac (e.g.Brom&Loeb 2002)..," This could leave a distinct imprint on the 21 cm background and the reionization of the universe \citep{furlanetto06,bl01}, as well as affect the observability of Pop III supernovae \citep[e.g.][]{bl02}. ."1120 Ultimately. this modulation might be inherited by the distributionof more massive objects forming at later times. thereby biasing large-scale structure estimates of cosmological parameters such as those related to the properties ofdark cucrey.," Ultimately, this modulation might be inherited by the distributionof more massive objects forming at later times, thereby biasing large-scale structure estimates of cosmological parameters such as those related to the properties of dark energy."1121Mesolensing can also discover or place limits on the existence of disk dark matter. and can contribute to surveys of the outermost regions of the solar system.,"Mesolensing can also discover or place limits on the existence of disk dark matter, and can contribute to surveys of the outermost regions of the solar system."1122 Under certain circumstances it can be used to study more distant masses in binaries. possibly including intermediate-mass black holes in our own Galaxy and the supermassive black holes found at the centers of galaxies Stefano 2007b).," Under certain circumstances it can be used to study more distant masses in binaries, possibly including intermediate-mass black holes in our own Galaxy and the supermassive black holes found at the centers of galaxies Stefano 2007b)."1123 One of the interesting results we have derived is the high rate of events possible with the coming generation of monitoring programs., One of the interesting results we have derived is the high rate of events possible with the coming generation of monitoring programs.1124" Key factors in increasing the rate are the fact that sensitive. photometry will allow smaller values of fy. while better spatial resolution will allow smaller values of 6,,,,. at least in fields crowded enough to contain stars in a surface area 02,,. This means that the rate of events due to nearby stars per square degree will be significantly higher than at present."," Key factors in increasing the rate are the fact that sensitive photometry will allow smaller values of $f_T,$ while better spatial resolution will allow smaller values of $\theta_{mon},$ at least in fields crowded enough to contain stars in a surface area $\theta_{mon}^2.$ This means that the rate of events due to nearby stars per square degree will be significantly higher than at present."1125 Pan-STARRS and LSST also naturally benefit from being able to monitor large areas., Pan-STARRS and LSST also naturally benefit from being able to monitor large areas.1126 We have used what appear to be realistically achievable values of the parameters fy. and Onon, We have used what appear to be realistically achievable values of the parameters $f_T$ and $\theta_{mon}$.1127 Even 1f the values eventually achieved are not optimal. the predicted rates are still high.," Even if the values eventually achieved are not optimal, the predicted rates are still high."1128 The detection efficiency then determines the fraction of events that will be successfully identified., The detection efficiency then determines the fraction of events that will be successfully identified.1129 Detection efficiencies for past monitoring programs have typically been in the range of tens of percent., Detection efficiencies for past monitoring programs have typically been in the range of tens of percent.1130 It is likely that new monitoring programs will be at least comparably efficient., It is likely that new monitoring programs will be at least comparably efficient.1131 Even though the cadences of wide-field monitoring may not be ideal for lensing. the greater photometric sensitivity means that events will typically last longer. providing more opportunities for detection.," Even though the cadences of wide-field monitoring may not be ideal for lensing, the greater photometric sensitivity means that events will typically last longer, providing more opportunities for detection."1132 The upshot is that the predicted rate of events caused by nearby stars will be high enough to ensure that many nearby lenses will be detected. and some will be studied in detail.," The upshot is that the predicted rate of events caused by nearby stars will be high enough to ensure that many nearby lenses will be detected, and some will be studied in detail."1133" It is interesting to note that. in general. we expect lensing events to be caused by nearby lenses. lenses in the background source field (""self-lensing"") and possibly by MACHOs."," It is interesting to note that, in general, we expect lensing events to be caused by nearby lenses, lenses in the background source field (“self-lensing”) and possibly by MACHOs."1134 Although our calculations were carried out for nearby lenses. the same considerations hold for other lenses as well. at least for a wide range of background fields.," Although our calculations were carried out for nearby lenses, the same considerations hold for other lenses as well, at least for a wide range of background fields."1135 It is therefore clear that future monitoring programs. especially Pan-STARRS and LSST will be important sources of lensing data.," It is therefore clear that future monitoring programs, especially Pan-STARRS and LSST will be important sources of lensing data."1136complicate the fitting procedure.,complicate the fitting procedure.1137 Visual inspection of the axial ratio fits yields a sample of 229 acceptable bar b/a measurements., Visual inspection of the axial ratio fits yields a sample of 229 acceptable bar b/a measurements.1138 Just as there is no dependence of A SFR on bar length. we also find no correlation with axial ratio.," Just as there is no dependence of $\Delta$ SFR on bar length, we also find no correlation with axial ratio."1139 It is well established that star formation enhancements in barrec galaxies are mostly seen amongst the early-type population (e.g. Huang et al., It is well established that star formation enhancements in barred galaxies are mostly seen amongst the early-type population (e.g. Huang et al.1140 1996: Ho et al., 1996; Ho et al.1141 1997)., 1997).1142 One of our principal results is that the enhancement in SER in barred galaxies ean be associated with the more fundamental parameter of galactic stellar mass., One of our principal results is that the enhancement in SFR in barred galaxies can be associated with the more fundamental parameter of galactic stellar mass.1143" The increase in SFR in bars is only evident in our sample a M,> 10! M..", The increase in SFR in bars is only evident in our sample at $_{\star}$$>$ $^{10}$ $_{\odot}$.1144" Earlier conclusions of morphology-dependent SFR enhancements follow from this mass dependence. since barrec galaxies with M, > 10! M. are dominated by early-types."," Earlier conclusions of morphology-dependent SFR enhancements follow from this mass dependence, since barred galaxies with $_{\star}$ $>$ $^{10}$ $_{\odot}$ are dominated by early-types."1145 Our results highlight that the dependence of morphological type on mass can complicate the interpretation of trends in barred galaxies., Our results highlight that the dependence of morphological type on mass can complicate the interpretation of trends in barred galaxies.1146 For example. Aguerri (1999) found that bar strength correlates with star formation rate.," For example, Aguerri (1999) found that bar strength correlates with star formation rate."1147 However. as discussed above. bar strength is known to correlate with Hubble type: low mass late-types having generally weaker bars than high mass early-types.," However, as discussed above, bar strength is known to correlate with Hubble type: low mass late-types having generally weaker bars than high mass early-types."1148 The correlation of SER and bar length found by Aguerri (1999) may therefore simply be a reflection of the mass-SER relation., The correlation of SFR and bar length found by Aguerri (1999) may therefore simply be a reflection of the mass-SFR relation.1149 Our results emphasize the importance of looking for trends at a given stellar mass. and we have tackled this by ealeulating SER otfsets from the unbarred SER-mass relation.," Our results emphasize the importance of looking for trends at a given stellar mass, and we have tackled this by calculating SFR offsets from the unbarred SFR-mass relation."1150" In contrast to Aguerri (1999), we do not find a correlation between SFR enhancement and bar length."," In contrast to Aguerri (1999), we do not find a correlation between SFR enhancement and bar length."1151" Instead. there seems to be a mass threshold of M, ~ LO! M. above which tibre SFRs are higher. on average. by ~ than unbarred galaxies of the same stellar mass."," Instead, there seems to be a mass threshold of $_{\star}$ $\sim$ $^{10}$ $_{\odot}$ above which fibre SFRs are higher, on average, by $\sim$ than unbarred galaxies of the same stellar mass."1152 This threshold corresponds to the mass at which the barred population transitions from late to early type barred galaxies., This threshold corresponds to the mass at which the barred population transitions from late to early type barred galaxies.1153 The nature of the bar itself changes at this morphological boundary. the late-types being exponential and the early-types being flat (Elmegreen Elmegreen 1985).," The nature of the bar itself changes at this morphological boundary, the late-types being exponential and the early-types being flat (Elmegreen Elmegreen 1985)."1154 Clues to understanding the ditferences in bars can be gleaned from simulations., Clues to understanding the differences in bars can be gleaned from simulations.1155 Combes Elmegreen (1993) found that late-type bars stop growing soon after their formation. whereas bars in early-types continue to gain in strength and length.," Combes Elmegreen (1993) found that late-type bars stop growing soon after their formation, whereas bars in early-types continue to gain in strength and length."1156 The morphological distinction is driven (in the simulations) by the more concentrated. mass profiles of early-types. whose bulges are more prominent than in the late types.," The morphological distinction is driven (in the simulations) by the more concentrated mass profiles of early-types, whose bulges are more prominent than in the late types."1157 Galaxies with high bulge fractions have their co-rotation radius well within the galactic disk and can therefore etfectively transfer angular momentum outwards and grow the bar., Galaxies with high bulge fractions have their co-rotation radius well within the galactic disk and can therefore effectively transfer angular momentum outwards and grow the bar.1158 In turn. a growing bar has continued access to the disks gas supply. so that early-type bars may experience extended inner star formation. regardless of the current length of the bar.," In turn, a growing bar has continued access to the disk's gas supply, so that early-type bars may experience extended inner star formation, regardless of the current length of the bar."1159was supported by NASA eraut NAC 5-3012. and the observations were obtained with the NASA/ESA Dubble Space Telescope operated by the Space Telescope Scieuce Iustitute managed by the Association of Universities for Research in Astronomy Tne. πας NASA coutract 26555.,"was supported by NASA grant NAG 5-3042, and the observations were obtained with the NASA/ESA Hubble Space Telescope operated by the Space Telescope Science Institute managed by the Association of Universities for Research in Astronomy Inc. under NASA contract NAS5-26555."1160 0.0611 Figure lad: NICMOS 1.10. 2.05. 2.12. aud2.15 pan images of the field of PSCIO2111I1721.," 0.06in Figure 1a–d: NICMOS 1.10, 2.05, 2.12, and 2.15 $\mu$ m images of the field of FSC10214+4724."1161 The are (Source 1) is nuresolved in width in all the nuages., The arc (Source 1) is unresolved in width in all the images.1162 Note that the noise iu the top left-hand corner of each nuage is due to the coronagraphic hole ou camera 2 of NICMOS., Note that the noise in the top left-hand corner of each image is due to the coronagraphic hole on camera 2 of NICMOS.1163 0.051, 0.05in1164"where 9,pcΕΕΚ) is the FFT of the LRG overdensity field and fy; are the Cartesian components of k.","where $\delta_{LRG,FFT}({\bf k})$ is the FFT of the LRG overdensity field and $k_i$ are the Cartesian components of ${\bf k}$."1165 Equ., Eqn.1166 23. corrects for FFT aliasing in the limit that (KdKy) is shot noise dominated. which is the case here.," \ref{Pest} corrects for FFT aliasing in the limit that $P({\bf k}+{\bf k_{N}})$ is shot noise dominated, which is the case here."1167 Finally. we average the values of Eqn.," Finally, we average the values of Eqn."1168" 23. over k-bands with Af,=0.0113. We use the spherical overdensity(SO) halo finder code described in ? with A=200p, io generate halo catalogs.", \ref{Pest} over k-bands with $\Delta k_{box} = 0.0113$ We use the spherical overdensity(SO) halo finder code described in \citet{tinker/etal:2008} with $\Delta = 200 \rho_b$ to generate halo catalogs.1169 Fig., Fig.1170 2. shows the ratio of the volume-weightecd SO mass function in our simulation set to the fitting function of 2. down to M=7.15x10AL..., \ref{fig:MFratall} shows the ratio of the volume-weighted SO mass function in our simulation set to the fitting function of \citet{tinker/etal:2008} down to $M = 7.15 \times 10^{12} M_{\sun}$.1171 There is good agreement al the level of accuracy claimed [or their analvtic fits (~5%)., There is good agreement at the level of accuracy claimed for their analytic fits $\sim 5\%$ ).1172 The overabundance of halos in the lowest mass bins is likely due (ο the small number of particles per halo in those bins., The overabundance of halos in the lowest mass bins is likely due to the small number of particles per halo in those bins.1173 This slight modilication of the mass functüon is unimportant lor our purposes. since there are no satellite LRGs in these mass bins. ancl changes in the mass function are degenerate wilh changes to the probability of hosting a central galaxy as a function of halo mass. VeenAL). We use the technique described in ? to produce mock catalogs for the NEAR (0.155 0.300). MID (0.300<z« 0.380). and FAR. (0.380<z« 0.474) redshift subsamples of 7..," This slight modification of the mass function is unimportant for our purposes, since there are no satellite LRGs in these mass bins, and changes in the mass function are degenerate with changes to the probability of hosting a central galaxy as a function of halo mass, $N_{cen}(M)$ We use the technique described in \citet{reid/spergel:2008} to produce mock catalogs for the NEAR $0.155 < z < 0.300$ ), MID $0.300 < z < 0.380$ ), and FAR $0.380 < z < 0.474$ ) redshift subsamples of \citet{tegmark/etal:2006}."1174 These samples contain roughly equal numbers of galaxies. aud (heir power spectra have roughly the same amplitude on large scales.," These samples contain roughly equal numbers of galaxies, and their power spectra have roughly the same amplitude on large scales."1175" We first review our LOD modeling assumptions. described in more detail in ο,"," We first review our HOD modeling assumptions, described in more detail in \citet{reid/spergel:2008}."1176" The Halo Occupation Distribution (LOD) model assumes that the probability: PON,pe;AL) OIN,pe; LRGs occupying a dark matter halo o£ mass Af ad redshilt z depends only on the halo mass (forareview.see.2).."," The Halo Occupation Distribution (HOD) model assumes that the probability $P(N_{LRG}|M)$ of $N_{LRG}$ LRGs occupying a dark matter halo of mass $M$ at redshift $z$ depends only on the halo mass \citep[for a review, see ][] {cooray/sheth:2002}."1177" Llowever. the application of the ILOD formalism requiresthat we make several further assumptions about PON,ge; AM)."," However, the application of the HOD formalism requiresthat we make several further assumptions about $P(N_{LRG}|M)$ ."1178 Detailed studies of dark matter halos and subhalos suggest a division of galaxies into central and satellite galaxies (?).., Detailed studies of dark matter halos and subhalos suggest a division of galaxies into central and satellite galaxies \citep{kravtsov/etal:2004}. .1179 The central, The central1180preliminary analysis of the echoes surrounding S CrA. From the information contained in the angular distance of the echoes versus time from outbursts we have been able to derive basic properties of the dust that is scattering the light-pulses.,preliminary analysis of the echoes surrounding S CrA. From the information contained in the angular distance of the echoes versus time from outbursts we have been able to derive basic properties of the dust that is scattering the light-pulses.1181 The dust must be concentrated in a region around 0000 AU from the star and the best geometry of the dust in terms of reproducing the observations Is an incomplete spherical shell or an inclined torus: a planar slab geometry appears to be ruled out by the observations. but 1t would require dust at à similar distance in order of magnitude.," The dust must be concentrated in a region around 000 AU from the star and the best geometry of the dust in terms of reproducing the observations is an incomplete spherical shell or an inclined torus; a planar slab geometry appears to be ruled out by the observations, but it would require dust at a similar distance in order of magnitude."1182 The best fit to the echo radi gives a distance from Earth to S CrA of 128 + 16 pe in the case of the spherical shell distribution. which is consistent with previous rough estimations of the distance to S CrA (seethedistancedis-cussioninNeuháuser&Forbrich2008) whereas the dust slab geometry gives a distance to S CrA that cannot be reconciled with other observations in the literature.," The best fit to the echo radii gives a distance from Earth to S CrA of 128 $\pm$ 16 pc in the case of the spherical shell distribution, which is consistent with previous rough estimations of the distance to S CrA \citep[see the distance discussion in][]{Neu2008} whereas the dust slab geometry gives a distance to S CrA that cannot be reconciled with other observations in the literature."1183 The derived distance implies that these are the closest echoes to the Earth that have ever been recorded., The derived distance implies that these are the closest echoes to the Earth that have ever been recorded.1184 Concerning the information extracted from the surface brightness of the echoes. the mass of the dust shell required in order to reproduce the observed echoes surface brightness is in the order of 2x107 and must be in the form of particles larger than 0.105 to explain the fading of the echoes as they grow in angular size.," Concerning the information extracted from the surface brightness of the echoes, the mass of the dust shell required in order to reproduce the observed echoes surface brightness is in the order of ${ 2\times10^{-3}}$ and must be in the form of particles larger than $\mu m$ to explain the fading of the echoes as they grow in angular size."1185 Such dust structure ts probably the remnant of the envelope typical of very young stars., Such dust structure is probably the remnant of the envelope typical of very young stars.1186 But because of the concentration near 10000 AU. we speculate that the dust particles might have been dynamically ejected from the star’s disk through the action of forming planets and ended up where they are now in a similar way as planetesimals have been ejected from the solar system to form the Oort cloud.," But because of the concentration near 10000 AU, we speculate that the dust particles might have been dynamically ejected from the star's disk through the action of forming planets and ended up where they are now in a similar way as planetesimals have been ejected from the solar system to form the Oort cloud."1187 We must caution the reader that we have presented just a first order model to explain the echoes around S CrA. A well sampled lighteurve of SCrA and high spatial resolution images would be needed in order to derive the detailed 3-dimensional structure of the dust surrounding S CrA., We must caution the reader that we have presented just a first order model to explain the echoes around S CrA. A well sampled lightcurve of SCrA and high spatial resolution images would be needed in order to derive the detailed 3-dimensional structure of the dust surrounding S CrA.1188"11805 (Lagrois&Joncas2009a),, mean electron densities (p), in the S* ionic volume, were obtained for each nebular-gas column (i.e., line-of-sight).","1805 \citep{Lag2009a}, mean electron densities $\rho$ ), in the $^{+}$ ionic volume, were obtained for each nebular-gas column (i.e., line-of-sight)."1189" Since uncertainties cannot be recovered from the use of the Fivel procedure,error bars on density measurements p were computed as follows."," Since uncertainties cannot be recovered from the use of the Fivel procedure,error bars on density measurements $\rho$ were computed as follows."1190" For each line of the [S textscii]doublet, density asreturnedbylhaGinuesiaroft"," For each line of the $[$ $]$ doublet, the uncertainty on the peak intensity, as returned by the Gaussian fit procedure, is provided by Equation of \citet{Lan1982}."1191peaecd unas spugeideqhadsauel spatialhaudman," From there, the statistical error on each line ratio is simply provided by the standard propagation of uncertainty."1192"etal.(1982) maximal (pmax) and minimal (pmin) densities, theuncertainty"," For each ratio, minimal and maximal plausible values are then easily obtained by respectively subtracting and adding this calculated uncertainty."1193"onthepeakintensity,associated to p, can be obtained via Fivel."," Using these lower and upper limits on $\frac{[\textnormal{S}\,\textsc{ii}]\,\lambda6716}{[\textnormal{S}\,\textsc{ii}]\,\lambda6731}$, maximal $\rho_{\textnormal{max}}$ ) and minimal $\rho_{\textnormal{min}}$ ) densities, associated to $\rho$, can be obtained via Fivel."1194 An asymmetrical error bar usually results where the upper (lower) uncertainty is provided by the difference between pmax (p) and p (pmin)., An asymmetrical error bar usually results where the upper (lower) uncertainty is provided by the difference between $\rho_{\textnormal{max}}$ $\rho$ ) and $\rho$ $\rho_{\textnormal{min}}$ ).1195 Only p values where both pmin and pmax are finite were retained (see § 4.2.2)., Only $\rho$ values where both $\rho_{\textnormal{min}}$ and $\rho_{\textnormal{max}}$ are finite were retained (see $\S$ 4.2.2).1196" According to Fivel, this implies that Pmin and Pmax must be greater than 10 cm? and lower than 150000 cm respectively (these two values mostly depend on our choice? of a constant electron temperature of 74400 K in 11805)."," According to Fivel, this implies that $\rho_{\textnormal{min}}$ and $\rho_{\textnormal{max}}$ must be greater than 10 $^{-3}$ and lower than 000 $^{-3}$ respectively (these two values mostly depend on our choice of a constant electron temperature of 400 K in 1805)."1197" Our method considers that the statistical error on p is entirely dominated by the data quality (i.e., S/N of the [S textscii]lines)andthattheuncertaintiesontheatomicparameters, u&edlI2)3 ifoe"," Our method considers that the statistical error on $\rho$ is entirely dominated by the data quality (i.e., S/N of the $[$ $]$ lines) and that the uncertainties on the atomic parameters, used by Fivel, are negligible."1198kyerenihg l'ogibltaH and pmin to calculate the statistical error on p probably overestimates the actual uncertainty on the electron density measurement.," However, using $\rho_{\textnormal{max}}$ and $\rho_{\textnormal{min}}$ to calculate the statistical error on $\rho$ probably overestimates the actual uncertainty on the electron density measurement."1199 The distribution of the retained electron densities is provided by the black curve in Figure (the blue and red distributions will be discussed in § 5.2.1)., The distribution of the retained electron densities is provided by the black curve in Figure (the blue and red distributions will be discussed in $\S$ 5.2.1).1200 The histogram has a mean of 155*22? cm where the error bars correspond to the mean upper ((Pmax?— p)) and lower ((p— pPmin)) uncertainty retrieved from the 0057 electron- points preserved.," The histogram has a mean of $^{+\,135}_{-\,75}$ $^{-3}$ where the error bars correspond to the mean upper $\left\langle \rho_{\textnormal{max}}\,-\,\rho \right\rangle$ ) and lower $\left\langle \rho\,-\,\rho_{\textnormal{min}} \right\rangle$ ) uncertainty retrieved from the 057 electron-density points preserved."

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