ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2" These QPOs can be qualitatively explained as gap and/or edge modes of sections 4 and 2, or even transient QPOs of section3°."," These QPOs can be qualitatively explained as gap and/or edge modes of sections 4 and 2, or even transient QPOs of section."3". However, this was only possible if the neutrons were decoupled from the Alfven waves in the core."," However, this was only possible if the neutrons were decoupled from the Alfven waves in the core."4" If the neutrons took part in the Alfven motion, then the effective mass of the Alfven modes shifted up by a factor of 20—40 and their frequencies shifted down by a factor 4—8 (Easson Pethick 1979, Alpar et al."," If the neutrons took part in the Alfven motion, then the effective mass of the Alfven modes shifted up by a factor of $20-40$ and their frequencies shifted down by a factor $4-8$ (Easson Pethick 1979, Alpar et al."5" 1984, van Hoven Levin 2008, Andersson et al."," 1984, van Hoven Levin 2008, Andersson et al."6 2009)., 2009).7" As a result, all modes at frequencies above ~50Hz were strongly damped (see Fig. 20))."," As a result, all modes at frequencies above $\sim 50$ Hz were strongly damped (see Fig. \ref{Figspec1}) )."8 Increasing the magnetic-field tension by a factor of 3 did not affect this conclusion (Fig 21))., Increasing the magnetic-field tension by a factor of 3 did not affect this conclusion (Fig \ref{Figspec3}) ).9 For the spherical magnetar models of section 4 we obtain similar results if couple the neutrons to the Alfven motion in the core., For the spherical magnetar models of section 4 we obtain similar results if couple the neutrons to the Alfven motion in the core.10" The key point that we would like the reader to appreciate is that Alfven modes in the core are key to determining the frequency and strength of the observable QPOs, and thus QPOs are very sensitive probe of the core interior. ("," The key point that we would like the reader to appreciate is that Alfven modes in the core are key to determining the frequency and strength of the observable QPOs, and thus QPOs are very sensitive probe of the core interior. ("11"2) A number of the high-frequency QPOs have been measured in the 2004 giant flare by Watts and Strohmayer (2006), the strongest among them being the QPO at 625 Hz.","2) A number of the high-frequency QPOs have been measured in the 2004 giant flare by Watts and Strohmayer (2006), the strongest among them being the QPO at $625$ Hz."12" This QPO is particularly strong and long-lived in the hard x-rays, reaching the amplitude of ~25% over the time interval of ~100 seconds (i.e., it persists for almost 10° oscillation periods!)"," This QPO is particularly strong and long-lived in the hard x-rays, reaching the amplitude of $\sim 25$ over the time interval of $\sim 100$ seconds (i.e., it persists for almost $10^5$ oscillation periods!)."13" Watts and Strohmayer (2006) argued that this frequency corresponds to the crustal shear mode with a single radial node (see also Piro 2005); this interpretation, if correct, would strongly constrain the thickness of the crust and rule out the fluid strange stars as magnetar candidates (Watts Reddy, 2007)."," Watts and Strohmayer (2006) argued that this frequency corresponds to the crustal shear mode with a single radial node (see also Piro 2005); this interpretation, if correct, would strongly constrain the thickness of the crust and rule out the fluid strange stars as magnetar candidates (Watts Reddy, 2007)."14" To investigate this suggestion, we have introduced several high-frequency low-j crustal modes into our square-box"," To investigate this suggestion, we have introduced several high-frequency low-j crustal modes into our square-box"15in all targets.,in all targets.16 The two bestestudied targets in our sample are IRASEF10211]L721 aud .the Cloverleaf (e... Ao et citevearaot8:: Darvaiuls ct citevearbar97T:: eet citevearwei03:: Bradford et 20093).," The two best-studied targets in our sample are F10214+4724 and the Cloverleaf (e.g., Ao et \\citeyear{ao08}; Barvainis et \\citeyear{bar97}; et \\citeyear{wei03}; Bradford et \citeyear{bra09}) )."17 Based on to oobservatious in the literature and our deletections. we can constrain the line radiative transfer hrough Large Velocity Gracicut (ΤΑ models. reating the eas kinetic temperature and density as free xuwanieters.," Based on to observations in the literature and our detections, we can constrain the line radiative transfer through Large Velocity Gradient (LVG) models, treating the gas kinetic temperature and density as free parameters."18 For all calculations. the IT» orthotopara ratio was fixed to 3:1. the cosmic mucrowave background cluperature was fixed to 8.95 aud ISIN (at :—2.286 and 2.558). aud the Flower (20011) CO collision rates were used.," For all calculations, the $_2$ ortho–to–para ratio was fixed to 3:1, the cosmic microwave background temperature was fixed to 8.95 and K (at $z$ =2.286 and 2.558), and the Flower \citeyear{flo01}) ) CO collision rates were used."19 For consistency with previous modcling of noth sources (Ao et citevearao(8:: Ricchers et citevearricllhj). πο adopted ai CO abundance o» velocity gradieut of 10νο 1 (e.g... citevearwei05h.. 2007: Ricchers citevearricG) ).," For consistency with previous modeling of both sources (Ao et \\citeyear{ao08}; Riechers et\\citeyear{rie11b}) ), we adopted a CO abundance per velocity gradient of ${\rm d}v/{\rm d}r) = 1 \times 10^{-5}\,{\rm pc}\,$ $^{-1}$ (e.g., \\citeyear{wei05b}, \citeyear{wei07}; Riechers \\citeyear{rie06}) )."20 Observations of both targets are fit very well by sinele-compoucut models (except the CO J=h »1fux in the Cloverleaf. which is likely too low due to calibration issucs related to the restricted bandwidth of these carly observations: Darvaiuis ct citevearbarO7:: see also A.etal. iu prep).," Observations of both targets are fit very well by single-component models (except the CO $J$ $\to$ 4 flux in the Cloverleaf, which is likely too low due to calibration issues related to the restricted bandwidth of these early observations; Barvainis et \\citeyear{bar97}; ; see also A., in prep.)."21" For IRASFFI10211]1721. we fit a representativo model with a kinetic eas temperature of Tigu=GOTIS aud a gas clensitv of Peas= LO? vielding a moderate optical depth Of Toor, yy=l.6 (Fig."," For F10214+4724, we fit a representative model with a kinetic gas temperature of $T_{\rm kin}$ K and a gas density of $\rho_{\rm22gas}$ $^{3.8}$ $^{-3}$ , yielding a moderate optical depth of $\tau_{\rm CO(1-0)}$ =1.6 (Fig."23 laa aud c)., \ref{f4}a a and c).24 For the Cloverleaf. we fit a representative model with Zii250IEI an Peas! OP ? vielding ai high optical depth of Toor υΗΞδ.Ι (Fig.," For the Cloverleaf, we fit a representative model with $T_{\rm kin}$ K and $\rho_{\rm25gas}$ $^{4.5}$ $^{-3}$, yielding a high optical depth of $\tau_{\rm CO(1-0)}$ =8.9 (Fig."26 Εν aud d)., \ref{f4}b b and d).27 While not formally excluding the presence of some colder gas (given the reaming uncertaimties). these models are consisten with previous fits based on the CO #23 transitions alone (Ao ct citevearaot8:: Bradford et citevearbrat9:: Riechers et citevemiellb)).," While not formally excluding the presence of some colder gas (given the remaining uncertainties), these models are consistent with previous fits based on the CO $J$$\geq$ 3 transitions alone (Ao et \\citeyear{ao08}; Bradford et \\citeyear{bra09}; Riechers et \\citeyear{rie11b}) )."28 They are also consistent with what is found for i1 quasars observed in eenission (Ricchers ct citevearric0G:: eet citevearwei07))., They are also consistent with what is found for $z$$>$ 4 quasars observed in emission (Riechers et \\citeyear{rie06}; et \\citeyear{wei07}) ).29 This Ποιος is in agreement with the ccluission in hieh-: quasars being associated with optically tlick ciission from the highly excited molecular gas detected in high-J. CO transitions. without auv evidence for significant additional excitation eas colponcuts.," This finding is in agreement with the emission in $z$ quasars being associated with optically thick emission from the highly excited molecular gas detected in $J$ CO transitions, without any evidence for significant additional low-excitation gas components."30 The eeniüssion m our targets appears to be associated witli hiehlv excited gas that has plivsical properties cousisteut with those found in the uuclei of nearby. ultra-luuineus infrared galaxies (ULIRGCs)., The emission in our targets appears to be associated with highly excited gas that has physical properties consistent with those found in the nuclei of nearby ultra-luminous infrared galaxies (ULIRGs).31 We thus calculate their eas misses assundng a ULIRG-likeconversion factor of Ocio + from Logsyy to Mas (Downes Solomon 1998))., We thus calculate their gas masses assuming a ULIRG-likeconversion factor of $\alpha_{\rm CO}$ $^{-1}$ from $L'_{\rm CO(1-0)}$ to $M_{\rm gas}$ (Downes Solomon \citeyear{ds98}) ).32" This vields leusiug-corrected molecular eas masses Of Aa =O.16. 3.1. 0.27. 114.7. and «101? Που TIRASFFLO211)1721. the Cloverleat. JJO9LL0551. SMML135|10277. aud 00751]2716. respectively,"," This yields lensing-corrected molecular gas masses of $M_{\rm gas}$ =0.46, 3.1, 0.27, 14.7, and $\times$ $^{10}$ for F10214+4724, the Cloverleaf, J0911+0551, J04135+10277, and 0751+2716, respectively."33"ISO JJO011235|10277 is now revealed as— the hieh-: quasar— with the highest AM, currently known.", J04135+10277 is now revealed as the $z$ quasar with the highest $M_{\rm gas}$ currently known.34 The gas massesof all svstenis he within the range found for other ligh-: quasars Qauuostly determined based ou observations of 7223 CO trausitious). with IRASFEFIO211]1721. aud RXJJO91110551 being situated at the low cud of the observed range (which can currently only be investigated with the aid of stroug gravitational leusiug: e.g.. Riechers 20113).," The gas massesof all systems lie within the range found for other $z$ quasars (mostly determined based on observations of $J$$\geq$ 3 CO transitions), with F10214+4724 and J0911+0551 being situated at the low end of the observed range (which can currently only be investigated with the aid of strong gravitational lensing; e.g., Riechers \citeyear{rie11c}) )."35" We have detected strong celission toward IRASFEFEI0211]|1721 (:=2.286). the Cloverleaf (:=2.558). JIJOOLL|O551 (:—2.7906). SMALIJOU35|10277. (2=2.8 16). and 00751|2716 (2=3.200),"," We have detected strong emission toward F10214+4724 $z$ =2.286), the Cloverleaf $z$ =2.558), J0911+0551 $z$ =2.796), J04135+10277 $z$ =2.846), and 0751+2716 $z$ =3.200)."36 Our EVLA observations lave spatially resolved the cimission toward IRASFFLO211)1721 and the Cloverleaf (Fie. 1))., Our EVLA observations have spatially resolved the emission toward F10214+4724 and the Cloverleaf (Fig. \ref{f1}) ).37 We finddine brightuess temperatures consistent with those measured iu J CO lines., We findline brightness temperatures consistent with those measured in $J$ CO lines.38 Excitation modeling indicates that the eenission is associated with the warm. highly excited eas in the star-formuus regions iu the host ealaxics that is also seen iu the higher-7 CO lines.," Excitation modeling indicates that the emission is associated with the warm, highly excited gas in the star-forming regions in the host galaxies that is also seen in the $J$ CO lines."39 This result sugeests that mid-7 CO lines are οσους indicators of the total amount of molecular gasin eas-vich high redshift quasar host galaxies. consistent with previous fiucdines based ou a stnaller sample of £z4E quasars (Riechers ct citevearrie06)). and exteudiug these studies to the peak epoch of cosumde star formation aud ACN activitv.," This result suggests that $J$ CO lines are good indicators of the total amount of molecular gasin gas-rich high redshift quasar host galaxies, consistent with previous findings based on a smaller sample of $z$$\gtrsim$ 4 quasars (Riechers et \\citeyear{rie06}) ), and extending these studies to the peak epoch of cosmic star formation and AGN activity."40 Iu contrast. recent studies of eenüsson iu :22 SM suggest that many ofthese ealaxies have substantial amounts of low-excitation gas (e.g.. Tainline et citevearluiu06:: Carilli et citevearcarlü: Harris et citevearharlO:: Ivison et citevearivilü.. 2011 Riechers et citevearriclO.. 2011b.. 20L1e)}.," In contrast, recent studies of emission in $z$$>$2 SMGs suggest that many ofthese galaxies have substantial amounts of low-excitation gas (e.g., Hainline et \\citeyear{hai06}; ; Carilli et \\citeyear{car10}; ; Harris et \\citeyear{har10}; ; Ivison et \\citeyear{ivi10}, , \citeyear{ivi11}; ; Riechers et \\citeyear{rie10}, , \citeyear{rie11}, , \citeyear{rie11d}) )."41 Such a difference is iu aerecluent with the picture that gasaich quasars aud SA[Gs veprescut different stages in the early evolution of massive galaxies., Such a difference is in agreement with the picture that gas-rich quasars and SMGs represent different stages in the early evolution of massive galaxies.42 Such an observational finding would be consistent with a high redshift analogue of the, Such an observational finding would be consistent with a high redshift analogue of the43"Eesc is generally a function of time t due to the evolution of Das, Rsh and Ush-","$\varepsilon_{\rm esc}$ is generally a function of time $t$ due to the evolution of $D_{\rm sh}$, $R_{\rm sh}$ and $u_{\rm sh}$."44 Fig., Fig.45 1 shows the electron spectrum assuming that only electrons and positrons above the escape energy €esc are injected instantaneously., 1 shows the electron spectrum assuming that only electrons and positrons above the escape energy $\varepsilon_{\rm esc}$ are injected instantaneously.46" The energy of electrons/positrons which is initially £e becomes Eesc/(1+ as a result of radiative cooling (where is the time béesctage)since the emission), and we can clearly see a tagesharp cutoff of the spectrum at that energy, which is the effect of energy-dependent escape of CR particles."," The energy of electrons/positrons which is initially $\varepsilon_{\rm esc}$ becomes $\varepsilon_{\rm esc}/(1+b\varepsilon_{\rm esc}t_{\rm age})$ as a result of radiative cooling (where $t_{\rm age}$ is the time since the emission), and we can clearly see a sharp cutoff of the spectrum at that energy, which is the effect of energy-dependent escape of CR particles."47" If such a spectrum is confirmed by the future experiments, it would be the strong support for the CR escape scenario of the particle acceleration process at the SNR, and we may also get the information of Εοις at the time of the source age tage."," If such a spectrum is confirmed by the future experiments, it would be the strong support for the CR escape scenario of the particle acceleration process at the SNR, and we may also get the information of $\varepsilon_{\rm esc}$ at the time of the source age $t_{\rm age}$."48 Let us consider the more sophisticated model than discussed in the previous section., Let us consider the more sophisticated model than discussed in the previous section.49 We consider a pulsar emitting electrons and positrons embedded in the SNR (i.e. it has not been evacuated from the SNR by the natal kick)., We consider a pulsar emitting electrons and positrons embedded in the SNR (i.e. it has not been evacuated from the SNR by the natal kick).50" A pulsar is considered to be an efficient € factory, because its rotating magnetic field would produce a strong electric field around the pulsar and then a large number of e* pairs would be produced via electromagnetic cascades."," A pulsar is considered to be an efficient $e^{\pm}$ factory, because its rotating magnetic field would produce a strong electric field around the pulsar and then a large number of $e^{\pm}$ pairs would be produced via electromagnetic cascades."51 The created pairs would stream away by centrifugal force as a pulsar wind that ends with a terminationa shock where the acceleration of electrons/positrons may occur., The created pairs would stream away by a centrifugal force as a pulsar wind that ends with a termination shock where the acceleration of electrons/positrons may occur.52 Hereafter we assume the e~ production rate per energy from a pulsar having a spectrum with a cutoff power-law shape: where the high energy break is fixed as €¢cut=10TeV.," Hereafter we assume the $e^{\pm}$ production rate per energy from a pulsar having a spectrum with a cutoff power-law shape: where the high energy break is fixed as $\varepsilon_{e,{\rm cut}}=10{\rm TeV}$."53" According to the gamma-ray observations of PWNe, the accelerated up to the energy of 10-100TeV seem to electrons/positronsexist in the nebulae (e.g., Aharonian et al."," According to the gamma-ray observations of PWNe, the electrons/positrons accelerated up to the energy of 10-100TeV seem to exist in the nebulae (e.g., Aharonian et al."54" 2006), so this assumption is reasonable."," 2006), so this assumption is reasonable."55 Here Qo(t) is given to satisfy where Lepr(t) is the electron/positron production luminosity and €¢min is set to be 1GeV.," Here $Q_0(t)$ is given to satisfy where $L_{e,{\rm pr}}(t)$ is the electron/positron production luminosity and $\varepsilon_{e,{\rm min}}$ is set to be $1{\rm GeV}$."56" We assume that this luminosity is proportional to the spin-down luminosity of the pulsar: where 7910?-4year is the spin-down timescale, which is related to the surface magnetic field of the pulsar (Shapiro Teukolsky 1983)."," We assume that this luminosity is proportional to the spin-down luminosity of the pulsar: where $\tau_0\sim 10^{2-4}{\rm year}$ is the spin-down timescale, which is related to the surface magnetic field of the pulsar (Shapiro Teukolsky 1983)."57" In order to evaluate the CR. spectrum in the escape scenario, we should assume the time evolution of &,.."," In order to evaluate the CR spectrum in the escape scenario, we should assume the time evolution of $\varepsilon_{\rm esc}$."58 In this study we adopt two models for the functional form of €esc., In this study we adopt two models for the functional form of $\varepsilon_{\rm esc}$.59" In the first model, we assume for €esc(t) a power-law behavior, and determine its normalization and power-law index according to the hypothesis that SNRs are responsible for the observed CRs with the energy from ~1GeV up to the knee energy (c10195eV)."," In the first model, we assume for $\varepsilon_{\rm esc}(t)$ a power-law behavior, and determine its normalization and power-law index according to the hypothesis that SNRs are responsible for the observed CRs with the energy from $\sim 1{\rm GeV}$ up to the knee energy $\sim 10^{15.5}{\rm eV}$ )."60 Then Eesc(t) should reach the knee energy at the end of the free expansion phase (i.e. the beginning of the Sedov phase; tgedov) and should decrease down to 1GeV at tc10°/?tgedov (i.e. the end of the SNR expansion; Gabici et al., Then $\varepsilon_{\rm esc}(t)$ should reach the knee energy at the end of the free expansion phase (i.e. the beginning of the Sedov phase; $t_{\rm Sedov}$ ) and should decrease down to 1GeV at $t\simeq 10^{5/2}t_{\rm Sedov}$ (i.e. the end of the SNR expansion; Gabici et al.61 2009; Ohira et al., 2009; Ohira et al.62" 2010a): As the second model for the evolution of Έα we adopt the one discussed by Ptuskin Zirakashvili (2005), which takes into account the modification of a shock structure due to the CR pressure, as well as the non- dissipation of magnetic turbulence."," 2010a): As the second model for the evolution of $\varepsilon_{\rm esc}$ we adopt the one discussed by Ptuskin Zirakashvili (2005), which takes into account the modification of a shock structure due to the CR pressure, as well as the non-linear dissipation of magnetic turbulence."63" They solve the steady-state equation which determines the energy density of the magnetohydrodynamic turbulence W: where u is the flow velocity (here it is equal to the shock velocity uan), k is the wave number of the turbulence, and Του, ΤΙ and Ty are the wave growth rate at the shock due to the CR streaming instability, the damping rate of waves in the background plasma due to the ion-neutral and electron-ion collisions (linear damping), and due to the wave-wave interactions (non-linear damping), respectively."," They solve the steady-state equation which determines the energy density of the magnetohydrodynamic turbulence $W$: where $u$ is the flow velocity (here it is equal to the shock velocity $u_{\rm sh}$ ), $k$ is the wave number of the turbulence, and $\Gamma_{\rm cr}$, $\Gamma_{\rm l}$ and $\Gamma_{\rm nl}$ are the wave growth rate at the shock due to the CR streaming instability, the damping rate of waves in the background plasma due to the ion-neutral and electron-ion collisions (linear damping), and due to the wave-wave interactions (non-linear damping), respectively."64" The mathematical expressions for these functions are shown in Ptuskin Zirakashvili (2005), and by solving this equation (while the term of linear damping is neglected), we obtain the threshold particle energy for escape as function of the shock velocity usp."," The mathematical expressions for these functions are shown in Ptuskin Zirakashvili (2005), and by solving this equation (while the term of linear damping is neglected), we obtain the threshold particle energy for escape as a function of the shock velocity $u_{\rm sh}$."65" Since we know the timea dependence of the shock radius and the shock velocity in the Sedov phase, we can derive as a function of time."," Since we know the time dependence of the shock radius and the shock velocity in the Sedov phase, we can derive $\varepsilon_{\rm esc}(t)$ as a function of time."66" When the age of the SNR is Eesc(t)younger than € 10°years, the evolution of e(t) in this model can be approximated as Fig."," When the age of the SNR is younger than $\lesssim 10^5{\rm years}$ , the evolution of $\varepsilon_{\rm esc}(t)$ in this model can be approximated as Fig."67 2 shows the evolutions of €esc(t) in two models described above., 2 shows the evolutions of $\varepsilon_{\rm esc}(t)$ in two models described above.68" Once we fix the time dependence of £,s.,"," Once we fix the time dependence of $\varepsilon_{\rm esc}$ ,"69our resulting mass estimates are therefore expected to be a [actor of 13 higher compared to theirs.,our resulting mass estimates are therefore expected to be a factor of $\sim 13$ higher compared to theirs.70 Our total mass estimates assuming a lower mass cut-olf of LAL. are referred toas Mus.," Our total mass estimates assuming a lower mass cut-off of $1 M_\odot$ are referred to as $M_{\rm tot,2}$."71 AC first comparison of our individually derived metallicity estimates shows that E02’s assumption of a mean cluster metallicity of O42. (based on spectroscopic metallicity. determinations by P93) is reasonable. except for a few clusters with significantly supersolar abundances.," A first comparison of our individually derived metallicity estimates shows that E02's assumption of a mean cluster metallicity of $0.472Z_\odot$ (based on spectroscopic metallicity determinations by P93) is reasonable, except for a few clusters with significantly supersolar abundances."73 Secondly. our low extinction values are also in line with our expectations for the cireumnuclear ring clusters: although the extinction. in the starburst rine varies in the range Pschy4 mag (CGrotheus Schmidt-Ixaler 1901). is has been shown that cireumnuclear ring clusters are often either almost fully obscured or virtually dust [ree (c.g... Maoz et al.," Secondly, our low extinction values are also in line with our expectations for the circumnuclear ring clusters; although the extinction in the starburst ring varies in the range $1 \lesssim A_V74\lesssim 4$ mag (Grotheus Schmidt-Kaler 1991), is has been shown that circumnuclear ring clusters are often either almost fully obscured or virtually dust free (e.g., Maoz et al."75 2001)., 2001).76 In addition. Meurer et al. (," In addition, Meurer et al. ("771995) estimate the average extinction in the NGC 3310 starburst regions to be in the range 0.18ECBV)0.23. based on the slope of the UY,"1995) estimate the average extinction in the NGC 3310 starburst regions to be in the range $0.18 \lesssim {\rm E}(B-V) \lesssim 0.23$, based on the slope of the UV"78theoretical Balmer line proliles.,theoretical Balmer line profiles.79 Profiles which are in reasonable agreement will observations were obtained., Profiles which are in reasonable agreement with observations were obtained.80 The calculated line profiles are slightly asvuunetric. wil blueshifted centroids. sometimes showing redshilted absorption components.," The calculated line profiles are slightly asymmetric, with blueshifted centroids, sometimes showing redshifted absorption components."81 However. Alencar&Basri(2000).. analvzing spectra from 30 CTTSs. noted that only of their sample showed inverse P Cveni proliles in (he studied lines.," However, \citet{alencar..00}, analyzing spectra from 30 CTTSs, noted that only of their sample showed inverse P Cygni profiles in the studied lines."82 Thev argued that winds. turbulence and rotation of the central star must be taken into account to filly explain the observations.," They argued that winds, turbulence and rotation of the central star must be taken into account to fully explain the observations."83 Dasri(1990) previously suggested Chat turbulence may be important in (he formation of line profiles., \citet{basri90} previously suggested that turbulence may be important in the formation of line profiles.84 Edwardsοἱal.(1994). suggested that Alfvénn waves can be the source of this turbulence.," \cite{edw..94}85 suggested that Alfvénn waves can be the source of this turbulence."86 Also. Johns&Dasri(1995).. when analvzing the spectra of SU Aur. found that a turbulent velocily component at the base of a wind is necessary in order to fit the observed spectra.," Also, \citet{johns..95}, when analyzing the spectra of SU Aur, found that a turbulent velocity component at the base of a wind is necessary in order to fit the observed spectra."87 The major uncertainty in (he radiative magnetospheric model caleulations is the temperatureprofile of the tube., The major uncertainty in the radiative magnetospheric model calculations is the temperatureprofile of the tube.88 Martin(1996.hereafterALA) caleulated the energy balance of the gas.," \citet*[hereafter MA]{martin}89 calculated the energy balance of the gas."90 He included heating by adiabatic compression of (he magnetic field lines. Balmer photoionization and aambipolar diffusion.," He included heating by adiabatic compression of the magnetic field lines, Balmer photoionization and ambipolar diffusion."91 However. the temperatures that he obtained are very low and cannot explain the observed line fIuxes.," However, the temperatures that he obtained are very low and cannot explain the observed line fluxes."92 Thus. an additional heating mechanism must take place in ihe tube.," Thus, an additional heating mechanism must take place in the tube."93 Combining tlie evidence for turbulence and the necessity of an additional heating mechanism. we suggest that the heating by Alfvénn waves is important in the magnetic flix tubes of CTTss.," Combining the evidence for turbulence and the necessity of an additional heating mechanism, we suggest that the heating by Alfvénn waves is important in the magnetic flux tubes of CTTSs."94 We first study the possibility that the waves are generated at the stars surface due to the shock produced by (he accreting matter. as suggested by (1988).," We first study the possibility that the waves are generated at the star's surface due to the shock produced by the accreting matter, as suggested by \citet{scheur..88}."95. A model in which the waves are generated locally is then studied. following the same approximation used in our previous paper (Vasconcelos.Jatenco-Pereira&Opher2000.alter.Paper I).," A model in which the waves are generated locally is then studied, following the same approximation used in our previous paper \citep*[ hereafter, Paper I]{vasc..00}."96. Independent of the generation mechanism. we calculate the damping length for the waves. investigating four dillerent damping mechanisms: 1) nonlinear: 2) turbulent (Paper D)): 3) collisional: aud 4) viscous-resistive (Osterbrock1961).," Independent of the generation mechanism, we calculate the damping length for the waves, investigating four different damping mechanisms: 1) nonlinear; 2) turbulent \citeauthor{vasc..00}) ); 3) collisional; and 4) viscous-resistive \citep{oster61}."97. The associated heating rates and the degree of turbulence are calculated., The associated heating rates and the degree of turbulence are calculated.98 We use a theoretical temperature prolile. varving Irom 1500 Ix (to ~8300 IX. which produces the observed line features.," We use a theoretical temperature profile, varying from $\sim 7500$ K to $\sim 8300$ K, which produces the observed line features."99 Various damping mechanisms for Alfvénn waves have been suggested in the literature. such as Alfvénn resonant heating of solar loops: wave damping bv phase mixing (also in the solar context): and evelotron. heating. occurring as an Alfvénn wave travels down a magnetic fiekl gradient until its frequency matches the decreasing ion exclotron resonance (magnetic beach).," Various damping mechanisms for Alfvénn waves have been suggested in the literature, such as Alfvénn resonant heating of solar loops; wave damping by phase mixing (also in the solar context); and cyclotron heating, occurring as an Alfvénn wave travels down a magnetic field gradient until its frequency matches the decreasing ion cyclotron resonance (magnetic beach)."100 In addition to the more conventional collisional and. viscous-resistive Alfvénn wave dampings. we concentrate on nonlinear and turbulent damping. which oureroup has investigated in: the solar wind (Jatenco-Pereira&Opher1989a:Jatenco-Dereira. 1994): protostellar winds (Jatenco-Pereira&Opler 1989b):: giant stars (Jatenco-Pereira&Opher 19890): Woll-Bavet sts," In addition to the more conventional collisional and viscous-resistive Alfvénn wave dampings, we concentrate on nonlinear and turbulent damping, which ourgroup has investigated in: the solar wind \citep{vera..89a,vera..94}; ; protostellar winds \citep{vera..89b}; ; late-type giant stars \citep{vera..89c}; ; Wolf-Rayet stars"101weight the simplifying assumptions used in our modeling of LPV 28579 against this future goal.,weight the simplifying assumptions used in our modeling of LPV 28579 against this future goal.102 Our study of the variation in model parameters demonstrates that we place reasonable constraints on the inner shell radius. the temperature at this radius. dust grain properties and the resulting mass-loss rates.," Our study of the variation in model parameters demonstrates that we place reasonable constraints on the inner shell radius, the temperature at this radius, dust grain properties and the resulting mass-loss rates."103 We discuss the results of our modeling in detail below., We discuss the results of our modeling in detail below.104 Figure 7— illustrates the good agreement between our model using an AmC+SiC dust composition and the overall continuum às well as the 11.3 jm feature observed in the spectrum., Figure \ref{fig:cagbmodel:totalfit} illustrates the good agreement between our model using an AmC+SiC dust composition and the overall continuum as well as the 11.3 $\mu$ m feature observed in the spectrum.105 Our combined gas+dust model improves on the pprediction by fitting the 13.7 jm absorption., Our combined gas+dust model improves on the prediction by fitting the 13.7 $\mu$ m absorption.106 We note two minor discrepancies: the silicon carbide feature seems broader than the model prediction. and the model fit systematically overestimates the flux at wavelengths longward of «20 jum. A broadening of the SiC feature may indicate self-absorption (see.e.g... corresponding to à high optical depth.," We note two minor discrepancies: the silicon carbide feature seems broader than the model prediction, and the model fit systematically overestimates the flux at wavelengths longward of $\sim$ 20 $\mu$ m. A broadening of the SiC feature may indicate self-absorption \citep[see, {\it e.g.}, corresponding to a high optical depth."107 The long-wavelength disagreement is probably due to the poor background subtraction (see Sect. 2.3)), The long-wavelength disagreement is probably due to the poor background subtraction (see Sect. \ref{subsec:cagbmodel:obs:sagespec}) )108 rather than due to a modeling issue., rather than due to a modeling issue.109 Given the low signal-to-noise of the spectrum. it is not certain if these discrepancies are real: we are therefore unable to justify a detailed refinement of our RT model.," Given the low signal-to-noise of the spectrum, it is not certain if these discrepancies are real; we are therefore unable to justify a detailed refinement of our RT model."110 Our best-fit model predicts a temperature of 1310 K at the inner radius of the dust shell. which is located at 4.4. R..," Our best-fit model predicts a temperature of 1310 K at the inner radius of the dust shell, which is located at 4.4 $R_*$."111 In Sect. 3.1.5..," In Sect. \ref{subsubsec:cagbmodel:parvar},"112" we estimate the inner edge to lie within (4.0—4.8) R. (corresponding to temperatures of 1260-1380 K). which is consistent with the theoretical predictions of Hófner(2007) for the condensation of amorphous carbon dust (7,,,,,21500 K. Rj,23 R.)."," we estimate the inner edge to lie within (4.0–4.8) $R_*$ (corresponding to temperatures of 1260–1380 K), which is consistent with the theoretical predictions of \citet{Hofner2007} for the condensation of amorphous carbon dust $T_{cond}$ =1500 K, $R_{\rm in}$ =3 $R_*$ )."113 The range of temperatures are slightly warmer than would be expected for LMC carbon stars of comparable loss rates (see.e.g... Fig.," The range of temperatures are slightly warmer than would be expected for LMC carbon stars of comparable mass-loss rates \citep[see, {\it e.g.}, Fig."114 4 and Equation |2009)., 4 and Equation 1.115 This may be due to the fact that we are using a warmer central star., This may be due to the fact that we are using a warmer central star.116 Here we are limited by the availability of the colder photospheres of comparable luminosity., Here we are limited by the availability of the colder photospheres of comparable luminosity.117 Moreover. as already. discussed. the moderate optical depth prevents us from using the observed near-IR colors to estimate the central star's effective temperature.," Moreover, as already discussed, the moderate optical depth prevents us from using the observed near-IR colors to estimate the central star's effective temperature."118" The KMH grain size distribution for the best-fit model is defined by y23.5. u,4,20.01 um aand eo21.0 jm. As noted in Sect. 3.1.3.."," The KMH grain size distribution for the best-fit model is defined by $\gamma$ =3.5, $a_{\rm min}$ =0.01 $\mu$ and $a_0$ =1.0 $\mu$ m. As noted in Sect. \ref{subsubsec:analysis:2dust:dprop},"119 the shape of the output SED ts sensitive to the size of the largest grains. but does not vary appreciably with changes in the miimum grain size up -θ.{ uim. About of the mass is cotained in grains with diameters exceeding | jm. depending on the minimum grain size.," the shape of the output SED is sensitive to the size of the largest grains, but does not vary appreciably with changes in the minimum grain size up $\sim$ 0.1 $\mu$ m. About of the mass is contained in grains with diameters exceeding 1 $\mu$ m, depending on the minimum grain size."120" For comparison. only of the dust mass ejected from IRC+10216 10? Li. 4,215 km sv! dust MLR ~8x1077 M. !) is in micron-sized particles (Jura1994)."," For comparison, only of the dust mass ejected from IRC+10216 $L\sim$$1.5\times 10^4$ $_\odot$, $\upsilon_{\rm exp}$ =15 km $^{-1}$, dust MLR $\sim$$8\times 10^{-8}$ $_\odot$ $^{-1}$ ) is in micron-sized particles \citep{Jura1994}."121 The SiC content derived from the best-fit model is comparable to values derived for dusty Galactic carbon stars (Groenewegenetal.1998)., The SiC content derived from the best-fit model is comparable to values derived for dusty Galactic carbon stars \citep{Groenewegenetal1998}.122. The lower metallicity of the LMC would imply a lower silicon abundance in general. and Groenewegenetal.(2007). find lower SiC/AmC ratios for the LMC compared to Galactic stars.," The lower metallicity of the LMC would imply a lower silicon abundance in general, and \citet{Groenewegenetal2007} find lower SiC/AmC ratios for the LMC compared to Galactic stars."123 By studying the effect of varying the SiC abundance on the output SED. we note that the SiC content can be in the range10-1656.," By studying the effect of varying the SiC abundance on the output SED, we note that the SiC content can be in the range."124. In this paper. we assume a gas:dust ratio V/2200.," In this paper, we assume a gas:dust ratio $\Psi$ =200."125 This value was determined for carbon stars in the solar neighbourhood (Jura1986)., This value was determined for carbon stars in the solar neighbourhood \citep{Jura1986}.126. An accurate determination of the gas:dust ratio is still to be made for LMC carbor stars., An accurate determination of the gas:dust ratio is still to be made for LMC carbon stars.127 Some observational. and theoretical studies (e.g... indicate that the carbon star gas:dust ratio may not be metallicity dependent.," Some observational and theoretical studies \citep[{\it e.g.}, indicate that the carbon star gas:dust ratio may not be metallicity dependent."128 In fact. recent studies (Groenewegenetal.2007;Wachteret2008;Mattsson2008) have found that the mass-loss rates of carbon stars may not be metallicity dependent.," In fact, recent studies \citep{Groenewegenetal2007,Wachteretal2008,Mattssonetal2008} have found that the mass-loss rates of carbon stars may not be metallicity dependent."129 The gas:dust ratio can be estimated from the mass fraction of SiC in the dust if we also know the fraction of the total Si mass that is in the dust., The gas:dust ratio can be estimated from the mass fraction of SiC in the dust if we also know the fraction of the total Si mass that is in the dust.130 Assuming that the οἱ abundance scales with metallicity (TheLMCsilicoiabundanceIsnotwellconstrained:seethediscussioninMatsuuraetal.2005) we obtain V in the range 200—570., Assuming that the Si abundance scales with metallicity \citep[The LMC silicon abundance is not well constrained; see the discussion in][]{Matsuuraetal2005} we obtain $\Psi$ in the range 200–570.131 However. we have assumed here that all of the S1 goes into the dust.," However, we have assumed here that all of the Si goes into the dust."132 In reality. the fraction of Si in dust depends indirectly on the amount of carbon in the dust.," In reality, the fraction of Si in dust depends indirectly on the amount of carbon in the dust."133 For example. if half of the carbon remaining after CO formation goes into dust. then of the Si is indust®.," For example, if half of the carbon remaining after CO formation goes into dust, then of the Si is in."134. The situation improves for higher C/O ratio — for C/Oz1.8. the Si dust fraction ts20-34%.," The situation improves for higher C/O ratio – for C/O=1.8, the Si dust fraction is."135. An alternative way to estimate the gas:dust ratio is to use the vanLoon(2000) relationship VY~ Z-- for carbon stars. which corresponds to 42300-1000 for the LMC.," An alternative way to estimate the gas:dust ratio is to use the \citet{vanLoon2000} relationship $\Psi\sim$ $^{-1\pm 0.3}$ for carbon stars, which corresponds to $\Psi$ =300–1000 for the LMC."136 Due tothe lack of constraints on the various quantities that determine the gas:dust ratio. we use 2200 when quoting a total mass-loss rate for LPV 28579. noting that the mass-loss rate could be up to about 5 times larger based on the calculations above.," Due tothe lack of constraints on the various quantities that determine the gas:dust ratio, we use $\Psi$ =200 when quoting a total mass-loss rate for LPV 28579, noting that the mass-loss rate could be up to about 5 times larger based on the calculations above."137 Our 2Dust model prediets a dust mass-loss rate of 2.5x107? M. yr!., Our ust model predicts a dust mass-loss rate of $2.5\times 10^{-9}$ $_\odot$ $^{-1}$.138 For a gas:dust ratio of 200. the total mass-loss rate is then 5x1077 M. yr!.," For a gas:dust ratio of 200, the total mass-loss rate is then $5\times 10^{-7}$ $_\odot$ $^{-1}$."139 This rate is on the low end of the vanLoonetal.(1999) mass-loss rates for the brightest. most obscured LMC carbon stars as well as the rates calculated for the Groenewegenetal.(2009) sample.," This rate is on the low end of the \citet{vanLoonetal1999} mass-loss rates for the brightest, most obscured LMC carbon stars as well as the rates calculated for the \citet{Groenewegenetal2009} sample."140 The mass-loss rates caleulated from the [3.6]-|8.0] and A-[8.0] colors of LPV 28579 using equations | and 2 of Matsuuraetal.(2009) are slightly higher (1.4107° Ma yr! and 2.5x107° M. yr! respectively)., The mass-loss rates calculated from the [3.6]–[8.0] and –[8.0] colors of LPV 28579 using equations 1 and 2 of \citet{Matsuuraetal2009} are slightly higher $1.4\times 10^{-6}$ $_\odot$ $^{-1}$ and $2.5\times 10^{-6}$ $_\odot$ $^{-1}$ respectively).141 However. our dust MLR is consistent with the value determined from the 8 jum flux — using the excess-MLR relation for extreme AGB stars from Paper [. we get a rate of 3.9x107 M. γη.," However, our dust MLR is consistent with the value determined from the 8 $\mu$ m flux – using the excess–MLR relation for extreme AGB stars from Paper I, we get a rate of $3.9\times 10^{-9}$ $_\odot$ $^{-1}$ ."142" Our total rate agrees with the values calculated using the period-MLR relations of Vassiliadis&Wood(1993) and Groenewegenetal.(1998) (107 M, γη) and 7.4x1077 M. vi! respectively. for a period of 356.24)."," Our total rate agrees with the values calculated using the period–MLR relations of \citet{VW93} and \citet{Groenewegenetal1998} $10^{-7}$ $_\odot$ $^{-1}$ and $7.4\times 10^{-7}$ $_\odot$ $^{-1}$ respectively, for a period of 356.2d)."143" The value obtained for the mass-loss rate is sensitive to the v, adopted (see Eq. 2)).", The value obtained for the mass-loss rate is sensitive to the $\upsilon_{\rm exp}$ adopted (see Eq. \ref{cagbmodel:MLR}) ).144 The outflow velocities for Galactie carbon, The outflow velocities for Galactic carbon145The second model had a primordial binary frequency of and was tailored to investigate the evolution and stellar populations of the old open cluster M67.,The second model had a primordial binary frequency of and was tailored to investigate the evolution and stellar populations of the old open cluster M67.146 It had 24000 menibers at birth and we will refer to this as the IX24-50 simulation.," It had $24\,000$ members at birth and we will refer to this as the K24-50 simulation."147 It had a half-life of about 2Gvr and after 4 Gyr of evolution only 2000 stars and binaries remained.," It had a half-life of about $2\,$ Gyr and after $4\,$ Gyr of evolution only $2\,000$ stars and binaries remained."148 The core density was about LO?starspe* on average. reaching a maximum of 350starspe* at 3480Myr with a corresponding core radius of 0.3 pe.," The core density was about $10^2 \, {\rm stars} \, {\rm pc}^{-3}$ on average, reaching a maximum of $350 \, {\rm stars} \, {\rm pc}^{-3}$ at $3\,480\,$ Myr with a corresponding core radius of $0.3\,$ pc."149 Figure Lbb shows the evolution of the core and Lagrangian radii for the IX24-50 simulation., Figure \ref{f:fig1}b b shows the evolution of the core and Lagrangian radii for the K24-50 simulation.150 To investigate the evolution of binary fractions across a range of star cluster models we will also make use of two simulations that have vet to be published., To investigate the evolution of binary fractions across a range of star cluster models we will also make use of two simulations that have yet to be published.151 These are a simulation that started with 90000 single stars ancl 10000 binaries (X100-10) ancl a simulation that started with 40000 single stars and 10000 binaries (50-20).," These are a simulation that started with $90\,000$ single stars and $10\,000$ binaries (K100-10) and a simulation that started with $40\,000$ single stars and $10\,000$ binaries (K50-20)."152 In Table 1 we summarize the properties of the four simulations., In Table \ref{t:table1} we summarize the properties of the four simulations.153 For each model the initial setup is as follows., For each model the initial setup is as follows.154 Masses for the single stars are drawn from the IAIF of Ixoupa. Tout Gilmore (1993) between (he mass limits of 0.1 and 50...," Masses for the single stars are drawn from the IMF of Kroupa, Tout Gilmore (1993) between the mass limits of 0.1 and $50 M_\odot$."155 Each binary mass is chosen from the IME of Ixroupa. Tout Gilmore (1991). as this had not been corrected for the effect of binaries. and the component masses are set bv choosing a [rom a uniform distribution.," Each binary mass is chosen from the IMF of Kroupa, Tout Gilmore (1991), as this had not been corrected for the effect of binaries, and the component masses are set by choosing a mass-ratio from a uniform distribution."156 We assume (hat all stars are on (he zero-age main sequence (ZAMS) when the simulation begins and that any residual gas from the star formation process has been removed., We assume that all stars are on the zero-age main sequence (ZAMS) when the simulation begins and that any residual gas from the star formation process has been removed.157 We use a Plummer density prolile (Aarseth. Hénnon Wielen 1974) and assume the stars and binaries are in virial equilibrium when assigning the initial positions and velocities.," We use a Plummer density profile (Aarseth, Hénnon Wielen 1974) and assume the stars and binaries are in virial equilibrium when assigning the initial positions and velocities."158 There is no primordial segregation by mass. binary properties. or any other discriminating [actor in these models.," There is no primordial segregation by mass, binary properties, or any other discriminating factor in these models."159 Each cluster is subject to a standard Galactic tidal field a civenlay orbit in the Solar neighborhood., Each cluster is subject to a standard Galactic tidal field – a circular orbit in the Solar neighborhood.160 Stars are removed. [rom the simulation when their distance from the density. centre exceeds twice that of the tidal radius of the cluster., Stars are removed from the simulation when their distance from the density centre exceeds twice that of the tidal radius of the cluster.161 The metallicity of the stars in the two simulations starting with 100000 stars and IX100-10) was set to be Z=0.001J. while both the IX24-50 and Ix50-20 simulations were assigned solar metallicity (7= 0.02).," The metallicity of the stars in the two simulations starting with $100\,000$ stars (K100-5 and K100-10) was set to be $Z = 0.001$ while both the K24-50 and K50-20 simulations were assigned solar metallicity $Z = 0.02$ )."162 The orbital separations of the 5000 primordial binaries in the IX100-5 simulation (Shara IIurley 2006) were drawn [rom the log-normal distribution suggested by Egeleton. Fitchett Tout (1989) with a peak at 30 au.," The orbital separations of the $5\,000$ primordial binaries in the K100-5 simulation (Shara Hurley 2006) were drawn from the log-normal distribution suggested by Eggleton, Fitchett Tout (1989) with a peak at $30\,$ au."163 This distribution is based on the properties of visual binaries in the Bright Star Catalogue (IHoffleit 1983) and is in agreement with the survey data of Duquennov AMavor (1991) for binaries in the solar neiglibourhood although the latter observations do not rule out a flat. distribution., This distribution is based on the properties of doubly-bright visual binaries in the Bright Star Catalogue (Hoffleit 1983) and is in agreement with the survey data of Duquennoy Mayor (1991) for binaries in the solar neighbourhood – although the latter observations do not rule out a flat distribution.164 Orbital eccentricities, Orbital eccentricities165intensely discussed. below.,intensely discussed below.166 Lt can be noted that a Poisson sample leads typically to a slope £2 and to a residual value Dy consistent with zero. Le. not. unexpectedA it is stronely dillerent from the void statistic of the LORS data.," It can be noted that a Poisson sample leads typically to a slope $\nu \approx 2$ and to a residual value $D_0$ consistent with zero, i.e. not unexpectedly, it is strongly different from the void statistic of the LCRS data."167 A similar relation for the mean voicl size of a Poisson sample of points in 3 dimensions. δω73À. was given in 7).," A similar relation for the mean void size of a Poisson sample of points in 3 dimensions, $D_{med} \approx 3\lambda$, was given in \citet{Li95}."168 The relation for the maximum: void size in Eq. (, The relation for the maximum void size in Eq. (1691) [rom 7). corresponds ο νz23 and no residual. value. which is typical for a Poisson point distribution.,"1) from \citet{RT84} corresponds to $\nu \approx 2-3$ and no residual value, which is typical for a Poisson point distribution."170 Obviously. a quite undersampled data set was used in their analysis.," Obviously, a quite undersampled data set was used in their analysis."171 Our relation in Eq. (, Our relation in Eq. (1722) seems more typical for the void size distribution in a clustered. galaxy. distribution. and an indication on a residual value is also seen in the void distribution of 2). (see Fig.,"2) seems more typical for the void size distribution in a clustered galaxy distribution, and an indication on a residual value is also seen in the void distribution of \citet{Li95} (see Fig."173 9 in their paper. where the relation of the void size and the galaxy number is shown).," 9 in their paper, where the relation of the void size and the galaxy number is shown)."174 The residual median void size. Dyz12h.!Mpe. is taken as a typical size of voids in well sampled. parts of the LORS.," The residual median void size, $D_0 \approx 12 \mhmpc$, is taken as a typical size of voids in well sampled parts of the LCRS."175 It substantially exceeds the corresponding values for the Poisson samples given. in the second. row of Table 2.., It substantially exceeds the corresponding values for the Poisson samples given in the second row of Table \ref{fit}.176 Also. the slope of the fractional increase of 10 vold size for diluted samples. 7 1. is significantly cüllerent [rom tha for the Poisson samples. £6z2.," Also, the slope of the fractional increase of the void size for diluted samples, $\nu177\approx 1$ , is significantly different from that for the Poisson samples, $\nu \approx 2$."178 Obviously. the void. sizes erow much more quickly in diluted data sets for the random samples than for the clustered data. and νz Lis a typica result that must be reproduced. by simulated. data sets.," Obviously, the void sizes grow much more quickly in diluted data sets for the random samples than for the clustered data, and $\nu \approx 1$ is a typical result that must be reproduced by simulated data sets."179 L is also remarkable that the inhomogeneous data set. 1H Lies on the same fit., It is also remarkable that the inhomogeneous data set 14 lies on the same fit.180 This means that some inhomogeneity in the galaxy sampling cloes not destroy the typical distribution of observed: voids., This means that some inhomogeneity in the galaxy sampling does not destroy the typical distribution of observed voids.181 There are no major cdillerences between the voi distributions for different bright galaxy samples. as the comparison of the void statistics of data sets 1 and 12 with the much brighter data sets 9. 11. and 13 demonstrates (see Fig.," There are no major differences between the void distributions for different bright galaxy samples, as the comparison of the void statistics of data sets 1 and 12 with the much brighter data sets 9, 11, and 13 demonstrates (see Fig."182 5 and Table 1)., 5 and Table 1).183 Pheir median sizes show no strong trend with the magnitude range. and only the maximum voicl size of set. 9 exceeds all the others due to its larger volume.," Their median sizes show no strong trend with the magnitude range, and only the maximum void size of set 9 exceeds all the others due to its larger volume."184 We do not regard the maximum void size às a reliable statistics for our comparison of data and simulations., We do not regard the maximum void size as a reliable statistics for our comparison of data and simulations.185 In Fig., In Fig.186 5 we show the median void sizes of the 14 data sets versus the lower limit of the absolute magnitude range Mj., 5 we show the median void sizes of the 14 data sets versus the lower limit of the absolute magnitude range $M_1$.187 There is a trend of increasing void sizes for more luminous galaxies., There is a trend of increasing void sizes for more luminous galaxies.188" llowever. this trend is masked by dillerences in the dilution factor. as seen by comparison of the data sets. sample with high (fini,2 0.35) and low (fi; 0.35) sampling rate."," However, this trend is masked by differences in the dilution factor, as seen by comparison of the data sets sampled with high $f_{min}>0.35$ ) and low $f_{min}<0.35$ ) sampling rate."189 Thus we shall use in the following analysis the mean galaxy separation in dilferent data sets as the argumen which determinesvoicl sizes., Thus we shall use in the following analysis the mean galaxy separation in different data sets as the argument which determinesvoid sizes.190" We studied Pearson's linear correlation r(see. e.g. 2))) of the median vold size D, aux the mean galaxy separation A. which is r=0.81 with error probability0."," We studied Pearson's linear correlation $r$(see, e.g. \citet{PTVF92}) ) of the median void size $D_{med}$ and the mean galaxy separation $\lambda$, which is $r = 0.81$ with error probability."191044... Phis indicates a clear correlation with high reliability., This indicates a clear correlation with high reliability.192" Taking the dependence of the median voic size {δη on the lower absolute magnitude limit M, anc the sampling fraction f,;,. we get much weaker correlation coellicients of ry=0.57 and r=0.56. with ancl error. probability. respectively."," Taking the dependence of the median void size $D_{med}$ on the lower absolute magnitude limit $M_1$ and the sampling fraction $f_{min}$, we get much weaker correlation coefficients of $r = 0.57$ and $r = 0.56$, with and error probability, respectively."193 Hence. basically. the firs dependence. {λα on A. shows a tight correlation.," Hence, basically, the first dependence, $D_{med}$ on $\lambda$, shows a tight correlation."194" This formal test shows that for the restricted range of AL, which could be tested with the given data the dependence of void sizes on the absolute magnitude limit cannot be established reliably.", This formal test shows that for the restricted range of $M_1$ which could be tested with the given data the dependence of void sizes on the absolute magnitude limit cannot be established reliably.195 An other important. effect. which plays a role is the wedege-like geometry of the LORS data sets i.e. the LORS slices are not rectangular volumes. but wedges with an opening angle of 1.5.," An other important effect which plays a role is the wedge-like geometry of the LCRS data sets – i.e, the LCRS slices are not rectangular volumes, but wedges with an opening angle of $1.5\dgr$."196 This leads to a slight density gradient over the survey plane ancl as shown by the scaling in Iq. (, This leads to a slight density gradient over the survey plane and – as shown by the scaling in Eq. (1972) to somewhat smaller voids in the more distant parts of the survey planes and to somewhat larger voids in the less dense sampled. parts of the nearby regions.,2) – to somewhat smaller voids in the more distant parts of the survey planes and to somewhat larger voids in the less dense sampled parts of the nearby regions.198 Phe addition of smal voids concerns less than half of the volume. whereas simal voids are less abundant in the other part due to the large volume occupied: by the big voids.," The addition of small voids concerns less than half of the volume, whereas small voids are less abundant in the other part due to the large volume occupied by the big voids."199 Tests with simulations show that the cumulative void cistribution in Eig., Tests with simulations show that the cumulative void distribution in Fig.200 3 is shiftec to larger void sizes D by (οrlO)., 3 is shifted to larger void sizes $D$ by $(5 - 10)\%$.201 This overestimate of void sizes also allects all mean characteristics of the vok distribution that are shown in Fig., This overestimate of void sizes also affects all mean characteristics of the void distribution that are shown in Fig.202 4 and given in Table 2.., 4 and given in Table \ref{fit}.203 The same effect occurs in the mock samples: ie. this elfec does not influence the comparison of the data with mocels.," The same effect occurs in the mock samples; i.e., this effect does not influence the comparison of the data with models."204 ‘Tests have shown that it is more reliable to keep a higher galaxy number in the volume limited samples rather than to reduce further the galaxy. number in order to ect samples with constant thickness., Tests have shown that it is more reliable to keep a higher galaxy number in the volume limited samples rather than to reduce further the galaxy number in order to get samples with constant thickness.205 Finally. we remarked above that the boundary. ellects of the survey tend to slightly reduce the typical void size Le. they vield a competing effect to that of the slices’ wedge-like geometry.," Finally, we remarked above that the boundary effects of the survey tend to slightly reduce the typical void size – i.e., they yield a competing effect to that of the slices' wedge-like geometry."206 Even so. as mentioned above. this competing influence is smaller (only =3%).," Even so, as mentioned above, this competing influence is smaller (only $\approx 3 \%$ )."207 For evaluation of our results we compare them with a set of numerical simulations anc corresponding mock samples of model galaxy. distributions in dillerent. CDM. models., For evaluation of our results we compare them with a set of numerical simulations and corresponding mock samples of model galaxy distributions in different CDM models.208 We compare the model galaxy distribution also with the 2- correlation function of galaxies with a similar range in brightness as that in the LCTUS., We compare the model galaxy distribution also with the 2-point correlation function of galaxies with a similar range in brightness as that in the LCRS.209 We emplov. particle mesh (PM). simulations in cillerent cosmological models., We employ particle mesh (PM) simulations in different cosmological models.210" First. we consider a COBLE normalized SCDAI model with ©,,=1 and climensionless Hubble constant f=0.5."," First, we consider a COBE normalized SCDM model with $\Omega_m=1$ and dimensionless Hubble constant $h=0.5$."211 bor the CODE normalization. we take the prescription of 2)..," For the COBE normalization, we take the prescription of \citet{BW97}."212 As an alternative. we take the same model at an earlier. time. SCDAIe. which fits the requirements of cluster normalization (see. c.g.. 7))).," As an alternative, we take the same model at an earlier time, SCDMc, which fits the requirements of cluster normalization (see, e.g., \citet{ECF96}) )."213" Further. we study more realistic mocels: ACDAL with £2,,= 0.3. h=0.65. and a cosmological term to provide spatial flatness: and anopen model. OCDAL with ον,= 0.5. h= 0.6."," Further, we study more realistic models: $\Lambda$ CDM with $\Omega_m=0.3$ , $h=0.65$, and a cosmological term to provide spatial flatness; and anopen model, OCDM with $\Omega_m=0.5$ , $h=0.6$ ."214 Finally. we consider a high. density CDM model with a more complex initial spectrum — one with a break in power between large and small scales. — denoted. as a," Finally, we consider a high density CDM model with a more complex initial spectrum – one with a break in power between large and small scales – denoted as a"215While the eieenfuunction c inside a uniforii density sphere las a roughly constant envelope (eq. [2.2.0].,"While the eigenfunction $\psi$ inside a uniform density sphere has a roughly constant envelope (eq. \ref{eq:psienv1}] ]),"216 c iu the power-law deusitv case behaves differeutly., $\psi$ in the power-law density case behaves differently.217 Followiug the saneoperation as in 82.2.0... one finds and Uu qu ," Following the sameoperation as in \ref{subsubsec:dispersion}, one finds and _i _i + )."218So. the eigeeufunction. c has an amplitude that rises toward the surface (when [0;|/> p).," So, the eigenfunction $\psi$ has an amplitude that rises toward the surface (when $|x_i| \rightarrow \mu$ )."219 In fact. its envelope scales with deusitv as ," In fact, its envelope scales with density as = _1 (x_1) _2 (x_2)."220Fig., Fig.221 9 shows one example of such a WISB cuvelope., \ref{fig:eigenfunction} shows one example of such a WKB envelope.222 We fud that the dispersion relation is also modified slightly from the case of a uniform deusity sphere., We find that the dispersion relation is also modified slightly from the case of a uniform density sphere.223 But qualitative features of equation remain., But qualitative features of equation remain.224" The density profile inside a planet typically traces out two different polvtropes: near the surface. the gas can be approximated as au ideal gas composed of diatomicmolecules. with a mean degree of freedom 5. so P4=GluP/Olup|,= 7/5. and the correct polvtrope uuuber is no2: in the interior of the planet. Coulomb pressure and electrou degeneracy mocity the equation of state aud raise Py to —2. while reducing the polvtrope uuuber to n~1l."," The density profile inside a planet typically traces out two different polytropes: near the surface, the gas can be approximated as an ideal gas composed of diatomicmolecules, with a mean degree of freedom $5$, so $\Gamma_1 ={\partial \ln P/\partial225\ln \rho}|_s = 7/5$ , and the correct polytrope number is $n \sim 2$; in the interior of the planet, Coulomb pressure and electron degeneracy modify the equation of state and raise $\Gamma_1$ to $\sim2262$, while reducing the polytrope number to $n \sim 1$."227 This motivates us to model Jupiters deusitv profile using two power-laws of the form in equation(23.005 5= Lin the interior and 3?=1.8 near the surface. with the transition occurring at a radius rτε0.98 (see Paper II).," This motivates us to model Jupiter's density profile using two power-laws of the form in equation: $\beta = 1$ in the interior and $\beta = 1.8$ near the surface, with the transition occurring at a radius $r228\approx 0.98$ (see Paper II)."229 This reproduces profiles iu realistic Jupiter models2001)., This reproduces profiles in realistic Jupiter models.230. The presence of a core or a phase transition complicates this picture., The presence of a core or a phase transition complicates this picture.231 We discuss them m more detail in Paper IL., We discuss them in more detail in Paper II.232 Iu general. equation is not separable under these density profiles.," In general, equation is not separable under these density profiles."233 However. we discover an approximate solution which is accurate to the secoud. order in wave-numbers (Q(1/A2) with Ao9 1). for the case when the density profile is power-law near the surface and sinoothly varving in the interior.," However, we discover an approximate solution which is accurate to the second order in wave-numbers ${\cal O}234(1/\lambda^2)$ with $\lambda \gg 1$ ), for the case when the density profile is power-law near the surface and smoothly varying in the interior."235 This is largely iuspired by the WISB result in 2.3.0., This is largely inspired by the WKB result in \ref{subsubsec:envelope}.236 We first iutroduce a fiducialdeusity paie Which satisfies equation with a power-law index taken to be that for the true density p near the surface., We first introduce a fiducialdensity $\rho_{\rm surf}$ which satisfies equation with a power-law index taken to be that for the true density $\rho$ near the surface.237 We also define X—pour/p so VNcmld near the surface and deviates from unity toward the center., We also define $X = \rho_{\rm surf}/\rho$ so $X \approx 1$ near the surface and deviates from unity toward the center.238 Inverse of the density scale height can be written as — | , Inverse of the density scale height can be written as = - = +.239Tutroducing a variable f. ta (xp yehr one fids. 2o sud ' 2.0ddu NES.dlaNvsTX ," Introducing a variable $t$, t = (x_1^2 - ^2-x_2^2) = ^2 ^2)(1-r^2), one finds, = - 2 r ^2 ^2) }."240Now repeat the same calculations that lead to equation(12).. we obtain yd~ NUT |," Now repeat the same calculations that lead to equation, we obtain _1 - - 2. ."241 uu 0. where the operator €; is defined in equation(13).," + + = 0, where the operator ${\cal E}_i$ is defined in equation."242. Tere. since Oefey;~ Ac. we can not ignore teris in the square parenthesis if we want to be accurate to OLA3) the finaleoal of our procedure.," Here, since $\partial \psi /\partial x_i \sim \lambda \psi$ , we can not ignore terms in the square parenthesis if we want to be accurate to ${\cal O} (1/\lambda^2)$, the finalgoal of our procedure."243 Tustead. πο experiment with the followiug decomposition for c.," Instead, we experiment with the following decomposition for $\psi$, = _0(x_1, x_2) = _0 (x_1, x_2)."244 This is mspied by the WIXB envelope preseuted iu equation(2., This is inspired by the WKB envelope presented in equation.245"3.0). Formally expressing E;o=a;OF|biefv; ee. Where the meanings of ειδι aud e; are clear frou equation (13).. we fiud Uo. Quo (20S NU"" Ui———' NNd ——' pb where = VX ."," Formally expressing ${\cal E}_i \psi = a_i {\partial^2246\psi}/{\partial x_i^2} + b_i {\partial \psi}/{\partial x_i} + c_i247\psi$ , where the meanings of $a_i, b_i$ and $c_i$ are clear from equation , we find _i =_0+ 2 a_i + ( a_i + b_i ) _0, where = ."248In this section we plot some of the (hermocdwnamie functions that were derived in the previous (wo sections.,In this section we plot some of the thermodynamic functions that were derived in the previous two sections.249 It is important (ο note that. although the results do depend on the numerical values of the parameters. the critical behaviors obviously do not.," It is important to note that, although the results do depend on the numerical values of the parameters, the critical behaviors obviously do not."250 In. addition. since most of the parameters were chosen to match onto known properties of quark-gluon matter al jc—0 and to dense nuclear matter al 7=0 the results should not be too far from what is al present impossibly difficult computations in QCD.," In addition, since most of the parameters were chosen to match onto known properties of quark-gluon matter at $\mu = 0$ and to dense nuclear matter at $T = 0$ the results should not be too far from what is at present impossibly difficult computations in QCD."251with scatter (frg)=0.517 mag.,with scatter $\sigma(\mu_B)=0.517$ mag.252 On Figure 3. our rjj and. luminosity (Mg) estimates for the racdio-selected: &alaxies are plotted. with the 7j;Ale relations from Equations 1. 2 and 3 For cach galaxy we calculated: ;NCAZg) as the dilference between the observed Ale and that given by the appropriate relation (i.e. Equation l for S4 and 16V30. Equation 3 for the other four) for the observed μι," On Figure 3, our $r_{hl}$ and luminosity $M_B$ ) estimates for the radio-selected galaxies are plotted with the $r_{hl}-M_B$ relations from Equations 1, 2 and 3 For each galaxy we calculated $\Delta(M_B)$ as the difference between the observed $M_B$ and that given by the appropriate relation (i.e. Equation 1 for S4 and 16V30, Equation 3 for the other four) for the observed $r_{hl}$."253 This provides a direct comparison between the rest-frame blue-band SB of our raclio-selected galaxies ancl that of normal field. galaxies., This provides a direct comparison between the rest-frame blue-band SB of our radio-selected galaxies and that of normal field galaxies.254 However. this is likely to be be an underestimate [or spirals seen close to cdge-on (i.e. 16V31 and 16V34). which would. require corrections for internal extinction.," However, this is likely to be be an underestimate for spirals seen close to edge-on (i.e. 16V31 and 16V34), which would require corrections for internal extinction."255 Lloerver. the central SD. (Vable 2). should be much less sensitive to the inclination angle. to local disk galaxies.," Hoerver, the central SB (Table 2), should be much less sensitive to the inclination angle, to local disk galaxies."256 Phe D-band central SB. corrected to z=0. can be estimated as For the disk galaxies. we calculated Aye as the the dillerence. between the observed. µρυ ancl the central SB given by Equation 4 for the Alp given by Equation 3 for the observed. ril Gol for the observed. Ale).," The $B$ -band central SB, corrected to $z=0$, can be estimated as For the disk galaxies, we calculated $\Delta\mu_B$ as the the difference between the observed $\mu_{B0}$ and the central SB given by Equation 4 for the $M_B$ given by Equation 3 for the observed $r_hl$ $not$ for the observed $M_B$ )."257 We see that. for the facc-on 16V25. XMpg and Ayre are very similar. but Aye is much greater for the edge-on. 16V31 and 16V34.," We see that, for the face-on 16V25, $\Delta M_B$ and $\Delta\mu_B$ are very similar, but $\Delta\mu_B$ is much greater for the edge-on 16V31 and 16V34."258 On the basis of these studies. the central SB of 16V22 is near the average for a disk galaxy of its size and recshilt. whereas 16V25. 16V31. 16V34 and SLO are ~1 mag above the average.," On the basis of these studies, the central SB of 16V22 is near the average for a disk galaxy of its size and redshift, whereas 16V25, 16V31, 16V34 and S10 are $\sim 1$ mag above the average."259 All four lic at about the top of the observed SB range of CERS/LDSS ealaxies in the pg—z plot of Lilly et al. (, All four lie at about the top of the observed SB range of CFRS/LDSS galaxies in the $\mu_B-z$ plot of Lilly et al. (2601998).,1998).261 The relatively high. SBs of these galaxies may then zwour the interpretation of their enhanced radio Luminosity as the result of starbursts., The relatively high SBs of these galaxies may then favour the interpretation of their enhanced radio luminosity as the result of starbursts.262 In all four. the high SD appears o be associated with the whole disk or with extended eatures. such as the bright rings of 16V31 and 16V34 (see xdow). and not with any central point-source.," In all four, the high SB appears to be associated with the whole disk or with extended features, such as the bright rings of 16V31 and 16V34 (see below), and not with any central point-source."263 16V22 has a more moderate SB. but its blue colours would be evidence or starbursting.," 16V22 has a more moderate SB, but its blue colours would be evidence for starbursting."264 However there is no indication that 84 is starbursting as its SB and red colours (Section. 6) are consistent with a passively evolving elliptical., However there is no indication that S4 is starbursting as its SB and red colours (Section 6) are consistent with a passively evolving elliptical.265 Two of the 9 galaxies appeared to be interacting with smaller companions. although we have no definite (i.e. with spectroscopic kinematics) confirmation of this.," Two of the 9 galaxies appeared to be interacting with smaller companions, although we have no definite (i.e. with spectroscopic kinematics) confirmation of this."266 S4 appeared to be an isolated galaxy in the BRLISO2 data. but the LIST reveals a much fainter (the demoerged SExtractor magnitude is £=22.67c 0.02). disk-twvpe companion 1.92 aresee to its SSE.," S4 appeared to be an isolated galaxy in the RLK02 data, but the HST reveals a much fainter (the demerged SExtractor magnitude is $I=22.67\pm 0.02$ ), disk-type companion 1.92 arcsec to its SSE."267 The luminosity ratio is 0.2l and projected separation 1945.1 kpe., The luminosity ratio is $0.2:1$ and projected separation $19.4 h_{50}^{-1}$ kpc.268 84 is not greatly disturbed but does show isophotal twist in the central kr«0.4 aresec., S4 is not greatly disturbed but does show isophotal twist in the central $r<0.4$ arcsec.269 16V21 has bright knots suggesting active star formation. and is very asymmetric.," 16V21 has bright knots suggesting active star formation, and is very asymmetric."270 It appears to be connected by a Luminous filament to a smaller. high-SB companion 3.24 arcsec to the SW. with £=24.05 (luminosity ratio 0.1:1).," It appears to be connected by a luminous filament to a smaller, high-SB companion 3.24 arcsec to the SW, with $I=24.05$ (luminosity ratio 0.4:1)."271 The other 7 galaxies have no obvious companions. but we investigate below the possibility that they show evidence of very recent interactions.," The other 7 galaxies have no obvious companions, but we investigate below the possibility that they show evidence of very recent interactions."272 Consclice. Bershacy anc Jangren (2000). presented. a quantitative measure of rotational asvnunetry. which can be used to distinguish between “normal. unclisturbed galaxies and those undergoing an interaction or merger.," Conselice, Bershady and Jangren (2000) presented a quantitative measure of rotational asymmetry, which can be used to distinguish between `normal', undisturbed galaxies and those undergoing an interaction or merger."273 The statistic they found to be most successful is evaluated as, The statistic they found to be most successful is evaluated as274 , 275One result of this paper is that our pressure-based model of star formation produces a standard SK with a knee at a σας surface density that depends on gas fraction in a way that resembles the metallicity dependence proposed by ? and ?..,One result of this paper is that our pressure-based model of star formation produces a standard SK with a knee at a gas surface density that depends on gas fraction in a way that resembles the metallicity dependence proposed by \cite{Krumholz09b} and \cite{Gnedin10}.276 If the molecular fraction is regulated by pressure. gas-rich galaxies become dominated by molecular gas at higher gas surface densities.," If the molecular fraction is regulated by pressure, gas-rich galaxies become dominated by molecular gas at higher gas surface densities."277" It is easy to show that the gas surface density at which MX, equates “ay. which we call “og. scales with the gas fraction f=Neots(MeottdMa). as: pa’"," It is easy to show that the gas surface density at which $\Sigma_{\rm mol}$ equates $\Sigma_{HI}$ , which we call $\Sigma_{\rm eq}$, scales with the gas fraction $\mu=\Sigma_{\rm278 cold}/(\Sigma_{\rm cold} + \Sigma_\star)$, as: = ."279" Here /1, is the normalization of equation 2..", Here $P_0$ is the normalization of equation \ref{eq:fmol}.280 In most chemical evolution models. sr is related to metallicity: for instance. in the simple closed-box model. Z=YIn(1/50)). where Y is the metal yield per stellar generation.," In most chemical evolution models, $\mu$ is related to metallicity; for instance, in the simple closed-box model, $Z=Y\ln (1/\mu)$, where $Y$ is the metal yield per stellar generation."281 Then. a pressure-based molecular fraction can mimic a metallicity dependence.," Then, a pressure-based molecular fraction can mimic a metallicity dependence."282" But the maximum value of M, is reached for ye=1. in which case Mouuas=VEIπανc34M.pe 7: this is the X, value of the SH simulation. that has a 99 per cent gas fraction."," But the maximum value of $\Sigma_{\rm eq}$ is reached for $\mu=1$, in which case $\Sigma_{\rm eq, max} = \sqrt{2P_0/\pi G} \simeq 34\ {\rm283 M}_\odot\ {\rm pc}^{-2}$ ; this is the $\Sigma_{\rm eq}$ value of the SH simulation, that has a 99 per cent gas fraction."284 According to 2.. Nag for the Large Magellanic Cloud is similar to 347. while for the Small Magellanic Cloud it is 1007.," According to \cite{Bolatto09}, , $\Sigma_{\rm eq}$ for the Large Magellanic Cloud is similar to 34, while for the Small Magellanic Cloud it is $\sim$ 100."285" This is confirmed by a quick comparison with Krumholtz et al's model: an increase in X, by a factor of 3. as large as the difference between MW and SH. is obtained by a decrease of metallicity by a similar factor. which is relatively modest."," This is confirmed by a quick comparison with Krumholtz et al's model: an increase in $\Sigma_{\rm eq}$ by a factor of 3, as large as the difference between MW and SH, is obtained by a decrease of metallicity by a similar factor, which is relatively modest."286 The same conclusion ean be reached by considering the saturation “yy value. that reaches ~20 for our SH dise while. for instance. ?. report higher values for a few low metallicity dwarf galaxies.," The same conclusion can be reached by considering the saturation $\Sigma_{\rm HI}$ value, that reaches $\sim20$ for our SH disc while, for instance, \cite{Fumagalli10} report higher values for a few low metallicity dwarf galaxies."287 We conclude that a pressure- molecular fraction cannot explain the whole observed range of variation of X.," We conclude that a pressure-driven molecular fraction cannot explain the whole observed range of variation of $\Sigma_{\rm288 eq}$."289 Because the motivation for molecular fraction being directly modulated by metallicity is very strong (butseethecommentsby 2). it is well conceivable to construct mixed scenarios where equation 2. is valid and the normalization 75 depends on metallicity.," Because the motivation for molecular fraction being directly modulated by metallicity is very strong \citep[but see the comments290 by][]{MacLow10}, it is well conceivable to construct mixed scenarios where equation \ref{eq:fmol} is valid and the normalization $P_0$ depends on metallicity."291 The search for aphysical interpretation of our results lead us to an expression for gas pressure in star-forming discs given by equation 6.., The search for aphysical interpretation of our results lead us to an expression for gas pressure in star-forming discs given by equation \ref{eq:Pfit}.292" Discs subject to this pressure have some interesting properties: for instance. neither Y, nor e, appear in the expression of pressure (though the gravity of stars enters in determining σα). gus effective height is related to the ratio of gas velocity dispersion and epicyclic frequency (equation 10)) and the sound crossing time of effective height is simply proportional to the orbital time (equation 113)."," Discs subject to this pressure have some interesting properties: for instance, neither $\Sigma_\star$ nor $\sigma_\star$ appear in the expression of pressure (though the gravity of stars enters in determining $\sigma_{\rm cold}$ ), gas effective height is related to the ratio of gas velocity dispersion and epicyclic frequency (equation \ref{eq:Heff}) ) and the sound crossing time of effective height is simply proportional to the orbital time (equation \ref{eq:tcross}) )."293 Comparison with data is not straightforward. as Foi Includes a major contribution from the sound speed of the hot phase (we give further comments below) and direct pressure estimates are hard to obtain.," Comparison with data is not straightforward, as $\sigma_{\rm cold}$ includes a major contribution from the sound speed of the hot phase (we give further comments below) and direct pressure estimates are hard to obtain."294 Nonetheless. these predictions can in principle be tested against observations of the Milky Way and nearby galaxies. so they may constitute a basis for a theory of the non-equilibrium vertical structure of dises effectively heated by feedback.," Nonetheless, these predictions can in principle be tested against observations of the Milky Way and nearby galaxies, so they may constitute a basis for a theory of the non-equilibrium vertical structure of discs effectively heated by feedback."295 Our simulated discs show total vertical velocity dispersions (figure 6)) that are well in excess of the ~10 value that is usually assumed to hold for dises., Our simulated discs show total vertical velocity dispersions (figure \ref{fig:sigma}) ) that are well in excess of the $\sim10$ value that is usually assumed to hold for discs.296 However. σι. in our simulations is dominated by the thermal sound speed (equation +)) computed at the particle effective temperature. and this last quantity is determined by the thermal content of the hot phase.," However, $\sigma_{\rm cold}$ in our simulations is dominated by the thermal sound speed (equation \ref{eq:scold}) ) computed at the particle effective temperature, and this last quantity is determined by the thermal content of the hot phase."297 This means that oi cannot be compared with the velocity dispersion of cold clouds in real galaxies., This means that $\sigma_{\rm cold}$ cannot be compared with the velocity dispersion of cold clouds in real galaxies.298 At the same time. vertical velocity dispersions of gas particles (computed without the sound speed) of MW and DW simulations show values that are in much better agreement with those measured in THINGS galaxies by ? (see figures 11 and 18 in paper D.," At the same time, vertical velocity dispersions of gas particles (computed without the sound speed) of MW and DW simulations show values that are in much better agreement with those measured in THINGS galaxies by \cite{Tamburro09} (see figures 11 and 18 in paper I)."299 In our simulations. multi-phase particles are composed by two phases at the sub-grid level. but are seen as a single entity by the SPH code.," In our simulations, multi-phase particles are composed by two phases at the sub-grid level, but are seen as a single entity by the SPH code."300 This means that. as long as a multi-phase cycle goes on. the hot phase is not free to leave the disc. while the cold phase is pulled by the former.," This means that, as long as a multi-phase cycle goes on, the hot phase is not free to leave the disc, while the cold phase is pulled by the former."301 This artificial entrainment results. at the macroscopic level. in a velocity dispersion of gas particles that is realistic and. from a detailed comparison of MW and MW.HHR. rather stable with resolution in that part of thedise that is well resolved in both simulations.," This artificial entrainment results, at the macroscopic level, in a velocity dispersion of gas particles that is realistic and, from a detailed comparison of MW and HR, rather stable with resolution in that part of thedisc that is well resolved in both simulations."302 This —means that our effective model is correctly producing a gas dise that is thermally warm but kinematically colder., This means that our effective model is correctly producing a gas disc that is thermally warm but kinematically colder.303 It must be noticed that the hot coronae we produce around the disces have temperatures ~3.10° K and densities ~107 . so their presence is likely ruled out by X-ray observations (e.g.2)..," It must be noticed that the hot coronae we produce around the discs have temperatures $\sim3\times10^6$ K and densities $\sim10^{-2}$ $^{-3}$, so their presence is likely ruled out by X-ray observations \citep[e.g.][]{Crain10}."304 However. insertion of metal cooling would change this energy balance in favour of kinetic energy. So we expect this hot corona to be less prominent when chemical evolution is properly taken into account.," However, insertion of metal cooling would change this energy balance in favour of kinetic energy, so we expect this hot corona to be less prominent when chemical evolution is properly taken into account."305 Our results thus suggest that a complete modeling of a disc heated by feedback must fully take into account the multi-phase nature of the ISM. where the ~kpe-height corona of warm/hot gas surrounding a spiral galaxy may have an important dynamical role.," Our results thus suggest that a complete modeling of a disc heated by feedback must fully take into account the multi-phase nature of the ISM, where the $\sim$ kpc-height corona of warm/hot gas surrounding a spiral galaxy may have an important dynamical role."306 A step forward in the modeling of a spiral disc subject to contiuous production and dissipation of energy was recently taken by ?.. who addressed the stability of a dise where energy is continually injected and dissipated over some multiple of the crossing time of turbulence.," A step forward in the modeling of a spiral disc subject to contiuous production and dissipation of energy was recently taken by \cite{Elmegreen11}, who addressed the stability of a disc where energy is continually injected and dissipated over some multiple of the crossing time of turbulence."307 However. in that paper only radial and tangential perturbations were considered and vertical equilibrium was assumed.," However, in that paper only radial and tangential perturbations were considered and vertical equilibrium was assumed."308 The results presented in this paper rely on how well the vertical structure of the dise is resolved in simulations., The results presented in this paper rely on how well the vertical structure of the disc is resolved in simulations.309 In the MW and DW cases effective dise heights are of the same order of the gravitational softening (that was kept of the same order as the one used in cosmological simulations with the same mass resolution). so numerical convergence of the results should be demonstrated.," In the MW and DW cases effective disc heights are of the same order of the gravitational softening (that was kept of the same order as the one used in cosmological simulations with the same mass resolution), so numerical convergence of the results should be demonstrated."310 We showed results for the MW.HHR simulation. and found no clear dependence on resolution in any of our results.," We showed results for the HR simulation, and found no clear dependence on resolution in any of our results."311 Moreover. the light disc forming out of the SH simulation has an effective height of ~1 kpe. with a gravitational softening of only 43 pe. so in this case the vertical structure 1s well resolved.," Moreover, the light disc forming out of the SH simulation has an effective height of $\sim1$ kpc, with a gravitational softening of only 43 pc, so in this case the vertical structure is well resolved."312 We conclude that. despite the vertical structure of the discs is barely resolved in some of our simulations. the results should be not strongly affected by resolution.," We conclude that, despite the vertical structure of the discs is barely resolved in some of our simulations, the results should be not strongly affected by resolution."313 Due to the difficulty in performing measures of gas pressure. observers typically use equation | to estimate pressure (often making strong assumptions on velocity dispersions}. but its validity has rarely been tested.," Due to the difficulty in performing measures of gas pressure, observers typically use equation \ref{eq:Pext} to estimate pressure (often making strong assumptions on velocity dispersions), but its validity has rarely been tested."314 ? compared this formula with simulations of turbulent ISM in a shearing disc., \cite{Koyama09} compared this formula with simulations of turbulent ISM in a shearing disc.315 In their simulations the gas dise is assumed to be much thinner than the stellar one. heating terms take account of cosmic rays. X-rays and He formation and destruction. while radiative feedback from massive stars is modeled as localized increases of heating rate. but no SNe are present.," In their simulations the gas disc is assumed to be much thinner than the stellar one, heating terms take account of cosmic rays, X-rays and $_2$ formation and destruction, while radiative feedback from massive stars is modeled as localized increases of heating rate, but no SNe are present."316 Their spatial resolution is of order of —1 pe., Their spatial resolution is of order of $\sim$ 1 pc.317 They found that midplane and mass-weighted pressures typically differ by an order of magnitude. and that equation | is very close to the armonic meanof the two.," They found that midplane and mass-weighted pressures typically differ by an order of magnitude, and that equation \ref{eq:Pext} is very close to the armonic meanof the two."318" Interestingly. their midplane pressure is a factorof three lower than /2.,,. which is what we find for Qiu.= I."," Interestingly, their midplane pressure is a factorof three lower than $P_{\rm ext}$ , which is what we find for $Q_{\rm tot}=1$ ."319" Our results are not comparable to their simulation. due to the vastly different resolution and to the much hotter state of our dises (they have 0,447-5 +)."," Our results are not comparable to their simulation, due to the vastly different resolution and to the much hotter state of our discs (they have $\sigma_{\rm cold} \sim5$ )."320 They also proposed an improved analytic, They also proposed an improved analytic3212005).,.322. The properties of individual red supereiant Ólavers vary significautlv from star to star. and a ereater sample of measurenienuts Is required to understaud what deteruines individual laver properties.," The properties of individual red supergiant layers vary significantly from star to star, and a greater sample of measurements is required to understand what determines individual layer properties."323 The processes by which red supergiaut stars form and accelerate dust. while crucial to mass-loss scenarios. are little understood.," The processes by which red supergiant stars form and accelerate dust, while crucial to mass-loss scenarios, are little understood."324 Existing models of stellar atinosplieres (0.8...Crustafssouetal.2008:Plez2010). caunot predict locatious for dust condensation. and attempts to model dust acceleration through radiation pressure lave also so far been unsuccessful (e...Woitke 2007)..," Existing models of stellar atmospheres \citep[e.g.,][]{gee+08,p10} cannot predict locations for dust condensation, and attempts to model dust acceleration through radiation pressure have also so far been unsuccessful \citep[e.g.,][]{w07}. ."325 Our inulti-epoch study. of a laver directly surrounding Betclecuse provides now insight iuto the processes involved iu red supergieunt niss-loss., Our multi-epoch study of a layer directly surrounding Betelgeuse provides new insight into the processes involved in red supergiant mass-loss.326 We have shown that the basic properties of the laver. even in Table 3. exhibit striking variability from vear to vear.," We have shown that the basic properties of the layer, given in Table 3, exhibit striking variability from year to year."327 The laver is found to decrease in size aud Increase iu optical depth over the vears 20062008. and increase in size and decrease in optical depth between 2009—2010.," The layer is found to decrease in size and increase in optical depth over the years $2006-2008$, and increase in size and decrease in optical depth between $2009-2010$."328 The laver temperature does not show such systematic variability. although the largest laver size (in 2010) does correspond to the highest temperature.," The layer temperature does not show such systematic variability, although the largest layer size (in 2010) does correspond to the highest temperature."329 The varnabilitv in the apparent nud-IR size of Deteleeuse reported by Townesetal.(2009). can also be interpreted to indicate variations in the lavers., The variability in the apparent mid-IR size of Betelgeuse reported by \citet{twh+09} can also be interpreted to indicate variations in the layers.330 Iutriguinely. a similar phenomenon was reported by Pease(1922).. who noted a decrease in the size of Detelgeuse at visible wavelengths followed by am increase.," Intriguingly, a similar phenomenon was reported by \citet{p22}, who noted a decrease in the size of Betelgeuse at visible wavelengths followed by an increase."331 Figure 5 shows incasuremenuts of the visual magnitude of Deteleeuse during between 2006 and 2010. as well as the ISI measurements of the total 11.15;1u fux density (also listed in Table 1).," Figure 5 shows measurements of the visual magnitude of Betelgeuse during between 2006 and 2010, as well as the ISI measurements of the total $\mu$ m flux density (also listed in Table 1)."332 The timespaus of the ISI observing epochs are also plotted., The timespans of the ISI observing epochs are also plotted.333= The visual nagnitude measurements were obtained from the online of the Ainerican Association of Variable Star Observers (AAVSO)., The visual magnitude measurements were obtained from the online of the American Association of Variable Star Observers (AAVSO).334 The data. collected by a uultitude of volunteer observers. were averaged over 30-day timespaus: cach timespan with less than 10 measurements was discarded.," The data, collected by a multitude of volunteer observers, were averaged over 30-day timespans; each timespan with less than 10 measurements was discarded."335 The visual variability. of Deteleeuse over our observing epochs was approsimatcly A9 imagnitudes., The visual variability of Betelgeuse over our observing epochs was approximately 0.9 magnitudes.336 The visual intensity of Betclecuse is iot likely to represent that of the plotosplere because he appareut stellar diameter at visible wavelengths is ereater than that at ucar-IR wavelengths (Youngctal.2000).., The visual intensity of Betelgeuse is not likely to represent that of the photosphere because the apparent stellar diameter at visible wavelengths is greater than that at near-IR wavelengths \citep{ybb+00}. .337 Also. using contemmporancous interferometric observations of Detelgeuse at different wavelcuetlis. Youngetal.(2000). found that hotspots evident in the visible were not present in the πο.," Also, using contemporaneous interferometric observations of Betelgeuse at different wavelengths, \citet{ybb+00} found that hotspots evident in the visible were not present in the near-IR."338 Observations of Deteleeuse at visible wavelengths could represent reeious within the laver observed at müud-IR wavelengths., Observations of Betelgeuse at visible wavelengths could represent regions within the layer observed at mid-IR wavelengths.339 It is interesting that the mid-IR flux density of Betclecuse. as well as the effective temperatures plotted in Figure 3. and the visual maguitude appear somewhat correlated. particularly iu their increase duriug the 2009 and 2010 epochs.," It is interesting that the mid-IR flux density of Betelgeuse, as well as the effective temperatures plotted in Figure 3, and the visual magnitude appear somewhat correlated, particularly in their increase during the 2009 and 2010 epochs."340 Previous authors (sissotal.2006)— have concluded that the visual variability of Detelgeuse is probably indicative of quasi-periodic pulsations. aud is too great to be explained by variations in the hotspot distribution.," Previous authors \citep{ksb06} have concluded that the visual variability of Betelgeuse is probably indicative of quasi-periodic pulsations, and is too great to be explained by variations in the hotspot distribution."341 The laver of material surrounding Detelgeuse is a candidate location for the onset of dust formation., The layer of material surrounding Betelgeuse is a candidate location for the onset of dust formation.342 A qmuuber of authors have identified the preseuce of aluniua dust directly above the plotosphere (Verhoclstetal.2006:Perrin2007:Verhoelst 2009).," A number of authors have identified the presence of alumina dust directly above the photosphere \citep{vdv+06,pvr+07,vvh+09}."343. The derived phlivsical parameters of the laver. such as the temperatures aud livdrogen mass deusities are suitable for the formation of amorphous alumina (Woitke2006:Dirksetal. 2008).," The derived physical parameters of the layer, such as the temperatures and hydrogen mass densities, are suitable for the formation of amorphous alumina \citep{w06,dss08}."344. While some aspects of the mocelect variability of the laver mielt be due to variations in the photosphere. measurements of changes in the appareut nud-IR appearance of Detelgeuse must be largely caused bv variations in the laver.," While some aspects of the modeled variability of the layer might be due to variations in the photosphere, measurements of changes in the apparent mid-IR appearance of Betelgeuse must be largely caused by variations in the layer."345 Tf abluuiua contributes sienificautly to the mudIR continuum opacity. these variations would represent variations in the dust couteut of the laver.," If alumina contributes significantly to the mid-IR continuum opacity, these variations would represent variations in the dust content of the layer."346" Our estimates of changes iu the mass of the laver. on the order of 10.ΑΗ, (see Table Uj. might indicate evolution in the laver."," Our estimates of changes in the mass of the layer, on the order of $10^{-4}M_{\odot}$ (see Table 4), might indicate evolution in the layer."347 The point sources we observe in the laver of material surrounding Detelgeuse and their changes sugecst that the lawer dvuaimics are anisotropic., The point sources we observe in the layer of material surrounding Betelgeuse and their changes suggest that the layer dynamics are anisotropic.348 Asvinunetries observed in the circuustclar caviromment of Betclecuse are eenerally luked to the preseuce of giant convection cells ou the stellar surface., Asymmetries observed in the circumstellar environment of Betelgeuse are generally linked to the presence of giant convection cells on the stellar surface.349 Such couvection cells are hought to shape the circumstellar cuviromment of Deteleeuse by clevating cool photospheric material (Linetal.1998) and driving large-scale chromospleric notions (Calliland&Dupree1996)., Such convection cells are thought to shape the circumstellar environment of Betelgeuse by elevating cool photospheric material \citep{lcw+98} and driving large-scale chromospheric motions \citep{gd96}.350. Our results indicate hat elant convection cells have a significant role in shaping the Betelecuse laver., Our results indicate that giant convection cells have a significant role in shaping the Betelgeuse layer.351 This i89 because the nechanisin that clevates the laver material above the shotosphere is clearly anisotropic., This is because the mechanism that elevates the layer material above the photosphere is clearly anisotropic.352 The laree mteusities of the observed point-source componcuts imply the action of laree-scale photospheric features. and their variability between observingepochs demonstrates thetransient nature of the cause of the point sources.," The large intensities of the observed point-source components imply the action of large-scale photospheric features, and their variability between observingepochs demonstrates thetransient nature of the cause of the point sources."353for non-saturated thermal conduction in which &(D7)=&oT7. where ky~9x10.Tergemtstyμε1 is the Spitzer conduction coellicient (Spitzer1962).,"for non-saturated thermal conduction in which $\kappa(T) =k_0 T^{5/2}$, where $k_0 \sim 9\times 10^{-7}354\rm erg\,cm^{-1}\,\!s^{-1}\,\!K^{-7/2}$ is the Spitzer conduction coefficient \citep{Spitzer62}."355. For saturated thermal conduction (qxpc?) uo constraint like Eq. (19)), For saturated thermal conduction $q \propto \rho c_s^3$ ) no constraint like Eq. \ref{eq:cond}) )356 is required because it does not require an extra coellicient with a non-vanishiug dimension., is required because it does not require an extra coefficient with a non-vanishing dimension.357 The constraint [rom a radiative cooling term μηACT) in the same equation depends ou the form of emissivity ΑΓ)., The constraint from a radiative cooling term $-n_{_H} n_e \Lambda(T)$ in the same equation depends on the form of emissivity $\Lambda(T)$.358" For optically thin primordial gas of temperature larger than 5-x2105irIN. for"" example. the emissivity.⋅⋅ cai be approximated⋅ as A(T)∣=ΑΓΙE! where Ay~-10MI7""ergemPsGΕν> τας the constraint.η becomes Iu general the cooling rate A(T) does uot have such a simple power law form. so the scaling relation is when combiued with Eq. (18))."," For optically thin primordial gas of temperature larger than $5\times 10^6 \rm\,K$, for example, the emissivity can be approximated as $\Lambda(T) = \Lambda_0 T^{1/2}$ where $\Lambda_0\sim 10^{-27}\, \rm erg\, cm^6\, s^{-1}\, K^{-1/2}$ and the constraint becomes In general the cooling rate $\Lambda(T)$ does not have such a simple power law form, so the scaling relation is when combined with Eq. \ref{eq:iT}) ),"359 which gives the unique scaling relation adopted by Sgro(1972).., which gives the unique scaling relation adopted by \citet{Sgro72}. .360" This scaling relation also makesEnnE an invariant (Le. 5j+2/4,= 0) as used in (1999)."," This scaling relation also makes $E_{sn} n_{0}^2$ an invariant (i.e., $i_E+2i_\rho=0$ ) as used in \cite{Shelton99}."361 Additional physical constraints other than those from the governing equations may need to be placed on the scalability., Additional physical constraints other than those from the governing equations may need to be placed on the scalability.362" For example. the scaling requires ¢p=O0 and/or 7,=0pal between solutions with an identical explosion energy and/or ambient density."," For example, the scaling requires $i_E$ =0 and/or $i_\rho$ =0 between solutions with an identical explosion energy and/or ambient density."363 Note that we have three degrees of freedom for all the power iudices. if the number of the constraints is less than three (i.e... at least oue iudex is [ree to change). the solution is then scalable: otherwise tle solution pertains only to a particular problem.," Note that we have three degrees of freedom for all the power indices, if the number of the constraints is less than three (i.e., at least one index is free to change), the solution is then scalable; otherwise the solution pertains only to a particular problem."364 Lhuplicit constraiuts on the scaling relation may be imposed by initial conditious as well., Implicit constraints on the scaling relation may be imposed by initial conditions as well.365 Specilically. when we scale oue solution [pgΣΕ Tu(ru.lu). ..] to another [pytrg.fy). Ρf2). ...]. the correspondiug initial condition needs to be scalediu the same way.," Specifically, when we scale one solution $\rho_a(r_a,t_a)$, $T_a(r_a,t_a)$, ...] to another $\rho_b(r_b,t_b)$, $T_b(r_b,t_b)$, ...], the corresponding initial condition needs to be scaled in the same way."366" For example. a particular scaling relation cau be determined by specilviug /3;. 75. and 7j. which in turn determines 7,. /, auc other indices via Eqs. (13))-(18))."," For example, a particular scaling relation can be determined by specifying $i_M$, $i_L$, and $i_t$, which in turn determines $i_v$, $i_\rho$ and other indices via Eqs. \ref{eq:ivb}) \ref{eq:iT}) )."367 This scaling relation demauds that the correspoudiug initial concditious should be related by auc other quautities [or [t is such demauds on the initial condition that often make one problem be unique from others (limiting the scalability of their solutions). even if all have the same goveruiug equations aud ebaracteristie quautities such as total energy aud mass (see 833.5 for further discussion).," This scaling relation demands that the corresponding initial conditions should be related by and other quantities for It is such demands on the initial condition that often make one problem be unique from others (limiting the scalability of their solutions), even if all have the same governing equations and characteristic quantities such as total energy and mass (see 3.5 for further discussion)."368 Iu the following we assume that the scalable solutious do have the required initial couditious unless being explicitly expressedotherwise., In the following we assume that the scalable solutions do have the required initial conditions unless being explicitly expressedotherwise.369aand temperature 26.5Κον as deteriunced incdependcutly from X-ray data (see Table 3)).,and temperature $\geq6.5~\mathrm{keV}$ as determined independently from X-ray data (see Table \ref{tab:xray}) ).370" The most distaut cluster detected by the jis aat 2=1.39. which has a total mass within rsyy of Ms)=LESOOsIOAZ, (Rosatietal.2009)."," The most distant cluster detected by the is at $z=1.39$, which has a total mass within $r_{500}$ of $M_{500}=4.4\pm1.0\times10^{14}$ \citep{rosati2009}."371.. Weak lensing observatious by Jeeetal.(2009)— indicate a total mass within 1 Mpe of 8.32:τιτν10HAZ..., Weak lensing observations by \cite{jee2009} indicate a total mass within 1 Mpc of $8.3\pm1.7\times10^{14}$.372 Similar lnasses are found for (May)=JOS30265.2!nESOHAL... Maughanetal. 2006)) and (Magy95.6d1.0104“theLamer etal. 2008)).," Similar masses are found for $M_{500}=5.2^{+1.0}_{-0.8}\times10^{14}$, \citealt{maughan2006}) ) and $M_{500}=5.6\pm1.0\times10^{14}$, \citealt{lamer2008}) )."373 The lack of SZ detectious« for other clusters strongly indicates they are lower ass svstenus: in particular. those S discovered in the infrared have Mí<5«OPAL (see Table 1)) aud their ull detection prevents investigation of optical-SZ scalings.," The lack of SZ detections for the other clusters strongly indicates they are lower mass systems; in particular, those originally discovered in the infrared have $M_{gas} < 5\times10^{12}$ (see Table \ref{tab:ubertable}) ) and their null detection prevents investigation of optical-SZ scalings."374 As a first step in investigating the SZmass scaling relationship at high redshift. we plot in Figure 2. the integrated. Compton Y values against the N-rav eas niass determinations. asuniue scltsimilar evolution.," As a first step in investigating the SZ–mass scaling relationship at high redshift, we plot in Figure \ref{fig:scaling} the integrated Compton $Y$ values against the X-ray gas mass determinations, assuming self-similar evolution."375 The clusters plotted include only those with robust N-rav eas nass constraints (sec Table 3))., The clusters plotted include only those with robust X-ray gas mass constraints (see Table \ref{tab:xray}) ).376 For comparison witli low redshift clusters. the solid lines in Figure 2 show the Y sscaling relationship prescuted in BOs and its lo unecrtaintics.," For comparison with low redshift clusters, the solid lines in Figure \ref{fig:scaling} show the $Y$ scaling relationship presented in B08 and its $1\sigma$ uncertainties."377 The figure illustrates that there is good agreement between the scaling of the ligh-z clusters aud that found in the low redshift sample., The figure illustrates that there is good agreement between the scaling of the high-z clusters and that found in the low redshift sample.378 Moasurenmeuts of amore clusters are needed. however. to make a more definitive comparison.," Measurements of more clusters are needed, however, to make a more definitive comparison."379 Oueoine SZ surveys from iustruinents such ACT (Fowlerctal.2007) and SPT (Carlstrvometal.2009) will provide much lareer siuuples of SZ-sclected clusters at high redshift (c.¢..Vau-derludeetal.2010).," Ongoing SZ surveys from instruments such as ACT \citep{fowler2007} and SPT \citep{carlstrom2009}380 will provide much larger samples of SZ-selected clusters at high redshift \citep[e.g.,][]{vanderlinde2010}."381 The operation of the SZA is supported by NSF through eraut AST-0601982 and AST-OS381587., The operation of the SZA is supported by NSF through grant AST-0604982 and AST-0838187.382 Partial support is also provided from eraut PITY-0111122 at a University of Chicago. aud bv NSF erauts AST-05075CARMA and AST-05-07161 to Columbia University.," Partial support is also provided from grant PHY-0114422 at the University of Chicago, and by NSF grants AST-0507545 and AST-05-07161 to Columbia University."383" operations are supported by the NSF under a cooperative agreement. and by the ΑΠΛΑ partner universities,"," CARMA operations are supported by the NSF under a cooperative agreement, and by the CARMA partner universities."384" SM acknowledges support from an NSF Astronomy, and Astrophysics Fellowship: CG. SM. aud AIS from NSF Caraduate Research Fellowships: DPAI frou NASA IIubble Fellowship eraut ITE-51259.01."," SM acknowledges support from an NSF Astronomy and Astrophysics Fellowship; CG, SM, and MS from NSF Graduate Research Fellowships; DPM from NASA Hubble Fellowship grant HF-51259.01."385stellar clusters. but rather that they were most likely ejected from these relatively recently.,"stellar clusters, but rather that they were most likely ejected from these relatively recently."386 Other luminous sources have been claimed to be compatible with the position of a young cluster. but none have a color consistent with stellar ages below [01 years te.g.2)..," Other luminous sources have been claimed to be compatible with the position of a young cluster, but none have a color consistent with stellar ages below $10^8$ years \citep[e.g.][]{Ptak2006}."387 In general ULXs are predominantly found in regions with high star-formation rates €?) and low metallicities €2?2)..," In general ULXs are predominantly found in regions with high star-formation rates \citep{Irwin2004} and low metallicities \citep{Pakull2002,Zampieri2009,Mapelli2010}."388 Observations of individual ULXs have found associations also with relatively poor stellar clusters (2).. and in some cases with large super-bubbles in the ISM (2)..," Observations of individual ULXs have found associations also with relatively poor stellar clusters \citep{Grise2008}, and in some cases with large super-bubbles in the ISM \citep{Pakull2003}."389 This clearly shows that ULXs are related to young stars. with ages of tens to a few hundred However. a number of ULXs have been found to reside in globular clusters (2?)..," This clearly shows that ULXs are related to young stars, with ages of tens to a few hundred However, a number of ULXs have been found to reside in globular clusters \citep{Maccarone2007,Maccarone2011}."390 These are likely BHs created during the early evolution of the globular clusters., These are likely BHs created during the early evolution of the globular clusters.391 The only other ULX that has been found to be spatially coincident with a massive young cluster is M82 X-l. which is claimed to be associated with the stellar cluster MGG-I1I.," The only other ULX that has been found to be spatially coincident with a massive young cluster is M82 X-1, which is claimed to be associated with the stellar cluster MGG-11."392 This was based on an analysis with an astrometric accuracy of ~| aresee (2)., This was based on an analysis with an astrometric accuracy of $\sim1$ arcsec \citep{Portegies2004}.393 Motivated by the results presented above. we revisit the astrometry of this source.," Motivated by the results presented above, we revisit the astrometry of this source."394 The region is covered well both by andHST., The region is covered well both by and.395 We select the two deepest archivalACLS observations of M82 X-1 COBSID 10542 and OBSID 10543)., We select the two deepest archival observations of M82 X-1 (OBSID 10542 and OBSID 10543).396 With ~20 Ks of exposure in each. they are deep enough to obtain a precise astrometric solution.," With $\sim120$ ks of exposure in each, they are deep enough to obtain a precise astrometric solution."397 We have compared them to the existingAST images in the vicinity of M82 X-I. and we find no secure matches that can be used for a direct registration of the images.," We have compared them to the existing images in the vicinity of M82 X-1, and we find no secure matches that can be used for a direct registration of the images."398 Instead we register the X-ray images to (SDSS). with 6 (5) matching sources in OBSID 10542 (10543).," Instead we register the X-ray images to (SDSS), with 6 (5) matching sources in OBSID 10542 (10543)."399 The results from the two observations agree within 0.05 arcsec. and we use the position from OBSID 10542 in the following.," The results from the two observations agree within 0.05 arcsec, and we use the position from OBSID 10542 in the following."400 We choose two observation sets that both have clear SDSS matches and where MGOG-11 is clearly observed., We choose two observation sets that both have clear SDSS matches and where MGG-11 is clearly observed.401 Archival NICMOS FI60W images obtained in April 1998 were used for the original matching (22). and three matches are found in SDSS.," Archival NICMOS F160W images obtained in April 1998 were used for the original matching \citep{McCrady2003,Portegies2004}, and three matches are found in SDSS."402 As an alternative we used archival WFC3 FlLOW images obtained November 2009., As an alternative we used archival WFC3 F110W images obtained November 2009.403 For these we find four SDSS matches (of which only two are the same as in the NICMOS images)., For these we find four SDSS matches (of which only two are the same as in the NICMOS images).404 Again the positions agree within 0.05 arcsec., Again the positions agree within 0.05 arcsec.405 Based on these. we translate the position of M82 X-I into theAST images with a precision x0.2 aresec.," Based on these, we translate the position of M82 X-1 into the images with a precision $\lesssim0.2$ arcsec."406 The results are shown in figure |.., The results are shown in figure \ref{fig:M82}.407 We find that MGG-11 is located ~0.65 aresec south of M82 X-I and that the positions are inconsistent at the 3 sigma level., We find that MGG-11 is located $\sim0.65$ arcsec south of M82 X-1 and that the positions are inconsistent at the 3 sigma level.408 NGC 7479 is located at a distance of 33 Mpe (We adopt a distance modulus of 32.65. assuming a radial velocity corrected for infall onto Virgo of 2443 km ! and a Hubble constant of 72 km | |).," NGC 7479 is located at a distance of 33 Mpc (We adopt a distance modulus of 32.65, assuming a radial velocity corrected for infall onto Virgo of 2443 km $^{-1}$ and a Hubble constant of 72 km $^{-1}$ $^{-1}$ )."409 It is a barred spiral galaxy (2). and contains a number of superclusters (e.g.2?) seen inAST images.," It is a barred spiral galaxy \citep{Sandage1987} and contains a number of superclusters \citep[e.g.][]{Zurita2001}410 seen in images."411 NGC 7479 has been observed two times with and two times withNewton., NGC 7479 has been observed two times with and two times with.412 It hosts several ULXs and we find that one of them is spatially coincident with a supercluster., It hosts several ULXs and we find that one of them is spatially coincident with a supercluster.413 The source is currently not found in theCatalog. and we label it CKOU J230453.0--121959 according to the naming based on the position of the source.," The source is currently not found in the, and we label it CXOU J230453.0+121959 according to the naming based on the position of the source."414 The absolute astrometry of both the and theAST images are uncertain at the ~| aresee level., The absolute astrometry of both the and the images are uncertain at the $\sim1$ arcsec level.415 We have therefore searched or sources that are both observed in X-rays and in the optical. and have a reliable position in both.," We have therefore searched for sources that are both observed in X-rays and in the optical, and have a reliable position in both."416 One such source exists. a bright foreground star.," One such source exists, a bright foreground star."417 While this is clearly not an ideal case. the distance of the reference source to ULX CXOU J230453.04+121959 is relatively small (~23 aresec). and it is therefore possible to use it o precisely match the X-ray images to the757 images.," While this is clearly not an ideal case, the distance of the reference source to ULX CXOU J230453.0+121959 is relatively small $\sim23$ arcsec), and it is therefore possible to use it to precisely match the X-ray images to the images."418 We use theFS/4W image jb4u53020 for the matching., We use the image jb4u53020 for the matching.419 As both heAST and the images are well-calibrated. we assume hat there is no distortions between the two images. and the rotation of theHST image was corrected using2MASS counterparts.," As both the and the images are well-calibrated, we assume that there is no distortions between the two images, and the rotation of the image was corrected using counterparts."420 The yositions of the Chandra images were then shifted to match the reference source in theHS7 image., The positions of the Chandra images were then shifted to match the reference source in the image.421 In figure 2 we show the position of the X-ray source on theAST image., In figure \ref{fig:position} we show the position of the X-ray source on the image.422 The thick black circle indicate the position found from OBSID 11230 (having the best statistics). and and the thin red circle indicates the position found from OBSID 10120.," The thick black circle indicate the position found from OBSID 11230 (having the best statistics), and and the thin red circle indicates the position found from OBSID 10120."423 The size of the circles indicate the statistical error on the position of the X-ray source and the boresight correction (~0.3 arcsec)., The size of the circles indicate the statistical error on the position of the X-ray source and the boresight correction $\sim 0.3$ arcsec).424 The positions of the stellar cluster and the ULX are consistent within the | sigma confidence limits., The positions of the stellar cluster and the ULX are consistent within the 1 sigma confidence limits.425 The ULX is therefore most likely related to the cluster. even if it could likely be located outside of it (similar to the other three ULXs discussed above).," The ULX is therefore most likely related to the cluster, even if it could likely be located outside of it (similar to the other three ULXs discussed above)."426 An older set ofΜΕΡΟΣ observations cover the same region., An older set of observations cover the same region.427 Comparison with these shows that the foreground reference star has a small proper motion ~0.01 arcsec per year., Comparison with these shows that the foreground reference star has a small proper motion $\sim0.01$ arcsec per year.428 The images used for the matching are taken «1 year after the X- observations. and the error due to this is therefore negligible.," The images used for the matching are taken $\sim$ 1 year after the X-ray observations, and the error due to this is therefore negligible."429 We have veritied the position using other optical intermediate images/catalogues. covering larger areas.," We have verified the position using other optical intermediate images/catalogues, covering larger areas."430 These have therefore more matching sources. but are less precise.," These have therefore more matching sources, but are less precise."431 The maximum number of matching sources found was 4 comparing the [1230 X-ray, The maximum number of matching sources found was 4 comparing the 11230 X-ray432Low Lass Nταν binaries (LAINBs) we interacting systems composed of a compact object. neutron star (NS) or black hole. which is accreting from a late-tvpe companion star. with mass generally <1 AL. and still ou the main sequence (or possibly sliebitlv evolved).,"Low mass X–ray binaries (LMXBs) are interacting systems composed of a compact object, neutron star (NS) or black hole, which is accreting from a late-type companion star, with mass generally $\la$ 1 $M_\odot$ and still on the main sequence (or possibly slightly evolved)."433 There exists however a απο of cases in which the donor star is actually a red giant: these. by analogy with the sviibiotie binaries which are formed by an evolved late-type star and a white dwarf. are dubbed syaubiotic Xorav binaries (SvXDs: sce c.g. Masetti et al.," There exists however a handful of cases in which the donor star is actually a red giant: these, by analogy with the symbiotic binaries which are formed by an evolved late-type star and a white dwarf, are dubbed symbiotic X–ray binaries (SyXBs; see e.g. Masetti et al."434 20062)., 2006a).435" Observationallv. these svstems are characterized bv appreciable. X-rav chussion⋅⋅ (107ao au10""_ ος 1. SCC Alasetti et al."," Observationally, these systems are characterized by appreciable X–ray emission $\sim$ $^{32}$ $^{34}$ erg $^{-1}$; see Masetti et al."436 2007 and references therein) positionallv associated with a red giant star which spectroscopically does not show uv abuormal features. with the possible exception of a continui excess in the blue and ultraviolet ranges.," 2007 and references therein) positionally associated with a red giant star which spectroscopically does not show any abnormal features, with the possible exception of a continuum excess in the blue and ultraviolet ranges."437 A notable outlier is the source CX L1£L. which clits up to —107 erg + and shows several emission lines iu the optical spectrum of the red eiut. companion (Chakrabarty Roche 1997: Απιια Zwitter 2002).," A notable outlier is the source GX 1+4, which emits up to $\sim$ $^{37}$ erg $^{-1}$ and shows several emission lines in the optical spectrum of the red giant companion (Chakrabarty Roche 1997; Munari Zwitter 2002)."438 This is nost likely ue to the fact that. in this latter case. accretion onto the compact object takes place via Roche lobe overflow rather than via a stellar wind (but see Iliukle et al.," This is most likely due to the fact that, in this latter case, accretion onto the compact object takes place via Roche lobe overflow rather than via a stellar wind (but see Hinkle et al."439 2006 for a different scenario)., 2006 for a different scenario).440 This allows the creation of a disk arouud the aceretor and makes the mass transfer phenomenon more efficieut in terms of production and reprocessing of Xrav enussion., This allows the creation of a disk around the accretor and makes the mass transfer phenomenon more efficient in terms of production and reprocessing of X–ray emission.441 Moreover. X.ray pulsations. with periods ranging frou lnudreds up to tens of thousands of seconds. were detected from). these systems: this indicates that the accreting conrpact object is a slowly rotating neutron star. the most extreme case beiug 1U 19511319 μμ~ 18100 s: Corbet et al.," Moreover, X–ray pulsations, with periods ranging from hundreds up to tens of thousands of seconds, were detected from these systems: this indicates that the accreting compact object is a slowly rotating neutron star, the most extreme case being 4U 1954+319 $P_{\rm spin} \sim$ 18400 s; Corbet et al."442 2008)., 2008).443 All the above characteristics make these svsteis rather unusual aud. iudeed. they are quite rare when compared o the uuuber of known LAINBs (about 190. according o Liu et al.," All the above characteristics make these systems rather unusual and, indeed, they are quite rare when compared to the number of known LMXBs (about 190, according to Liu et al."444 2007): up to now. ouly 6 svstenis are firmly included im this subclass of LAINBs (see Masetti ct al.," 2007): up to now, only 6 systems are firmly included in this subclass of LMXBs (see Masetti et al."445 2007. Nespoli et al.," 2007, Nespoli et al."446 2010 aud references theorem) hrough coincidence between optical aud X.rav positions and subsequent confirmation via optical or near-infrared (NIB) spectroscopy., 2010 and references therein) through coincidence between optical and X–ray positions and subsequent confirmation via optical or near-infrared (NIR) spectroscopy.447 Three more cases however exist. jiviue cither the confirmation still peudiug due to the lack of optical or NIR spectroscopy (ARNS 273932: Nucita et al.," Three more cases however exist, having either the confirmation still pending due to the lack of optical or NIR spectroscopy (1RXS $-$ 273932: Nucita et al."448 2007: 2NMM 290337: Farrell et al., 2007; 2XMM $-$ 290337: Farrell et al.449 2010). or with a still debated nature TCR 1613: see Nespoli et al.," 2010), or with a still debated nature (IGR $-$ 4643: see Nespoli et al."450 2010. but also Thompson et al.," 2010, but also Thompson et al."451 2006 aud Corbet et al., 2006 and Corbet et al.452 2010 or a different source classification as a supergiaut hielh-muass Xrav ary)., 2010 for a different source classification as a supergiant high-mass X–ray binary).453 Therefore. given the sinall πο of known SvXBs. each new possible member of this subclass of LAINBs should be the object of an in-depth imultivaveleusth study to expand the sample.," Therefore, given the small number of known SyXBs, each new possible member of this subclass of LMXBs should be the object of an in-depth multiwavelength study to expand the sample."454" We thus focused our attention on star CGCS 5926, which was classified by Machara Sovauo (1987) ax a pP- lL8 mag carbon star (thus a late-type eiant) in the Cassiopeia region: according to the 2MLASS catalog (Skrutskie et al."," We thus focused our attention on star CGCS 5926, which was classified by Maehara Soyano (1987) as a $V$ = 14.8 mag carbon star (thus a late-type giant) in the Cassiopeia region; according to the 2MASS catalog (Skrutskie et al."455" 2006). this object has NTR iaenitucdes J = S821+0.023. IT = LOOEO.02 and A, = 12+0.02|."," 2006), this object has NIR magnitudes $J$ = $\pm$ 0.023, $H$ = $\pm$ 0.042 and $K_{\rm s}$ = $\pm$ 0.024."456 Qur interest iu this star was drawn by the fact that (see Fie., Our interest in this star was drawn by the fact that (see Fig.457" 1} if is positionally inside he 20"" error circle of the soft Xrav source IRNS J231515.9|625256 helougine to theROSAT Al-Skv Survey Faint Source Catalog (Voecs et al.", 1) it is positionally inside the $''$ error circle of the soft X–ray source 1RXS J234545.9+625256 belonging to the All-Sky Survey Faint Source Catalog (Voges et al.458 2000). which makes COCS 5926 à SvXND cauclidate due to its optical spectral classification and its possible Xray endssion.," 2000), which makes CGCS 5926 a SyXB candidate due to its optical spectral classification and its possible X–ray emission."459 However. the lack of further information at optical. Xorav and other waveleusths does not mnake a secure case for melusionu of this star in the SvXD subclass.," However, the lack of further information at optical, X–ray and other wavelengths does not make a secure case for inclusion of this star in the SyXB subclass."460 It is therefore worthy of further analysis * imenus of a specific spectrophotometric campaign in the optical range. as well as of a pointed observation with the use of au X satellite affording localizatious with a wrecision better than a few areseconds.," It is therefore worthy of further analysis by means of a specific spectrophotometric campaign in the optical range, as well as of a pointed observation with the use of an X--ray satellite affording localizations with a precision better than a few arcseconds."461BD136∙⋅ 1867∖⋅↼ was mistakenly: observed when iutending. to measure the webyd standard star BD136 L868.,BD+36 4867 was mistakenly observed when intending to measure the $uvby\beta$ standard star BD+36 4868.462" This error cae from confusion of the coordinates of the two stars in the SIMBAD data base at the time of the meastwements,", This error came from confusion of the coordinates of the two stars in the SIMBAD data base at the time of the measurements.463 The Strémmeren indices of BD136 L867 axe listed for completeness in Table 6. indicatingc» a iid C-type star.," The Strömmgren indices of BD+36 4867 are listed for completeness in Table 6, indicating a mid G-type star."464" The pupublished V. MEREmagnitudes of NCCUt 1893m 196 vary,UU between 12.30 aud 12.79.", The published $V$ magnitudes of NGC 1893 196 vary between 12.30 and 12.79.465 This unusually wide range raises the suspicion of stellar ↸↸↸variability., This unusually wide range raises the suspicion of stellar variability.466 DcTable [lists V—12.637 i P=∡⋯≼↧↗−⋅∙↓↸≺↧↸↥⋯⋯↕∐≺↕↸∡⊓↴∖↴∖↥∪∐⊓↕⋅↖≺↥∪⊓↸∐2.411., Table 4 lists $V=12.637$ and $\beta=2.441$.467 The lattervalue Πιοισαος stronghyvdrogeu- line. CUSSION.∙∙ as demonstrated spectroscopically∙ (Marco et al. 2001)).," The latter value indicates strong hydrogen-line emission, as demonstrated spectroscopically (Marco et al. \cite{MBN01}) )."468 The ranges m which the trausformation cquatious are valid are examined in 1., The ranges in which the transformation equations are valid are examined in 1.469 It shows the distributions of the standard aud target star measurements with respect to the different «0559.7 colour indices aud reddening., It shows the distributions of the standard and target star measurements with respect to the different $uvby\beta$ colour indices and reddening.470 The routines by Napiwotzki. Schounberner. Weuske (1993)) were used to derive the latter.," The routines by Napiwotzki, Schönnberner, Wenske \cite{NSW93}) ) were used to derive the latter."471 The (by) values of all but one target star (Boslund 2 13. a ναν red object) are contained within the ranec spanned by the standard stars.," The $(b-y)$ values of all but one target star (Roslund 2 13, a very red object) are contained within the range spanned by the standard stars."472 The same comment is true for the e4 parameter aud reddening L()—yg)., The same comment is true for the $c_1$ parameter and reddening $E(b-y)$.473 Sixteen 11043) of the targets have more positive iy values than any standard star., Sixteen ) of the targets have more positive $m_1$ values than any standard star.474 These are stars of later spectral types than AO which are not the prime interest of this work., These are stars of later spectral types than A0 which are not the prime interest of this work.475 As far as {1 is concerned. five stars with values below 2.55 were observed. includiug two (supposed) staudar aud three target stars.," As far as $H_\beta$ is concerned, five stars with values below 2.55 were observed, including two (supposed) standard and three target stars."476 Both standard stars were rejectec after deteriuning the transformation equations due to Hel residual deviations., Both standard stars were rejected after determining the transformation equations due to high residual deviations.477 It is suspected that all five of hese stars are Be stars., It is suspected that all five of these stars are Be stars.478 The hydrogen due emission of such stars is often variable (6.5... AleSwain. UWnaue. Cues 2009)) which explains the hieh residuals aac uakes the tabulated values unrelable.," The hydrogen line emission of such stars is often variable (e.g., McSwain, Huang, Gies \cite{MHG09}) ) which explains the high residuals and makes the tabulated values unreliable."479 They are listed for completeness ouly., They are listed for completeness only.480 Considering the distribution in £(boy). about two hinds of the stars with the simallest reddening are along heKepler targets: the satellite’s field of view deliberately excludes the ceutral ealactic plane.," Considering the distribution in $E(b-y)$, about two thirds of the stars with the smallest reddening are among the targets: the satellite's field of view deliberately excludes the central galactic plane."481 Two of the remaimine arects are 3 Cephei stars of rather high ealactic latitude. and the remainder are cool main sequence stars in fhe orcerouud of some of the target open clusters.," Two of the remaining targets are $\beta$ Cephei stars of rather high galactic latitude, and the remainder are cool main sequence stars in the foreground of some of the target open clusters."482 In Tables 1-6 the colour indices that are outside the range of those spanned by the standard stars are marked with colous aud should be used with caution., In Tables 4 - 6 the colour indices that are outside the range of those spanned by the standard stars are marked with colons and should be used with caution.483 Before2ofore inferringfemmine plivsicalxe parametersqvstare of: theEavoptuze targets. it1 aust. be made sure that the data are coiuuensurate with the αποκτά system.," Before inferring physical parameters of the targets, it must be made sure that the data are commensurate with the standard system."484" It is a subtle process to obtain accurate “tandard photometry of reddened carly-type stars, sec, 68e Crawford (1991)) for a disenssion."," It is a subtle process to obtain accurate standard photometry of reddened early-type stars, see, e.g., Crawford \cite{Cr99}) ) for a discussion."485 One test is fo compare published (€BY colours with (ub) values from Stróuunugreu indices (see Crawford 1991)) aud to compare the resultiug: relation: with: the one defined wi ostandard stars., One test is to compare published $(U-B)$ colours with $(u-b)$ values from Strömmgren indices (see Crawford \cite{Cr94}) ) and to compare the resulting relation with the one defined by standard stars.486 This is done in 22. using the results⋅ for target stars with⋅⋅ existing⇁⇁ UDV photometry.," This is done in 2, using the results for target stars with existing UBV photometry."487 ↽∏↕⋠∖∏ -D) values for the target stars were taken from the General Catalogne of Photometric Data (Meruilliod. Alexiuilliod. Tauck 1997)).," The $(U-B)$ values for the target stars were taken from the General Catalogue of Photometric Data (Mermilliod, Mermilliod, Hauck \cite{MMH97}) )."488 For easier visual inspection. the slope of the (UFDB) πμ μμ απμμ fit," For easier visual inspection, the slope of the $(U-B)$ $(u-b)$ relation was removed by a linear fit."489 heresidualsarceom parcd with typestars(C rawfordl975 \jand forbrightstarsearlierthan BSC ra," The residuals are compared with those of the standard values for reddened O-type stars (Crawford \cite{Cr75}) ) and for bright stars earlier than B5 (Crawford, Barnes, Golson \cite{CBG71}) ), which are on the average considerably less reddened than the O stars."490u," For better illustration, we only show a fit to the relations defined by the standard stars for comparison with the data of the target stars."491sky areas for point sources.,sky areas for point sources.492 As part of a Κον programme monitoring campaign on the SAIC and 47 Tuc. INPECGRAL observed the SAIC and Magellanic Bridge for approximately 90 ks per satellite revolution (73 davs) from 2008 November 1l to 2009 June 25 - see Table 1. for a detailed journal of all the observation dates and exposures.," As part of a key programme monitoring campaign on the SMC and 47 Tuc, INTEGRAL observed the SMC and Magellanic Bridge for approximately 90 ks per satellite revolution $\sim$ 3 days) from 2008 November 11 to 2009 June 25 - see Table \ref{tab:expo} for a detailed journal of all the observation dates and exposures."493 Individual pointings (science windows) were processet using the INPEGRAL Ollline Science Analysis v.7.0 (OSA. Coldwurm et al.," Individual pointings (science windows) were processed using the INTEGRAL Offline Science Analysis v.7.0 (OSA, Goldwurm et al."494 2003) and were mosaiced using the weight mean of the Hux in the 310 keV. (JEALN) and. 1535 keV (1119) energy ranges., 2003) and were mosaiced using the weighted mean of the flux in the 3–10 keV (JEM-X) and 15–35 keV (IBIS) energy ranges.495 Proprietary software was use to mosaic the observations [rom successive revolutions to improve the exposure and thereby the sensitivity to fain sources., Proprietary software was used to mosaic the observations from successive revolutions to improve the exposure and thereby the sensitivity to faint sources.496 Lighteurves in these energv bands were generate on science window ( 2000 s) and revolution time-scales., Lightcurves in these energy bands were generated on science window ( 2000 s) and revolution time-scales.497 The IBIS energy band. was chosen to maximise the detection significance of SAIC X-1. ancl hence other SAIC accreting X-ray pulsars. which have similar spectral shapes to SAIC X-1 in this energy range.," The IBIS energy band was chosen to maximise the detection significance of SMC X-1, and hence other SMC accreting X-ray pulsars, which have similar spectral shapes to SMC X-1 in this energy range."498 An IBIS mosaic of data [rom revolutions 752756 in the 1535 keV is shown in MeDride et al (2010)., An IBIS mosaic of data from revolutions 752–756 in the 15–35 keV is shown in McBride et al (2010).499 A list of all the definite source detections and when they occurred is presented in Table 2.., A list of all the definite source detections and when they occurred is presented in Table \ref{tab:sources}.500 As à neutron star accreting from a supergiant overfilling its ltoche lobe. SAIC N-1 is the only. persistent acercting X-rav pulsar in the SAIC.," As a neutron star accreting from a supergiant overfilling its Roche lobe, SMC X-1 is the only persistent accreting X-ray pulsar in the SMC."501 This transfer of angular momentunm serves to spin up the pulsar. and SMC X-1 has demonstrated consistent spin up over the last 40 vears.," This transfer of angular momentum serves to spin up the pulsar, and SMC X-1 has demonstrated consistent spin up over the last 40 years."502 Ht has a dd orbital period with eclipses lasting 1.12 dd (Wojdowskl et al., It has a d orbital period with eclipses lasting $1.12$ d (Wojdowski et al.503 1998) and also shows superorbital modulation at 60 cid. thought to be the result. of a precessing. warped accretion disk (Clarkson et al.," 1998) and also shows superorbital modulation at $\sim60$ d, thought to be the result of a precessing, warped accretion disk (Clarkson et al."504 2003)., 2003).505 The first set of IBIS observations cover almost a full superorbital evele. while the subsequent observations occur predominantly in the superorbital low state.," The first set of IBIS observations cover almost a full superorbital cycle, while the subsequent observations occur predominantly in the superorbital low state."506 See Fig., See Fig.507 1. for the whole lightcurve and Figure 2. for details of the binary eclipse., \ref{Fig:smcx1_revlc} for the whole lightcurve and Figure \ref{Fig:smcx1_ecl} for details of the binary eclipse.508 Folding data from revolutions 745 to 749 on the orbital ephemeris from. Wojdowski ct al. (, Folding data from revolutions 745 to 749 on the orbital ephemeris from Wojdowski et al. (5091998). resulted in an orbital profile cluring superorbital high state. (,1998) resulted in an orbital profile during superorbital high state. (510Sec Figure 2. top panel).,See Figure \ref{Fig:smcx1_ecl} top panel).511 For comparison. an orbital profile during superorbital low state was generated using data from revolutions 751 to 756 and S12 to SIS.," For comparison, an orbital profile during superorbital low state was generated using data from revolutions 751 to 756 and 812 to 818."512 There are significant differences between the eclipse profiles during these two superorbital phases., There are significant differences between the eclipse profiles during these two superorbital phases.513 Eclipse ingress ancl egress are steep. almost square. during superorbital high state. while they are much more gradual (almost 0.1 phase longer) during superorbital low state.," Eclipse ingress and egress are steep, almost square, during superorbital high state, while they are much more gradual (almost 0.1 phase longer) during superorbital low state."514 These results are in agreement with the orbital profile as a function of superorbital phase oesented in “Trowbridge. Nowak Wilms (2007).," These results are in agreement with the orbital profile as a function of superorbital phase presented in Trowbridge, Nowak Wilms (2007)."515 These authors use softer. N-rav. data kkeV) to show that he eclipse is wide and shallow during superorbital low state while it is narrow and deep during superorbital high state., These authors use softer X-ray data keV) to show that the eclipse is wide and shallow during superorbital low state while it is narrow and deep during superorbital high state.516 From these data there is no evidence that 1e eclipse in jud X-rays kkeV) is shorter than in soft N-ravs kkeV. Trowbridge. Nowak Wilms 2007). which may be expected due to the increased transpareney of the supergiant xhotosphere to hard. X-ray. photons.," From these data there is no evidence that the eclipse in hard X-rays keV) is shorter than in soft X-rays keV, Trowbridge, Nowak Wilms 2007), which may be expected due to the increased transparency of the supergiant photosphere to hard X-ray photons."517 Fhere mas. however. be some evidence for asvmmetry of ingress ancl ceress curing he high superorbital state eclipse.," There may, however, be some evidence for asymmetry of ingress and egress during the high superorbital state eclipse."518 The eclipse profile in Figure 2 shows a similar shape to kkeV. eclipse profile in MeDride et al. (, The eclipse profile in Figure \ref{Fig:smcx1_ecl} shows a similar shape to keV eclipse profile in McBride et al. (5192007).,2007).520 An IBIS observation at NJD 54797. during. the superorbital bright phase. was used to determine the current spin period. of the pulsar. in SAIC δα.," An IBIS observation at MJD 54797, during the superorbital bright phase, was used to determine the current spin period of the pulsar in SMC X-1."521 This was determined using an epoch folding technique to be 0.702010+ 0.000008 ancl is plotted above the arrow in Fie 3..," This was determined using an epoch folding technique to be $0.702010\pm0.000008 $ s, and is plotted above the arrow in Fig \ref{fig:smc2}."522 A straight line ss.model does not fit the period evolution very well. but. gives à. good. idea. of the general spin. up of the system over its lifetime. which can be estimated. as ~ιδ αι...," A straight line model does not fit the period evolution very well, but gives a good idea of the general spin up of the system over its lifetime, which can be estimated as $\sim-3.8\times10^{-4}$ s/yr."523 Α source καν detected. ino INTEGRAL at ᾱ- position coincident with SXP756 (Coo Ecdec. 2004) within an uncertainty of ~1 areminute over (wo satellite orbits (ALJD54941 - 54941).," A source was detected in INTEGRAL at a position coincident with SXP756 (Coe Edge, 2004) within an uncertainty of $\sim$ 1 arcminute over two satellite orbits (MJD54941 - 54947)."524 Follow-up RNPE observations (ALJD54943) revealed evidence for weak pulsations around τοθ-εῦς. the relatively large. uncertainty rellecting the fact that the observation extended over I3ks and therefore does," Follow-up RXTE observations (MJD54943) revealed evidence for weak pulsations around $\pm$ 5s, the relatively large uncertainty reflecting the fact that the observation extended over 13ks and therefore does"525of the virial ratios of the subclusters from all snapshots. as well as hose from the last snapshot. which are shown as the shaded region.,"of the virial ratios of the subclusters from all snapshots, as well as those from the last snapshot, which are shown as the shaded region."526 Only of the subclusters are unbound when excluding the gas. while remains subvirial.," Only of the subclusters are unbound when excluding the gas, while remains subvirial."527 When considering the subclusters Tom all snapshots. a Gaussian fit to the distribution of virial ratios gives a mean of Qi=0.59 and a standard deviation of 0.16.," When considering the subclusters from all snapshots, a Gaussian fit to the distribution of virial ratios gives a mean of $Q_{\rm vir}=0.59$ and a standard deviation of $\sigma_Q=0.16$ ."528 As in Fig. 4..," As in Fig. \ref{fig:virial},"529" the gradual decrease of the mean virial ratio owards Q,;;=0.5 is also visible in Fig. 6..", the gradual decrease of the mean virial ratio towards $Q_{\rm vir}=0.5$ is also visible in Fig. \ref{fig:virial2}.530 A comparison of the wo histograms shows that the subclusters in the last snapshot are closer to being virialised than the population of subclusters from all snapshots., A comparison of the two histograms shows that the subclusters in the last snapshot are closer to being virialised than the population of subclusters from all snapshots.531 These virial ratios imply that the eSFE is close to unity. i.e. the majority of subclusters will not be strongly affected by gas expulsion (see Sect. 4).," These virial ratios imply that the eSFE is close to unity, i.e. the majority of subclusters will not be strongly affected by gas expulsion (see Sect. \ref{sec:exp}) )."532 Replacing hard binaries and higher order multiples by their centre of mass particles is essential to obtain a reliable picture of the subcluster dynamies., Replacing hard binaries and higher order multiples by their centre of mass particles is essential to obtain a reliable picture of the subcluster dynamics.533 The disruption of the subclusters during gas expulsion is controlled by the dynamical state of the binary centres of mass rather than the binaries themselves., The disruption of the subclusters during gas expulsion is controlled by the dynamical state of the binary centres of mass rather than the binaries themselves.534corrected for binaries or higher order multiples. the measures for the dynamical state of the subelusters would fluctuate with the orbital phase of a few tightly bound and eccentric binaries.," for binaries or higher order multiples, the measures for the dynamical state of the subclusters would fluctuate with the orbital phase of a few tightly bound and eccentric binaries."535 The bound mass fraction of the subclusters is not strongly affected by the presence of binaries (unbound sink particles are generally single). but because binaries are in virial or slightly subvirial. the mean virial ratio of the subclusters from all snapshots is decreased by 0.1—0.2 if it is not corrected for multiples.," The bound mass fraction of the subclusters is not strongly affected by the presence of binaries (unbound sink particles are generally single), but because binaries are in virial or slightly subvirial, the mean virial ratio of the subclusters from all snapshots is decreased by 0.1–0.2 if it is not corrected for multiples."536 About two thirds of this difference is due to binaries. while the remaining third is accounted for by triples and quadruples.," About two thirds of this difference is due to binaries, while the remaining third is accounted for by triples and quadruples."537 This shift of the virial ratio means that without correcting for binaries. the subelusters could be incorrectly interpreted as being slightly (Qa.~0.45-0.50). and the entire simulation would be close to virialised (Qi;~0.60-0.65) instead of the marginally bound state that is shown in Fig. +.," This shift of the virial ratio means that without correcting for binaries, the subclusters could be incorrectly interpreted as being slightly $Q_{\rm vir}\sim 0.45$ –0.50), and the entire simulation would be close to virialised $Q_{\rm vir}\sim 0.60$ –0.65) instead of the marginally bound state that is shown in Fig. \ref{fig:virial}."538 With respect to the binary-corrected results from Fig. 4..," With respect to the binary-corrected results from Fig. \ref{fig:virial},"539 this rather modest difference arises because the finite smoothing length used in the simulation inhibits the formation of very hard binaries., this rather modest difference arises because the finite smoothing length used in the simulation inhibits the formation of very hard binaries.540 Nonetheless. the correction for binaries improves the accuracy of our analysis. and therefore all results shown in this paper are corrected for binaries and higher order multiple systems.," Nonetheless, the correction for binaries improves the accuracy of our analysis, and therefore all results shown in this paper are corrected for binaries and higher order multiple systems."541 The key question is the subclusters are so close to virial equilibrium when neglecting the gas potential., The key question is the subclusters are so close to virial equilibrium when neglecting the gas potential.542 An obvious answer would be that the subclusters are generally gas-poor. which would imply that they are hardly affected by the gas potential in the first place.," An obvious answer would be that the subclusters are generally gas-poor, which would imply that they are hardly affected by the gas potential in the first place."543" To assess the gas potential and its time evolution. we have analysed the distribution of the gas in two snapshots of the simulation. at times fj,=O442 Myr (when star formation is ongoing) and t»=0.641 Myr tthe last snapshot of the simulation. after one free-fall time: also see Fig. 33)."," To assess the gas potential and its time evolution, we have analysed the distribution of the gas in two snapshots of the simulation, at times $t_1=0.442$ Myr (when star formation is ongoing) and $t_2=0.641$ Myr (the last snapshot of the simulation, after one free-fall time; also see Fig. \ref{fig:meanmcl}) )."544 For each of the identified subclusters in these snapshots. we calculate the fraction of the total mass within thestellar half-mass radius of the stellar distribution that is constituted by gas.," For each of the identified subclusters in these snapshots, we calculate the fraction of the total mass within the half-mass radius of the stellar distribution that is constituted by gas."545 The distribution of these gas fractions is shown in Fig. 7..," The distribution of these gas fractions is shown in Fig. \ref{fig:gas},"546 which contirms that the subclusters are indeed sus-poor on their typical length scales. with gas fractions of few) 0-0.2.," which confirms that the subclusters are indeed gas-poor on their typical length scales, with gas fractions of $\langle f_{\rm gas} \rangle=0$ –0.2."547 Because the simulation does not include feedback. his means that the accretion of gas onto the sink particles can keep up with the overall gas inflow towards the subclusters.," Because the simulation does not include feedback, this means that the accretion of gas onto the sink particles can keep up with the overall gas inflow towards the subclusters."548 Another mechanism that naturally leads to gas-poor subelusters is heir accretion-driven shrinking (222)... which increases the density contrast between the subclusters and the surrounding gas.," Another mechanism that naturally leads to gas-poor subclusters is their accretion-driven shrinking \citep{bonnell98,moeckel10,moeckel11}, which increases the density contrast between the subclusters and the surrounding gas."549 Gas accretion and the time evolution of the structural woperties of the population of subclusters both further decrease he gas fraction as time progresses., Gas accretion and the time evolution of the structural properties of the population of subclusters both further decrease the gas fraction as time progresses.550 This evolution isillustrated by comparing the data of the two snapshots in Fig. 7.. ," This evolution isillustrated by comparing the data of the two snapshots in Fig. \ref{fig:gas}, ,"551corresponding o times fj;=0.442 Myr and t»=0.641 Myr., corresponding to times $t_1=0.442$ Myr and $t_2=0.641$ Myr.552 During the enclosed, During the enclosed553AST-0808001.,AST-0808001.554 The MALT90 project team gratefully acknowledges the use of dense core positions supplied by ATLASGAL., The MALT90 project team gratefully acknowledges the use of dense core positions supplied by ATLASGAL.555" ATLASGAL is a collaboration between the Max Planck Gesellschaft (MPG: Max Planck Institute for Radioastronomy, Bonn and the Max Planck Institute for Astronomy, Heidelberg), the European Southern Observatory (ESO) and the University of Chile."," ATLASGAL is a collaboration between the Max Planck Gesellschaft (MPG: Max Planck Institute for Radioastronomy, Bonn and the Max Planck Institute for Astronomy, Heidelberg), the European Southern Observatory (ESO) and the University of Chile."556 Thanks to Anita Titmarsh and the duty astronomers and staff at the Paul Wild Observatory for their assistance during the observations., Thanks to Anita Titmarsh and the duty astronomers and staff at the Paul Wild Observatory for their assistance during the observations.557The alternative for computing the forces in Fourier space is. to calculate them in real space as gradients of the mesh-defined potential.,"The alternative for computing the forces in Fourier space is, to calculate them in real space as gradients of the mesh-defined potential."558 This would induce additional errors and therefore we prefer the first method., This would induce additional errors and therefore we prefer the first method.559 In our application of the PAL method. we compute the (periodic) to the force ancl the potential and adel this to the solution for the isolated. svstem. which is obtained vie direct summation onGRAPE.," In our application of the PM method, we compute the (periodic) to the force and the potential and add this to the solution for the isolated system, which is obtained via direct summation on."560 This procedure ensures proper treatment of periodic boundary conditions., This procedure ensures proper treatment of periodic boundary conditions.561 The Green's function for the PM scheme can be constructed directly. in Fourier space (οσον Eastwood 1988)., The Green's function for the PM scheme can be constructed directly in Fourier space (Hockney Eastwood 1988).562 Llowever. for the correction force and potential. this is rather complicated and it is more intuitive and straightforward to ooceed the following wav: We obtain the Green's function or each force component as the Fourier transform of ther. jy and. z-component. respectively. of the mesh-cdelined pairwise »eriodie correction force £4. defined in IE5qn. 9..," However, for the correction force and potential, this is rather complicated and it is more intuitive and straightforward to proceed the following way: We obtain the Green's function for each force component as the Fourier transform of the $x$, $y$ and $z$ -component, respectively, of the mesh-defined pairwise periodic correction force ${\bf f}_{\rm cor}$, defined in Eqn. \ref{corr-force}."563" Anc for the »otential correction. the appropriate Cireen's function is the Fourier transform of o, in Eqn. 10.."," And for the potential correction, the appropriate Green's function is the Fourier transform of $\phi_{\rm cor}$ in Eqn. \ref{corr-pot}."564 Ehe Green's 'unction is thus the offset between the Green's function for he periodic svstem Όρων and the isolated one Gis. Or with other words. fo and Oo. the Green's functions with the right. properties and only have to be transformed into. Fourier. space for. convolution with the densitv.," The Green's function is thus the offset between the Green's function for the periodic system $\cal{G}_{\rm per}$ and the isolated one $\cal{G}_{\rm iso}$, Or with other words, ${\bf f}_{\rm cor}$ and $\phi_{\rm cor}$ the Green's functions with the right properties and only have to be transformed into Fourier space for convolution with the density."565 Using the Fourier transform of the Ewald forces as periodic Cireen's function was proposed by A. Luss (private communication) and it is straightforward to extend this for handling the [force by subtracting the isolated solution., Using the Fourier transform of the Ewald forces as periodic Green's function was proposed by A. Huss (private communication) and it is straightforward to extend this for handling the force by subtracting the isolated solution.566 Note. in order to obtain thezsofaled solution in Fourier space. one has to double the linear dimensions ofthe grid andpad the additional grid. points to avoid contamination rom implicitly assumed. periodicity (see Press et al.," Note, in order to obtain the solution in Fourier space, one has to double the linear dimensions of the grid and the additional grid points to avoid contamination from implicitly assumed periodicity (see Press et al."567 1989)., 1989).568 For example. to solve Poisson's equation for a cubic density ield with volume £. we have to use a grid of size (2L). assign the densitv field to one octant of the large box and fill the remaining eric points with zero.," For example, to solve Poisson's equation for a cubic density field with volume $L^3$, we have to use a grid of size $(2L)^3$, assign the density field to one octant of the large box and fill the remaining grid points with zero."569 The Green's unction. however. has to be defined on the complete grid. ic. G(r)=1r for the potential. with Lxr.g.z2xL.," The Green's function, however, has to be defined on the complete grid, i.e. ${\cal G}({\bf r}) = 1/|{\bf r}|$ for the potential, with $-L \leq x,y,z \leq L$."570 On he other hand. theperiodic Green's function is delined on he original erid. with £/2crg.zxL2.," On the other hand, the Green's function is defined on the original grid, with $-L/2 \leq x,y,z \leq L/2$."571 bor alignment with the isolated solution. we have to extend the periodic solution into the larger cube.," For alignment with the isolated solution, we have to extend the periodic solution into the larger cube."572 To obtain the right correction Green's function. e.g. for the force. we replicate the table of pairwise Ewald forces (defined on the small cube) into all octants of the large cube.," To obtain the right correction Green's function, e.g. for the force, we replicate the table of pairwise Ewald forces (defined on the small cube) into all octants of the large cube."573 Then we subtract the isolated force Ποια (defined on the large cube) and transform into Fourier space., Then we subtract the isolated force field (defined on the large cube) and transform into Fourier space.574 This procedure is illustrated in Fig. l..," This procedure is illustrated in Fig. \ref{fig-green},"575" it plots £, in the vz-plane at. =0: a) is the Ewalel periodic force computed on a 32-grid ancl replicated. four time into a erid. b) is the isolated solution defined on the large erid ancl ο) is the cüllerence. the final correction force."," it plots $F_x$ in the yz-plane at $x=0$: a) is the Ewald periodic force computed on a 32-grid and replicated four time into a 64-grid, b) is the isolated solution defined on the large grid and c) is the difference, the final correction force."576 The Green's Function finally is the Fourier transform of this force matrix., The Green's function finally is the Fourier transform of this force matrix.577 Convolution with the zero padded: density field. results. in the right force correction., Convolution with the zero padded density field results in the right force correction.578 The procedure is analogue for the potential., The procedure is analogue for the potential.579 In practice. it is sullicient to compute the Cireen's function once at the beginning of a simulation run and store it as a table.," In practice, it is sufficient to compute the Green's function once at the beginning of a simulation run and store it as a table."580 The total force acting on an individual particle during one timestep then stems from the particle svstem inside the simulation cube. computed by direct summation onGRAPE. the contribution from an infinite set of. periodically nmürrored systems. computed via the method described above.," The total force acting on an individual particle during one timestep then stems from the particle system inside the simulation cube, computed by direct summation on, the contribution from an infinite set of periodically mirrored systems, computed via the method described above."581 For smoothed particle hyclrodyvnamies. one also has to adel pressure ancl viscous forces.," For smoothed particle hydrodynamics, one also has to add pressure and viscous forces."582 We compute the periodic and the isolated solution on a eric. subtract the latter from the first ancl add the isolated forces calculated withGRAPE.," We compute the periodic and the isolated solution on a grid, subtract the latter from the first and add the isolated forces calculated with."583 The two isolated. solutions cancel out and one can ask the question. what have we eained?," The two isolated solutions cancel out and one can ask the question, what have we gained?"584 For a svstem with more or less homogeneous density a pure PAL scheme is sulficient., For a system with more or less homogeneous density a pure PM scheme is sufficient.585 However. the advantage of using is evident when computing strongly structure: systems.," However, the advantage of using is evident when computing strongly structured systems."586 Unlike in PM schemes. the spacial resolution with is not limited to a given. cell size. but adapts to the density distribution due to its Lagrangian nature.,"	 Unlike in PM schemes, the spacial resolution with is not limited to a given cell size, but adapts to the density distribution due to its Lagrangian nature."587 1 is limited only by the gravitational smoothing length. or equivalently. by the choice of the minimum timestep.," It is limited only by the gravitational smoothing length, or equivalently, by the choice of the minimum timestep."588 Since the potential of strong density peaks is dominated: by πο eravity and the influence of periodic boundaries (and thus of the Ewalel correction) becomes weak. it is sullicient to compute this correction term on a relatively coarse eric which keeps the additional computational cost. low.," Since the potential of strong density peaks is dominated by self gravity and the influence of periodic boundaries (and thus of the Ewald correction) becomes weak, it is sufficient to compute this correction term on a relatively coarse grid which keeps the additional computational cost low."589 bor a relatively smooth density clistribution. a relatively wide mesh is sullicient anvhow.," For a relatively smooth density distribution, a relatively wide mesh is sufficient anyhow."590 The scheme proposed here unites both. high resolution with and the periodicity of a PM scheme.," The scheme proposed here unites both, high resolution with and the periodicity of a PM scheme."591 In addition. applying a Courant-Eriedrichs-Lewy like criterion. we typically do not have to compute the FET at cach smallest. timestep. but. can use. stored Correction values from the previous call.," In addition, applying a Courant-Friedrichs-Lewy like criterion, we typically do not have to compute the FFT at each smallest timestep, but can use stored correction values from the previous call."592 This reduces the computational expense further., This reduces the computational expense further.593 The contributions to the total acceleration of one particle are computed by two distinct methods: by direct summation on he board for the isolated solution and by applying a particle-mesh scheme for the periodic correction term., The contributions to the total acceleration of one particle are computed by two distinct methods: by direct summation on the board for the isolated solution and by applying a particle-mesh scheme for the periodic correction term.594 Compared to the host computer. the chips hereby aave only limited numerical accuracy (see Sect. 4.1)).," Compared to the host computer, the chips hereby have only limited numerical accuracy (see Sect. \ref{opt-resol}) )."595 The spacial resolution of the PAL scheme is limited. by. the number of erid zones and the choice of the assignment unction (Sect. 4.22)., The spacial resolution of the PM scheme is limited by the number of grid zones and the choice of the assignment function (Sect. \ref{opt-assign}) ).596 ALL this may leacl to spurious residuals, All this may lead to spurious residuals597"accuracy, MDM auc CDAL lead to the same gravitational wave spectra.","accuracy, MDM and CDM lead to the same gravitational wave spectra."598 Changing the number of degrees of freedom iu massless neutri or TIDAL also induces very stall differences of the order of., Changing the number of degrees of freedom in massless neutrini or HDM also induces very small differences of the order of.599. Takiug into accom that an experineut always just measures the sun of tensor and scalar contributions and first las to disentangle the probably sieuificantly smaller gravitational wave contribution. we can disregard such small οects. even if the experiuenutal eror is as small as possible. dominated by cosmüe variance.," Taking into account that an experiment always just measures the sum of tensor and scalar contributions and first has to disentangle the probably significantly smaller gravitational wave contribution, we can disregard such small effects, even if the experimental error is as small as possible, dominated by cosmic variance."600 The relevant parameers to be considered are thus O3;=ος|Op.Ox aud My.," The relevant parameters to be considered are thus $\Om_M=\Om_C+\Om_H,~601\Om_\La$ and $h_0$."602 Iu the & dependence of h an additional effect comes iuto play: Due to the mode depenudeuce of ty. the oscillations in fy at a fixe fraction f=ffy of fy have dicerent waveleugths if measured in units of fy.," In the $k$ dependence of $\dot{h}$ an additional effect comes into play: Due to the model dependence of $t_0$, the oscillations in $\dot{h}$ at a fixed fraction $t=ft_0$ of $t_0$ have different wavelengths if measured in units of $t_0$."603" Models wi ha larger cosmological coustaut oscillate slower in A7, than inodels with sinall cosmological constaut.", Models with a larger cosmological constant oscillate slower in $kt_0$ than models with small cosmological constant.604 Therefore. the cauceation due to oscillatious in the integral (2)) is nore severe for models with simall cosmological coustaut.," Therefore, the cancelation due to oscillations in the integral \ref{II}) ) is more severe for models with small cosmological constant."605 This eect finally dominates over the arecr amplitude of 5 which models with large A actually have., This effect finally dominates over the larger amplitude of $\dot{h}$ which models with large $ \La$ actually have.606 In Fig., In Fig.607" 3 we show tlje C, spectra or several models aud 1 ra Fie.", 3 we show the $C_{\ell}$ spectra for several models and in a Fig.608 1 the relative differences are indicated., 4 the relative differences are indicated.609 The A-11o« els shown iu yaues (a) of Fies., The $\La$ -models shown in frames (a) of Figs.610 3 aud 1 show a slightly increasi1ο aüuplitude with increasingBi A., 3 and 4 show a slightly increasing amplitude with increasing $\La$.611 As can be secu in frames (b) of Fies., As can be seen in frames (b) of Figs.612 3 and d increasing Pg. which docs not lead to an increase in the relative oscillation frequency. jus decreases the fuctuatious due to stronger damping.," 3 and 4, increasing $h_0$, which does not lead to an increase in the relative oscillation frequency, just decreases the fluctuations due to stronger damping."613 The detailed model xuiunueters of the frames (b) are just given for iformation., The detailed model parameters of the frames (b) are just given for information.614 The ouly parameters which really natter are O4 and fy., The only parameters which really matter are $\Om_\La$ and $h_0$.615 The variatious induced by changing the other parameters are on the evel and thus swamped Y* cosnide Varlalce., The variations induced by changing the other parameters are on the level and thus swamped by cosmic variance.616 The variation of the eusor C; spectrui for different cosmological models with fixed IImbble xuineter which are uo already. excluded by other observations than CAB anisotropics never exceed for 6<60. while variations of the Tibble paramecter can lead to chauges in the spectrum of up to," The variation of the tensor $C_{\ell}$ spectrum for different cosmological models with fixed Hubble parameter which are not already excluded by other observations than CMB anisotropies never exceed for $\ell617<60$, while variations of the Hubble parameter can lead to changes in the spectrum of up to."618 We have calculated the tensor contribution to the CMD anisotropies iu mixed dark matter models with aud without cosmological coustaut., We have calculated the tensor contribution to the CMB anisotropies in mixed dark matter models with and without cosmological constant.619 We have included a previously neglected source terii in the evolution equation for metric perturbations., We have included a previously neglected source term in the evolution equation for metric perturbations.620 Our findings are however quite modest: By reasons of cosmic variance. the statistical relative error in C5 measured from only one point iu the universe is alwavs 1/2|1.," Our findings are however quite modest: By reasons of cosmic variance, the statistical relative error in $C_{\ell}$ measured from only one point in the universe is always $1/\sqrt{2\ell+1}$."621 This is a very significant uncertainty. especially for the gravitational wave contribution which peaks around (~20 aud has already dropped by a factor of about 2 at f=60 (see Fig.," This is a very significant uncertainty, especially for the gravitational wave contribution which peaks around $\ell\sim62220$ and has already dropped by a factor of about 2 at $\ell=60$ (see Fig."623 3)., 3).624" Iu non of the considqd nodels the influence of the anisotropic stress source becomes large enough to induce a cifference iu the C, spectrum which is larger than cosmic variance.", In non of the considered models the influence of the anisotropic stress source becomes large enough to induce a difference in the $C_{\ell}$ spectrum which is larger than cosmic variance.625 The same is true for hot dark matter contributions., The same is true for hot dark matter contributions.626 Only an extremely large cosmological coustaut or a cifference in the IIubble paranueter can induce chauges iu the gravitational wave spectra which are in principle observable but nevertheless small., Only an extremely large cosmological constant or a difference in the Hubble parameter can induce changes in the gravitational wave spectrum which are in principle observable but nevertheless small.627 This finding has oue neeative and one positive aspect: Unfortunately. the gravitational wave contribution docs not contain detailed information about the cosmological parameters considered here and can thus not be used to measure them with high accuracy.," This finding has one negative and one positive aspect: Unfortunately, the gravitational wave contribution does not contain detailed information about the cosmological parameters considered here and can thus not be used to measure them with high accuracy."628" Ou the other hand. since this contribution is so model independent. if couserves its information about the initial condition aud thus about the amplitude' and spectral iudex which it iuherited during. ο,ο,, au inflationary epoch."," On the other hand, since this contribution is so model independent, it conserves its information about the initial condition and thus about the amplitude and spectral index which it inherited during, e.g., an inflationary epoch."629 T. Wauhiashvili would like to express her thanks to the University of Geneva for hospitality., T. Kanhiashvili would like to express her thanks to the University of Geneva for hospitality.630 Tus. is erateful to R. Valdarnimi aud II. \Gheeva for helpful remarks., T.K. is grateful to R. Valdarnini and H. Miheeva for helpful remarks.631 It is a pleasure to thauk also, It is a pleasure to thank also632by stellar evolutionary models.,by stellar evolutionary models.633 ? showed that by artilically enhancing the opacity over the temperature range 1.5xLON«T<810K by a [actor of 2.5 it was possible to remove the diserepaney., \cite{Andreasen88} showed that by artifically enhancing the opacity over the temperature range $1.5\times10^{5}K<T<8\times10^{5}K$ by a factor of 2.5 it was possible to remove the discrepancy.634 More. detailed modelling of opacities bv the OPAL (?)| and the Opacity Project (72). confirmed an increase in (his temperature range due to metal opacitv., More detailed modelling of opacities by the OPAL \citep{Rogers92} and the Opacity Project \citep{Seaton94} confirmed an increase in this temperature range due to metal opacity.635 The implementation of new opacities largely resolved (he bump Cepheid mass discrepancy (?).., The implementation of new opacities largely resolved the bump Cepheid mass discrepancy \citep{Moskalik92}.636 However. despite convergence. a number of subsequent studies have shown that the discrepancy remains significant. and requires explanation.," However, despite convergence, a number of subsequent studies have shown that the discrepancy remains significant and requires explanation."637 Studies of Galactic (??).. LAIC (22???) and SAIC (7) Cepheics have shown that the masses determined. via pulsation modelling are ~15-20% less massive than those expected from evolutionary models.," Studies of Galactic \citep{Natale07,Caputo05}, LMC \citep{Wood97,Keller02,Keller06,Bono02} and SMC \citep{Keller06} Cepheids have shown that the masses determined via pulsation modelling are $\sim$ less massive than those expected from evolutionary models."638 Dynamical masses lor Cepheids are diffieult to obtain given the low spatial density of Cepheids., Dynamical masses for Cepheids are difficult to obtain given the low spatial density of Cepheids.639 The works of 2???— present dynamical masses [for six Cepheids.," The works of \citet{Benedict07,Evans07, Evans06, Evans98} present dynamical masses for six Cepheids."640 Albeit with large associated uncertainties. (hese results confirm the conclusions drawn for pulsation modelling: that the evolutionary masses appear ~15% larger.," Albeit with large associated uncertainties, these results confirm the conclusions drawn for pulsation modelling; that the evolutionary masses appear $\sim15$ larger."641 From an evolutionary perspective. Cepheids are understood to be post-red giant stars crossing (he instability strip on so-called blue loops [ουντας the initiation of core-Ile burning.," From an evolutionary perspective, Cepheids are understood to be post-red giant stars crossing the instability strip on so-called blue loops following the initiation of core-He burning."642 To ascribe an evolutionary mass one takes the Cepheid's luminosity and. using a mass-luuinosity (AI-L) relation that is derived from evolutionary models. derives the mass of the Cepheid.," To ascribe an evolutionary mass one takes the Cepheid's luminosity and, using a mass-luminosity (M-L) relation that is derived from evolutionary models, derives the mass of the Cepheid."643 The M-L relation can be modified substantially bx the treatment of internal mixing and mass-loss., The M-L relation can be modified substantially by the treatment of internal mixing and mass-loss.644 Both processes feature complex hydrodvuamical and radiative mechanisms for which we. al present. only possess empirical approximations.," Both processes feature complex hydrodynamical and radiative mechanisms for which we, at present, only possess empirical approximations."645 The treatment of internal mixing mocdifies the size of the helium core established during (he stars main-sequence (AIS) evolution., The treatment of internal mixing modifies the size of the helium core established during the star's main-sequence (MS) evolution.646 Overshoot at the edge of the convective core of the Cepheicl progenitor mixes additional hydrogen into the core aud hence increases the helium core mass., Overshoot at the edge of the convective core of the Cepheid progenitor mixes additional hydrogen into the core and hence increases the helium core mass.647 As a consequence the post-M$ evolution occurs at a higher Iuminositv., As a consequence the post-MS evolution occurs at a higher luminosity.648 Mass loss. in an ad-hoc manner at least. offers a mechanism to modifv the M-L. relation by directly reducing (he mass of a Cepheicl.," Mass loss, in an ad-hoc manner at least, offers a mechanism to modify the M-L relation by directly reducing the mass of a Cepheid."649 The properlies of pulsation. on the other hand. are dependent on the structure of the atmosphere of the Cepheid.," The properties of pulsation, on the other hand, are dependent on the structure of the atmosphere of the Cepheid."650 ? show that the morphology. of a bump Cepheid light. curve is highlv sensitive to the mass. huminositw. effective temperature and metallicity.," \citet{Keller06} show that the morphology of a bump Cepheid light curve is highly sensitive to the mass, luminosity, effective temperature and metallicity."651 Hence modelling of the light curve can be used to determine a pulsation Cepheid mass Chat is entirely independent of stellar evolution calculations., Hence modelling of the light curve can be used to determine a pulsation Cepheid mass that is entirely independent of stellar evolution calculations.652 In the work of ? and ? it is proposed that mass-loss can account for the mass discrepancy between pulsation and evolutionary masses., In the work of \cite{Bono02} and \cite{Caputo05} it is proposed that mass-loss can account for the mass discrepancy between pulsation and evolutionary masses.653 ?.— also conclude that models that incorporate additional internal mixing in (he vicinity of the convective core are not. able to explain the mass discrepancy., \citet{Caputo05} also conclude that models that incorporate additional internal mixing in the vicinity of the convective core are not able to explain the mass discrepancy.654 I (his paper we revisit (hese conclusions and present a, In this paper we revisit these conclusions and present a655high spectral resolution is needed to measure the line shapes more accurately. this preliminary application shows intriguing potential.,"high spectral resolution is needed to measure the line shapes more accurately, this preliminary application shows intriguing potential."656 Here we apply our synthetic line profile approach to the case of  Vel consisting of à WCS star with an O7.5 companion., Here we apply our synthetic line profile approach to the case of $\gamma$ Vel consisting of a WC8 star with an O7.5 companion.657 Adopted parameters for the WR wind and the orbit are given in Table 4.., Adopted parameters for the WR wind and the orbit are given in Table \ref{tab4}.658 This eolliding wind system has been studied extensively., This colliding wind system has been studied extensively.659 The star and wind parameters come from de Marco (2000). and the orbital parameters come from the interferometric study by North (2007).," The star and wind parameters come from de Marco (2000), and the orbital parameters come from the interferometric study by North (2007)."660 Note that an independent study by Millour (2007) vields mostly similar parameters., Note that an independent study by Millour (2007) yields mostly similar parameters.661 Four forbidden lines were observed with/SO: [Catv]. [Neri]. [Nett]. and [Srv] (see Dessart 22000 and Ignace 22001).," Four forbidden lines were observed with: ], ], ], and ] (see Dessart 2000 and Ignace 2001)."662 In contrast to WR 147. the orbital parameters are quite well-known. and so . Vel constitutes a significant test case for our modeling.," In contrast to WR 147, the orbital parameters are quite well-known, and so $\gamma$ Vel constitutes a significant test case for our modeling."663 We note that the adopted opening angle of 7=δη” is significantly larger than the value for an adiabatic shock at =45° (see eq. [22]]), We note that the adopted opening angle of $\beta = 85^\circ$ is significantly larger than the value for an adiabatic shock at $\approx 45^\circ$ (see eq. \ref{eq:beta}] ])664 or a radiative shock at z35 (see Canto 11996)., or a radiative shock at $\approx 35^\circ$ (see Canto 1996).665 We use this larger value based on the X-ray study by Henley (2005)., We use this larger value based on the X-ray study by Henley (2005).666 There are a number of new issues that arise in the case of  Vel that are different from the wide binary WR 147. notably that Gu the winding radius is comparable to the critical radii of the observed forbidden lines and (b) the critical radit of most lines are only somewhat larger than the orbital semi-mayor (within a factor of about 10). and for [ον]. the critical radius is nearly equal to the separation of the stars at apastron.," There are a number of new issues that arise in the case of $\gamma$ Vel that are different from the wide binary WR 147, notably that (a) the winding radius is comparable to the critical radii of the observed forbidden lines and (b) the critical radii of most lines are only somewhat larger than the orbital semi-major (within a factor of about 10), and for ], the critical radius is nearly equal to the separation of the stars at apastron."667 The three primary scale lengths of the problem — rw. Morb. and re — are somewhat comparable for all four lines of interest.," The three primary scale lengths of the problem – $r_{\rm668w}$, $r_{\rm orb}$, and $r_{\rm c}$ – are somewhat comparable for all four lines of interest."669 As a result. the single greatest deficiency of our model becomes potentially important. namely the treatment of the bow shock head.," As a result, the single greatest deficiency of our model becomes potentially important, namely the treatment of the bow shock head."670 Our treatment of the shape of the bow shock interior to the instantaneous position of the companion star is extremely rough., Our treatment of the shape of the bow shock interior to the instantaneous position of the companion star is extremely rough.671 We determine the stagnation point ro based on equation (21)., We determine the stagnation point $r_0$ based on equation \ref{eq:stag}) ).672 The emissivity “cavity” extends inward in a conical fashion from the companion star to the stagnation point., The emissivity `cavity' extends inward in a conical fashion from the companion star to the stagnation point.673 This is à gross misrepresentation of the rounded shape that the bow shock should take., This is a gross misrepresentation of the rounded shape that the bow shock should take.674 However. this sector of the bow shock is the portion where the two winds intersect most nearly head-on and which produces the observed X-ray emissions (e.g.. Skinner 22001: Henley," However, this sector of the bow shock is the portion where the two winds intersect most nearly head-on and which produces the observed X-ray emissions (e.g., Skinner 2001; Henley"675consider only this case.,consider only this case.676" Then. we have 6<0 because B,BQ!«dQ’> 0."," Then, we have $\delta < 0$ because $B_s B_{\varphi} \Omega' \propto \delta \Omega' > 0$ ."677 The r.h.s., The r.h.s.678 of Eq. (, of Eq. (67935) is à monotonously inereasing function of ΚΗ and is a minimum for the minimal possible value of &H.,35) is a monotonously increasing function of $kH$ and is a minimum for the minimal possible value of $kH$.680 Since a short-wavelength approximation applies only if KH>l. we can estimate the domain of instability supposing KH=| in imequality (35).," Since a short-wavelength approximation applies only if $kH > 1$, we can estimate the domain of instability supposing $kH=1$ in inequality (35)."681 Then. in order to fulfill the instability condition (35) for short-wavelength perturbations with KH>|. the rotation shear has to satisfy. at least. the inequality: In Fig.," Then, in order to fulfill the instability condition (35) for short-wavelength perturbations with $kH >1$, the rotation shear has to satisfy, at least, the inequality: In Fig."682 1. we plot the regions of instability given by Eq. (," 1, we plot the regions of instability given by Eq. ("68336) for different negative values of ὁ.,36) for different negative values of $\delta$.684 At given 6. the instability can occur ifthe value of [H5€/c4| is above the corresponding curve (note that O' is negative in Fig.," At given $\delta$, the instability can occur ifthe value of $|H s \Omega' /c_A|$ is above the corresponding curve (note that $\Omega'$ is negative in Fig."685 1)., 1).686" If the magnetic and thermal energies are comparable and departures from the Keplerian disk are not large. then c4/H.-c,/H.~ο. and Η΄οι~sQ’/Qx 3/2."," If the magnetic and thermal energies are comparable and departures from the Keplerian disk are not large, then $c_A/H \sim c_s/H \sim \Omega$, and $H s \Omega'/c_s \sim s \Omega' /687\Omega \approx 3/2$ ."688" Inequality (36) can be satisfied only for relatively small values of j/Hc4«|o .orjo]~B,/B. I/Re,,."," Inequality (36) can be satisfied only for relatively small values of $\eta / H c_A < |\delta|$, or $|\delta| \sim B_s/B_{\varphi} 689> 1/ {\rm Re}_m$ ."690 For a non-Keplerian disk. the quantity HsQ’/c can vary in à wider range even if the magnetic ad thermal energies are comparable. but condition (36) still cannot be satisfied for relatively large values of 77/He..," For a non-Keplerian disk, the quantity $H s \Omega'691/ c_{A}$ can vary in a wider range even if the magnetic and thermal energies are comparable, but condition (36) still cannot be satisfied for relatively large values of $\eta/ H c_{A}$."692 By analogy. we can also transform condition (34).," By analogy, we can also transform condition (34)."693 The minimal unstable rotation. shear. corresponds again to the maximal possible wavelength., The minimal unstable rotation shear corresponds again to the maximal possible wavelength.694 Again. the maximum wavelength can be estimated from the condition KH.~l|.," Again, the maximum wavelength can be estimated from the condition $kH \sim 1$."695 For such wavevectors. Eq. (," For such wavevectors, Eq. ("69636) can be transformed into: whereB=cie.,36) can be transformed into: where $\beta = c_{s}^2/c_{A}^2$.697 In Fig., In Fig.698 2. we show the region of parameters where the instability can occur in accordance with Eq. (," 2, we show the region of parameters where the instability can occur in accordance with Eq. ("69937).,37).700" Inequality (37) is quadratic in AsQ’/e, and can be satisfied if this parameter 1s larger/smaller than the largest/smallest root of the corresponding quadratic equation.", Inequality (37) is quadratic in $H s \Omega'/c_A$ and can be satisfied if this parameter is larger/smaller than the largest/smallest root of the corresponding quadratic equation.701 Therefore. for a given combination of B and 6. the regions of instability lie above the upper line and below the lower line.," Therefore, for a given combination of $\beta$ and $\delta$, the regions of instability lie above the upper line and below the lower line."702" To calculate the instability growth rate. it is convenient to introduce dimensionless quantities. (we assume B,B,.O'> 0)."," To calculate the instability growth rate, it is convenient to introduce dimensionless quantities, (we assume $B_s B_{\varphi} \Omega' >0$ )."703 Then. Eq. (," Then, Eq. ("70424) transforms into The dependence on the wavelength is characterized by the parameter A7 in this equation.,24) transforms into The dependence on the wavelength is characterized by the parameter $x^{2}$ in this equation.705" The parameter « is of the order of 1/Re,,.", The parameter $\alpha$ is of the order of $1/{\rm Re}_m$ .706 We solved eq. (, We solved eq. (70738) numerically for different values of the parameters by computing the eigenvalues of thematrix,38) numerically for different values of the parameters by computing the eigenvalues of thematrix708of protons even if the UV fluxes are assumed at a low level.,of protons even if the UV fluxes are assumed at a low level.709 The high ionization degree can be explained as the consequence of low mass loss rate., The high ionization degree can be explained as the consequence of low mass loss rate.710 Even if the UV flux is al same level. the mass loss rate of WD 1359733b should be lower than that of IID 209455b due to the larger potential well of IID 189733b.," Even if the UV flux is at same level, the mass loss rate of HD 189733b should be lower than that of HD 209458b due to the larger potential well of HD 189733b."711 Thus. for ILD 189733b. the low mass loss leads to the low optical depth and high ionization degree.," Thus, for HD 189733b, the low mass loss leads to the low optical depth and high ionization degree."712 Given (he energy. equation. il is clear that the photoionization heating is proportional to the number density of neutral hydrogen.," Given the energy equation, it is clear that the photoionization heating is proportional to the number density of neutral hydrogen."713 With the assuniption of energy-limit most of the UV radiation energy is deposited as heat (due to the low ionization degree). which is used to lift material out of the gravitational potential well.," With the assumption of energy-limit most of the UV radiation energy is deposited as heat (due to the low ionization degree), which is used to lift material out of the gravitational potential well."714 Thus. the condition of energv-limit results in higher mass loss rates.," Thus, the condition of energy-limit results in higher mass loss rates."715 In the case of ionizecl wind (he material is mainly composed of protons., In the case of ionized wind the material is mainly composed of protons.716 Only a little of UV radiation can be transformed as heat. and further goes into PdV work.," Only a little of UV radiation can be transformed as heat, and further goes into PdV work."717 Miurav-Clav. et al. (, Murray-Clay et al. (7182009) found that at high. Frey the flow is racdiation-recombination-limited (at low flux MxFS high flux AMx FI). and an almost isothermal wind is predicted.,"2009) found that at high $F_{UV}$ the flow is radiation-recombination-limited (at low flux $\dot{M} \propto719F_{UV}^{0.9}$; at high flux $\dot{M} \propto F_{UV}^{0.6}$ ), and an almost isothermal wind is predicted."720 In contrast to the case of radiation-recombination-limit. our results show a “normal” temperature profile.," In contrast to the case of radiation-recombination-limit, our results show a ""normal"" temperature profile."721 It hints that heating is balanced by PAV work rather (han radiation cooling., It hints that heating is balanced by PdV work rather than radiation cooling.722 Thus. we can summarize that the modified energv-Iimit approach can be used in the case of low or moderate ionization degree. but is unsuccessful for the high ionization winds.," Thus, we can summarize that the modified energy-limit approach can be used in the case of low or moderate ionization degree, but is unsuccessful for the high ionization winds."723 The conclusion can be validated by comparison with ILD 209458b. we find that the mass loss rate calculated by Equation (23) can predict a reasonable observation value for IID 209458b.," The conclusion can be validated by comparison with HD 209458b, we find that the mass loss rate calculated by Equation (23) can predict a reasonable observation value for HD 209458b."724 The interesting results motivated us to fit the mass loss rate as a function of UV flux in the case of ionized wind., The interesting results motivated us to fit the mass loss rate as a function of UV flux in the case of ionized wind.725 Seen from Figure 6. it is clear (hat the straight line can depict the lower part. and the upper part can be fitted by using a polynomial (a jump appears al Fyy= 2000).," Seen from Figure 6, it is clear that the straight line can depict the lower part, and the upper part can be fitted by using a polynomial (a jump appears at $F_{UV}=2000$ )."726 Finally. (he mass loss rate can be express as," Finally, the mass loss rate can be express as"727range. giveu the total Na profile observed.,"range, given the total Na profile observed."728 Since the low-altitude pressure is au upper lait constrained by Rayleigh scattering. a lower pressure would have an effect ou the lower temperature profile. increase the lower Na iuixiug ratio. aud decrease the condeusate pressure deteriuued in our transit fit.," Since the low-altitude pressure is an upper limit constrained by Rayleigh scattering, a lower pressure would have an effect on the lower temperature profile, increase the lower Na mixing ratio, and decrease the condensate pressure determined in our transit fit."729" Whatever the true pressure 2. or additional absorption sources, however. the basic atmospheric characteristics of Na determined here would remain the same."," Whatever the true pressure $P_{s}$ or additional absorption sources, however, the basic atmospheric characteristics of Na determined here would remain the same."730 Namely. the muddle atmosphere has a greatly reduced amount of Na with a temperature below Na»S coudoeusatiou. while the lower aud higher atimuospheres are warmer than the condensation temperature with the lower atmosphere contaimine a solar-like Na abundance and higher one a sieuificautlv reduced Na abunclance.," Namely, the middle atmosphere has a greatly reduced amount of Na with a temperature below $_2$ S condensation, while the lower and higher atmospheres are warmer than the condensation temperature with the lower atmosphere containing a solar-like Na abundance and higher one a significantly reduced Na abundance."731 Given the large uncertainties iiodeliug hot-Jupiter Na photoionization. we choose not to enplov a complex ionization model. but rather follow the results of Fortuevetal.(2003). and assume in our model that neutral Na can be suddenly ionized above a given altitude leading to the observed Na depletion.," Given the large uncertainties modeling hot-Jupiter Na photoionization, we choose not to employ a complex ionization model, but rather follow the results of \cite{Fortney03} and assume in our model that neutral Na can be suddenly ionized above a given altitude leading to the observed Na depletion."732" The ionization depth fouud bv Fortneyetal.(2003) is around 1.7 παν, close to the pressure we find for a Na abundance change iu the coudensation model. indicating the effects could be oeuportant at those pressures and such a aodel is viable."," The ionization depth found by \cite{Fortney03} is around 1.7 mbar, close to the pressure we find for a Na abundance change in the condensation model, indicating the effects could be important at those pressures and such a model is viable."733 A inodel with Na ionization effectively lifts the constraint of the temperature profile dropping below 1ο Na condcusation curve. which the condensation uodel uses to deplete atomic Na.," A model with Na ionization effectively lifts the constraint of the temperature profile dropping below the Na condensation curve, which the condensation model uses to deplete atomic Na."734" Effectively a model with Na ionization leaves a wide range of temperatures yossible iu the uiddle atmosphere (corresponding in our inodel to 7,,) as the collisional broadened Na xofle at those altitudes (1.000 - 2.000. ki) contains ιο temperature Information."," Effectively, a model with Na ionization leaves a wide range of temperatures possible in the middle atmosphere (corresponding in our model to $T_{m}$ ) as the collisional broadened Na profile at those altitudes (1,000 - 2,000 km) contains no temperature information."735 The correspouding IL Ravleigh scattering slope (below ~3.100 A) is at the edee of the spectrum and also provides no uscful widdle atmospheric temperature coustraiuts;," The corresponding $_2$ Rayleigh scattering slope (below $\sim$ 3,400 ) is at the edge of the spectrum and also provides no useful middle atmospheric temperature constraints."736" Within the yamework of equilibrium chemistry. the temperature T,, is likely below that of the TiO/VO condensation curve aud above that ofthe NaoS condensation curve."," Within the framework of equilibrium chemistry, the temperature $T_{m}$ is likely below that of the TiO/VO condensation curve and above that of the $_2$ S condensation curve."737 However. Ravleigh scattering stil implies a lieh temperature of 2.2004260 IK at 3345 mbar aud the deep narrow Na suggest high altitude temperatures of iuouud τοcores IK. Without a strong constraint on the muddle ονatmosphere temperature. T-P profile fit» are dominated by these upper aud lower atmospheric constrains. leading to anomalously high temperature T-P profiles fit to be everywhere above 2.000 IX. Thoug[um echuically good fits to the data. such profiles cam Ὡς ruled out as the temperatures would be evervwher üeher than the davside temperature mversion seen wit[um Spitzer (Ikuutsonetal.2008:Burrowsoet2007a).," However, Rayleigh scattering still implies a high temperature of $\pm$ 260 K at $\pm$ 5 mbar and the deep narrow Na cores suggest high altitude temperatures of around $^{+500}_{-570}$ K. Without a strong constraint on the middle atmosphere temperature, T-P profile fits are dominated by these upper and lower atmospheric constrains, leading to anomalously high temperature T-P profiles fit to be everywhere above 2,000 K. Though technically good fits to the data, such profiles can be ruled out as the temperatures would be everywhere higher than the dayside temperature inversion seen with Spitzer \citep{Knut08,Burrows07}."738. Additionally. the lack of observed Ca Tat AL227 in tle ow resolution data further suggests temperatures reac[um values lower than that required for Ca-Ti and Ca-Al-)'arnue condeusates (Loders&Feeley2006).," Additionally, the lack of observed Ca I at $\lambda$ 4,227 in the low resolution data further suggests temperatures reach values lower than that required for Ca-Ti and Ca-Al-bearing condensates \citep{Lodd06}."739". ""Though the current data lacks enough constraints for a uique T-P profile solution iu the photoionization moclel. he ionization pressure. [μι can be estimated eiven the ikelv rauge of temperatures."," Though the current data lacks enough constraints for a unique T-P profile solution in the photoionization model, the ionization pressure, $P_{ion}$, can be estimated given the likely range of temperatures."740" We fit various isothermal uodels fitting 5, ax free parameter along with the Na abundances (taken to be coustaut) above aud below that pressure.", We fit various isothermal models fitting $P_{ion}$ as free parameter along with the Na abundances (taken to be constant) above and below that pressure.741 The resulting ionization pressure varices from 0.5 mbar to 5 mbar for temperatures of 1.100 aud 2.000 I& respectively.," The resulting ionization pressure varies from 0.5 mbar to 5 mbar for temperatures of 1,100 and 2,000 K respectively."742 Higher temperature fits result in sanaller wppecr-atinospheric Na abuudances aud larger Na abundance coutrasts., Higher temperature fits result in smaller upper-atmospheric Na abundances and larger Na abundance contrasts.743" The abundauces found in the lower temperature fits are in general aerecimeut with those found in the Na condeusatiou model while the upper temperature fits find much πα]: uppoer-abuncdauces, with the 2.000 I& model eiviug an upper Na abuudauce 1580 times less than solar."," The abundances found in the lower temperature fits are in general agreement with those found in the Na condensation model, while the upper temperature fits find much smaller upper-abundances, with the 2,000 K model giving an upper Na abundance 180 times less than solar."744 Thus. à Na abundance drop bx a factor of ten cau be considered as a lower limit. aud may be much larger depending ou the depletion mechaisiun.," Thus, a Na abundance drop by a factor of ten can be considered as a lower limit, and may be much larger depending on the depletion mechanism."745 A 0.1 absorption of Na indicates that ou transmission spectra probes an altitude range of ~3.500 kan.," A $\sim$ absorption of Na indicates that our transmission spectra probes an altitude range of $\sim$ 3,500 km."746 Such a laree altitude range with our slaut transit ecolctry indicates we are sensitive to pressures between Ls of mbar and ~0.001 mbar., Such a large altitude range with our slant transit geometry indicates we are sensitive to pressures between 10's of mbar and $\sim$ 0.001 mbar.747 These hub pressures are in agreenient with those found from Fortneyal.(2003).. who analyzed the original Clarbouneanctal.(2002) inediun resolution Na mcasuremeuts.," These limb pressures are in agreement with those found from \cite{Fortney03}, who analyzed the original \cite{Charby} medium resolution Na measurements."748 At oressures ligher than 30-50 mbar. our transmission spectra is optically thick to Ravleigh scattering by the abundant molecule Πο. providing a firm upper pressure nut.," At pressures higher than 30-50 mbar, our transmission spectra is optically thick to Rayleigh scattering by the abundant molecule $_{2}$, providing a firm upper pressure limit."749 Such pressure restrictions. im addition to the strong narrow Na liue cores. facilitate the necessity of a hot high-altitude temperature (above 71.500). which hen naturally provides the observed altitude range due o an increased scale height.," Such pressure restrictions, in addition to the strong narrow Na line cores, facilitate the necessity of a hot high-altitude temperature (above $\sim$ 1,500), which then naturally provides the observed altitude range due to an increased scale height."750 Our hieh altitude high ub temperature may point toward the atmospheric escape mechanisin beime felt. which necessitates larec eniperature rises to perhaps 10.000 or 15.000 Ix in the exosphere (Yelle2001:Vidal-Macdjaretal.2003.2001).," Our high altitude high limb temperature may point toward the atmospheric escape mechanism being felt, which necessitates large temperature rises to perhaps 10,000 or 15,000 K in the exosphere \citep{Yelle,Vidal02,Vidal03}."751 The highest altitudes probed here are dependent ou he Na core. however. auc thus have a correspondingly arecr associated error.," The highest altitudes probed here are dependent on the Na core, however, and thus have a correspondingly larger associated error."752 The laree error coupled with he possible Nai depletion mechanisias leaves open a wide range of possible upper atimospheric teniperature xofiles., The large error coupled with the possible Na depletion mechanisms leaves open a wide range of possible upper atmospheric temperature profiles.753 However. a high altitude temperature rise can ο seen When analyzing the narrowest Na wavelenetl wands alouc. scusitive to high altitudes well above he condensationionization altitude. makiug the ligh-altitude temperature measurement independent of the depletion 1iechauisui.," However, a high altitude temperature rise can be seen when analyzing the narrowest Na wavelength bands alone, sensitive to high altitudes well above the condensation/ionization altitude, making the high-altitude temperature measurement independent of the depletion mechanism."754 The hot high-altitude teuiperature is illustrated in Fie., The hot high-altitude temperature is illustrated in Fig.755 Lo which shows photometric Na neasurenients frou Charbomuneauctal.(2005) and Sineetal.(2008) overplotted with various constant abundance isothermal models.," 4, which shows photometric Na measurements from \cite{Charby} and \cite{Sing08a} overplotted with various constant abundance isothermal models."756 A single isothermal model fits through the 12 aud 17 bands. indicating that he temperature and Na abuudance do not chauge senificautlv between those altitudes (~2.000 to 2.200 -uj.," A single isothermal model fits through the 12 and 17 bands, indicating that the temperature and Na abundance do not change significantly between those altitudes $\sim$ 2,000 to 2,200 km)."757 However. the absorptions measured in the Ll aud So bands. which probe higher in altitude (~2.700 to L700 Km). rise much faster than the isothermal model fittine the lower altitudes of the 12 and 17 lands. indicating that warmer temperatures are needed.," However, the absorptions measured in the 4.4 and 8.8 bands, which probe higher in altitude $\sim$ 2,700 to 3,700 km), rise much faster than the isothermal model fitting the lower altitudes of the 12 and 17 bands, indicating that warmer temperatures are needed."758 Tn the ionization Na depletion scenario. there are ess temperature constraints for the middle atmosphere compared to the Na coucdensation model.," In the ionization Na depletion scenario, there are less temperature constraints for the middle atmosphere compared to the Na condensation model."759 However. linab cluperatures evervwhereabove —1.500 In are unlikely. and im contradiction with Spitzer iueasurements of infrared brightuess temperature.," However, limb temperatures everywhereabove $\sim$ 1,500 K are unlikely, and in contradiction with Spitzer measurements of infrared brightness temperature."760 T-P profiles applicable, T-P profiles applicable761frequencies v; and normalizations A; and phases ὁ;. 1.8. On the other hand the Fourier transform of a ltghteurve can also be represented by a superposition of individual sinusoids.,"frequencies $\nu_i$ and normalizations $A_i$ and phases $\phi_i$, i.e. On the other hand the Fourier transform of a lightcurve can also be represented by a superposition of individual sinusoids."762 By drawing the amplitudes and phases of these sinusoids from a normal distribution and calculating the inverse Fourier transformation of these values. a linear. stochastic lightcurve can easily be simulated (Timmer&Kónig.1995)..," By drawing the amplitudes and phases of these sinusoids from a normal distribution and calculating the inverse Fourier transformation of these values, a linear, stochastic lightcurve can easily be simulated \citep{timmer95a}."763 To obtain a simulated lightcurve resembling observational data. randomly drawn amplitudes and phases of each frequency are weighted by a filter function that describes the frequency spectrum of the observed data.," To obtain a simulated lightcurve resembling observational data, randomly drawn amplitudes and phases of each frequency are weighted by a filter function that describes the frequency spectrum of the observed data."764 This filter function is given by the shape of the periodogram of the data. as only real values are important for the lightcurve (Uttleyetal..2005)..," This filter function is given by the shape of the periodogram of the data, as only real values are important for the lightcurve \citep{uttley05a}."765 According to the central limit theorem. the simulated lightcurve will have a normal brightness distribution. because it can be written as the sum of random numbers drawn from the same probability distribution.," According to the central limit theorem, the simulated lightcurve will have a normal brightness distribution, because it can be written as the sum of random numbers drawn from the same probability distribution."766 Uttleyetal.(2005) pointed out that in much the same way. a lighteurve with a log-normal brightness distribution can be simulated by using the product instead of the sum of randomized sinusoids.," \citet{uttley05a} pointed out that in much the same way, a lightcurve with a log-normal brightness distribution can be simulated by using the product instead of the sum of randomized sinusoids."767 This is most easily achieved by taking the exponential function of alinear lighteurve., This is most easily achieved by taking the exponential function of alinear lightcurve.768 Uttleyetal.(2005) used the method by Timmer&Kónig(1995) to obtain the linear lighteurve. an approach we also adopted for our analysis.," \citet{uttley05a} used the method by \citet{timmer95a} to obtain the linear lightcurve, an approach we also adopted for our analysis."769 In order to evaluate the shape of the power spectral density (PSD) of Vela X-1 we extracted a lightcurve with 6ssee resolution in the kkeV energy range and divided it into segments of evenly spaced data of ssec (214x6 ssec)., In order to evaluate the shape of the power spectral density (PSD) of Vela X-1 we extracted a lightcurve with sec resolution in the keV energy range and divided it into segments of evenly spaced data of sec $2^{13}\times6$ sec).770 In order to obtain evenly spaced lighteurves. we interpolated over small gaps around the slew time scale of ~ ssec.," In order to obtain evenly spaced lightcurves, we interpolated over small gaps around the slew time scale of $\sim$ sec."771 This interpolation reduces spurious power on the ScW timescale., This interpolation reduces spurious power on the ScW timescale.772 The average PSD for all segments drawn from data of Rev. 373-383 (Block 2) is shown in Fig. 5..," The average PSD for all segments drawn from data of Rev. 373–383 (Block 2) is shown in Fig. \ref{fig:psd_fit.eps},"773 together with the best- model consisting of a constant plus a power law and 6 Lorentzian lines., together with the best-fit model consisting of a constant plus a power law and 6 Lorentzian lines.774 The Lorentzians are characterized by their peak frequency. their width and their normalization. describing the overall contribution to the PSD.," The Lorentzians are characterized by their peak frequency, their width and their normalization, describing the overall contribution to the PSD."775 They are necessary to model the contribution of the strong pulse with a pulse period of 283.5ssec and its harmonies. as marked in Fig. 5..," They are necessary to model the contribution of the strong pulse with a pulse period of sec and its harmonics, as marked in Fig. \ref{fig:psd_fit.eps}."776 The frequencies of the Lorentzians were fixed to multiples of the pulse frequency., The frequencies of the Lorentzians were fixed to multiples of the pulse frequency.777 The first two Lorentzians are both located at the pulse frequency. with Lorentz | modeling a broad base. while Lorentz 2 models the narrow spike.," The first two Lorentzians are both located at the pulse frequency, with Lorentz 1 modeling a broad base, while Lorentz 2 models the narrow spike."778 The inclusion of the broad component drastically improves our fit., The inclusion of the broad component drastically improves our fit.779 Α similar superposition of two Lorentzians at the pulse frequency was also seen in. V. 0332-53 by Mowlavietal.(2000). who interpreted 1t as a quasi periodic oscillation (ΟΡΟ).," A similar superposition of two Lorentzians at the pulse frequency was also seen in V $+$ 53 by \citet{mowlavi06a}, who interpreted it as a quasi periodic oscillation (QPO)."780 A detailed analysis of this feature in Vela X-1 1s. however. beyond the scope of this paper.," A detailed analysis of this feature in Vela X-1 is, however, beyond the scope of this paper."781 It is interesting to note that the power at half the pulse period (7.05x107 HHz) is more than 4 times higher than at the actual pulse period., It is interesting to note that the power at half the pulse period $7.05\times10^{-3}$ Hz) is more than 4 times higher than at the actual pulse period.782 This effect is caused by the pulse shape in the regarded spectral energy range consisting of two very similar pulses. which could easily be misunderstood as pulsations with half the actual pulse period (Kreykenbohmetal. 1999).," This effect is caused by the pulse shape in the regarded spectral energy range consisting of two very similar pulses, which could easily be misunderstood as pulsations with half the actual pulse period \citep{kreykenbohm99a}."783". The underlying continuum of the PSD can be modeled accurately with the constant and the power law component of the model. with the power law having the shape v7"", where y=1.19."," The underlying continuum of the PSD can be modeled accurately with the constant and the power law component of the model, with the power law having the shape $\nu^{-\gamma}$, where $\gamma = 1.19$."784 All fit parameters are listed in Table 2.., All fit parameters are listed in Table \ref{tab:psdmodel}.785 The noise level of ISGRI PSDs is poorly understood. but a comparison with PCA PSDs shows that for instrumental reasons it is not purely Poissonian.," The noise level of ISGRI PSDs is poorly understood, but a comparison with PCA PSDs shows that for instrumental reasons it is not purely Poissonian."786 We are currently m the process of analyzing other data of other HMXB to investigate ISGRI’s broad band timing capabilities., We are currently in the process of analyzing other data of other HMXB to investigate ISGRI's broad band timing capabilities.787 For the present analysis. however. only the slope of the power law of the PSD is important. which is independent of the overall noise level.," For the present analysis, however, only the slope of the power law of the PSD is important, which is independent of the overall noise level."788 We compared the ISGRI result to PCA PSDs of Vela X-1 and found a value of y~1.4 for the latter., We compared the ISGRI result to PCA PSDs of Vela X-1 and found a value of $\gamma \sim 1.4$ for the latter.789 The difference does not change the outcome of the simulation., The difference does not change the outcome of the simulation.790 Contributions from the pulse period to the PSD can also be neglected. as the sampling rate of the lightcurve is chosen to eliminate them.," Contributions from the pulse period to the PSD can also be neglected, as the sampling rate of the lightcurve is chosen to eliminate them."791" The simulation was then carried out using a PSD of the shape i? ana taking care that the emerging statistical parameters (x), and c, are the same as for the input data.", The simulation was then carried out using a PSD of the shape $\nu^{-1.19}$ and taking care that the emerging statistical parameters $\left<x\right>_\text{sim}$ and $\tilde \sigma_\text{sim}$ are the same as for the input data.792 A part of the simulated lighteurve is shown in the lower panel of Fig. l.., A part of the simulated lightcurve is shown in the lower panel of Fig. \ref{fig:lc_20-60_4xx.pdf}.793 The overall behavior of the data. showing short. strong flares can be very well described with the model.," The overall behavior of the data, showing short, strong flares can be very well described with the model."794 The PSD has a relatively large power at low frequencies. showing up in notable variations in the statistical parameters of the emerging lightcurve between individual runs of the simulation.," The PSD has a relatively large power at low frequencies, showing up in notable variations in the statistical parameters of the emerging lightcurve between individual runs of the simulation."795 To determine the size of these variations. we simulated 250 lightcurves with the same parameters (x) and &.," To determine the size of these variations, we simulated 250 lightcurves with the same parameters $\left<x\right>$ and $\tilde\sigma$ ."796 As the simulated lighteurve incorporates a frequency, As the simulated lightcurve incorporates a frequency797T5N2 is that the high Nray luminosity is produced by the active nucleus. which is obscured at longer wavelengths by dust located in the cireununuclear regions: the heating of the dust bv the starburst produces the farautrared cnussion.,"7582 is that the high X–ray luminosity is produced by the active nucleus, which is obscured at longer wavelengths by dust located in the circumnuclear regions; the heating of the dust by the starburst produces the far-infrared emission."798 The availallity of the data longward of LOO pan allowed the detection of a very cold (1T IN) compoucut oei the SED of the disk., The availability of the data longward of 100 $\mu$ m allowed the detection of a very cold (17 K) component in the SED of the disk.799 This very cold compoucut is ue to dust beate by the interstellar radiation field aud --- dominates the dust mass of the galaxy: its inclusion oeicreases the dust mass detected now by a factor of 7., This very cold component is due to dust heated by the interstellar radiation field and it dominates the dust mass of the galaxy; its inclusion increases the dust mass detected now by a factor of 7.800of far-infrared emission. the presence of large amourts of molecular gas (Evansetal.1999)... ancl enission lines iu their optical spectra (see Figure 3ce).,"of far-infrared emission, the presence of large amounts of molecular gas \citep{evan1999}, and emission lines in their optical spectra (see Figure \ref{fig-3}c c)."801 The remaining radio galaxy which appears to be fairly isolated is 3C 386., The remaining radio galaxy which appears to be fairly isolated is 3C 386.802 Although the argumens are weaker. it lias some similarities with 3€ 293 and 3C 3+)05.," Although the arguments are weaker, it has some similarities with 3C 293 and 3C 305."803 Its radio morphology is that of a relaxed double. with a bright core ποιος by diffuse emission over a large area.," Its radio morphology is that of a relaxed double, with a bright core surrounded by diffuse emission over a large area."804 Consequently. i is not a classical FR I type radio source.," Consequently, it is not a classical FR I type radio source."805 Au additional three of the radio 2aaxles have LINER spectra (B2 0222--36. B2 02584-35. aud B2 1122-26).," An additional three of the radio galaxies have LINER spectra (B2 0222+36, B2 0258+35, and B2 1422+26)."806 In geteral. these ai'e also located tu poorer environments tha the classical FR I radio sources.," In general, these are also located in poorer environments than the classical FR I radio sources."807 Both B2 0258+35 and B2 1122-26 iive ouly five confirmed relmbers. and B2 0222-36 resides in a sysem with 11 conΠιο members.," Both B2 0258+35 and B2 1422+26 have only five confirmed members, and B2 0222+36 resides in a system with 14 confirmed members."808 However. the local environimeit of this latter source nay be moο complicated.," However, the local environment of this latter source may be more complicated."809 It is not the uxightest galaxy in its field. aud. appears to have a velocity which is «MIset E'On systeliic velocity.," It is not the brightest galaxy in its field, and appears to have a velocity which is offset from systemic velocity."810 The siuall uumber of velocities prohibits any statistical statements. bit thi115 sysien inicht be a pair of groups — one which iucludes the radio ealaxy aud another wlie liCdes the brighter galaxy.," The small number of velocities prohibits any statistical statements, but this system might be a pair of groups — one which includes the radio galaxy and another which includes the brighter galaxy."811 The rest of the radiο eaxies generally show classical FR E morphologies. inclucirο jets of radio eiuissiou which extend past the optical boundaries of the galaxies.," The rest of the radio galaxies generally show classical FR I morphologies, including jets of radio emission which extend past the optical boundaries of the galaxies."812 Optically. they all have absorptiou-line spectra itxlicaive of older stellar populatious.," Optically, they all have absorption-line spectra indicative of older stellar populations."813 With the exceptjon o. B2 13224-36. all of these galaxies have velocity disyersious in excess of 200 kin 1 iudicatiug jeir presence in structures raigiug [from the size ol eroups on up through poor Abell clusters. wl virial inasses [rom about 2x10! t0 3x10! AL..," With the exception of B2 1322+36, all of these galaxies have velocity dispersions in excess of 200 km $^{-1}$ indicating their presence in structures ranging from the size of groups on up through poor Abell clusters, with virial masses from about $2 \times 10^{13}$ to $3 \times 10^{14}$ $_\odot$."814 Thiis result is in agreement with the couclusi X Paper 1: he presence of a LER Eradk) SOULCEe Is al excellent indicator of an underlying grou j»oor, This result is in agreement with the conclusions of Paper 1: the presence of an FR I radio source is an excellent indicator of an underlying group or poor.815" Two of the FR I ""aclio sources (B2 1621438 aidà 16154351) have NAT 1‘phologies.", Two of the FR I radio sources (B2 1621+38 and 1615+351) have NAT morphologies.816 They are located it two of tle richer enviro1111011s of the sample. aid each have associe dilluse λος emission (Ferettietal.1995).," They are located in two of the richer environments of the sample, and each have associated diffuse X-ray emission \citep{fere1995}."817". BlitoLeal.(]LOOS) exanined NAT sources drawn froi 1a large samy of Abell clusers and noted that ¢ers with NATs were more likely to have su5ructure tlall ""adio-quiet custers.", \citet{blit1998} examined NAT sources drawn from a large sample of Abell clusters and noted that clusters with NATs were more likely to have substructure than radio-quiet clusters.818 Ckyalescence of slbstructures cai produce the large relative moions between AT. host galaxies ancl the intracluster gas uecessary to explain the radio morphologies of sich sources., Coalescence of substructures can produce the large relative motions between NAT host galaxies and the intracluster gas necessary to explain the radio morphologies of such sources.819 For B2 1621438. there is only slight evidence for substructure. a result undoubtedly related o the somewhat limite| number of velocites (21) in our study.," For B2 1621+38, there is only slight evidence for substructure, a result undoubtedly related to the somewhat limited number of velocites (24) in our study."820 The situation is iuproved [or 16154-351. with its 38 velociles producing several siguiicant results (see Section ??)).," The situation is improved for 1615+351, with its 38 velocities producing several significant results (see Section \ref{sec:rgmove}) )."821 In addition. he radio [n]galaxy 1s the seco brightest galaxy in the Ποια. with the brightest beiug NGC 6107.," In addition, the radio galaxy is the second brightest galaxy in the field, with the brightest being NGC 6107."822 This galaxy is also a radiο 50‘ce (Ekersetal.1978).. athough it is weaker than 16154-3251.," This galaxy is also a radio source \citep{eker1978}, although it is weaker than 1615+351."823 Figure |. plots the galaxy. clistriutl1 for 16154-351., Figure \ref{fig-4} plots the galaxy distribution for 1615+351.824 The eloieation is evident. ruuniug from SW to NE (whichisalsoconsistentwilhecliffIseX-rayeimissioiFerettietal.1905).," The elongation is evident, running from SW to NE \citep[which is also consistent with the diffuse X-ray emission;][]{fere1995}."825.. A elump of galaxies at lower velocities thau tl ecuster cener is seen to the NE., A clump of galaxies at lower velocities than the cluster center is seen to the NE.826 For relereuce. tle racio emissiou poiuts away [rom the galaxy. tovVal he NW.," For reference, the radio emission points away from the galaxy toward the NW."827 Iu total. these results indicate that the NATs in our study appear to be found in clisters with sibstructure. consistent with the findiugs for NATs in Abell," In total, these results indicate that the NATs in our study appear to be found in clusters with substructure, consistent with the findings for NATs in Abell"828lasst isks. and thus it seems possible that even modest. X-ray. emission could make such low uiass disks entirely active. increasing the amount of viscous evolution and draining the disk onto the centra nass nost rapicly to vielcl low accretion rates at ages of about 1 Myr.,"mass disks, and thus it seems possible that even modest X-ray emission could make such low mass disks entirely active, increasing the amount of viscous evolution and draining the disk onto the central mass most rapidly to yield low accretion rates at ages of about 1 Myr."829 More rapid. viscous evolution ineans that tle accretion rates of the vouugest brown dwarls must be much higher. by a signifiaut factor.," More rapid viscous evolution means that the accretion rates of the youngest brown dwarfs must be much higher, by a significant factor."830 Thus this model predicts that the decline of mass accretion rates with age should be faster iu brown dwaTs than iu the nearly solar-inass T Tauri stars (Harmann 1998)., Thus this model predicts that the decline of mass accretion rates with age should be faster in brown dwarfs than in the nearly solar-mass T Tauri stars (Hartmann 1998).831 In ackdition. he brown dwarls with t1e very low mass accretiou rates should liwe very low muu-wave emission ixcdicatiug (roiehly) very low-uiass disks. although the faintuess of he emission will make this precii‘lion difficult to test.," In addition, the brown dwarfs with the very low mass accretion rates should have very low mm-wave emission indicating (roughly) very low-mass disks, although the faintness of the emission will make this prediction difficult to test."832 Obse‘vations so [ar inclicate i0 reason why young brown «walls acc‘ele inae alitative cifferei1 uanuer [rom that characteristic of T Taur stars., Observations so far indicate no reason why young brown dwarfs accrete in a qualitatively different manner from that characteristic of T Tauri stars.833 Thus. sole of these isstes can |yO explore dlNw studies of very low mass T Tauri stars. which will be brighter and eas]er to studs.," Thus, some of these issues can be explored by studies of very low mass T Tauri stars, which will be brighter and easier to study."834 TI »edictiois of the previcius paragraph cau be tested by obtaining nuch larger samples ο: lulDi-wav CLUISSLO1 aud accretion rate estimates for 0.3—0.1AZ. stars., The predictions of the previous paragraph can be tested by obtaining much larger samples of mm-wave emission and accretion rate estimates for $0.3 - 0.1 \msun$ stars.835 If viscous evolution is faster in stars. one shoulc ¢observe a steeper decline of mass ace'etiou rate with age thai shown in tle uegher-hass samples «iscussed by Hartiuaun (1998). aid imuu-wave enmission sοι correlate strougly with accretion rate: the cur'eu data are not conchsive on this pOlnt. gelsren. the limited jiunber of «etectec ‘own clwarl disks (Ixlein 2003: Sclιοί 2006). the incertalutles in 'elatiug this eimnissico to disk mass. aud uicertainties in the 1lass accretion lae cleterminatious.," If viscous evolution is faster in lower-mass stars, one should observe a steeper decline of mass accretion rate with age than shown in the higher-mass samples discussed by Hartmann (1998), and mm-wave emission should correlate strongly with accretion rate; the current data are not conclusive on this point, given the limited number of detected brown dwarf disks (Klein 2003; Scholz 2006), the uncertainties in relating this emission to disk mass, and uncertainties in the mass accretion rate determinations."836 Laverec accellon with dead zoues is more likely to occur in higher-mass systems., Layered accretion with dead zones is more likely to occur in higher-mass systems.837 The existence of dead (or heal dead zoues is iiuportaut for planet formation. especially ist the 1-10 AU racial range: the |ighe wlace deusities are likely to vield Laster «ust grain erowtl auc settling to the midplane. axd il eclange inthe distribution of disk mass as a function of radius could slow down the so-called Type II viscous migratiou of gap-opeuiug planets (e.g.. Lit Papaloizou 1956).," The existence of dead (or nearly) dead zones is important for planet formation, especially in the 1-10 AU radial range; the higher surface densities are likely to yield faster dust grain growth and settling to the midplane, and the change in the distribution of disk mass as a function of radius could slow down the so-called Type II viscous migration of gap-opening planets (e.g., Lin Papaloizou 1986)."838 Finally. the possibility of inargitally gravitatjionally-uustable T Tauri disks siould 1ot be discounted given the uncertalnties in dust opacities.eS. at least [or the most massive systens.," Finally, the possibility of marginally gravitationally-unstable T Tauri disks should not be discounted given the uncertainties in dust opacities, at least for the most massive systems."839 The research of L.H. and N.C. was supported in part by NASA eransS NACÓ-9670. NACÓ- NAGS5-10515. atd grant AR-0952LOI-A from the Space Telescope Science Institute.," The research of L.H. and N.C. was supported in part by NASA grants NAG5-9670, NAG5-13210, NAG5-10545, and grant AR-09524.01-A from the Space Telescope Science Institute."840 PD ackuowledges grants frou Papii/UNAM aud CONACYT. Néxxico.," PD acknowledges grants from Papiit/UNAM and CONACyT, Méxxico."841 Suppor for this work was also provided by NASA thieο Contract Number 1257181 issued by JPL/Caltech and through the Spitzer Fellowship Progaig under award 011 508-001., Support for this work was also provided by NASA through Contract Number 1257184 issued by JPL/Caltech and through the Spitzer Fellowship Program under award 011 808-001.842"The following Table 1. presents the mean and median depth of the 2AIRS (A4,=11.25 mag) and 2MÁÀSS NSC (Aquas=13.5 mag) for the LF as given by ?..",The following Table \ref{Tab:depth} presents the mean and median depth of the 2MRS $K_\mathrm{max}=11.25$ mag) and 2MASS XSC $K_\mathrm{max}=13.5$ mag) for the LF as given by \cite{6dF_Fi}.843 The difference between the mean and (he median is in that case of the order of a lew percent., The difference between the mean and the median is in that case of the order of a few percent.844 The effective depth of a flux-limited survey is however not a good measure of the effective ol a thin shell in flux space. (in whieh the third coordinate is the flux. bv analogy. with the redshift space) that we seek.," The effective depth of a flux-limited survey is however not a good measure of the effective of a thin shell in `flux space' (in which the third coordinate is the flux, by analogy with the redshift space) that we seek."845 What we need is the mean value of distances of all galaxies 5., What we need is the mean value of distances of all galaxies $S$.846 The mean that we calculate will be (hus a conditional one., The mean that we calculate will be thus a conditional one.847 This derivation is qualitatively the sanie as for (he mean redshift of galaxies with a given flux. presented on pages 120121 of ?..," This derivation is qualitatively the same as for the mean redshift of galaxies with a given flux, presented on pages 120–121 of \cite{Pe93}."848 We start bv deriving the joint probability.distribution of galaxy distances + ad fluxes ο., We start by deriving the joint probabilitydistribution of galaxy distances $r$ and fluxes $S$.849 It is easily obtained bv differentiating (CX1)) with respect to Iuminositv L., It is easily obtained by differentiating \ref{eq:mathcalN}) ) with respect to luminosity $L$ .850 Hence. the differential number d2.N of galaxies with a LF &(£) in a volume element 9V. is eiven bv with. oV.x=ἐπDoδη ," Hence, the differential number $\delta^2 N$ of galaxies with a LF $\Phi(L)$ in a volume element $\delta V$ is given by with $\delta V=4\pi r^2\,\delta r$."851Now.- passing. trom. lIuminositv: to flux. £=σοι42775. forϱ fixed. r we have OL—4Axr? 05.," Now, passing from luminosity to flux, $L=4\pi r^2 S$, for fixed $r$ we have $\delta L=4\pi r^2\, \delta S$ ."852 This gives thejoint probability as The conditional probability for r given 5$ is, This gives thejoint probability as The conditional probability for $r$ given $S$ is853By calculating the likelihood over a range of power spectrum parameters. (he maximum ikelihood values of (he parameters can be determined.,"By calculating the likelihood over a range of power spectrum parameters, the maximum likelihood values of the parameters can be determined."854" If these values differ substantially from {he initial ""guess"" used to calculate the moments. then the moments should be recaleulated using the maximum likelihood. values."," If these values differ substantially from the initial “guess” used to calculate the moments, then the moments should be recalculated using the maximum likelihood values."855" This process can be iterated until the maximum ikelihood values are close to (he initial ""guess: (hiis ensures (hat (he moments are optimum rear (he peak of the likelihood function.", This process can be iterated until the maximum likelihood values are close to the initial “guess”; this ensures that the moments are optimum near the peak of the likelihood function.856" since our goal has been (o reduce (he sensitivity of our data to nonlinear velocities. it is of interest (ο examine the contributions to the individual moments uw, from different scale nodes."," Since our goal has been to reduce the sensitivity of our data to nonlinear velocities, it is of interest to examine the contributions to the individual moments $u_n$ from different scale modes."857 By substituting Eq. (22)), By substituting Eq. \ref{Rnm}) )858 in Eq. (2)).," in Eq. \ref{Rij}) ),"859 the variance for a given moment αμ can be willlen as term is the contribution to the due (ο , the variance for a given moment $u_{n}$ can be written as The second term is the contribution to the moment due to noise.860"The first term is the contributionThe to secondthe moment from the velocity field:moment this term cannoise, be further expanded as where we have defined the window funetion for the nth moment as where Wh) is given in Eq. (A7))", The first term is the contribution to the moment from the velocity field; this term can be further expanded as where we have defined the window function for the $n$ th moment as where $W^{2}_{ij}(k)$ is given in Eq. \ref{Wtsq}) )861 in the appendix., in the appendix.862 The window function W72() tell ux (he sensitivity of the moment {ο the scale corresponding to the wave number /., The window function $W^{2}_{n}(k)$ tell us the sensitivity of the moment $u_{n}$ to the scale corresponding to the wave number $k$.863" This gives us a check on our method: ideally. the moments that we retain should have window functions that are maximum at large scales and relatively small in the region Aj;>h£I, (see Sec. 5))."," This gives us a check on our method; ideally, the moments that we retain should have window functions that are maximum at large scales and relatively small in the region $k_{nl}\ge k \ge k_{c}$ (see Sec. \ref{sec-pow}) )."864 llowever. since we have chosen our moments by their insensitivitv (o small scales. there is no guarantee (hat thev will necessarily be sensitive (o large scales.," However, since we have chosen our moments by their insensitivity to small scales, there is no guarantee that they will necessarily be sensitive to large scales."865 Indeed. we have found that in some cases a small number of the modes found by this method turn out to be insensitive to almostalf scales.," Indeed, we have found that in some cases a small number of the modes found by this method turn out to be insensitive to almost scales."866 This can occur when a mode is either dominated bv far away galaxies with huge errors or by à close pair of galaxies: a moment representing the difference of the velocities of two closely spaced. galaxies is sensiüve only (o scales which are smaller (han (he separation., This can occur when a mode is either dominated by far away galaxies with large errors or by a close pair of galaxies; a moment representing the difference of the velocities of two closely spaced galaxies is sensitive only to scales which are smaller than the separation.867 Since the moments are normalized to have unit variance. (he ones with low signal to noise can be found by examining the contribution to the variance of each moment from the noise part of (he covariance matrix: moments wilh a noise contribution above some threshold. can be discarded.," Since the moments are normalized to have unit variance, the ones with low signal to noise can be found by examining the contribution to the variance of each moment from the noise part of the covariance matrix; moments with a noise contribution above some threshold can be discarded."868 One concern is that the same smallscale. nonlinear effects (hat we are (rving to remove can also lead to deviations from Gaussianitv. which our method does not account lor.," One concern is that the same small–scale, nonlinear effects that we are trying to remove can also lead to deviations from Gaussianity, which our method does not account for."869 While ib is plausible (hat (hese deviations are small enough in twpical velocity survevs as (o nol significantly bias the results. the only way to be sure about (his is to test the method on realistic simulated catalogs.," While it is plausible that these deviations are small enough in typical velocity surveys as to not significantly bias the results, the only way to be sure about this is to test the method on realistic simulated catalogs."870at approximately L in the quasar luminosity function (equation 12)).,at approximately $L^*$ in the quasar luminosity function (equation \ref{eqn:Lstar}) ).871 The turn-over is less pronounced for higher redshift quasars. [attening somewhat and even increasing to veh luminosities at z=d.," The turn-over is less pronounced for higher redshift quasars, flattening somewhat and even increasing to high luminosities at $z=4$."872 Due to the simplicity and transpareney of the model we know exactly why model quasar lifetimes behave in this wav: quasars occupy a narrower range of halo masses at late times relative to early times (skip forward to figure LO to see this)., Due to the simplicity and transparency of the model we know exactly why model quasar lifetimes behave in this way: quasars occupy a narrower range of halo masses at late times relative to early times (skip forward to figure \ref{fig:evolution} to see this).873 Because of this. low redshift bright quasars are rare amongst he abundant ~LOMAL. mass halos they oceupy (hence the urnover at bright luminosities). whereas high redshift bright quasars are [frequent among their rare ~LOMAL. mass halo josts (hence fo remains flat).," Because of this, low redshift bright quasars are rare amongst the abundant $\sim 10^{13} M_\odot$ mass halos they occupy (hence the turnover at bright luminosities), whereas high redshift bright quasars are frequent among their rare $\sim 10^{13} M_\odot$ mass halo hosts (hence $t_Q$ remains flat)."874 Painter quasars (those with ~Lox L*) tend to always commonly. populate mostly abundant halos. again resulting in a relatively constant fo.," Fainter quasars (those with $\sim L_Q<L^*$ ) tend to always commonly populate mostly abundant halos, again resulting in a relatively constant $t_Q$ ."875 We will return to this point in Section 4.2.., We will return to this point in Section \ref{sec:application}.876 Physically speaking. it is important to realise that the trends seen in figure 5. do not result. from the explicit modelling of a changing Ecldineton accretion fraction. as has often. been explored. (e.g.2)...," Physically speaking, it is important to realise that the trends seen in figure \ref{fig:tQ} do not result from the explicit modelling of a changing Eddington accretion fraction, as has often been explored \citep[e.g.][]{Hopkins2005d}."877 Quasars in our mocel are assumed. to always accrete at a fixed. fraction. of the Eddington rate across the quasarlifetime., Quasars in our model are assumed to always accrete at a fixed fraction of the Eddington rate across the quasar.878 This is a kev difference between our model and. many. previous works. and may explain its ability to simultaneously match such a wide range of observations.," This is a key difference between our model and many previous works, and may explain its ability to simultaneously match such a wide range of observations."879 For example. ? find an over-production of bright quasars at low redshift.," For example, \cite{Wyithe2003} find an over-production of bright quasars at low redshift."880 In our model. such quasars have very short lifetimes. ancl hence are. not commonly seen in surveys.," In our model, such quasars have very short lifetimes, and hence are not commonly seen in surveys."881 This may simply arise due to the diwindling supply of cold gas in massive systems at [ate times (?).., This may simply arise due to the dwindling supply of cold gas in massive systems at late times \citep{Fabian1994}.882 Observations suggest that a black hole gains the majority of its mass while in the active high accretion (quasar) shase (2).., Observations suggest that a black hole gains the majority of its mass while in the active high accretion (quasar) phase \citep{Heckman2004}.883 The cumulative ellect of such mass growth over cosmic time is measurable in the local (passive) black hole x»pulation., The cumulative effect of such mass growth over cosmic time is measurable in the local (passive) black hole population.884 Our model makes a prediction for the active slack hole mass function., Our model makes a prediction for the active black hole mass function.885 It is important to note that this oedietion. arises via the dual constraint of linking quasar umiinosity to halo virial mass through the mig@ relation (equation 7)). and from matching the abundance of black roles to the quasar luminosity function. (Section 2.2)) at various redshifts.," It is important to note that this prediction arises via the dual constraint of linking quasar luminosity to halo virial mass through the $m_{\rm BH} - \sigma$ relation (equation \ref{eqn:mass2mag}) ), and from matching the abundance of black holes to the quasar luminosity function (Section \ref{sec:selection}) ) at various redshifts."886 We did not tune the model in this regard o force a particular outcome., We did not tune the model in this regard to force a particular outcome.887 1n figure G6 we show the observed cumulative black hole mass function for both z=O passive and z=2 active jack holes., In figure \ref{fig:BHMF} we show the observed cumulative black hole mass function for both $z=0$ passive and $z=2$ active black holes.888 Εις figure is adoptedl from figure 6 of ?.., This figure is adopted from figure 6 of \cite{McLure2004}.889 The upper thin solid. and. dashed.l lines show the local observed results inferred from the mpy bulge luminosity relation and mpgc0 relation. respectively.," The upper thin solid and dashed lines show the local observed results inferred from the $m_{\rm BH}-$ bulge luminosity relation and $m_{\rm BH}-\sigma$ relation, respectively."890 Phe three data points show the cumulative SDSS quasar mass function at >=2 for three different limiting black hole masses., The three data points show the cumulative SDSS quasar mass function at $z=2$ for three different limiting black hole masses.891 The upward. pointing arrows on each indicate that the space density measured in each bin is incomplete. and hence provide only a lower limit to the true mass clonsity.," The upward pointing arrows on each indicate that the space density measured in each bin is incomplete, and hence provide only a lower limit to the true mass density."892 The three thick lines in figure 6/— show the moclel prediction for our. complete sample of quasar black holes at redshifts 0.5. 2.0. and 4.0. as indicated in the legend.," The three thick lines in figure \ref{fig:BHMF} show the model prediction for our complete sample of quasar black holes at redshifts $0.5$, $2.0$, and $4.0$, as indicated in the legend."893 For black holes more massive than logmigzi9.0 at z=2 our model is close to the lower limit found in the SDSS data., For black holes more massive than $\log m_{\rm BH}\simgt 9.0$ at $z=2$ our model is close to the lower limit found in the SDSS data.894 Η true. the model indicates (perhaps unsurprisingly) that much of the massive end of the black holemass function forms solely from accretion during this time of peak activity.," If true, the model indicates (perhaps unsurprisingly) that much of the massive end of the black holemass function forms solely from accretion during this time of peak activity."895"of this study was an analytical prescription for the heating ratio Q,/Q.(J,.T,/T.). a fiction of ouly two plasiia parameters. the proton placa beta ἐν aud the protou-to-clectrou temperature ratio T,/7,.","of this study was an analytical prescription for the heating ratio $Q_p/Q_e(\beta_p, T_p/T_e)$, a function of only two plasma parameters, the proton plasma beta $\beta_p$ and the proton-to-electron temperature ratio $T_p/T_e$."896 The linits of validity of this heating ratio prediction were giveu as a constraint on the minium scale of turbuleut energy injection (assuming anu isotropic driviug nechanisni for the turbulence)., The limits of validity of this heating ratio prediction were given as a constraint on the minimum scale of turbulent energy injection (assuming an isotropic driving mechanism for the turbulence).897" This paper describes the application of the Howes(2000). heating prescription topredict the proton-to- turbulent heating rate |Qe) for the high- solar windand compares Q,/(GQ,the resulting prediction to the empirical estimate of Cranmeretal.(2009)."," This paper describes the application of the \citet{Howes:2010d}898 heating prescription topredict the proton-to-total turbulent heating rate $Q_p/(Q_p+Q_e)$ for the high-speed solar windand compares the resulting prediction to the empirical estimate of \citet{Cranmer:2009}."899. This section describes the prediction of the ratio of he proton-to-total turbulent heating Ορ|Q.) iu he high-speed solar wind as a function of heliocentric radius Rousing the turbulent heating prescription bv Howes(2010).., This section describes the prediction of the ratio of the proton-to-total turbulent heating $Q_p/(Q_p+Q_e)$ in the high-speed solar wind as a function of heliocentric radius $R$ using the turbulent heating prescription by \citet{Howes:2010d}.900" Since this prescription cepeuds on the asma parameters 3, aud it is uecessary to construct a imodel of the high-speed0/2). solar wind to deteriuue the variation of these plasma parameters with welioceutric radius."," Since this prescription depends on the plasma parameters $\beta_p$ and $T_p/T_e$, it is necessary to construct a model of the high-speed solar wind to determine the variation of these plasma parameters with heliocentric radius."901 In82.1... we describe the solar wiud uodel.," In, we describe the solar wind model."902 In§2.2.. we review the theoretical framework of low-frequency. anisotropic turbulence in a uaenetized. weakly collisional plasina that uuderlies he turbulent heating prescription.," In, we review the theoretical framework of low-frequency, anisotropic turbulence in a magnetized, weakly collisional plasma that underlies the turbulent heating prescription."903" This prescription is cluploved to predict the protou-to-total turbulent eating Q,/(Q,|Q.) in§2.", This prescription is employed to predict the proton-to-total turbulent heating $Q_p/(Q_p+Q_e)$ in.9043.. Tn82. we estimate the evolution of the width of the inertial rangeL. in the lieh-speed solar wind iu order to verify the validitv of the urbulent heating prescription im82.," In, we estimate the evolution of the width of the inertial range in the high-speed solar wind in order to verify the validity of the turbulent heating prescription in."9055.. We adopt the same specific model for the ligh-specd solar wind used by Crammerctal.(2009) to facilitate the conrparisou to their enipirical turbulent heating estimate., We adopt the same specific model for the high-speed solar wind used by \citet{Cranmer:2009} to facilitate the comparison to their empirical turbulent heating estimate.906" This model is uxed to specify. as a function of helioceutric radius HR. the two key plasma parameters required by the turbulent heating prescription: the proton plasma bota j, aud the protou-to-clectron temperature ratio Τρ1ο."," This model is used to specify, as a function of heliocentric radius $R$ , the two key plasma parameters required by the turbulent heating prescription: the proton plasma beta $\beta_p$ and the proton-to-electron temperature ratio $T_p/T_e$."907 Analvtic fits to mncastreinents of the high-speed solar wind (faster than 600 km 1)from the aud spacecraft over the range 0.29AU<R«5.1 were used by Crammeretal.(2009) to generate equations for the proton and electron temperatures as function of helioceutric radius A. where «—ιδAU).," Analytic fits to measurements of the high-speed solar wind (faster than 600 km $^{-1}$ )from the and spacecraft over the range $0.29\mbox{ AU} <R<5.4\mbox{908AU}$ were used by \citet{Cranmer:2009} to generate equations for the proton and electron temperatures as function of heliocentric radius $R$, where $x \equiv \ln(R/1\mbox{ AU})$."909" Iu addition to the proton temperature. we need to specity the form of the proton density and magnetic field strength to determine the proton plasina beta 3,=Soul, B?."," In addition to the proton temperature, we need to specify the form of the proton density and magnetic field strength to determine the proton plasma beta $\beta_p= 8 \pi n_p T_p/B^2$ ."910 Following Crammerotal.(2009).. we take a proton deusity of the form where ay=2.5cur7.," Following \citet{Cranmer:2009}, we take a proton density of the form where $n_0 = 2.5\mbox{ cm}^{-3}$."911 The empirical turbuleut heating constraints calculated by Crammeretal.(2009) used a colatitude 0=15° to model the high-latitude measurements., The empirical turbulent heating constraints calculated by \citet{Cranmer:2009} used a colatitude $\theta=15^\circ$ to model the high-latitude measurements.912" For the lelioceutric distances covered by this model. the winding of the maguetic field iuto the Parker spiral for the high-speed streams at this colatitude is relatively weak. so a simple monopolar model for the magnetic field strength is a reasonable approximation. with By22.5«106, "," For the heliocentric distances covered by this model, the winding of the magnetic field into the Parker spiral for the high-speed streams at this colatitude is relatively weak, so a simple monopolar model for the magnetic field strength is a reasonable approximation, with $B_0 = 2.5 \times 10^{-5}\mbox{ G}$."913"Using these fuuctions for T,. τοι αν. aud DB in ligh- solar wind streams. we fiud that the proton plasina beta varies from ἐν=0.92 at 0.29 AU to J,=31 at 5.1 AU. aud the protou-to-clectron temperature ratio varies from T,/T.=3.9 at 0.29 AU to T/T.=1.5 at 5.1 AU."," Using these functions for $T_p$, $T_e$, $n_p$, and $B$ in high-speed solar wind streams, we find that the proton plasma beta varies from $\beta_p=0.92$ at 0.29 AU to $\beta_p=34$ at 5.4 AU, and the proton-to-electron temperature ratio varies from $T_p/T_e=3.9$ at 0.29 AU to $T_p/T_e=1.3$ at 5.4 AU."914 The heating prescription preseuted iu Iowes(2010) is determined using a model for the turbulent cascade of enerev in a magnetized. weakly collisional plasima (ITowes," The heating prescription presented in \citet{Howes:2010d} is determined using a model for the turbulent cascade of energy in a magnetized, weakly collisional plasma \citep{Howes:2008b}."915 The cascade model determines the steady state form of the maguetic οσον spectruii of fluctuations. based on three primary assumptions: (1) the IKohuogorov hypothesis that the energv cascade is determined by local interactions (Ixoliiogorov1910): (2) the turbulence maintains a state of critical balance at all scales (Coldveich&Sridhar1905): aud (3) the linear kinetic damping rates are applicable in the uoulincarly turbulent plasma.," The cascade model determines the steady state form of the magnetic energy spectrum of fluctuations, based on three primary assumptions: (1) the Kolmogorov hypothesis that the energy cascade is determined by local interactions \citep{Kolmogorov:1941}; (2) the turbulence maintains a state of critical balance at all scales \citep{Goldreich:1995}; and (3) the linear kinetic damping rates are applicable in the nonlinearly turbulent plasma."916 The dependence of the nonlinear cnerey trauster rate on the local turbulent fluctuations in the cascade model (lowesetal.2008a) ids inspired by the following theoretical picture of low-frequency. anisotropic turbulence in a magnetized. weakly collisional plasiua (ILlowes2008:Schekochihimetal.2009).," The dependence of the nonlinear energy transfer rate on the local turbulent fluctuations in the cascade model \citep{Howes:2008b} is inspired by the following theoretical picture of low-frequency, anisotropic turbulence in a magnetized, weakly collisional plasma \citep{Howes:2008c,Schekochihin:2009}."917. The cucrey of fluctuations is injected into the turbulence isotropically at a scale much lareer than the ion Larmor radius. Ly29ρε. corresponding to an isotropic diving wavemuuber hyp;l.," The energy of fluctuations is injected into the turbulence isotropically at a scale much larger than the ion Larmor radius, $L_0 \gg \rho_i$, corresponding to an isotropic driving wavenumber $k_0 \rho_i \ll9181$."919 Since the damping of fluctuations at this laree scale by wave-xuwticle interactions in a weakly collisional plasma is icelieible. the turbulent fluctuations rise to sufficient auplitudes that noulinear iuteractious between counter-oxopagatine wave packets transfer the turbuleut Huctuation energv to simaller scales.," Since the damping of fluctuations at this large scale by wave-particle interactions in a weakly collisional plasma is negligible, the turbulent fluctuations rise to sufficient amplitudes that nonlinear interactions between counter-propagating wave packets transfer the turbulent fluctuation energy to smaller scales."920 This sets τι critically-balanced. anisotropic cascade of MIID. waves over all scales down to the perpeucdicular scale of he ion Larmor radius. τρις1 (Goldreich&Sridhar1995:Boldyvrev2005) field.," This sets up a critically-balanced, anisotropic cascade of MHD waves over all scales down to the perpendicular scale of the ion Larmor radius, $k_\perp \rho_i \lesssim 1$ \citep{Goldreich:1995,Boldyrev:2005} ."921.. Even in a weakly collisional plasina. the dynamics of his wave cascade is rigorously described by tle equations of reduced MIID. (Schekochihiuetal. 2009)..," Even in a weakly collisional plasma, the dynamics of this wave cascade is rigorously described by the equations of reduced MHD \citep{Schekochihin:2009}. ."922" At the perpendicular scale of the jon Larimerradius hop,c αν the turbulence transitions to a critically valaniced. anisotropic cascade of kinetic waves over the perpendicular scales τρις 1."," At the perpendicular scale of the ion Larmorradius $k_\perp \rho_i \sim 1$ , the turbulence transitions to a critically balanced, anisotropic cascade of kinetic waves over the perpendicular scales $k_\perp \rho_i \gtrsim 1$ ."923 The range of scales traversed by the MOTD wave cascade. between the driving scale and the ion Larmor radius scale. is conunonly designated the “inertial range” (Xohnogorov1911). of MOTD ie... the rane," The range of scales traversed by the MHD wave cascade, between the driving scale and the ion Larmor radius scale, is commonly designated the “inertial range” \citep{Kolmogorov:1941} of MHD , the range"924 The range of scales traversed by the MOTD wave cascade. between the driving scale and the ion Larmor radius scale. is conunonly designated the “inertial range” (Xohnogorov1911). of MOTD ie... the ranec," The range of scales traversed by the MHD wave cascade, between the driving scale and the ion Larmor radius scale, is commonly designated the “inertial range” \citep{Kolmogorov:1941} of MHD , the range"925these ΠΡΟΣ sorted in ascending order. M is the median mean of data.c;,"these numbers sorted in ascending order, M is the median mean of data $x$."926" Then the estimate of 1l/—5j quautile of the distribution of τρ, is ay=Wi.", Then the estimate of $1-\beta$ quantile of the distribution of $W_{(i)}$ is $\widehat{\omega _{\beta}}=W_{(m)}$.927 Now set aud in which case the bend nidvariuice is where Fie., Now set and in which case the bend midvariance is where Fig.928 lg shows the relative enmipirical influence functions for variances computed with 7s., 1g shows the relative empirical influence functions for variances computed with $T_{8}$.929" The LOSS= 0.96, ", The $LOSS=0.96$ .930This estimate is described iu (Shurygin.2000)., This estimate is described in \citep{shur01}.931. Mean is estimated as a solution of the equation and variance is defined as a solution of the equation where q;—αμfr)?fo2., Mean is estimated as a solution of the equation and variance is defined as a solution of the equation where $q_{i}=(x_{i}-\widehat{\mu_{r}})^{2}/\widehat{\sigma ^{2}}$.932 Fie., Fig.933 dh shows the relative enipirical influence fictions for variances computed with 75., 1h shows the relative empirical influence functions for variances computed with $T_{9}$.934 The LOSS=0.95., The $LOSS=0.98$.935 D. A. Lax performed a Monte Carlo study. of nore than 150 variance estimators., D. A. Lax performed a Monte Carlo study of more than 150 variance estimators.936 Seventeen of hese estimators were selected as beg cither ΟΙΊο or commonly used (Lax 1985)., Seventeen of these estimators were selected as being either promising or commonly used \citep {lax85}.937. The results of our computer simulation are iu agrecmicut with this test (LaxL985).. especially concerning he high cfiiciency of estimate { aud T7 and the ow efficiency. of T3.," The results of our computer simulation are in agreement with this test \citep {lax85}, especially concerning the high efficiency of estimate $T_{1}$ and $T_{7}$ and the low efficiency of $T_{3}$."938 The choice of a particular estimate depends ou the type and iuteusitv of ΠΕΙ. the type of observations aud the method of implementation (hardware or software).," The choice of a particular estimate depends on the type and intensity of RFI, the type of observations and the method of implementation (hardware or software)."939 Zs aud T5 are the best estimates from the point of view of LOSS., $T_{8}$ and $T_{9}$ are the best estimates from the point of view of $LOSS$.940 T3 and Ts remove outliers in a most effective way (high value of the breakdown poit)., $T_{3}$ and $T_{5}$ remove outliers in a most effective way (high value of the breakdown point).941 Number sorting and permutations of pairwise nieasurenments which are necessary in several algoritlius require more conrputational time aud computer niemory., Number sorting and permutations of pairwise measurements which are necessary in several algorithms require more computational time and computer memory.942 This section preseuts computer simulations of ΠΕΙ initigation using algorithms which were eniploved in observations (Section L)., This section presents computer simulations of RFI mitigation using algorithms which were employed in observations (Section 4).943" Two estimators frou, the the previous section have. οσο. chosen: Winsorization and exponential weighting.", Two estimators from the the previous section have been chosen: winsorization and exponential weighting.944 The reasons for this choice are as follows., The reasons for this choice are as follows.945" All algorithDius described in Section 3. give estimates of variance. Ίνοι, they work as total power detectors (TPD) iu radiotechuical terminology."," All algorithms described in Section 2 give estimates of variance, i.e., they work as total power detectors (TPD) in radiotechnical terminology."946 They can be applied in single dish observations both iu οσομα and in spectral observations., They can be applied in single dish observations both in continuum and in spectral observations.947 Tn the same manner they can substitute for TPDs which are already installed in existing radio telescopes., In the same manner they can substitute for TPDs which are already installed in existing radio telescopes.948 Nowadays it is practically impossible for technical and oreanizational reasons., Nowadays it is practically impossible for technical and organizational reasons.949Iu future radio relescopes nav be equipped with some REI wiutigation fechniques and these variance estimators could then be implemented in hardware or software shape.,In future radio relescopes may be equipped with some RFI mitigation techniques and these variance estimators could then be implemented in hardware or software shape.950 But at the present time any experiuenut with RFEIauitigatiou at existing ratio elescopes must take the technical constraiuts of inpleieutation iuto account., But at the present time any experiment with RFI mitigation at existing ratio telescopes must take the technical constraints of implementation into account.951 Therefore only those estimators from Section 2 were chosen which could xovide uot only estimates of variance but also vclean data which could be applied further to TPD or to the correlator already i use ina radio clescope backend., Therefore only those estimators from Section 2 were chosen which could provide not only estimates of variance but also “clean” data which could be applied further to TPD or to the correlator already in use in a radio telescope backend.952 Winsorization with the paramcter 5=0.05 was chosen mainly because nuapulse-lihke REI iu the temporal domain was predonmuünaut durus observations made at Effelsbere prescuted in Fie., Winsorization with the parameter $\gamma=0.05$ was chosen mainly because impulse-like RFI in the temporal domain was predominant during observations made at Effelsberg presented in Fig.953 S., 8.954 Tt was strong aud sparse., It was strong and sparse.955 The percentage of RET in the whole volume of data was not large (<<5%)., The percentage of RFI in the whole volume of data was not large $(<5\%)$.956" Both wiusorization aud παπο can provide raw data without outhers but trinus iucounvenieutlv reduces the nuuber of samples because of this Huplementation problem: c""fiuiugis distorted."," Both winsorization and trimming can provide raw data without outliers but trimming inconveniently reduces the number of samples because of this implementation problem: “timing”is distorted,"957The most important consequence is that the field settles into a the tension force can be estimated by B.VB-—kK~KB?kuB onthe average.,The most important consequence is that the field settles into a the tension force can be estimated by $\vB\cdot\nabla\vB\sim \kpar B^2 \sim KB^2 \sim\kd B^2$ on the average.958 A simple|B argument can be envisioned to further support this statement., A simple argument can be envisioned to further support this statement.959 Let us write the evolution equation for F=B:VB: VF=F 4να... where the diffusion terms are again dropped.," Let us write the evolution equation for $\vF=\vB\cdot\nabla\vB$: = +, where the diffusion terms are again dropped."960 Suppose for a moment that the field is chaotically tangled. te. F~ with &|~ko»Κω.," Suppose for a moment that the field is chaotically tangled, i.e. $F\sim\kpar B^2$ with $\kpar\sim\kperp\gg\kd$."961 Then the term in that involves kBthe second derivatives of the velocity field can be neglected and becomes formally identical to the evolution equation for B., Then the term in that involves the second derivatives of the velocity field can be neglected and becomes formally identical to the evolution equation for $\vB$.962 The moments of F must. therefore. grow at the same rates as the moments of B. and we estimate (F)/(B5x(B75(B5. which decays exponentially fast in time.," The moments of $\vF$ must, therefore, grow at the same rates as the moments of $\vB$, and we estimate $\Fsq/\Bfr\propto\Bsq/\Bfr$, which decays exponentially fast in time."963" An exact statistical/ calculation for the Kazantsev—Kraichnan velocity. shows that. indeed. MK, asymptotically with time. starting from any mitial conditions (SCMMO02)."," An exact statistical calculation for the Kazantsev–Kraichnan velocity, shows that, indeed, ^2 asymptotically with time, starting from any initial conditions (SCMM02)."964 The convergence is exponentially fast at the stretching (eddy-turnover) rate., The convergence is exponentially fast at the stretching (eddy-turnover) rate.965 We conclude that even an initially chaotically tangled magnetic field will quickly develop the folding structure., We conclude that even an initially chaotically tangled magnetic field will quickly develop the folding structure.966 Thus. the nonlinear saturation. which is due to the Lorentz tension balancing the stretching action of the flow. occurs when the energy of the field becomes comparable to the energy of the turbulent eddies.," Thus, the nonlinear saturation, which is due to the Lorentz tension balancing the stretching action of the flow, occurs when the energy of the field becomes comparable to the energy of the turbulent eddies."967 Note that in a hypothetical chaotically tangled field with &j~Κι. the tension would be much larger: B.VB-— so saturation would be possible already at very low magnetic kB.energies.," Note that in a hypothetical chaotically tangled field with $\kpar\sim \kperp$, the tension would be much larger: $\vB\cdot\nabla\vB\sim \kres B^2$, so saturation would be possible already at very low magnetic energies."968 o satisfactory analytical description of the nonlinear state is as yet available. so one must be guided by results of numerical experiments.," No satisfactory analytical description of the nonlinear state is as yet available, so one must be guided by results of numerical experiments."969 The main obstacle in the way of a definitive numerical study is the tremendously wide range of scales that must be resolved in order to adequately simulate the large-Pr MHD: indeed. one must resolve scaling intervals. the hydrodynamic inertial range and the subviscous magnetic one.," The main obstacle in the way of a definitive numerical study is the tremendously wide range of scales that must be resolved in order to adequately simulate the large-Pr MHD: indeed, one must resolve scaling intervals, the hydrodynamic inertial range and the subviscous magnetic one."970 Since this is not feasible. we propose to simulate the initial stage of the nonlinear evolution up to the point when thesore! energy of the magnetic field equalizes with the energy of the viscous-scale turbulent eddies.," Since this is not feasible, we propose to simulate the initial stage of the nonlinear evolution up to the point when the energy of the magnetic field equalizes with the energy of the viscous-scale turbulent eddies."971 This stage can be studied in the where the hydrodynamic Reynolds number Re is order one and the external forcing models the energy supply from the larger eddies (cf.Catta-neo.Hughes.&Kim1996:Kinneyetal.2000).," This stage can be studied in the where the hydrodynamic Reynolds number $\Re$ is order one and the external forcing models the energy supply from the larger eddies \citep[cf.][]{Cattaneo_Hughes_Kim,Kinney_etal}."972. Moreover. one can argue (MCMO02.Schekochihinetal.2002b) that once the magnetic energy does equalize with that of the smallest eddies. the following scenario takes place.," Moreover, one can argue \citep[MCM02,][]{SCHM_ssim} that once the magnetic energy does equalize with that of the smallest eddies, the following scenario takes place."973 The magnetic back reaction leads to suppression of the shearing motions associated with the viscous-scale eddies., The magnetic back reaction leads to suppression of the shearing motions associated with the viscous-scale eddies.974 Larger-scale eddies. which are more energetic (but have slower turnover rates). continue to drive the small-scale magnetic fluctuations by the same stretching mechanism that the viscous-scale ones did. until the magnetic field becomes strong enough to suppress these eddies as well.," Larger-scale eddies, which are more energetic (but have slower turnover rates), continue to drive the small-scale magnetic fluctuations by the same stretching mechanism that the viscous-scale ones did, until the magnetic field becomes strong enough to suppress these eddies as well."975 This process continues until all field-stretching motions throughout the inertial range are suppressed (seeSchekochi-hinetal.2002b.forfurtherdiscussion)..., This process continues until all field-stretching motions throughout the inertial range are suppressed \citep[see][for further discussion]{SCHM_ssim}.976 Speculatively. this could be thought of as some effective renormalization of Re. so that the final statistics of the magnetic field would again be described by the low-Re MHD model.," Speculatively, this could be thought of as some effective renormalization of Re, so that the final statistics of the magnetic field would again be described by the $\Re$ MHD model."977 Some numerical evidence supporting this picture is given by MCMO2., Some numerical evidence supporting this picture is given by MCM02.978 In our simulations. we choose the parameters so that the forcing and the viscous scales are comparable and the statistics of the subviscous-range magnetic fluctuations can be studied already at 128? resolution.," In our simulations, we choose the parameters so that the forcing and the viscous scales are comparable and the statistics of the subviscous-range magnetic fluctuations can be studied already at $128^3$ resolution."979 The numerical set-up and the spectral MHD code used are exhaustively described. in MCMO02., The numerical set-up and the spectral MHD code used are exhaustively described in MCM02.980 The foreing ts large scale. nonhelical. and white in time.," The forcing is large scale, nonhelical, and white in time."981 The units are based on the box size | and the forcing power |., The units are based on the box size 1 and the forcing power 1.982 In these units. setting 725«10 effectively leads to Re—I.," In these units, setting $\nu=5\cdot10^{-2}$ effectively leads to $\Re\sim1$."983 After the initial kinematic growth stage. saturation. Is achieved where the total magnetic and hydrodynamic energies are We then measure the PDFs of the magnetic-field strength and curvature in the saturated state.," After the initial kinematic growth stage, saturation is achieved where the total magnetic and hydrodynamic energies are We then measure the PDFs of the magnetic-field strength and curvature in the saturated state."984 Our findings are as follows., Our findings are as follows.985Llubble as this is mainly correlated. to the inclination of galaxies rather than any intrinsic properties of the galaxies.,Hubble as this is mainly correlated to the inclination of galaxies rather than any intrinsic properties of the galaxies.986 These authors developed two main classes for cllipticals and several branches within each type., These authors developed two main classes for ellipticals and several branches within each type.987 As a subjective scheme however. the classes are not robust and many galaxies have properties that belong to multiple classes or none at. all.," As a subjective scheme however, the classes are not robust and many galaxies have properties that belong to multiple classes or none at all."988 lxormendy&Dender(1996) attribute these inconsistencies to heterogeneous formation histories., \citet{KB:96} attribute these inconsistencies to heterogeneous formation histories.989 More recentlv. automated classification schemes such as Artificial Neural Networks (ANNs) (Naimetal.19972:3azell2000:Odewahnctal.9005} have been used to acconimodate the vast. quantities of galaxies that require Classification and to a large extent ANNs eliminate. any subjective bias in the classification process. as well as being verv accurate (Balletal.2004).," More recently automated classification schemes such as Artificial Neural Networks (ANNs) \citep{NRG:97a,Baz:00,Ode:02} have been used to accommodate the vast quantities of galaxies that require classification and to a large extent ANNs eliminate any subjective bias in the classification process, as well as being very accurate \citep{Bal:04}."990.. ANNs cannot create a new Classification system but. rather replicate visual classification and with much higher consistency., ANNs cannot create a new classification system but rather replicate visual classification and with much higher consistency.991 These systems require a “lest sample” previously classified by a human expert on which to base classifications which has the disadvantage of allowing the same human biases anc [laws of the classification svstem to propagate.," These systems require a “test sample"" previously classified by a human expert on which to base classifications which has the disadvantage of allowing the same human biases and flaws of the classification system to propagate."992 The use of Self Organising Maps by Naimetal.(1997h) however. eliminates the need for a test sample and any human inlluence in the classification. process.," The use of Self Organising Maps by \citet{NRG:97b} however, eliminates the need for a test sample and any human influence in the classification process."993 Photometric decomposition techniques which analyse the observed. distributions of photometric intensity (Simardatal.2002:Penget2002) and Fourier analysis techniques that quantify luminosity distributions of galaxies (Ocdewahnetal.2002:Trinidad1998) have had moderate success in dillerentiating galaxies into their respective classes.," Photometric decomposition techniques which analyse the observed distributions of photometric intensity \citep{Sea:02,Pea:02} and Fourier analysis techniques that quantify luminosity distributions of galaxies \citep{Ode:02,Trin:98} have had moderate success in differentiating galaxies into their respective classes."994 Non-parametric approaches such as. the CAS Classification scheme have hack success in objectively separating galaxies into Llubble’s classes as well as being applicable at high redshifts (z=3) (Consclice2003:Abrahametal. 1996).," Non-parametric approaches such as the CAS classification scheme have had success in objectively separating galaxies into Hubble's classes as well as being applicable at high redshifts (z=3) \citep{Cons:03,Aea:96}."995. Phe scheme uses 3 properties. concentration. asvnunetry and elumpiness. which quantify aspects of galaxy morphology.," The scheme uses 3 properties, concentration, asymmetry and clumpiness, which quantify aspects of galaxy morphology."996 These quantities identify formation histories. merging activity and areas of high star formation activity (Conselice2003).," These quantities identify formation histories, merging activity and areas of high star formation activity \citep{Cons:03}."997.. This technique can be easilv applied. to the decomposition of the distribution of other physical propertics in galaxies., This technique can be easily applied to the decomposition of the distribution of other physical properties in galaxies.998 Phe inclusion of additional parameters such as a Cini Coellicient has been shown to produce more refined. separations of galaxies but at the expense of increasing the dimensionality of the classification scheme (Lotzetal.2004.2006).," The inclusion of additional parameters such as a Gini Coefficient has been shown to produce more refined separations of galaxies but at the expense of increasing the dimensionality of the classification scheme \citep{LPM:04,Lea:06}."999. Classification of galaxies by physical properties alone las not been extensively carried out. although new echniques such as Pixel-z have emerged that enable. the extraction of information about the physical properties of galaxies by fitting spectral energy. distribution. (SED) emplates derived from stellar population evolution Muzual&Charlot2002:Contietal.2003).," Classification of galaxies by physical properties alone has not been extensively carried out, although new techniques such as Pixel-z have emerged that enable the extraction of information about the physical properties of galaxies by fitting spectral energy distribution (SED) templates derived from stellar population evolution \citep{BC:03,Con:03}."1000. Each pixel is fitted. with templates. eiving a localised analysis of the ohvsical properties within the galaxy. (Welikalaetal.2007.2008. 2009)..," Each pixel is fitted with templates, giving a localised analysis of the physical properties within the galaxy \citep{Wel:07,Wel:08,Wel:09}."1001 Shapelet decomposition promises a new approach in the morphological classification of galaxies., Shapelet decomposition promises a new approach in the morphological classification of galaxies.1002 Shapelets are Gaussian-weighted Lermite polynomials (Refregier 2003).., Shapelets are Gaussian-weighted Hermite polynomials \citep{Ref:03}. .1003 They are also the cigenstates of the Quantum Harmonic Oscillator (QUO) Lamiltonian. ancl are thus well understood. (Itefregier2003).," They are also the eigenstates of the Quantum Harmonic Oscillator (QHO) Hamiltonian, and are thus well understood \citep{Ref:03}."1004.. They. have been shown to be useful in image simulation and gravitational lensing measurements (Chang&Re-[regier2002:Refregier&Bacon2003).," They have been shown to be useful in image simulation and gravitational lensing measurements \citep{CR:02,RB:03}."1005. Shapelets use all the information about the shape of a galaxy. and. form a complete set thus making them an ideal candidate to be used in the morphological classification of galaxies (Ixellv&Alelxay.2004)., Shapelets use all the information about the shape of a galaxy and form a complete set thus making them an ideal candidate to be used in the morphological classification of galaxies \citep{KM:04}.1006. Shapelets are a central component in a new objectively developed. anc automated. classification. svstem known as the Quantitative Multiwaveleneth Morphology (QAMAL)., Shapelets are a central component in a new objectively developed and automated classification system known as the Quantitative Multiwavelength Morphology (QMM).1007 QAIAL uses shapelets to decompose the galaxy images and a Principal Component Analwsis (PCA) to reduce the dimensionality of the data followed by a Mixture-of-Gaussian models to objectively identify particular morphological classes of galaxies (ον&Melxay2004.2005).," QMM uses shapelets to decompose the galaxy images and a Principal Component Analysis (PCA) to reduce the dimensionality of the data followed by a Mixture-of-Gaussian models to objectively identify particular morphological classes of galaxies \citep{KM:04,KM:05}."1008. Shapelets are not a compact form of/ classification and require a PCA to account. for. this., Shapelets are not a compact form of classification and require a PCA to account for this.1009 The technique uses galaxy images in multiple filters. and currently images in the Sloan Digital Sky Survey (SDSS) filter set. (ugriz) has been used.," The technique uses galaxy images in multiple filters, and currently images in the Sloan Digital Sky Survey (SDSS) filter set (ugriz) has been used."1010 Welly& Melxav.(2004) and. Welly&Alelxay(2005) show that this technique consistently reveals previously established: relationships such as that. between Llubble ἵνρο and colour. as well as broad. connections between morphology and the physical properties of galaxies.," \citet{KM:04} and \citet{KM:05}1011 show that this technique consistently reveals previously established relationships such as that between Hubble type and colour, as well as broad connections between morphology and the physical properties of galaxies."1012 We aim to identify relationships between the physical properties. measured with Pixel-z and quantified using CAS. and the morphological properties quantified using OMM.," We aim to identify relationships between the physical properties, measured with Pixel-z and quantified using CAS, and the morphological properties quantified using QMM."1013 Our initial objective is to extract the physical. properties from galaxy images and then quantify the spatial distributions of these physical properties., Our initial objective is to extract the physical properties from galaxy images and then quantify the spatial distributions of these physical properties.1014 The tools used for this process are Pixel-z (κουWelikalaetal.2007.2008. 2009).. [or extracting the physical properties. and CAS (Conselice2003).. t0 quantify their spatial clistribution (the collective process will be known as CCAS herein).," The tools used for this process are Pixel-z \citep[see][]{Wel:07,Wel:08,Wel:09}, for extracting the physical properties, and CAS \citep{Cons:03}, to quantify their spatial distribution (the collective process will be known as CAS herein)."1015 These quantities are then compared: with the results of the QAIAT analysis of the same galaxy images. through a regression. analysis. to analyse how well QAIAL deseribes the spatial distribution of the physical properties in galaxies.," These quantities are then compared with the results of the QMM analysis of the same galaxy images, through a regression analysis, to analyse how well QMM describes the spatial distribution of the physical properties in galaxies."1016 This indicates the extent to which we can use QAIAL to connect physical and morphological properties of galaxies. providing us with the possibility. of developing. a comprehensive galaxy classification scheme that incorporates both physical anc morphological properties of galaxics.," This indicates the extent to which we can use QMM to connect physical and morphological properties of galaxies, providing us with the possibility of developing a comprehensive galaxy classification scheme that incorporates both physical and morphological properties of galaxies."1017 The data was obtained. from. the fourth cata release (DRA) of the Sloan Digital Sky Survey (SDSS)., The data was obtained from the fourth data release (DR4) of the Sloan Digital Sky Survey (SDSS).1018 The SDSS used. a dedicated: 2.5n1 telescope located at Apache Point Observatory in New Mexico. USA together with a 142 megapixel camera in drift-scan mode to obtain images ancl spectroscopy over abouta quarter of the sky. (formorede- Using the Pixel-z output. from Welikalactal.(2008) we quantified the distribution of the physical properties in galaxies through the CAS technique developed by," The SDSS used a dedicated 2.5m telescope located at Apache Point Observatory in New Mexico, USA together with a 142 megapixel camera in drift-scan mode to obtain images and spectroscopy over abouta quarter of the sky \citep[for more details, see][]{Yokea:00,Hogea:01,Smtea:02,1019Subea:02,Pirea:03,Izcea:04,Tkrea:06}1020 Using the Pixel-z output from \citet{Wel:08} we quantified the distribution of the physical properties in galaxies through the CAS technique developed by"1021 (22) (?).. Εν. (2°22). (?277?).. (?2).. (7).," \citep{sre98,str04} \citep{lat10}. \citep{pad93,ste93,sal94,chi95,ste96,kaz97,chi98,muk99,muc00,gio06,nt06,der07,pv08,ino09,ven09, ven10,aba10}, \citep{pav02, fie10, mak10}, \citep{tho07, ste06, mak10}. \citep{har99,1cat}, \citep{bla79},"1022 spectrum radio quasars (FSROs) and BL Lacertac-type objects., spectrum radio quasars (FSRQs) and BL Lacertae-type objects.1023 It is expected that since blazars comprise the largest class of identified extragalactic sources. unresolved blazars should coutribute significantly to the EGD.," It is expected that since blazars comprise the largest class of identified extragalactic sources, unresolved blazars should contribute significantly to the EGB."1024 Additionally. just as our Galaxy produces 2-ravs. it ds expected that are produced in other galaxies. and as such. unresolved salaxies might also contribute o the ECD with the most significant coutributiou originating from the population of actively star-forming ealaxies (27777)..," Additionally, just as our Galaxy produces $\gamma$ -rays, it is expected that are produced in other galaxies, and as such, unresolved galaxies might also contribute to the EGB with the most significant contribution originating from the population of actively star-forming galaxies \citep{ste75, pav01,pav02,fie10,mak10}."1025 Tuteresting truly diffuse miechlianisuis hat could contribute to the EGD involve cosmic rav interactions with intergalactic gas aud the cosmic vackeround radiatiou (2???) and electromagnetic cascades produced by interactious of ναν high aud ultrahieh cucerey particles with the extragalactic ckeround light (2777). as well as more exotic scenarios such as dark matter aunibhilation (777777?) aud decay erm?...," Interesting truly diffuse mechanisms that could contribute to the EGB involve cosmic ray interactions with intergalactic gas and the cosmic background radiation \citep{faz66,ste73,dar07,kes03} and electromagnetic cascades produced by interactions of very high and ultrahigh energy particles with the extragalactic background light \citep{kal09, ber10, ahl10,ven10}, as well as more exotic scenarios such as dark matter annihilation \citep{sil84, ste85, rud88, ste89, ste89a, rud91,ull02} and decay \citep{oli85,ste86, iba08}."1026 Tn this paper. we estimate the contributions to the EGB from unresolved extragalactic sources of various types aud compare them with the ECB obtained from analysis of data.," In this paper, we estimate the contributions to the EGB from unresolved extragalactic sources of various types and compare them with the EGB obtained from analysis of data."1027 In doiug so. we also take iuto consideration the effects of both the completcness of the flux limited blazar survey and the importaut effect of source confusion owing to the cuerey depeudent angular resolution of the Ferim-LAT detector.," In doing so, we also take into consideration the effects of both the completeness of the flux limited blazar survey and the important effect of source confusion owing to the energy dependent angular resolution of the -LAT detector."1028 We will then briefly discuss the nuplicatious of possible truly diffuse cussion mecha, We will then briefly discuss the implications of possible truly diffuse emission mechanisms to the EGB.1029uisui, In Figure \ref{fig:logN/logSdata} we plot the number of blazars observed per square degree blazar flux integrated above $100$ MeV for both EGRET \citep{rei01} and \citep{1cat}.1030s to the ECB.," In the case of, the source spectra were extrapolated from a power-law fit above a fiducial energyof $1$ GeV\citep{pop10}..The offset between the resolved source count data"1031We have reviewed the current evidence of star-plaiot maenetic interaction in stellar anosplieresphotospheres.,We have reviewed the current evidence of star-planet magnetic interaction in stellar atmospheres.1032 Unfortunately. the curTOLnf resiIts so furt10r dedicated observations are nec to assess the reality and clarity the properties of the related ]21101101110la.," Unfortunately, the current results so further dedicated observations are needed to assess the reality and clarify the properties of the related phenomena."1033 Space-borue lous-teriu plotometiv Scl as flat uade possible ly MOST. CoRoT. Kepler (and later PLATO) provides unique data sets to investigate he presence of photospheric sarspots related with a rot Jupiter. as we discussed 1ji the cases of 2. CoRoT-Ll. CoBRoT-6. and Kepler targets;," Space-borne long-term photometry such as that made possible by MOST, CoRoT, Kepler (and later PLATO) provides unique data sets to investigate the presence of photospheric starspots related with a hot Jupiter, as we discussed in the cases of CoRoT-2, CoRoT-4, CoRoT-6, and Kepler targets."1034 Cuaround-sed searches should concentrate ou the nonitorius of chromospheric proxies. such as Ca IT IT Ix. line core clussion. to obtain a sufficient statistics on the xoperties of chromospheric hot spots.," Ground-based searches should concentrate on the monitoring of chromospheric proxies, such as Ca II H K line core emission, to obtain a sufficient statistics on the properties of chromospheric hot spots."1035 Theoretical models should clarify the iiecladslus for he interaction and this requires a map of he coroial Geld structure., Theoretical models should clarify the mechanisms for the interaction and this requires a map of the coronal field structure.1036 As in the case of tle Sun. it 1s possie ο extrapoate he field components meastred at 1C shotosphere.," As in the case of the Sun, it is possible to extrapolate the field components measured at the photosphere."1037 Since he hieh-order multipoles of shotospheric fied decay rapidly with the distauce. oilv he low-order compoucuts. sav dipole aud cΠινηνJIC. are relevau at he distance of the planet.," Since the high-order multipoles of the photospheric field decay rapidly with the distance, only the low-order components, say dipole and quadrupole, are relevant at the distance of the planet."1038 This mica hat the roseit photospheric feld recoistructkDERI sed onssectropolarimetric techniques are adequate ο extrapolate fιο field at the distauce ο ‘the planetary uagnetospwere (e.g.Aloutouctal.2007:Faresetal. 2010).," This means that the present photospheric field reconstructions based on spectropolarimetric techniques are adequate to extrapolate the field at the distance of the planetary magnetosphere \citep[e.g., ][]{Moutouetal07,Faresetal10}."1039". The simultancous observations of a chromospheric hot spot aud the phoospheric feld ο extrapoate the coronal configuratioj will provide ""uique information to understand the iiferaction (sceLauza20049.for details)."," The simultaneous observations of a chromospheric hot spot and the photospheric field to extrapolate the coronal configuration, will provide unique information to understand the interaction \citep[see ][ for details]{Lanza09}."1040 The )ossibilitv that he planet somehow trigecrs the ciergence of uew lewnetie fux frou the interior. appearing as starspots or faculae iu the plotosphere. caauuuot ο excluded: aux secnus tfo be supported bv the observatious of the CoRoT targets ciscussecL above.," The possibility that the planet somehow triggers the emergence of new magnetic flux from the interior, appearing as starspots or faculae in the photosphere, cannot be excluded and seems to be supported by the observations of the CoRoT targets discussed above."1041 Π coufinued in other systems. this will ope τα new view οi stellar dvwuamos. planetary magnetic fields aud star-planet interaction iuakiug this area of research of the highest imterest for the advaiceineut of stellar aud planetary astroplivsics.," If confirmed in other systems, this will open a new view on stellar dynamos, planetary magnetic fields and star-planet interaction making this area of research of the highest interest for the advancement of stellar and planetary astrophysics."1042" Tus paper has been developed frou, a review orig)willy presented at the 2wl CoRoT SiuYOSMIUL.", This paper has been developed from a review originally presented at the 2nd CoRoT Symposium.1043 The author wishes to thank. he SOC for tlidr kiud invitation to attend the Conerence and review the status star-panet iuteraction studies., The author wishes to thank the SOC for their kind invitation to attend the Conference and review the status star-planet interaction studies.1044 The autior also wishes to thank Prof. M. Dehul. Prof. J. Liuskw. Dy. C. Moutou. aud Dr. A. S. Bonomo for interesting disciSSLOLLS Orseveral aspects o‘the star-plane uaegnetici interaction.," The author also wishes to thank Prof. M. Deluil, Prof. J. Linsky, Dr. C. Moutou, and Dr. A. S. Bonomo for interesting discussions on several aspects of the star-planet magnetic interaction."1045 Many thauks also o the Editor iu Chicf of Astroplivsies and Space Science. Prof. M. A. Dovita. for lis kind inviation to subinit his paper as au invited review.," Many thanks also to the Editor in Chief of Astrophysics and Space Science, Prof. M. A. Dopita, for his kind invitation to submit this paper as an invited review."1046 Last but not least. fje dusightful coniueuts bv au anonviuous referee proved to be a great help in inuproviug this work.," Last but not least, the insightful comments by an anonymous referee proved to be a great help in improving this work."1047versatility of the scheme relative to the inclusion of specific prior information on the signal in the minimization problems.,versatility of the scheme relative to the inclusion of specific prior information on the signal in the minimization problems.1048 This versatility allows the detinition of image reconstruction techniques which are significantly more powerful than standard deconvolution algorithm called CLEAN used in the context of radio astronomy., This versatility allows the definition of image reconstruction techniques which are significantly more powerful than standard deconvolution algorithm called CLEAN used in the context of radio astronomy.1049 In Section 2.. we pose the inverse problem for image reconstruction from radio-interferometric data and. discuss the standard image reconstruction techniques used in radio astronomy.," In Section \ref{sec:Radio-interferometry}, we pose the inverse problem for image reconstruction from radio-interferometric data and discuss the standard image reconstruction techniques used in radio astronomy."1050 In Section 3.. we concisely describe the central results of the theory of compressed sensing regarding the definition of a sensing basis and the accurate reconstruction of sparse or compressible signals.," In Section \ref{sec:Compressed-sensing-perspective}, we concisely describe the central results of the theory of compressed sensing regarding the definition of a sensing basis and the accurate reconstruction of sparse or compressible signals."1051 In Section 4.. we firstly comment on the exact compliance of radio interferometric measurements with compressed sensing.," In Section \ref{sec:Applications}, we firstly comment on the exact compliance of radio interferometric measurements with compressed sensing."1052" We hen study the reconstruction performances of various compressed sensing imaging techniques relative to CLEAN on simulations of wo kinds of signals of interest for astrophysics and cosmology,", We then study the reconstruction performances of various compressed sensing imaging techniques relative to CLEAN on simulations of two kinds of signals of interest for astrophysics and cosmology.1053 We tinally conclude in Section 5.., We finally conclude in Section \ref{sec:Conclusion}.1054 Notice that a first application of compressed sensing in astronomy was very recently proposed for non-destructive data compression on board the future Herschel space S? .l(u). wCS. 2004)., Notice that a first application of compressed sensing in astronomy was very recently proposed for non-destructive data compression on board the future Herschel space $\textnormal{S}^{2}$ $A(\omega)$ $\omega\in\textnormal{S}^{2}$ .1055". At each instant of observation. each telescope pair identified by an index b measures a complex visibility jy,cC€."," At each instant of observation, each telescope pair identified by an index $b$ measures a complex visibility $y_{b}\in\mathbb{C}$."1056 This visibility is defined as the correlation between incoming electric fields /7 at the positions of the two telescopes in the three-dimensional space. b).boCIzEN In this relation. / denotes the time variable and the brackets 3 denote an average over a time Af long relative to the period of the radio wave detected.," This visibility is defined as the correlation between incoming electric fields $E$ at the positions of the two telescopes in the three-dimensional space, $\vec{b}_{1},\vec{b}_{2}\in\mathbb{R}^{3}$: In this relation, $t$ denotes the time variable and the brackets $\langle\cdot\rangle_{\Delta t}$ denote an average over a time $\Delta t$ long relative to the period of the radio wave detected."1057" We consider a monochromatic signal with a wavelength of emission A, and made up of incoherent sources."," We consider a monochromatic signal with a wavelength of emission $\lambda$, and made up of incoherent sources."1058 We also consider a standard interferometer with an illumination function whose angular support is small enough so that the field of view may be identified to a planar patch of the celestial sphere: 2?©127., We also consider a standard interferometer with an illumination function whose angular support is small enough so that the field of view may be identified to a planar patch of the celestial sphere: $P\subset\mathbb{R}^{2}$.1059 The signal and the illumination function thus respectively appear as ‘unctions £(p) and -AQp)of the angular variable seen as a two-dimensional vector p€I7 with an origin at the pointing direction of the array., The signal and the illumination function thus respectively appear as functions $I(\vec{p})$ and $A(\vec{p})$of the angular variable seen as a two-dimensional vector $\vec{p}\in\mathbb{R}^{2}$ with an origin at the pointing direction of the array.1060" The vector n=Dob,[25 defining the relative yosition between the two telescopes is called the baseline. and its wojection on the plane perpendicular to the pointing direction of he instrument may be denoted as nC[27,"," The vector $\vec{B}_{b}=\vec{b}_{2}-\vec{b}_{1}\in\mathbb{R}^{3}$ defining the relative position between the two telescopes is called the baseline, and its projection on the plane perpendicular to the pointing direction of the instrument may be denoted as $\vec{B}_{b}^{\perp}\in\mathbb{R}^{2}$."1061 One also makes the additional assumption that the maximum projection of the baselines in the pointing direction itself is small2008)., One also makes the additional assumption that the maximum projection of the baselines in the pointing direction itself is small.1062. In his context. the so-called van Cittert-Zernike theorem states that he visibility measured identifies with the two-dimensional Fourier ransform of the image multiplied by the illumination function -1/ at the single spatial frequency i.e. for any two-dimensional vector 72°.," In this context, the so-called van Cittert-Zernike theorem states that the visibility measured identifies with the two-dimensional Fourier transform of the image multiplied by the illumination function $AI$ at the single spatial frequency i.e. for any two-dimensional vector $\vec{u}\in\mathbb{R}^{2}$."1063" Interferometric arrays thus probe signals at a resolution equivalent to that of a single telescope with a size /? essentially equivalent to. the maximum projected baseline on the plane perpendicular to the pointing direction: 2max,Hi.", Interferometric arrays thus probe signals at a resolution equivalent to that of a single telescope with a size $R$ essentially equivalent to the maximum projected baseline on the plane perpendicular to the pointing direction: $R\simeq\max_{b}\vec{B}_{b}^{\perp}$.1064 This expresses the essence of aperture synthesis2004)., This expresses the essence of aperture synthesis.1065 In the course of an observation. the projected baselines on the plane perpendicular to the pointing direction change thanks to the Earth's rotation and run over an ellipse in the Fourier plane of the original image. whose parameters are linked to the parameters of observation.," In the course of an observation, the projected baselines on the plane perpendicular to the pointing direction change thanks to the Earth's rotation and run over an ellipse in the Fourier plane of the original image, whose parameters are linked to the parameters of observation."1066 The total number 2/2 of spatial frequencies probed by all pairs of telescopes of the array during the observation provides some Fourier coverage characterizing the interferometer., The total number $m/2$ of spatial frequencies probed by all pairs of telescopes of the array during the observation provides some Fourier coverage characterizing the interferometer.1067 Any interferometer is thus simply identified by a binary mask in Fourier equal to 1 for each spatial frequency probed and 0 otherwise., Any interferometer is thus simply identified by a binary mask in Fourier equal to $1$ for each spatial frequency probed and $0$ otherwise.1068 The visibilitiesmeasuredmay be denoted as a vector of m/2 complex Fourier coefficients yj0cextn——FD=[yu Ετος possibly affected by complex noise values ηC of astrophysical or instrumental origin.," The visibilitiesmeasuredmay be denoted as a vector of $m/2$ complex Fourier coefficients $y\in\mathbb{C}^{m/2}=\{y_{b}=\widehat{AI}(\vec{u}_{b})\}_{1\leq b\leq m/2}$ , possibly affected by complex noise values $n\in\mathbb{C}^{m/2}=\{n_{b}=n(\vec{u}_{b})\}_{1\leq b\leq m/2}$ of astrophysical or instrumental origin."1069 Considering that the signal / and the illumination function, Considering that the signal $I$ and the illumination function1070where mtr)=nAzEidr is the mass. contained within the radius r. and the prime denotes radial derivative.,"where $ m(r) = \int_{0}^{r} 4\pi Er^2 dr $ is the mass, contained within the radius $r$, and the prime denotes radial derivative."1071" In order to solve equations (2) - (4). we rewrite the linear EOS mentioned in the last section Since. the various SOM models considered. in. the present study (corresponding το dilferent values of. the parameters e ancl f, shown in Table 2) are very precisely approximated by this EOS (Zdunik 2000: Gondek-Itosisska et al 2000)."," In order to solve equations (2) - (4), we rewrite the linear EOS mentioned in the last section Since, the various SQM models considered in the present study (corresponding to different values of the parameters $a$ and $E_s$ shown in Table 2) are very precisely approximated by this EOS (Zdunik 2000; Gondek-Rosińsska et al 2000)."1072 Moreover. this form also turns out to be exact for massless quarks (free or interacting) corresponding to à value of e=1/3.," Moreover, this form also turns out to be exact for massless quarks (free or interacting) corresponding to a value of $a = 1/3$."1073" The first three pairs of the parameters e and ££. shown in Table 2 represent the MEE bag models of SOM corresponding to: the mass of à strange quark m.=200 MeV. a value of QCD coupling constant a,=0.2 and a bag constant B= ? (indicated as SQALL in Table 2): m,=100 MeV. a,=0.6 and D = 40\McVin (indicated as SCQM2 in Table 2): m,= 0.60,=0 and B = (indicated as SQAIO in Table 2)."," The first three pairs of the parameters $a$ and $E_s$ shown in Table 2 represent the MIT bag models of SQM corresponding to: the mass of a strange quark $m_s = 200$ MeV, a value of QCD coupling constant $\alpha_c = 0.2$ and a bag constant B = $^{-3}$ (indicated as SQM1 in Table 2); $m_s = 100$ MeV, $\alpha_c = 0.6$ and B = $^{-3}$ (indicated as SQM2 in Table 2); $m_s = 0$ $\alpha_c = 0$ and B = $^{-3}$ (indicated as SQM0 in Table 2)."1074" The last two entries (indicated"" as S82 and SSL in Table 2). however. represent the SQAL models of Day et al (1998) corresponding to density dependent quark masses and a color dependent vector interquark potential."," The last two entries (indicated as SS2 and SS1 in Table 2), however, represent the SQM models of Day et al (1998) corresponding to density dependent quark masses and a color dependent vector interquark potential."1075 Equation (5) is solved. together with the coupled equations (2) - (4) for five pairs of the parameters e and fey (shown in Table 2) until the pressure vanishes at. the surface of the configuration., Equation (5) is solved together with the coupled equations (2) - (4) for five pairs of the parameters $a$ and $E_s$ (shown in Table 2) until the pressure vanishes at the surface of the configuration.1076 At the surface. kr=2. we obtain The results of the caleulations are shown in Table 3 - 7 and the AlRL diagram is presented in Fig.1.," At the surface, $r = R$, we obtain and The results of the calculations are shown in Table 3 - 7 and the $M-R$ diagram is presented in Fig.1."1077" lt follows from Table 3 that along the stable branch of the SQMO sequence. the maximum value of mass (Adis&1.06524...) corresponds to the maxinium ‘stable’ value of Mun2O.2707 and the corresponding ""local value of (Li)uστ L5974."," It follows from Table 3 that along the stable branch of the SQM0 sequence, the maximum value of mass $M_{\rm max} \simeq 1.9654M_\odot$ ) corresponds to the maximum `stable' value of $u_{\rm max} 1078\simeq 0.2707$ and the corresponding `local' value of $(\Gamma_1)_0 \simeq 1.5974$ ."1079 Although. this value of (Pyjo turns out to be consistent with that of the absolute upper bound on (oODoauasans&1.7766). the maximum ‘stable’ value of MunCz0.2107 is Found to be inconsistent. with that of the absolute upper bound on tins(inax.abs20.2356).," Although, this value of $(\Gamma_1)_0$ turns out to be consistent with that of the absolute upper bound on $(\Gamma_1)_0 ((\Gamma_1)_{0,\rm max, abs} \simeq 1.7766)$, the maximum `stable' value of $u_{\rm max} \simeq 0.2707$ is found to be inconsistent with that of the absolute upper bound on $u_{\rm max} (u_{\rm max,abs} \simeq 0.2356)$."1080 Thus the configuration turns out to be inconsistent with that of the lindings of the last section., Thus the configuration turns out to be inconsistent with that of the findings of the last section.1081 ]t is seen from Table 4 (which presents the results for SQALL sequence) that along the stable branch. of the sequence. the maximum value of mass (Mis&1.7OOGAL. ) corresponds to the maximum ‘stable’ πμ. &0.2608 and the corresponding ‘local’ value of (Pyjy21.5531.," It is seen from Table 4 (which presents the results for SQM1 sequence) that along the stable branch of the sequence, the maximum value of mass $M_{\rm max} \simeq 1.7996M_\odot$ ) corresponds to the maximum `stable' value of $u_{\rm max} 1082\simeq 0.2608$ and the corresponding `local' value of $(\Gamma_1)_0 \simeq 1.5531$."1083 The xur of these values. however. show inconsistency with that of the pair of absolute upper bounds migans(z0.2244) and (LioasesabsCR1.7346).," The pair of these values, however, show inconsistency with that of the pair of absolute upper bounds $u_{\rm max,abs} (\simeq 0.2244)$ and $(\Gamma_1)_{0,\rm max,abs} (\simeq 1.7346)$."1084 HC follows. therefore. that the Al2 relation corresponding to the SQMI EOS does not. provide a necessary ancl sullicient condition for dvnamical stability or the equilibrium configurations.," It follows, therefore, that the $M-R$ relation corresponding to the SQM1 EOS does not provide a necessary and sufficient condition for dynamical stability for the equilibrium configurations."1085 The results of the calculations for SQAI2 sequence is »esented in Table 5., The results of the calculations for SQM2 sequence is presented in Table 5.1086 lt follows from this table that along the stable branch of the sequence. the maximum value of mass (Aas&2.2859M 1) corresponds to the maximum ‘stable’ value of thins&0.2684 and the corresponding ‘local’ value of (L'i)o21.5798.," It follows from this table that along the stable branch of the sequence, the maximum value of mass $M_{\rm max} \simeq 2.2859M_\odot$ ) corresponds to the maximum `stable' value of $u_{\rm max} 1087\simeq 0.2684$ and the corresponding `local' value of $(\Gamma_1)_0 \simeq 1.5798$."1088 Phe pair of these values is also found to be inconsistent. with that of the pair of absolute upper bounds μισο0.2325) and (Vouas(01.7645) obtained for he SQAI2 sequence in the last section.," The pair of these values is also found to be inconsistent with that of the pair of absolute upper bounds $u_{\rm max,abs} (\simeq 0.2325)$ and $(\Gamma_1)_{0,\rm max,abs} (\simeq 1.7645)$ obtained for the SQM2 sequence in the last section."1089 Lt follows. therefore. hat the AJA! relation corresponding to the SQAIZ EOS does not provide a necessary ancl sullicient condition for dynamical stability for the equilibrium configurations.," It follows, therefore, that the $M-R$ relation corresponding to the SQM2 EOS does not provide a necessary and sufficient condition for dynamical stability for the equilibrium configurations."1090" The maximum value of mass (Maso— 14358.) models vields the maximum value of s(n,44)c0.2999 andthe corresponding value of (D1Ju.21.7793 as shown in Table 6.", The maximum value of mass $M_{\rm max} \simeq 1.4358M_\odot$ ) models yields the maximum value of $u (u_{\rm max}) \simeq 0.2999$ andthe corresponding value of $(\Gamma_1)_0 \simeq 1.7793$ as shown in Table 6.1091 “Phe pair of these values. however. also. show," The pair of these values, however, also show"1092best fit to the KCAB dataset.,best fit to the KCAB dataset.1093 Kroupaetal.(2003) suggest that the field mass function mar be consistent will a cutoll (a steep drop in number density) at or near the stellar/substellar boundary., \citet{kru03} suggest that the field mass function may be consistent with a cutoff (a steep drop in number density) at or near the stellar/substellar boundary.1094 We test this hypothesis using our Bavesian formulation. which uses identical likelihood functions and prior distributions as those given in §33.3.1. but with new mass function models given by Equation 2.," We test this hypothesis using our Bayesian formulation, which uses identical likelihood functions and prior distributions as those given in 3.3.1, but with new mass function models given by Equation 2."1095 Figure 10. displays the resultant 2D posterior distribution., Figure \ref{fig:ka5} displays the resultant 2D posterior distribution.1096" The maximum is at the lower edge of the 4, range. 0.01A.. with as~0.25."," The maximum is at the lower edge of the $m_{cut}$ range, $0.01~M_{\odot}$, with $\alpha_2 \sim 0.25$."1097 Our results agree better will the Ixroupaetal.(2003) mass function that includes no lower mass cutolt. rather than a cutoff near the hvdrogen burning limit: 0.05A. is the highest eutoff mass that is consistent with our analvsis.," Our results agree better with the \citet{kru03} mass function that includes no lower mass cutoff, rather than a cutoff near the hydrogen burning limit; $0.05~M_{\odot}$ is the highest cutoff mass that is consistent with our analysis."1098 This upper limit is approximately (he lowest mass probed by average field T cwarts., This upper limit is approximately the lowest mass probed by average field T dwarfs.1099 The posterior distribution for the cutoff model peaks more narrowly (han (he posterior distribution of the (wo-seegment power law. and it too is not stronglv dependent on (he prior distribution.," The posterior distribution for the cutoff model peaks more narrowly than the posterior distribution of the two-segment power law, and it too is not strongly dependent on the prior distribution."1100 Fieure 11. displays the same four altered prior distributions and (heir resultant posterior distributions as in 833.3.1. but for the cutoff power law mass function.," Figure \ref{fig:cop} displays the same four altered prior distributions and their resultant posterior distributions as in 3.3.1, but for the cutoff power law mass function."1101 The posterior distributions show similar behavior to those of the (wo-seement power law mass function., The posterior distributions show similar behavior to those of the two-segment power law mass function.1102 The Bavesian result of (his mass function formulation is similar to the previous one. (hat the data weakly constrain the model parameter values.," The Bayesian result of this mass function formulation is similar to the previous one, that the data weakly constrain the model parameter values."1103 We apply our Bavesian analvsis to a third set of model luminosity functions based on a log normal mass function., We apply our Bayesian analysis to a third set of model luminosity functions based on a log normal mass function.1104 As with the power law analvses. there are (wo [ree parameters: the characteristic mass. my. which is allowed to span (he range —1.4«1ος)<—0.4: ancl the width. o. which spans 0.35 to 1.35.," As with the power law analyses, there are two free parameters: the characteristic mass, $m_0$, which is allowed to span the range $-1.4 < \log(m_0) < -0.4$; and the width, $\sigma$, which spans 0.35 to 1.35."1105 The nominal prior distribution uses the values of those parameters eiven by Chabrier(2003) (logG4)=—1.12:0.1 and 6=0.692: 0.05)., The nominal prior distribution uses the values of those parameters given by \citet{chab03} $\log(m_0) = -1.1\pm0.1$ and $\sigma = 0.69\pm0.05$ ).1106 The log normal mass functions generate similar luminosity [functions to those from power law mass function models through the T dwarf regime. but they diverge at fainter magnitudes (see 2 53.3.4).," The log normal mass functions generate similar luminosity functions to those from power law mass function models through the T dwarf regime, but they diverge at fainter magnitudes (see ${\S}3.3.4$ )."1107 As noted above. this stems from the turnover in the log normal mass functions ad low masses.," As noted above, this stems from the turnover in the log normal mass functions at low masses."1108 The Bavesian analysis of (his mass function model vields similar results to those outlined in the previous seclions., The Bayesian analysis of this mass function model yields similar results to those outlined in the previous sections.1109 Figure 12 clisplavs (he posterior distributions on log(ig) Lor four variations of the my prior distribution., Figure \ref{fig:lnp} displays the posterior distributions on $\log(m_0)$ for four variations of the $m_0$ prior distribution.1110 Unlike the previous analyses. the posterior distribution stvonely mirrors the input prior distribution. which means that we cannol constrain the mass funetion in this case.," Unlike the previous analyses, the posterior distribution strongly mirrors the input prior distribution, which means that we cannot constrain the mass function in this case."1111 The reason for this is that the KCAB data are not at the peak of the log normal distribution., The reason for this is that the KCAB data are not at the peak of the log normal distribution.1112 This effectively means we (rv to fit the falling slope of the mass function., This effectively means we try to fit the falling slope of the mass function.1113 The result is that a wide range of possible parameter values are, The result is that a wide range of possible parameter values are1114re SER given by the FUR both extinction free tracers of rw current. SER.,the SFR given by the FIR both extinction free tracers of the current SFR.1115 The size of the SNR is about 2 times argcr than the size of the largest SNR detected in AL 82 indicating that the star forming event in NGC 3077 is older iun the one in AL 82., The size of the SNR is about 2 times larger than the size of the largest SNR detected in M 82 indicating that the star forming event in NGC 3077 is older than the one in M 82.1116 The other detected source with the characteristics of a compact LIL region. coincides with the X-ray source 83. an X-ray binary svstem.," The other detected source with the characteristics of a compact HII region, coincides with the X-ray source S3, an X-ray binary system."1117 We estimate a lux density of 747 pdx for this source., We estimate a flux density of 747 $\mu$ Jy for this source.1118 Assuming that all us cnerey has a thermal origin we estimate that only a few massive stars are necessary (o ionize the observed nebula., Assuming that all this energy has a thermal origin we estimate that only a few massive stars are necessary to ionize the observed nebula.1119" A massive ancl voung stellar cluster observed by the Llubble Space ""Telescope coincides with the position of both the $3 A-ray source and the LUE region.", A massive and young stellar cluster observed by the Hubble Space Telescope coincides with the position of both the S3 X-ray source and the HII region.1120 ALERLIN is a national facility operated by the University of Manchester at Jodrell Bank Observatory on behalf. of PPABC., MERLIN is a national facility operated by the University of Manchester at Jodrell Bank Observatory on behalf of PPARC.1121 E gratefully acknowledges the advice and technical support given by Peter Thomasson. Anita Richards and other members of the Jocrell Bank Observatory.," I gratefully acknowledges the advice and technical support given by Peter Thomasson, Anita Richards and other members of the Jodrell Bank Observatory."1122 L also hank Elena ‘Terlevich. Cillermo Tenorio-Tagle.. Roberto ‘Verlevich. Divakara Mayyva. Paul O'Neill ancl Antonio Garcfaa Barreto for useful discussions.," I also thank Elena Terlevich, Gillermo Tenorio-Tagle, Roberto Terlevich, Divakara Mayya, Paul O'Neill and Antonio a Barreto for useful discussions."1123 An extensive report rom an anonvmous referee ercathy improved the final version of the paper., An extensive report from an anonymous referee greatly improved the final version of the paper.1124The gravitational field acts as a lens.,The gravitational field acts as a lens.1125" Hlowever. since for ravs passing through the exterior gravitational fields of the Sun. the deflection angle decreases will increasing impact parameter (as shown by Eq.(1))). the lens does not have a true optical point but only a caustic line beginning at the distance of Fy=F(R.)RZ(2r,546AU from the Sun."," However, since for rays passing through the exterior gravitational fields of the Sun, the deflection angle decreases with increasing impact parameter (as shown by \ref{eqdef}) )), the lens does not have a true optical point but only a caustic line beginning at the distance of ${\cal1126F}_0 \equiv {\cal F}({\cal R}_\odot) = {\cal R}^2_\odot /2 r_g = 546 ~AU$ from the Sun."1127 Geomelric oplics gives the optical distance as a function of the impact parameter: By rigorously applving (he methods of wave optics il was shown by that the space behind the Sun max formally be separated into the three physically different regions. namely. (1) the shadow. (2) the region of geometric optics (where only one rav passes through each point of space). aud (3) the region of interference (where (wo ravs are passing through each point) as shown in Figure 6..," Geometric optics gives the optical distance as a function of the impact parameter: By rigorously applying the methods of wave optics it was shown by \citet{her76} that the space behind the Sun may formally be separated into the three physically different regions, namely, (1) the shadow, (2) the region of geometric optics (where only one ray passes through each point of space), and (3) the region of interference (where two rays are passing through each point) as shown in Figure \ref{fig:sl}."1128 The solar shadowing effect prohibits focusing of light at distances shorter then Fy from the Sun., The solar shadowing effect prohibits focusing of light at distances shorter then ${\cal F}_0$ from the Sun.1129 On the other hand. the most interesting ellects. such as amplification of light. may only be observed in the third region the region interference.," On the other hand, the most interesting effects, such as amplification of light, may only be observed in the third region – the region interference."1130 Hence. in discussing the solar gravity lens. we shall be interested only in the solar region of interference.," Hence, in discussing the solar gravity lens, we shall be interested only in the solar region of interference."1131 This region is defined to be at the distance F such as: F>Fy and 8«xLP ," This region is defined to be at the distance ${\cal F}$ such as: ${\cal F} \ge {\cal F}_0 $ and $\theta1132\le |\theta_{0\,\tt gr}|$."1133This region may further be sub-divided onto several physically. interesting regions., This region may further be sub-divided onto several physically interesting regions.1134 The most intriguing of (hose. is the region of extreme intensity. for which the following condition in the image plane (perpendicularto the optical axis) issatisfied: zx>vr«θαNr. For small departures p of the observer from the optical axis p<\/2ryF solution may be obtained by the stationary phase method (see ILerltaudStephani (1976))) which vields the following expression for the gain Gp.A) of this lens: Jy being a Bessel function of zero-order.," The most intriguing of those, is the region of extreme intensity, for which the following condition in the image plane (perpendicularto the optical axis) is: ${\lambda\over 2\pi}/{ \sqrt{2r_g{\cal F}}}1135\ll \theta \ll \sqrt{{r_g/ {\cal F}}}.$ For small departures $\rho$ of the observer from the optical axis $\rho\ll\sqrt{2r_g{\cal F}}$ solution may be obtained by the stationary phase method (see \cite{her76}) ) which yields the following expression for the gain $G(\rho,\lambda)$ of this lens: $J_0$ being a Bessel function of zero-order."1136 The corresponding gain as a function of the optical distance and a possible observation wavelength is presented in Figure 7.., The corresponding gain as a function of the optical distance and a possible observation wavelength is presented in Figure \ref{fig:gain}. .1137 Note (that. gain G(p.A) has its maximum on the axis," Note that gain $G(\rho,\lambda)$ has it's maximum on the axis"1138Pegasus has two detected. HII regions (Skillinan. Bomaus. Iobuluicky 1997) aud the fornal calculation of τρως lor Pegasus vields a value of 22200QCivi?.,"Pegasus has two detected HII regions (Skillman, Bomans, Kobulnicky 1997) and the formal calculation of $\tau_{gas}$ for Pegasus yields a value of 3220."1139. Until recently. an optical radial velocity was unavallable for Phoenix. aud it was nol clear whether tje. HI detected in the direction of Phoeulx was directly associated with it (Carignan. Demers. Cotté 1991: Oosterloo et 11996. You18 Lo 1997. St-Cermai1 et 11999).," Until recently, an optical radial velocity was unavailable for Phoenix, and it was not clear whether the HI detected in the direction of Phoenix was directly associated with it (Carignan, Demers, Côtté 1991; Oosterloo et 1996, Young Lo 1997, St-Germain et 1999)."1140 However. Gallar et ((2001) have now oxovided au optical radial velocity o“52 + 6lLans LF which is relatively close to the HI cloud separated from Phoeix by 6 with a velocity of —23 km and (dey conclude that the properties o “this HI cloud are cousistent with |aviug een recently lost by Phoenix.," However, Gallart et (2001) have now provided an optical radial velocity of $-$ 52 $\pm$ 6 km $^{-1}$, which is relatively close to the HI cloud separated from Phoenix by $\arcmin$ with a velocity of $-$ 23 km $^{-1}$, and they conclude that the properties of this HI cloud are consistent with having been recently lost by Phoenix."1141 The recent Weasurement ¢X the optical radial velocity of Phoeiix of — 132 9 kins by Irwin Tolstoy (2002) strenetheus tle COinection between the HI clotd aud the galaxy., The recent measurement of the optical radial velocity of Phoenix of $-$ 13 $\pm$ 9 km $^{-1}$ by Irwin Tolstoy (2002) strengthens the connection between the HI cloud and the galaxy.1142 Note tha the stellar population study by Holtzuan. Smith. Crillmair (200()) iudic:ies that Phoenix has experienced star formation up uutil rotelly 100 inilio1 vears ago which imXies that Phoenix mitst have had sole gas until very recentN.," Note that the stellar population study by Holtzman, Smith, Grillmair (2000) indicates that Phoenix has experienced star formation up until roughly 100 million years ago which implies that Phoenix must have had some gas until very recently."1143 For the galaxies with the very low valies of SER (or high vaues OL Tyas aud Tropa) Le precise value of the current SER is probably uot very meaniugful.," For the galaxies with the very low values of SFR (or high values of $\tau_{gas}$ and $\tau_{form}$ ), the precise value of the current SFR is probably not very meaningful."1144 The conversion [ron Ha Íux to SFR calculated by Ixenuicutt e (1991) is owed on a Lully poplated. IMF. and witl1 so few HII 'eelons. it is clea “that the whole range of Inassive stars is noti ‘epresented.," The conversion from $\alpha$ flux to SFR calculated by Kennicutt et (1994) is based on a fully populated IMF, and with so few HII regions, it is clear that the whole range of massive stars is not represented."1145 Siice the presence or absence of a few HII 'eglons can move al extremely low luiilosity galaxy belween the dl and rausitlou catego‘Tes. hey may have mucl in common.," Since the presence or absence of a few HII regions can move an extremely low luminosity galaxy between the dI and transition categories, they may have much in common."1146 One also has to cousider the Πο introduced by the diffe'ences between the Ha [hixes caleulated from the sum oft he HII 'eelons ancl hose calculated Grom he entire image (includiug the diffuse component) whicl can |© slgenificant or these very quiescent galaxies., One also has to consider the uncertainty introduced by the differences between the $\alpha$ fluxes calculated from the sum of the HII regions and those calculated from the entire image (including the diffuse component) which can be significant for these very quiescent galaxies.1147 There are at leas two clillereuo evolutionary paths that a dl galaxy cau take to become a ransition galaxy., There are at least two different evolutionary paths that a dI galaxy can take to become a transition galaxy.1148 Oue possibility is for the galaxy to lose enough of its cold gas to halt preseut star ormation., One possibility is for the galaxy to lose enough of its cold gas to halt present star formation.1149" A second possibility is o have suflicieut gas for star formation. but to be simply ""iu jetweeu"" episodes of star [ormiation."," A second possibility is to have sufficient gas for star formation, but to be simply “in between” episodes of star formation."1150 Phoeuix may be a local example of the first case (as discissed yw CGallart et 22001). while Atilia. DDO 210. LOS-:)). and Pegasus may be exauples of the second case.," Phoenix may be a local example of the first case (as discussed by Gallart et 2001), while Antlia, DDO 210, LGS-3, and Pegasus may be examples of the second case."1151 Typically. dE galaxies rave Mj;/L ratios of about one in solar units (SkiLiman 1996).," Typically, dI galaxies have $_{HI}$ /L ratios of about one in solar units (Skillman 1996)."1152 Thus. galaxies with similar Mjj;/L but no current star formation could be what woud normally be called cls. but are simply. between episodes of galaxy formation.," Thus, galaxies with similar $_{HI}$ /L but no current star formation could be what would normally be called dIs, but are simply between episodes of galaxy formation."1153 Simply based ou tlje munber of stars aid the average liletimes of HIT regious. the sinaller the dl galaxy. the higher tje. likelihood that it could be found in such a phase.," Simply based on the number of stars and the average lifetimes of HII regions, the smaller the dI galaxy, the higher the likelihood that it could be found in such a phase."1154 Note that all five of the Local Group trausiion galaxies, Note that all five of the Local Group transition galaxies1155uniform rotation of their radiative zones.,uniform rotation of their radiative zones.1156 For the sake of generalitv. we derive the basic set of equations Lor the case of 3D perturbations in a compressible. eravitationallv stratifiel MIID fluid.," For the sake of generality, we derive the basic set of equations for the case of 3D perturbations in a compressible, gravitationally stratified MHD fluid."1157 This formalism will be presented in the next (2.1) subsection., This formalism will be presented in the next (2.1) subsection.1158 Later on (subsection 2.2). we will restrict. the consideration to (he somewhat simpler case of 2D perturbations in an incompressible medium.," Later on (subsection 2.2), we will restrict the consideration to the somewhat simpler case of 2D perturbations in an incompressible medium."1159 Besides. the wil be used and the stationary shear flow will be considered.," Besides, the will be used and the stationary shear flow will be considered."1160" In our model. the geometry of the considered problem is simplified in (he Iollowing wav: the equilibrium flow U is supposed to be plane-parallel. to be directed along the r-axis. and to have both a horizontal 1,) and a vertical A.) shear: The uniform gravitv g is assed (o be directed along the negative direction of the l-aXls: We consider a simplified model and assume that the equilibrium magnetic field Bo is toroidal. parallel to U and that it is possessing the gravitv-induced vertical stratification: The set of equations of one-fhiud ideal magnetohyvdrodynamies (MIDID). governing, the physics of the {low is:"," In our model, the geometry of the considered problem is simplified in the following way: the equilibrium flow ${\bf {U}}$ is supposed to be plane-parallel, to be directed along the $x$ -axis, and to have both a horizontal $A_y$ ) and a vertical $A_z$ ) shear: The uniform gravity ${\bf g}$ is assumed to be directed along the negative direction of the $z$ -axis: We consider a simplified model and assume that the equilibrium magnetic field ${\bf B_0}$ is toroidal, parallel to $\bf {U}$ and that it is possessing the gravity-induced vertical stratification: The set of equations of one-fluid ideal magnetohydrodynamics (MHD), governing the physics of the flow is:"1161Lt is important to compare anc contrast these results with studies of 6-30-15 in its normal state.,It is important to compare and contrast these results with studies of $-$ 6-30-15 in its normal state.1162 In their paper that originally identified the Deep Minimum. state. Dwasawa et al. (," In their paper that originally identified the Deep Minimum state, Iwasawa et al. ("11631996) used to show that the iron line profile was substantially broader in the Deep Minimum than at other times.,1996) used to show that the iron line profile was substantially broader in the Deep Minimum than at other times.1164 More recently. Fabian et al. (," More recently, Fabian et al. ("11652002: hereafter 1702) examined an independent and long kksec) observation of 6-30-15 which mostly. caught it in its normal Dux state.,2002; hereafter F02) examined an independent and long ksec) observation of $-$ 6-30-15 which mostly caught it in its normal flux state.1166 In agreement with the expectation from Iwasawa ct al. (, In agreement with the expectation from Iwasawa et al. (11671996). E02 found the iron line profile to be generally. narrower than in the Deep Minimum state of Paper L. although they clearly noted an extreme recd-tail extending down to  3kkeV. Fitting the iron line with a near-extreme Ixerr. black hole model (@= 0.998) using a broken-powerlaw cnussivity profile indicated a rather Lat cnussivity. profile (3~ 2.5) for rc Gre. breaking to a steep profile (3~ 5) within this radius.,"1996), F02 found the iron line profile to be generally narrower than in the Deep Minimum state of Paper I, although they clearly noted an extreme red-tail extending down to $\sim 3$ keV. Fitting the iron line with a near-extreme Kerr black hole model $a=0.998$ ) using a broken-powerlaw emissivity profile indicated a rather flat emissivity profile $\beta\sim 2.5$ ) for $r>6r_{\mathrm1168g}$ , breaking to a steep profile $\beta\sim 5$ ) within this radius."1169 Thus. the principal difference in the shape of the emissivity profile between the Deep Minimum and normal states of 6-30-15 appears to lie bevonel some radius àGry.," Thus, the principal difference in the shape of the emissivity profile between the Deep Minimum and normal states of $-$ 6-30-15 appears to lie beyond some radius $r\sim 6r_{\mathrm g}$."1170 While it is bevond the scope of this paper to fit our physical accretion clisk mocdels to the long data set. it is clear that a toreque-dominated disk around a rapidly spinning black hole cannot reproduce the normal state emissivity. profile.," While it is beyond the scope of this paper to fit our physical accretion disk models to the long data set, it is clear that a torque-dominated disk around a rapidly spinning black hole cannot reproduce the normal state emissivity profile."1171 There are also interesting differences in the spectral variability properties of the two states., There are also interesting differences in the spectral variability properties of the two states.1172 Careful analysis of the RNTEAPCA data for 6-30-15 during the normal state clearly showed that the iron line. Lux underwent significant variations but was not correlated with the continuum [lux (Lee et al., Careful analysis of the -PCA data for $-$ 6-30-15 during the normal state clearly showed that the iron line flux underwent significant variations but was not correlated with the continuum flux (Lee et al.1173 2000: Hevnolds 2000: Vaughan Edelson 2001)., 2000; Reynolds 2000; Vaughan Edelson 2001).1174 This was confirmed in a rather clirect manner bv Shih. bvasawaFabian (2002) who usec the," This was confirmed in a rather direct manner by Shih, IwasawaFabian (2002) who used the"1175"the energy fiux in the sound waves decavs faster than in the Cartesian two-dimensional case,",the energy flux in the sound waves decays faster than in the Cartesian two-dimensional case.1176" Thus. our 2D simulation uueht give amore radially distributed heating rate (xr1) compared to a 3D calculation (where the wave energy flux scales as xor 2),"," Thus, our 2D simulation might give a more radially distributed heating rate $\propto r^{-1}$ ) compared to a 3D calculation (where the wave energy flux scales as $\propto1177r^{-2}$ )."1178 However. since the dissipation rate per uit lass is inversely proportional to deusitv » while the cooling rate per unit mass is X5. a slight stecpenine of the density profile (by ~or 7) should. compensate for the extra power of r+ iu the cucrey flux.," However, since the dissipation rate per unit mass is inversely proportional to density $n$ while the cooling rate per unit mass is $\propto n$, a slight steepening of the density profile (by $\sim r^{-1/2}$ ) should compensate for the extra power of $r^{-1}$ in the energy flux."1179 Note that the scaling of heating and cooling with density does not necessarily Πρι instability., Note that the scaling of heating and cooling with density does not necessarily imply instability.1180 The densest ceutral regions. which cool the fastest. are in fact heated more effectively because the velocity fluctuations are stronger in the cluster core.," The densest central regions, which cool the fastest, are in fact heated more effectively because the velocity fluctuations are stronger in the cluster core."1181 The amount of eucrgv injected to the cluster shoul also be regulated bv the central cooling rate., The amount of energy injected to the cluster should also be regulated by the central cooling rate.1182 That is. increased cooling rate should lead to more accretion onto he ceutral AGN.," That is, increased cooling rate should lead to more accretion onto the central AGN."1183 Accretion of eas outo the center wouk hen cause ACN outbursts leading to a reduced ceutra cooling rate., Accretion of gas onto the center would then cause AGN outbursts leading to a reduced central cooling rate.1184" If acoustic heating is truly able to stabilize radiative cooling. then the density and the luminosity of he central AGN should adjust automatically, as it was shown to do iu the 1D ZEUS simulations of effervesceu reatine by Ruszkowski Beecluan (2002)."," If acoustic heating is truly able to stabilize radiative cooling, then the density and the luminosity of the central AGN should adjust automatically, as it was shown to do in the 1D ZEUS simulations of effervescent heating by Ruszkowski Begelman (2002)."1185 We also expect cherectically “equivalent” bubbles to grow to nore rapidly in 2D than iu 3D. Thus it is not surprisiug hat the bubbles iu our 2D simulations are larecr than he X-rav holes at the ceuter of the Perseus Cluster. despite our attempt to roughly match conditious.," We also expect energetically “equivalent"" bubbles to grow to more rapidly in 2D than in 3D. Thus it is not surprising that the bubbles in our 2D simulations are larger than the X-ray holes at the center of the Perseus Cluster, despite our attempt to roughly match conditions."1186 We decided to carry out two-dimensional simulations first jecause they are computationally iumch less demanding and allow us to explore a wider range of parameters., We decided to carry out two-dimensional simulations first because they are computationally much less demanding and allow us to explore a wider range of parameters.1187" However, we are planning to report a lanited sot of 3D simulations separately"," However, we are planning to report a limited set of 3D simulations separately."1188 Preliminary results sugecst that main conclusions drawn from the threc-dimensional siuulatiouns are consistent with those obtained from 2D Iu sunny. we have demonstrated that viscous heatiug by an intermittent AGN located at the center of a cooling flow cluster can balance radiative cooling aud. thus. quench the cooling flow.," Preliminary results suggest that main conclusions drawn from the three-dimensional simulations are consistent with those obtained from 2D In summary, we have demonstrated that viscous heating by an intermittent AGN located at the center of a cooling flow cluster can balance radiative cooling and, thus, quench the cooling flow."1189 Energy is trausterred to the gas by viscous dissipation of waves produced by iuteruuütteut AGN activity with a duty cevele much shorter than the cooling time., Energy is transferred to the gas by viscous dissipation of waves produced by intermittent AGN activity with a duty cycle much shorter than the cooling time.1190 Iu the proposed heating 1iechauisui. heating is eeutle. spatially-distributed iu a sviunietric fashion aud delivered to the eas located within the cooling radius faster than the cooling timescale.," In the proposed heating mechanism, heating is gentle, spatially-distributed in a symmetric fashion and delivered to the gas located within the cooling radius faster than the cooling timescale."1191" Iu this first attempt to simulate the effects of dissipation of waves in the ICAL we have assumed Spitzer viscosity, but we have to concede that the value of viscositv in the ICAL is poorly constrained."," In this first attempt to simulate the effects of dissipation of waves in the ICM, we have assumed Spitzer viscosity, but we have to concede that the value of viscosity in the ICM is poorly constrained."1192 Nevertheless. our results show that this heating mechanisi is broadly consistent with the asstuuptions of the effervesceut heating model (Beechuanu2001:Ruszkowski&Beechnan2002).. in which dissipation of waves plavs an important role (Beechnan2003).. and can be applied to recently reported observations of ripples in the Perseus (Fabianctal.2003a.b) aud Vireo (Formanetal.2003) clusters.," Nevertheless, our results show that this heating mechanism is broadly consistent with the assumptions of the effervescent heating model \citep{beg01,rus02}, in which dissipation of waves plays an important role \citep{beg03}, and can be applied to recently reported observations of ripples in the Perseus \citep{fab03a,fab03b} and Virgo \citep{for03} clusters."1193 We thank the auonviuous referee for παν usefu conunents and Phil Armitage for his words of wiscdoi., We thank the anonymous referee for many useful comments and Phil Armitage for his words of wisdom.1194 Iu particular. the anonvinous referee is ackuowledged for his/her contribution to the discussion of the couversion of the iuput enerev to the enerev iu the ICAL (paragraph j in section 3).," In particular, the anonymous referee is acknowledged for his/her contribution to the discussion of the conversion of the input energy to the energy in the ICM (paragraph 6 in section 3)."1195 We are grateful to Andy Fabian iix Clais Reynolds for their comunents. which improvec the paper.," We are grateful to Andy Fabian and Chris Reynolds for their comments, which improved the paper."1196 We also thank Peter Ruprecht aud Alark Tamusica for technical support., We also thank Peter Ruprecht and Mark Tamisiea for technical support.1197 The software used iu this work was in part developed bv the DOE-supportec ASCT/Alliance Couter for Astrophysical Theruouuclear Flashes at the University of Chicago., The software used in this work was in part developed by the DOE-supported ASCI/Alliance Center for Astrophysical Thermonuclear Flashes at the University of Chicago.1198 We acknowledge support from the W. ML deck Foundation. which purchased the JILA 7l-processor Keck Cluster.," We acknowledge support from the W. M. Keck Foundation, which purchased the JILA 74-processor Keck Cluster."1199 Some of the calculations presented iu this work were performed at National Center for Supercomputing Applications at the University of Hlinois at Urbana-Champaign. which is funded through the PACT Program at the National Scieuce Foundation.," Some of the calculations presented in this work were performed at National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, which is funded through the PACI Program at the National Science Foundation."1200 Support for this work was provided by National Science Foundation eraut AST-0307502 aud the National Aeronautics aud Space Acuninistration throughChandra Fellowship Award Number PF3-10029) issued bv the Chandra N-rayv Observatory Ceuter. which is operated by the Simithsonian Astrophysical Observatory for and on behalf of the National Aeronautics aud Space Achuinistration under contract NASS-39073.," Support for this work was provided by National Science Foundation grant AST-0307502 and the National Aeronautics and Space Administration through Fellowship Award Number PF3-40029 issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics and Space Administration under contract NAS8-39073."

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