ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 This is also illustrated in Figure 3. which dots the softness ratio as a function of total pn count rate. he correlation is significant at z-09.99 confidence using a Spearman-Rank test.," This is also illustrated in Figure 3, which plots the softness ratio as a function of total pn count rate, the correlation is significant at $>99.99$ confidence using a Spearman-Rank test."3 We also constructed cross correlation functions in order o search for any soft to hard time lags using both the aand delata., We also constructed cross correlation functions in order to search for any soft to hard time lags using both the and data.4 No delays were found. the upper-limit was «1 ksec.," No delays were found, the upper-limit was $<1$ ksec."5 It appears that both the soft (0.31.0) keV and hard (2-10 keV) bands vary coherently on timescales much shorter than that of the overall Hare duration., It appears that both the soft (0.3-1.0) keV and hard (2-10 keV) bands vary coherently on timescales much shorter than that of the overall flare duration.6 For simple reprocessing models. where the thermal dise emission is Compton up-scattered to reproduce the hard. X-ray. power-law (e.g. Czerny. Elvis 1987). this implies that the size of the reprocessing region is «1055 em or «GLA (for à Thomson depth of 7~ 1).," For simple reprocessing models, where the thermal disc emission is Compton up-scattered to reproduce the hard X-ray power-law (e.g. Czerny Elvis 1987), this implies that the size of the reprocessing region is $<10^{13}$ cm or $<0.1R_S$ (for a Thomson depth of $\tau\sim1$ )."7 The spectral softening appears consistent with observations of some ACN. where the X-ray spectra are generally softer at higher lluxes (e.g. Vaughan Edelson 2001).," The spectral softening appears consistent with observations of some AGN, where the X-ray spectra are generally softer at higher fluxes (e.g. Vaughan Edelson 2001)."8 Using light-crossing arguments. anc assuming that relativistic beaming is unimportant. one can calculate the overall size of the X-ray emitting region in PDS 456 from the expression /2cf/(1|7). where t is the rise-time of the Hares ancl 7 is the Phomson depth of the X-ray emitting region.," Using light-crossing arguments, and assuming that relativistic beaming is unimportant, one can calculate the overall size of the X-ray emitting region in PDS 456 from the expression $l=ct/(1+ \tau)$, where t is the rise-time of the flares and $\tau$ is the Thomson depth of the X-ray emitting region."9 Past multi-wavelength studies have shown that PDS 456 has a total bolometric Luminosity of 107 erg sf. peaking in the optical-UV. band. (Simpson 1999. Reeves 2000).," Past multi-wavelength studies have shown that PDS 456 has a total bolometric luminosity of $10^{47}$ erg $^{-1}$ , peaking in the optical-UV band (Simpson 1999, Reeves 2000)."10 With the assumption of isotropic, With the assumption of isotropic11the magnetized plasma.,the magnetized plasma.12 Thus Doppler shifts of the Stokes I and Q.U.V profiles reflect average line-of-sight (LOS) velocities of plasmas in the whole resolution element and those within magnetic regions. respectively (e.g..Solanki1986).," Thus Doppler shifts of the Stokes $I$ and $Q, U, V$ profiles reflect average line-of-sight (LOS) velocities of plasmas in the whole resolution element and those within magnetic regions, respectively \citep[e.g.,][]{Solanki1986A&A...168..311S}."13 Asymmetries of Stokes profiles are a powerful diagnostics of the height and spatial properties ofmagnetic and flow fields (e.g..Grigorev&Katz1975).," Asymmetries of Stokes profiles are a powerful diagnostics of the height and spatial properties ofmagnetic and flow fields \citep[e.g.,][]{Grigorev+Katz1975SoPh...42...21G}."14 Under a restrictive Milne-Eddington atmosphere where magnetohydrodynamie (MHD) conditions (e.g.. plasma velocity. magnetic. field vector. and temperature) are constant with depth and the source function. varies linearly with optical depth (Unno1956:LandiDeglinnocenti& 1985).. the Zeeman-split Stokes 7.Q.U profiles are symmetric. while V is antisymmetric about the line center.," Under a restrictive Milne-Eddington atmosphere where magnetohydrodynamic (MHD) conditions (e.g., plasma velocity, magnetic field vector, and temperature) are constant with depth and the source function varies linearly with optical depth \citep{Unno1956, Landi+Landi1985}, the Zeeman-split Stokes $I,Q,U$ profiles are symmetric, while $V$ is antisymmetric about the line center."15 Most of the observed Stokes spectra. however. deviate from the ideal forms and exhibit notable difference. between the blue and red wings in amplitude and/or area.," Most of the observed Stokes spectra, however, deviate from the ideal forms and exhibit notable difference between the blue and red wings in amplitude and/or area."16 Therefore the Stokes asymmetry is able to reveal the inhomogeneous nature of the solar atmosphere (e.g..[lingetal.1974a.b)..," Therefore the Stokes asymmetry is able to reveal the inhomogeneous nature of the solar atmosphere \citep[e.g.,][]{illing+landmann+mickey1974A&A....35..327I, illing+landmann+mickey1974A&A....37...97I}."17 Direct observations (e.g..Balasubramaniametal.1997;Sigwarth2001) and modeling of synthetic Stokes profiles (e.g..Solanki&Pahlkeetal.2000;Steiner2000) have found possible physical conditions for producing asymmetric Stokes spectra. such às gradients of flow velocity and/or magnetic field vector along the LOS direction and nonuniform atmosphere that contains two or more distinct magnetic and/or flow components in one resolution element.," Direct observations \citep[e.g.,][]{Balasubramaniam+etal1997ApJ...482.1065B, Sigwarth2001} and modeling of synthetic Stokes profiles \citep[e.g.,][]{Solanki+Pahlke1988A&A...201..143S, SanchezAlmeida+Lites1992ApJ...398..359S, Solanki+Montavon1993A&A...275..283S, SanchezAlmeida+etal1996ApJ...466..537S, Grossmann-Doerth+etal2000, Steiner2000SoPh..196..245S} have found possible physical conditions for producing asymmetric Stokes spectra, such as gradients of flow velocity and/or magnetic field vector along the LOS direction and nonuniform atmosphere that contains two or more distinct magnetic and/or flow components in one resolution element."18 A more comprehensive study by LópezArtiste(2002) based on the analytical solution for the generalized transfer equation explicitly demonstrates that the velocity gradients are the necessary and sufficient condition for Stokes profile asymmetries., A more comprehensive study by \citet{LopezAriste2002ApJ...564..379L} based on the analytical solution for the generalized transfer equation explicitly demonstrates that the velocity gradients are the necessary and sufficient condition for Stokes profile asymmetries.19 The addition of other effects or gradients of other MHD parameters (e.g.. magnetic field and temperature) could enhance the asymmetries and give different characteristics of asymmetries.," The addition of other effects or gradients of other MHD parameters (e.g., magnetic field and temperature) could enhance the asymmetries and give different characteristics of asymmetries."20 For example. strong Stokes / and V asymmetries are usually found around magnetic flux. concentrations in. the photosphere. which is attributed to the presence of the “magnetic canopy” (Grossmann-Doerthetal.1988.1989:Solanki1989;Leka&Steiner 2001)..," For example, strong Stokes $I$ and $V$ asymmetries are usually found around magnetic flux concentrations in the photosphere, which is attributed to the presence of the “magnetic canopy” \citep{grossmanndoerth+schuessler+solanki1988A&A...206L..37G, grossmanndoerth+schuessler+solanki1989A&A...221..338G, Solanki1989A&A...224..225S, leka+steiner2001}."21 Strong gradients in both magnetic and flow fields are naturally generated because the “magnetic canopy” spatially separates the field-free convective downdrafts from the more static flux tube that fans out above the photosphere., Strong gradients in both magnetic and flow fields are naturally generated because the “magnetic canopy” spatially separates the field-free convective downdrafts from the more static flux tube that fans out above the photosphere.22 The aforementioned analyses of Stokes profiles predominantly use photospherie spectral lines., The aforementioned analyses of Stokes profiles predominantly use photospheric spectral lines.23 In retrospect.— only few such attempts using chromospheric Stokes spectra have been reported.," In retrospect, only few such attempts using chromospheric Stokes spectra have been reported."24" As examples. Briand&Solanki(1998) inferred fast down flows concentrated in narrow lanes surrounding the flux tube below the “magnetic canopy"" by using Stokes V asymmetries of bb: line in additional to photospherie lines."," As examples, \citet{Briand+Solanki1998A&A...330.1160B} inferred fast down flows concentrated in narrow lanes surrounding the flux tube below the “magnetic canopy” by using Stokes $V$ asymmetries of $_2$ line in additional to photospheric lines."25 Gosain&Choud-hary(2003) compared the Stokes V asymmetries between photospheric llines and chromospheric llines and found differences in their spatial distribution within a simple sunspot., \citet{Gosain+Choudhary2003SoPh..217..119G} compared the Stokes $V$ asymmetries between photospheric lines and chromospheric lines and found differences in their spatial distribution within a simple sunspot.26 Additional investigation of chromospheric Stokes spectra in. conjunction with photospherie measurements would improve our understanding— of 3D magnetic topology and plasma flows., Additional investigation of chromospheric Stokes spectra in conjunction with photospheric measurements would improve our understanding of 3D magnetic topology and plasma flows.27 In this paper. we study Doppler shifts and asymmetries of Stokes profiles of three spectral lines simultaneously observed in an active region close to the disk center.," In this paper, we study Doppler shifts and asymmetries of Stokes profiles of three spectral lines simultaneously observed in an active region close to the disk center."28" The three spectral lines. 6630.25 nm (g,;;= 2.5). 6630.15 nm (g,;;= 1.67). and bb. are formed at partially overlapping atmospheric layers spanning from the photosphere to the low chromosphere."," The three spectral lines, 630.25 nm $_{eff} = 2.5$ ), 630.15 nm $_{eff} = 1.67$ ), and $_2$, are formed at partially overlapping atmospheric layers spanning from the photosphere to the low chromosphere."29 Even though both are regarded as photospheric lines. the 6630.15 nm line often forms above the 630.25 nm line (e.g..Khomenko&Collados 2007)..," Even though both are regarded as photospheric lines, the 630.15 nm line often forms above the 630.25 nm line \citep[e.g.,][]{Khomenko+Collados2007ApJ...659.1726K}."30 Combining data from multiple atmospheric. heights using these spectral lines thus enables us to shed new light on the properties of magnetic and flow structures associated with different magnetic features., Combining data from multiple atmospheric heights using these spectral lines thus enables us to shed new light on the properties of magnetic and flow structures associated with different magnetic features.31 The plan of this paper is as follows: in ?? and ??. we introduce the observations and present the procedure for data reduction.," The plan of this paper is as follows: in \ref{sec:observation} and \ref{sec:reduction}, we introduce the observations and present the procedure for data reduction."32 In ?? the results of comparison of profile shifts and asymmetries among the three spectral lines are described and discussed., In \ref{sec:results} the results of comparison of profile shifts and asymmetries among the three spectral lines are described and discussed.33 We summarize our major findings and present some prospects for future studies ing 22., We summarize our major findings and present some prospects for future studies in \ref{sec:summary}.34 We obtained the spectropolarimetric data sets using the 76 em Dunn Solar Telescope and its associated Adaptive Optics system (Rimmele2004).. along with the High Altitude Observatory/National Solar Observatory Advanced. Stokes Polarimeter (HAO/NSOASP.Elmoreetal.1992;Lites1996;Skumanichetal. 1997).," We obtained the spectropolarimetric data sets using the 76 cm Dunn Solar Telescope and its associated Adaptive Optics system \citep{rimmele2004a}, along with the High Altitude Observatory/National Solar Observatory Advanced Stokes Polarimeter \citep[HAO/NSO ASP,][]{Elmore+etal1992, Lites1996, skumanich+etal1997}."35. The observations were obtained on 2001 October 17 under excellent seeing conditions., The observations were obtained on 2001 October 17 under excellent seeing conditions.36 The ASP is a slit-grating spectropolarimeter., The ASP is a slit-grating spectropolarimeter.37" The 1.6"" « sslit was oriented in. the solar north-south direction and scanned in the east-west direction.", The $^{\prime}$ $\times$ slit was oriented in the solar north-south direction and scanned in the east-west direction.38 Each whole scan took 280 steps with a step size of 0.6”.. which results in a field of view (FOV) of 1.6 « 2.8 that covers the near disk center (NI4°.," Each whole scan took 280 steps with a step size of , which results in a field of view (FOV) of $^{\prime}$ $\times$ $^{\prime}$ that covers the near disk center $^\circ$ ,"39"this corresponds to objects farther than about a tenth of a parsec; therefore, beyond a parsec lensing strongly dominates.","this corresponds to objects farther than about a tenth of a parsec; therefore, beyond a parsec lensing strongly dominates."40 If the source is a giant in the bulge its angular radius is typically about 20 pas., If the source is a giant in the bulge its angular radius is typically about 20 $\mu$ as.41" More distant sources will appear smaller; however, they would be difficult if not impossible to detect with the SKA."," More distant sources will appear smaller; however, they would be difficult if not impossible to detect with the SKA."42" If the lens lies well below the blue line (Rg/D=0.02 mas) and the source is a bulge giant, then the optical light curve would be similar to that of a point source."," If the lens lies well below the blue line $R_E/D=0.02$ mas) and the source is a bulge giant, then the optical light curve would be similar to that of a point source."43" If the lens lies above or near the black line Rg/(fD)=0.02 mas), the fringes would begin to be washed out due to the finite size of the source; therefore, if a lensing event on a bulge star lacks finite-size effects in the optical and lacks fringes at one-metre, then the lens must lie the wedge well above the black line and well below the blue line."," If the lens lies above or near the black line $\pi44R_E/(f D)=0.02$ mas), the fringes would begin to be washed out due to the finite size of the source; therefore, if a lensing event on a bulge star lacks finite-size effects in the optical and lacks fringes at one-metre, then the lens must lie the wedge well above the black line and well below the blue line."45" One could look for fringes at lower frequencies to further restrict the properties of the lens; however, the sources might be difficult to detect at such low frequencies refsec:sources))."," One could look for fringes at lower frequencies to further restrict the properties of the lens; however, the sources might be difficult to detect at such low frequencies \\ref{sec:sources}) )."46 More tantalizing than a null result would be the detection of fringes (Fig. 2)), More tantalizing than a null result would be the detection of fringes (Fig. \ref{fig:sample}) )47 or a lack of magnification at the longer wavelength., or a lack of magnification at the longer wavelength.48 By comparing the optical light curve (green in Fig 2)) to the light curve at lower frequencies one could determine the value of f for the lens at the lower frequency., By comparing the optical light curve (green in Fig \ref{fig:sample}) ) to the light curve at lower frequencies one could determine the value of $f$ for the lens at the lower frequency.49" Even if the fringes are diluted by finite source effects, the diffraction does still cause the light curve to vary."," Even if the fringes are diluted by finite source effects, the diffraction does still cause the light curve to vary."50" Typically if there are six fringes across the disk of the source (red curve), the difference between the light curve according to geometric optics and the diffractive result is a few percent."," Typically if there are six fringes across the disk of the source (red curve), the difference between the light curve according to geometric optics and the diffractive result is a few percent."51" For twenty fringes over the stellar disk, the difference is a few parts per thousand."," For twenty fringes over the stellar disk, the difference is a few parts per thousand."52" If the source is a bulge giant (with a radius twenty times that of the sun), this would correspond to the uppermost black line labelled “A6s,=0.002mas.”"," If the source is a bulge giant (with a radius twenty times that of the sun), this would correspond to the uppermost black line labelled $\Delta\theta_\mathrm{fr}=0.002$ mas.”"53 For values of f<1 there is typically little magnification., For values of $f<1$ there is typically little magnification.54 The absence of magnification at a particular wavelength would restrict the lens to have a Schwarzschild radius less than that wavelength — a low mass lens., The absence of magnification at a particular wavelength would restrict the lens to have a Schwarzschild radius less than that wavelength — a low mass lens.55" On the other hand, the detection of some magnification along with fringes would determine the value of f constraining the lens to lie on one of the vertical lines in Fig."," On the other hand, the detection of some magnification along with fringes would determine the value of $f$ constraining the lens to lie on one of the vertical lines in Fig."56 1 and giving the mass of the lens., \ref{fig:regimes} and giving the mass of the lens.57 The distance to the lens would also be constrained by the relative amplitude of the fringing if the angular size of the source is comparable or larger than that of fringes., The distance to the lens would also be constrained by the relative amplitude of the fringing if the angular size of the source is comparable or larger than that of fringes.58" For wavelengths less than a metre and lens masses greater than a tenth of a Jupiter mass, the value of f is much greater than unity."," For wavelengths less than a metre and lens masses greater than a tenth of a Jupiter mass, the value of $f$ is much greater than unity."59 In this limit the fringe pattern approaches a simple cosine dependence (Eq. 6)), In this limit the fringe pattern approaches a simple cosine dependence (Eq. \ref{eq:4}) )60 as can be seen in Fig. 3.., as can be seen in Fig. \ref{fig:fringe}.61 In the limit of large f the peak magnification is simply af while in the geometric optics limit the magnification diverges as the source lens and observer become aligned., In the limit of large $f$ the peak magnification is simply $\pi f$ while in the geometric optics limit the magnification diverges as the source lens and observer become aligned.62" According to Fig. 4,,"," According to Fig. \ref{fig:ampl},"63 the relative amplitude of the variation is approximately equal to (f0./05) for large values of f and (f0./0rE)., the relative amplitude of the variation is approximately equal to $(f \theta_s/\theta_E)^{-1.5}$ for large values of $f$ and $(f\theta_s/\theta_E)$.64" The amplitude of .?the power-law relation depends on what portion of the light curve is examined; however, the exponent comes simply from the integral of a sinusoid (Eq. 6))"," The amplitude of the power-law relation depends on what portion of the light curve is examined; however, the exponent comes simply from the integral of a sinusoid (Eq. \ref{eq:4}) )"65 over the circular source where k«xf0s/0g., over the circular source where $k\propto f \theta_S/\theta_E$.66 The final proportionality holds for values of k much greater than one., The final proportionality holds for values of $k$ much greater than one.67" The derivation of this expression clearly only makes sense if f>>1 and 0s<0g More generally the relative amplitude of the variation can be taken to be a power law to give for f, ]νά and f>>1 and where"," The derivation of this expression clearly only makes sense if $f\gg 1$ and $\theta_S \ll68\theta_E$ More generally the relative amplitude of the variation can be taken to be a power law to give for $f_\nu > f_{\nu,d}$ and $f \gg 1$ and where"69"While the earliest Pop III stars are most likely to form in the main progenitor halo of the Galaxy, the majority may form in other, smaller progenitor haloes.","While the earliest Pop III stars are most likely to form in the main progenitor halo of the Galaxy, the majority may form in other, smaller progenitor haloes."70 Here we evaluate the probability of accretion onto low-mass Pop III stars in these haloes., Here we evaluate the probability of accretion onto low-mass Pop III stars in these haloes.71" For this purpose, we employ the extended Press-Schechter (e.g. Lacey Cole 1993) formalism to construct a merger tree of the progenitor haloes of a Milky Way-like halo, with a mass of 1013 Mo at z = 0."," For this purpose, we employ the extended Press-Schechter (e.g. Lacey Cole 1993) formalism to construct a merger tree of the progenitor haloes of a Milky Way-like halo, with a mass of $^{12}$ $_{\odot}$ at $z$ = 0."72" In particular, we employ the Monte-Carlo method suggested by Somerville Kolatt (1999)."," In particular, we employ the Monte-Carlo method suggested by Somerville Kolatt (1999)."73" As we have shown, in haloes of lower mass, accretion is more likely to occur, due principally to the fact that a star moving at lower velocity v. ~ Umax can accrete gas at a lower density, which in turn has a larger volume-filling factor faoua."," As we have shown, in haloes of lower mass, accretion is more likely to occur, due principally to the fact that a star moving at lower velocity $v_{\rm *}$ $\sim$ $v_{\rm max}$ can accrete gas at a lower density, which in turn has a larger volume-filling factor $f_{\rm cloud}$."74" Therefore, the minimum halo mass for which accretion of metals can take place is a critical parameter in our calculation."," Therefore, the minimum halo mass for which accretion of metals can take place is a critical parameter in our calculation."75" As discussed in Section 4.1, a minimum halo mass of 105 Mo is likely a good estimate (e.g. Greif et al."," As discussed in Section 4.1, a minimum halo mass of $^{8}$ $_{\odot}$ is likely a good estimate (e.g. Greif et al."76" 2010b), as this is the typical mass of a halo that is able to re- the metal-enriched ejecta of the first Pop III SNe, which typically occur in the 10° - 10’ Mo progenitors of these haloes (e.g. Bromm Larson 2004; Trenti Stiavelli 2009)."," 2010b), as this is the typical mass of a halo that is able to re-capture the metal-enriched ejecta of the first Pop III SNe, which typically occur in the $^6$ - $^7$ $_{\odot}$ progenitors of these haloes (e.g. Bromm Larson 2004; Trenti Stiavelli 2009)."77" Similar to the case of the main progenitor halo described in Section 4.2.1, we estimate the probability of accretion onto a low-mass Pop III star by integrating equation (15) from z — 0 to the redshift at which a halo with the minimum mass forms."," Similar to the case of the main progenitor halo described in Section 4.2.1, we estimate the probability of accretion onto a low-mass Pop III star by integrating equation (15) from $z$ = 0 to the redshift at which a halo with the minimum mass forms."78" However, to account for the numerous halo mergers that alter the orbital parameters of a star, and in particular the apogalactic distance of its orbit, instead of assuming rap = 0.1 ryir as before, we now use rap = Nyand Tvir, Where Nrana is a random number between zero and unity that is updated after each merger."," However, to account for the numerous halo mergers that alter the orbital parameters of a star, and in particular the apogalactic distance of its orbit, instead of assuming $r_{\rm ap}$ = 0.1 $r_{\rm vir}$ as before, we now use $r_{\rm ap}$ = $N_{\rm rand}$ $r_{\rm vir}$, where $N_{\rm rand}$ is a random number between zero and unity that is updated after each merger."79 T'his yields the orbital period of a star in a given halo torn = Nrana Tvir / Umax., This yields the orbital period of a star in a given halo $t_{\rm orb}$ = $N_{\rm rand}$ $r_{\rm vir}$ / $v_{\rm max}$.80" Also, as in Komiya et al. ("," Also, as in Komiya et al. ("81"2010), we account for the delay in a star being incorporated into its new host halo after a merger, which is taken to be the timescale for dynamical friction given by Springel et al. (","2010), we account for the delay in a star being incorporated into its new host halo after a merger, which is taken to be the timescale for dynamical friction given by Springel et al. ("822001).,2001).83" Similar to the case of accretion onto Pop III stars with no winds considered by Komiya et al.,"," Similar to the case of accretion onto Pop III stars with no winds considered by Komiya et al.,"84" we find that the accounting for this delay results in somewhat higher accretion probabilities, especially for stars formed in haloes at relatively low z that undergo mergers with much more massive haloes (see discussion below)."," we find that the accounting for this delay results in somewhat higher accretion probabilities, especially for stars formed in haloes at relatively low $z$ that undergo mergers with much more massive haloes (see discussion below)."85 Figure 2 shows the probability that low-mass Pop III stars within haloes with mass > 10? Mo accrete metal-enriched gas during the assembly of the Galaxy., Figure 2 shows the probability that low-mass Pop III stars within haloes with mass $\ge$ $^8$ $_{\odot}$ accrete metal-enriched gas during the assembly of the Galaxy.86" The left panel shows the probability of accretion onto stars hosted by all of the 10° Mo progenitor haloes, as a function of the redshift at which they form."," The left panel shows the probability of accretion onto stars hosted by all of the $^8$ $_{\odot}$ progenitor haloes, as a function of the redshift at which they form."87" The right panel shows the distribution of these probabilities; assuming that each 10? Mo halo hosts the same number of low-mass Pop III stars, this can be translated as the distribution of probabilities of accretion onto all Pop III stars in the halo of the Galaxy today."," The right panel shows the distribution of these probabilities; assuming that each $^8$ $_{\odot}$ halo hosts the same number of low-mass Pop III stars, this can be translated as the distribution of probabilities of accretion onto all Pop III stars in the halo of the Galaxy today."88" As shown by the black histogram in the right panel,"," As shown by the black histogram in the right panel,"89theoretical expectations for the light curves.,theoretical expectations for the light curves.90 These are 0<tonsc LOO. LOO<taps 200. aud 200ctaps<100. davs.," These are $0<t_{obs}<100$ $100<t_{obs}<200$ , and $200<t_{obs}<400$ days."91 In addition to the practical convenieuce of analyzing these data in this comparamecutalized fashion. it also anticipates the possibility that some trausicut-source lielt curves may be truncated by either cud of our 2.2 vear baseline by different timescales.," In addition to the practical convenience of analyzing these data in this comparamentalized fashion, it also anticipates the possibility that some transient-source light curves may be truncated by either end of our 2.2 year baseline by different timescales."92 We remind the reader that the light curves of all sources are larecly ciscoutignous because the precise pointing (aud orieutation) varies epoch by epoch., We remind the reader that the light curves of all sources are largely discontiguous because the precise pointing (and orientation) varies epoch by epoch.93 This also affects the precise depth of cach epoch. and changes the on-sky orientation of the IRAC diffraction patteru essentially leading to rotating cliffraction spikes across nuages.," This also affects the precise depth of each epoch, and changes the on-sky orientation of the IRAC diffraction pattern essentially leading to rotating diffraction spikes across images."94 We find that the photometry of objects near bright stars is systematically coutaminated by these rotating diffraction spikes., We find that the photometry of objects near bright stars is systematically contaminated by these rotating diffraction spikes.95 Therefore we identify the stars auc the sources close enough to them to be affected. and explicitly remove them frou our master catalog.," Therefore we identify the stars and the sources close enough to them to be affected, and explicitly remove them from our master catalog."96 huagine with //ACS FalW was obtained between November December 2006. one vear after the end of the TRAC dataset described here.," Imaging with /ACS F814W was obtained between November December 2006, one year after the end of the IRAC dataset described here."97 With this data. a plot of the Source. EXtractor (Bertin&Arnouts1996) value versus aperture magnitude photometry clearly separates the ridge of unresolved sources from resolved galaxies. because unresolved sources lave sinaller than galaxies at uu even naenuitude.," With this data, a plot of the Source EXtractor \citep{bertin96} value versus aperture magnitude photometry clearly separates the ridge of unresolved sources from resolved galaxies, because unresolved sources have smaller than galaxies at any given magnitude."98" This imoethod identifies 1117 uuresolved sources,", This method identifies 1147 unresolved sources.99" We empirically deteruine a radius of à=0.06<53,654, aaresee (but no greater than aaresec). to ask out a circular area around cach star also removing au additional 5858 sources which were in close proximity."," We empirically determine a radius of $r=0.06\times S_{3.6\mu m}$ arcsec (but no greater than arcsec), to mask out a circular area around each star also removing an additional 5858 sources which were in close proximity."100 Given the relative non-hoimosenueitv in the survey's depth and cadence saiupliug. we apply several criteria O removeerroneous sources.," Given the relative non-homogeneity in the survey's depth and cadence sampling, we apply several criteria to removeerroneous sources."101 1) We impose an Hux density ΠΠ of LOgJy. which is an cmpirically determined practical threshold for removing aceditional objects that are affected by diffraction spike artifacts. vevoud the masked radii. aud object de-bleudiug issues.," 1) We impose an flux density limit of $\mu$ Jy, which is an empirically determined practical threshold for removing additional objects that are affected by diffraction spike artifacts, beyond the masked radii, and object de-blending issues."102 2) For all sources we ouly inchide epochs which have a 5o detection of >LyJy., 2) For all sources we only include epochs which have a $\sigma$ detection of $>$ $\mu$ Jy.103 3) We do not cousider sources hat appear in only a epoch., 3) We do not consider sources that appear in only a epoch.104 L) Sources detected iu ouly two or three epochs are oulv included iu our search if they have 56 doetectious of 71 py in epochs., 4) Sources detected in only two or three epochs are only included in our search if they have $\sigma$ detections of $>$ $\mu$ Jy in epochs.105 5) For any object with multiple epoch detections. we require the 3.6400 photometric uncertainty to be less than iu at least half of its detected epochs.," 5) For any object with multiple epoch detections, we require the ${3.6\mu m}$ photometric uncertainty to be less than in at least half of its detected epochs."106 This eusures that this source is not rejected ou the basis of large uncertainties in a πα umber of epochs (e.g. due to some epochs being particularly shallow relative to the others)., This ensures that this source is not rejected on the basis of large uncertainties in a small number of epochs (e.g. due to some epochs being particularly shallow relative to the others).107 6) Finally. we require at least two siguificaut uou-detections. to eusure a clear transicut signal.," 6) Finally, we require at least two significant non-detections, to ensure a clear transient signal."108 After application of cach of these criteria. 650 candidates remained that warranted more careful follow-up.," After application of each of these criteria, 650 candidates remained that warranted more careful follow-up."109 The 36425 light) curves and the corresponding TRAC and imaging were all visually inspected by ceustoni-built software that clearly identified all salieut aspects for the object iu the master database., The ${3.6\mu m}$ light curves and the corresponding IRAC and imaging were all visually inspected by custom-built software that clearly identified all salient aspects for the object in the master database.110 No a priori restrictions were placed ou the shape of the light curve., No a priori restrictions were placed on the shape of the light curve.111" Several objects with otherwise flat πο curves were found to lave a dramatic ""fhue-up in a single epoch.", Several objects with otherwise flat light curves were found to have a dramatic “flare-up” in a single epoch.112 Careful inspection of the individual IRAC. sx exposures of that epoch showed the spike to be a cosmic rav incident., Careful inspection of the individual IRAC s exposures of that epoch showed the spike to be a cosmic ray incident.113 The remaimine candidates were found to have resolved-source counterparts in the data. and are therefore candidate low-redshift active galactic uuclei. which though extremely interesting in their own right. ave clearly not Pop HIE SNe candidates.," The remaining candidates were found to have resolved-source counterparts in the data, and are therefore candidate low-redshift active galactic nuclei, which though extremely interesting in their own right, are clearly not Pop III SNe candidates."114 At the end of this careful analysis and vetting procedure. viable candidates survived.," At the end of this careful analysis and vetting procedure, viable candidates survived."115 In the next Section we calculate the formal Linits implied by our search., In the next Section we calculate the formal limits implied by our search.116 No Pop III SNe candidates to our sensitivity liit of HyjaAD)~21 were identified., No Pop III SNe candidates to our sensitivity limit of $m_{\rm 3.6\mu m}(\rm AB) \sim 24$ were identified.117 For the areal search over a total of Laarcuminutes?. the rate limit is below ?yvr 1.," For the areal search over a total of $^2$ , the rate limit is below $^{-2}$ $^{-1}$."118 Using the same area but also modeling this nou-cdetection limit as a Poisson distribution. the The Wise&Abel(2005). and Ieeeretal.(2002) 2=10 predicted differential rates of αλ— 0.31ddegv | and ~0.2ddee 7vyy +. respectively. are not ruled out. even if they appear at lower redshifts which may be above our sensitivity linüt.," Using the same area but also modeling this non-detection limit as a Poisson distribution, the The \citet{wiseabel05} and \citet{heger02} $z=10$ predicted differential rates of $dN/dz\sim0.34$ $^{-2}$ $^{-1}$ and $\sim$ $^{-2}$ $^{-1}$ , respectively, are not ruled out, even if they appear at lower redshifts which may be above our sensitivity limit."119 Caven that our search is most effectively probing 2~3.5. the differential rate of Welmmanun&Lilly(2005) of 25 2yyr bati= Sis broadly comparable to our limit.," Given that our search is most effectively probing $z\sim3-5$, the differential rate of \cite{weinmann04} of 25 $^{-2}$ $^{-1}$ at $z=5$ is broadly comparable to our limit."120 It should be noted the very hDmuuimous PISNe that we would be seusitive to i this survey may be only a simall fraction of all hiel-+vedshift superuova events., It should be noted the very luminous PISNe that we would be sensitive to in this survey may be only a small fraction of all high-redshift supernova events.121 There is a distinction currently being made between Pop IIL1 aud IIL2 stars. where the former class are of fully primorcial i»udauce. and formin dark matter mini-lialos. resulting in the pre-requisite stellar masses of above ~100A. to produce PISNe (Joliusou&Drouun2006.. McI&ee&Tau 2008)).," There is a distinction currently being made between Pop III.1 and III.2 stars, where the former class are of fully primordial abundance, and form in dark matter mini-halos, resulting in the pre-requisite stellar masses of above $\sim100\,M_{\odot}$ to produce PISNe \citealt{jobro06}, \citealt{mcktan08}) )."122 These are distinct from the Pop IIL2 stars. which are expected to fox through atomic cooling processes. producing only LOAL. progenitors (Cweif&Dronuu 2006).," These are distinct from the Pop III.2 stars, which are expected to form through atomic cooling processes, producing only $\sim 10\,M_{\odot}$ progenitors \citep{grebro06}."123. The PISNe Pop ΤΗ. progenitors nav cousist of oulv some of Pop III SNe (Croif&Brom2006)., The PISNe Pop III.1 progenitors may consist of only some of Pop III SNe \citep{grebro06}.124. Furthermore. the “pristine” Pop IIL1 progenitors cau suffer dramatic negative feedback citealtiicktan(08)). which παν additionally liuüt their relative nunibers.," Furthermore, the “pristine” Pop III.1 progenitors can suffer dramatic negative feedback \\citealt{mcktan08}) ), which may additionally limit their relative numbers."125 These were all considerations not vet taken in the predictions by Alackeyetal.(2003).. which led to the high expectation rates.," These were all considerations not yet taken in the predictions by \citet{mackey03},, which led to the high expectation rates."126 To do a search for Pop III SNe usiug (or a future platform with similarcapabilities) would require a survey area of1 dee? with exposures of 5000 seconds (50«LOO ssexposures) per point on the sky., To do a search for Pop III SNe using (or a future platform with similarcapabilities) would require a survey area of1 $^2$ with exposures of 5000 seconds $50\times100$ sexposures) per point on the sky.127 This would reach map~26 at the 0 level. depending," This would reach $m_{\rm AB}\sim26$ at the $\sigma$ level, depending"128our estimates in Section 6 suggest that these under-counting effects only account for roughly 10% of the discrepancy in estimates of low-luminosity 150 MHz radio halos.,our estimates in Section \ref{sec:rh_counts} suggest that these under-counting effects only account for roughly $10 \%$ of the discrepancy in estimates of low-luminosity 150 MHz radio halos.129 While the combined effects of the lack of steep-spectrum halos and our limited simulation volume, While the combined effects of the lack of steep-spectrum halos and our limited simulation volume130dig=35000480 and logg=8.175250.03.,$T_{\rm eff} = 35000\pm80$ and $\log{g} = 8.75\pm0.03$.131 And finally the eric of models that include Lyman satellites and use EP result in a best fitwith Zip=34800290 and logg=9.1350.04., And finally the grid of models that include Lyman satellites and use IT result in a best fitwith $T_{\rm eff} = 34800\pm90$ and $\log{g} = 9.13\pm0.04$.132 The series of analyses show that the two dillerent treatments of line merging produces a dillerence of zz0.1 in the surface eravity. and that the inclusion of Lyman satellites increases the measured. surface. gravity by z0.3.," The series of analyses show that the two different treatments of line merging produces a difference of $\approx 0.1$ in the surface gravity, and that the inclusion of Lyman satellites increases the measured surface gravity by $\approx 0.3$."133 We find that the best agreement with Vennesetal.(1905) is obtained using moclels that include the Lyman satellites however the fit is unsatislactory as several predicted features are stronger than observed., We find that the best agreement with \citet{ven1998} is obtained using models that include the Lyman satellites however the fit is unsatisfactory as several predicted features are stronger than observed.134 Similar cilliculties were encountered. by in the analysis of Lyman line profiles of the ultramassive DAp PG 1658| 441., Similar difficulties were encountered by in the analysis of Lyman line profiles of the ultramassive DAp PG $+$ 441.135 Emploving the mass-radius relations for DA white dwarfs (Benvenuto&Althaus1999).. we determined. the mass and absolute magnitude of the white dwarl 1.08LetM. and Ady=10.96.11.76.," Employing the mass-radius relations for DA white dwarfs \citep{ben1999}, we determined the mass and absolute magnitude of the white dwarf, $M=1.08 - 1.24\ M_\odot$ and $M_V=10.96 - 11.76$."136 Vennesetal.(1998) already concluded that the distance modulus derived from the Hipparcos parallax of the AS star would be consistent with the predicted. distance modulus for an dwarf., \citet{ven1998} already concluded that the distance modulus derived from the Hipparcos parallax of the A8 star would be consistent with the predicted distance modulus for an .137 To our knowledge. the case of LURS210 is rather unique," To our knowledge, the case of HR8210 is rather unique"138Here a significant fraction of the total dust mass is located at larger radii and directly heated by the AGN.,Here a significant fraction of the total dust mass is located at larger radii and directly heated by the AGN.139" We plot the light curves as a function of the intrinsic time scale fau;=rgo/c, which corresponds to the light-travel time from the source to the sublimation radius rp."," We plot the light curves as a function of the intrinsic time scale $t_\mathrm{sub} = r_\mathrm{sub}/c$, which corresponds to the light-travel time from the source to the sublimation radius $r_\mathrm{sub}$."140" In this way the variability signal from the AGN can be considered a tomographic device to map out the brightness distribution in the torus, and elapsed time and distance from the AGN become equivalent independent of the object's luminosity (tsub=rap/ce L'/?, see Sect. ??))."," In this way the variability signal from the AGN can be considered a tomographic device to map out the brightness distribution in the torus, and elapsed time and distance from the AGN become equivalent independent of the object's luminosity $t_\mathrm{sub} = r_\mathrm{sub}/c \propto L^{1/2}$ , see Sect. \ref{sec:var}) )."141 The near-IR (2.2 um) light curves in Fig.," The near-IR $2.2\,\micron$ ) light curves in Fig."142" 2 show that the more concentrated distributions are stronger peaked, while the distributions with @ closer to 0 have longer tails."," \ref{fig:lc} show that the more concentrated distributions are stronger peaked, while the distributions with $\alpha$ closer to 0 have longer tails."143 In the very compact objects almost all of the near-IR light comes from the peak emission of the hottest dust., In the very compact objects almost all of the near-IR light comes from the peak emission of the hottest dust.144" When the dust distribution becomes more extended, then the Wien tails of the cooler dust emission start to contribute relatively more since the relative amount of hot dust decreases."," When the dust distribution becomes more extended, then the Wien tails of the cooler dust emission start to contribute relatively more since the relative amount of hot dust decreases."145 The behavior in the near-IR has its correspondence at longer wavelength., The behavior in the near-IR has its correspondence at longer wavelength.146 The mid-IR (8.5m) light curves with a compact brightness profile are peaked in the inner torus where the hot dust is located.," The mid-IR $8.5\,\micron$ ) light curves with a compact brightness profile are peaked in the inner torus where the hot dust is located."147" Over time the brightness decays quickly, however not as fast as in the near-IR."," Over time the brightness decays quickly, however not as fast as in the near-IR."148" As the brightness distribution becomes shallower (more extended), the initial peak at rsyp/c vanishes, the light curves get flatter, and for α>-—0.5 they keep on increasing out to >10xry/c."," As the brightness distribution becomes shallower (more extended), the initial peak at $r_\mathrm{sub}/c$ vanishes, the light curves get flatter, and for $\alpha>-0.5$ they keep on increasing out to $\ge10\times r_\mathrm{sub}/c$."149 The difference between the mid-IR and the near-IR is that in the mid-IR the emission comes predominantly from either the Rayleigh-Jeans tail of hot dust emission in the inner torus or from the peak black-body emission of cooler dust at larger distances., The difference between the mid-IR and the near-IR is that in the mid-IR the emission comes predominantly from either the Rayleigh-Jeans tail of hot dust emission in the inner torus or from the peak black-body emission of cooler dust at larger distances.150 In the near-IR the flux originates predominantly in the black-body peak of hot dust with little contribution from the steeply dropping Wien tail of cooler dust., In the near-IR the flux originates predominantly in the black-body peak of hot dust with little contribution from the steeply dropping Wien tail of cooler dust.151" For steep brightness profiles, the hot-dust Rayleigh-Jeans tail dominates the mid-IR emission due to the lack of extended dust."," For steep brightness profiles, the hot-dust Rayleigh-Jeans tail dominates the mid-IR emission due to the lack of extended dust."152" Around α«-1, the contribution of the black-body peak from extended dust becomes about equal to the hot dust Rayleigh-Jeans tail, which takes over for even shallower brightness profiles."," Around $\alpha\approx -1$, the contribution of the black-body peak from extended dust becomes about equal to the hot dust Rayleigh-Jeans tail, which takes over for even shallower brightness profiles."153" Since the contribution from different emission regions changes as a function of wavelength and brightness distribution, we can expect delays between the peak of the emission in light-curves."," Since the contribution from different emission regions changes as a function of wavelength and brightness distribution, we can expect delays between the peak of the emission in light-curves."154" Classical reverberation mapping tries to quantify the lag time between the AGN variation and its correspondence in the IR by means of the cross correlation function (CCF) where| fx(t) and fy(t) are light curves at wavebands X and Y, and At is the introduced time lag between both light curves."," Classical reverberation mapping tries to quantify the lag time between the AGN variation and its correspondence in the near-IR by means of the cross correlation function (CCF) where $f_X(t)$ and $f_Y(t)$ are light curves at wavebands $X$ and $Y$, and $\Delta t$ is the introduced time lag between both light curves."155" This method can be applied, in principle, also to the mid-IR."," This method can be applied, in principle, also to the mid-IR."156 We note that in the framework of this paper we define lag times as the peak in the CCF., We note that in the framework of this paper we define lag times as the peak in the CCF.157 In Fig., In Fig.158" 3 we show the CCF of the AGN variability signal with the 2.2um and 8.5um light curves, respectively."," \ref{fig:ccf_agn} we show the CCF of the AGN variability signal with the $2.2\,\micron$ and $8.5\,\micron$ light curves, respectively."159" As expected the time lag between AGN variability and near-IR emission is close to r,,5/c and the CCF is quite narrow.", As expected the time lag between AGN variability and near-IR emission is close to $r_\mathrm{sub}/c$ and the CCF is quite narrow.160" The fact that it is actually slightly larger than unity is in part a result of the used variability function (step function with width 1/2t,5) and the smoothened-out response by the dust.", The fact that it is actually slightly larger than unity is in part a result of the used variability function (step function with width $1/2 t_\mathrm{sub}$ ) and the smoothened-out response by the dust.161" It is seen that the lag time depends slightly on a, so that extended emission profiles show slightly longer lag times (~1.5X rgup/c) while the most compact brightness distributions are at ~1.1Xrsup/c."," It is seen that the lag time depends slightly on $\alpha$, so that extended emission profiles show slightly longer lag times $\sim 1.5\times r_\mathrm{sub}/c$ ) while the most compact brightness distributions are at $\sim 1.1 \times r_\mathrm{sub}/c$."162 The mid-IR light curves show a different behavior., The mid-IR light curves show a different behavior.163" If the brightness distribution is compact, the peak in the CCF is still well-defined and close to rgyp/c."," If the brightness distribution is compact, the peak in the CCF is still well-defined and close to $ r_\mathrm{sub}/c$."164" However when the distribution becomes more extended, the CCF becomes very broad."," However when the distribution becomes more extended, the CCF becomes very broad."165 For —0.5 the peak is no longer well defined and shifts to very long time lags., For $\alpha \le -0.5$ the peak is no longer well defined and shifts to very long time lags.166 This is expected from the light curves and reflects the change in contribution from hot and cooler dust to the mid-IR emission (see Sec. ??))., This is expected from the light curves and reflects the change in contribution from hot and cooler dust to the mid-IR emission (see Sec. \ref{sec:lc}) ).167 The change in CCF (or light curve) with a may be used to distinguish between compact and extended dust distributions., The change in CCF (or light curve) with $\alpha$ may be used to distinguish between compact and extended dust distributions.168" Interestingly, since the near-IR CCFs and light curves are peaked around rj/c for all o, it is not necessary to take the AGN variability signal as a reference, but instead use the near-IR as the CCF-reference signal for the mid-IR."," Interestingly, since the near-IR CCFs and light curves are peaked around $r_\mathrm{sub}/c$ for all $\alpha$, it is not necessary to take the AGN variability signal as a reference, but instead use the near-IR as the CCF-reference signal for the mid-IR."169" While the actual size of rs) cannot be determined in that way, the dust distribution relative torj is still accessible."," While the actual size of $r_\mathrm{sub}$ cannot be determined in that way, the dust distribution relative to$r_\mathrm{sub}$ is still accessible."170 In Fig., In Fig.171 4 we, \ref{fig:ccf_k} we172 L220inthefirstcondilionof& 4.2.2).,$>$ 20 in the first condition of $\S$ 4.2.2).173 ncerlainliesonthemeanarmdolience standarddeciationofbothhislogramsarestatislicaluncertainliesieelmietedla&ssLimi ber ή, Uncertainties on the mean and one-standard deviation of both histograms are statistical uncertainties retrieved assuming normal distributions \citep[Chapter 5]{Bev1969}.174 apterb).[eb ren i. below 2 or well-above 4. were not measured.," Extreme values for $\frac{[\textnormal{N}\,\textsc{ii}]\,\lambda6584}{[\textnormal{N}\,\textsc{ii}]\,\lambda6548}$ i.e., below 2 or well-above 4, were not measured."175 Hence. Condition 5. listed. in 5 4.2.2. was not used in this work to reject: particular emission-line profiles although it could used by other authors for future. similar studies.," Hence, Condition 5, listed in $\S$ 4.2.2, was not used in this work to reject particular emission-line profiles although it could used by other authors for future, similar studies."176 Considering the relatively high S/N. used. here (above 20 for the thick-line histogram of Figure 14 hence suggesting avery good signal quality). deviations from eteJNDNanMnsNonds on22 seem genuine and will be addressed in & 5.1.," Considering the relatively high S/N used here (above 20 for the thick-line histogram of Figure 11 hence suggesting a very good signal quality), deviations from $\frac{[\textnormal{N}\,\textsc{ii}]\,\lambda6584}{[\textnormal{N}\,\textsc{ii}]\,\lambda6548}$ $\sim$ 3 seem genuine and will be addressed in $\S$ 5.1."177 Panels (a) of Figures 12 to 14 provide a series of line-ratio diagnostic diagrams commonly used in optical observations., Panels (a) of Figures 12 to 14 provide a series of line-ratio diagnostic diagrams commonly used in optical observations.178 Each diagram contains the 30057 points already. discussec int; 3 and 4.2.4., Each diagram contains the 057 points already discussed in $\S$$\S$ 4.2.3 and 4.2.4.179" Areas labeled regions’. “SNRs”. and. 7PNe"" were all reproduce according to Figures | to 3 of Sabbadinοἱa£. (1971).."," Areas labeled regions”, “SNRs”, and “PNe” were all reproduced according to Figures 1 to 3 of \citet{Sab1977}. ."180 Long-dashed lines. in Figures and indicate the lower and upper limits for SUENOTIGAGTSL that. provide finite values of electron densities p given a constant temperature of 4400 Ix in 11805 (see § 4.2.8).," Long-dashed lines, in Figures and indicate the lower and upper limits for $\frac{[\textnormal{S}\,\textsc{ii}]\,\lambda6716}{[\textnormal{S}\,\textsc{ii}]\,\lambda6731}$ that provide finite values of electron densities $\rho$ given a constant temperature of 400 K in 1805 (see $\S$ 4.2.3)."181" In all three ciagranis. crosses. colored in blue. are use to represent points found (in majority) within the regions"" area."," In all three diagrams, crosses, colored in blue, are used to represent points found (in majority) within the regions” area."182 Phe relatively high numbers of crosses is not surprising for 11805. already. cataloged as an region.," The relatively high numbers of crosses is not surprising for 1805, already cataloged as an region."183 A certain fraction of the sample. however. falls outside this area.," A certain fraction of the sample, however, falls outside this area."184 These points are svmbolized as red filled. circles ancl point approximately toward the “SNRs” sugecsting evidence for shock excitation in the ΗΕ Ποο πι," These points are symbolized as red filled circles and point approximately toward the “SNRs” area, hence suggesting evidence for shock excitation in the targeted ISM volume."185 Ημ Gp S689, This will be discussed in $\S$ 5.2.186 of the 30057 points retained for this study. respectively 134 (4.40)). 67 (2.2:4)). ancl S4 ()) are clisplavecl as red filled. circles in Figures tolta.," Out of the 057 points retained for this study, respectively 134 ), 67 ), and 84 ) are displayed as red filled circles in Figures to."187 Panels (b). in all three figures. provide the spatial clistribution of all crosses (shown as blue dots) ane circles (shown as red dots) clisplaved in the diagnostic. diagram of their respective Panel (a).," Panels (b), in all three figures, provide the spatial distribution of all crosses (shown as blue dots) and circles (shown as red dots) displayed in the diagnostic diagram of their respective Panel (a)."188 As in Figure106. a black-anc-white reproduction of Figure 4 was used.," As in Figure, a black-and-white reproduction of Figure 4 was used."189 Ited dots in Figures to all point at the same areas and reveal that the southern portions of the bright. central structure - ⋅⋅∣⋅⋅∕⋅∕∕ ↿∖↙↘∣⊐⊔∩∩⋮↻↻↓−≽≼⊢⊰∪⊐⊔↓⋜↧∙∖⇁⋖⋅⊔≼⇍∪⊔↓↓≻⋜↧⊳∖⊳∖⋖⊾∠⇂⊔↓⋜⋯⋅↓⋅⋯⇂≱∖⊔∣⋡≯⇃⋯∙↥↿∪ ⋠ ⊲ ionization by shocks.," Red dots in Figures to all point at the same areas and reveal that the southern portions of the bright, central structure $\delta_{2000}$ $<$ $\arcdeg$ $\arcmin$ $\arcsec$ ) may encompassed material subject to ionization by shocks."190 As demonstrated in 5S 4.2.4. values for the NuηςNone\GSLS line ratio above 3.5 and approaching 4 are partially attributed to poorer data quality especially alfecting the lower-signal. noisy N Lextscii] A6548 A line (c.g.. sce Figure 2).," As demonstrated in $\S$ 4.2.4, values for the $\frac{[\textnormal{N}\,\textsc{ii}]\,\lambda6584}{[\textnormal{N}\,\textsc{ii}]\,\lambda6548}$ line ratio above 3.5 and approaching 4 are partially attributed to poorer data quality especially affecting the lower-signal, noisy $[$ $]$ $\lambda$ 6548 $\mbox{\AA}$ line (e.g., see Figure 2)."191 Figure 1 indicates that the use of profiles whose emission. lines are strictly characterized by verv high. S/N (in our case. greater than 20) contributes to attenuatethe right. tail of the distribution.," Figure 11 indicates that the use of profiles whose emission lines are strictly characterized by “very” high S/N (in our case, greater than 20) contributes to attenuatethe right tail of the distribution."192 The asvmmetrv. coellicient (Lo. skewness) is reduced from roughly 0.4 to 0.2.," The asymmetry coefficient (i.e., skewness) is reduced from roughly 0.4 to 0.2."193 ConsequentIs. the width of," Consequently, the width of"194We represent DIHs in the code by collisionless sink particles of initially very small mass. and we allow them to grow Via eas accretion and through mergers. with other DIIS hat happen to get sullicienthy close.,"We represent BHs in the code by collisionless sink particles of initially very small mass, and we allow them to grow via gas accretion and through mergers with other BHs that happen to get sufficiently close."195 During the growth ol structure. we seed every new dark matter halo above a certain mass threshold (e.g. 5Lot? tAL.) with a central Bll of mass 1075.1M. provided the halo does not contain any BIL vet.," During the growth of structure, we seed every new dark matter halo above a certain mass threshold (e.g. $5 \times 10^{10}\,h^{-1}196{\rm M}_\odot$ ) with a central BH of mass $10^{5}\,h^{-1} {\rm197M}_\odot$, provided the halo does not contain any BH yet."198 The seeding is accomplished on-the-[hy by requenthy invoking a parallel fricnels-of-friends algorithm., The seeding is accomplished on-the-fly by frequently invoking a parallel friends-of-friends algorithm.199 Once seeded. DIIs can then grow by local gas accretion. with an accretion rate estimated with the Bondi-LHovle-Lyttleton ormula (?222).," Once seeded, BHs can then grow by local gas accretion, with an accretion rate estimated with the Bondi-Hoyle-Lyttleton formula \citep{Hoyle1939, Bondi1944,200Bondi1952}."201. We impose a limit equal to the Eddington rate on the maximum allowed BILAR., We impose a limit equal to the Eddington rate on the maximum allowed BHAR.202 As for the 111 feedback processes. we assume that they are composed. of two physically distinct. modes. depending on the BILAN. itself.," As for the BH feedback processes, we assume that they are composed of two physically distinct modes, depending on the BHAR itself."203 At high. accretion rates. Le. above 107 in Eddington units. we assume that the DII is in a raciativelv οποιο phase. where a small fraction of the bolometric accretion Luminosity is coupled thermally to the local gas particles around the BLL with an cllicieney of 54 and a spherical injection kernel.," At high accretion rates, i.e. above $10^{-2}$ in Eddington units, we assume that the BH is in a radiatively efficient phase, where a small fraction of the bolometric accretion luminosity is coupled thermally to the local gas particles around the BH, with an efficiency of $5\%$ and a spherical injection kernel."204 Instead. at low BLLARs. we conjecture that the BLL growth is characterized by a raciatively inellicient accretion flow. where most of the feedback is in a mechanical form. manifesting itself. by hot buovant bubbles that rise through the intragroup or intracluster medium.," Instead, at low BHARs, we conjecture that the BH growth is characterized by a radiatively inefficient accretion flow, where most of the feedback is in a mechanical form, manifesting itself by hot buoyant bubbles that rise through the intragroup or intracluster medium."205 We relate the bubble energy. content. radius and dutv evele with the BIL physics. ancl adopt a somewhat higher ellicieney of mechanical feedback: of 204.," We relate the bubble energy content, radius and duty cycle with the BH physics, and adopt a somewhat higher efficiency of mechanical feedback of $20\%$."206 We note that 2). recently showed that there exists a tight correlation between the Bondi accretion rates calculated based: on observed gas temperature. ancl gas density profiles ancl estimated. DII masses. ancl the actual power emereing from these svstems in relativistic jets.," We note that \citet{Allen2006} recently showed that there exists a tight correlation between the Bondi accretion rates calculated based on observed gas temperature and gas density profiles and estimated BH masses, and the actual power emerging from these systems in relativistic jets."207 This lends observational support to our simple estimates of the BUARs., This lends observational support to our simple estimates of the BHARs.208 We represent. the CR population in cach gaseous [uid clement by à. relativistic population of protons. which we approximately describe. with an isotropic power-law distribution function in momentum space.," We represent the CR population in each gaseous fluid element by a relativistic population of protons, which we approximately describe with an isotropic power-law distribution function in momentum space."209 In the simple formalism adopted. here. this distribution function is fully defined by the power lav slope a. its normalization €'. and a dimensionless low momentum cut-olf q: απρ=Cp“Alp— q).," In the simple formalism adopted here, this distribution function is fully defined by the power law slope $\alpha$, its normalization $C$, and a dimensionless low momentum cut-off $q$: ${\rm210d}n/{\rm d}p \,=\,Cp^{-\alpha} \theta(p-q)$ ."211 Mere 066p) denotes Heaviside step function and the dimensionless momenta are expressed. in units of myc.," Here $\theta(x)$ denotes Heaviside step function and the dimensionless momenta are expressed in units of $m_{\rm p}\,c$."212 We assume for clarity that the only source of Clits is eiven by the racliatively inellicient. accretion mode of BIIs. while we neglect. other contributions from. supernovac or particle acceleration at cosmic structure formation shocks. which have been extensively discussed. in previous work (??T??T)..," We assume for clarity that the only source of CRs is given by the radiatively inefficient accretion mode of BHs, while we neglect other contributions from supernovae or particle acceleration at cosmic structure formation shocks, which have been extensively discussed in previous work \citep{Jubelgas2007, Pfrommer2006, Pfrommer2007a,213Pfrommer2007b, Pfrommer2007c}."214 We include. CI. loss processes in the form. of thermalization by Coulomb interactions and. losses due to hadronic interactions., We include CR loss processes in the form of thermalization by Coulomb interactions and losses due to hadronic interactions.215 We expect that within dilute bubbles hese loss mechanisms should play a subdominant role compared to the pressure loss due to aciabatic expansion of he buovantly rising bubbles., We expect that within dilute bubbles these loss mechanisms should play a subdominant role compared to the pressure loss due to adiabatic expansion of the buoyantly rising bubbles.216 Therefore. we believe that our simulations also are representative. at least qualitatively. of he case of a radio plasma that is dominated by a relativistic electron-positron population.," Therefore, we believe that our simulations also are representative, at least qualitatively, of the case of a radio plasma that is dominated by a relativistic electron-positron population."217 Even though in the present implementation of CR orocesses in.CLADGIZTE-2. accounting for Cl. dillusion is in xinciple possible. in this study we refrain from. trving to model it because this treatment of dilfusion is only isotropic at present.," Even though in the present implementation of CR processes in, accounting for CR diffusion is in principle possible, in this study we refrain from trying to model it because this treatment of diffusion is only isotropic at present."218 Nevertheless. during the rise of a bubble. CR diffusion should. be significantly. suppressed. perpendicular to the magnetic field lines that drape around the bubbles. only allowing CRs to diffuse ellicientlv in the wake of the bubbles. (seee.g.??7)..," Nevertheless, during the rise of a bubble, CR diffusion should be significantly suppressed perpendicular to the magnetic field lines that drape around the bubbles, only allowing CRs to diffuse efficiently in the wake of the bubbles \citep[see e.g.][]{Sanders2007, Ruszkowski2007}."219" ""Phus. isotropic. Cl diffusion would be a rather poor representation of this process. and neglecting diffusion altogether probably mimies the possible influence of magnetic draping ellects with higher realism."," Thus, isotropic CR diffusion would be a rather poor representation of this process, and neglecting diffusion altogether probably mimics the possible influence of magnetic draping effects with higher realism."220 Note. however. that the impact. of magnetic fields on CT dilfusion out of the bubbles is still poorly understood and is a matter of debate. hence a detailed treatment of this issue is bevond the scope of this work.," Note, however, that the impact of magnetic fields on CR diffusion out of the bubbles is still poorly understood and is a matter of debate, hence a detailed treatment of this issue is beyond the scope of this work."221 In the numerical framework we adopted for the description of CRs. we need to determine the power lav slope a of 10 momentum spectrum representative for our system. its injection cut-oll dig. and the fraction. for of the energy released by the DII that actually goes into the CRs.," In the numerical framework we adopted for the description of CRs, we need to determine the power law slope $\alpha$ of the momentum spectrum representative for our system, its injection cut-off $q_{\rm inj}$, and the fraction $f_{\rm CR}$ of the energy released by the BH that actually goes into the CRs."222 Once jose values have been chosen we can follow the bubble’s ΝΟΤο and the loss processes of the CR. component and. compare with the case where the riven bubbles are purely thermal.," Once these values have been chosen we can follow the bubble's evolution and the loss processes of the CR component self-consistently, and compare with the case where the AGN-driven bubbles are purely thermal."223 For the slope a we have tested. values. from. 2.1 to 2.4. where a steeper power-law slope corresponds to a distribution with more low-energv Clits.," For the slope $\alpha$ we have tested values from $2.1$ to $2.4$, where a steeper power-law slope corresponds to a distribution with more low-energy CRs."224" These can thermalize faster ancl have a less relativistic equation of state that is closer to the ""harder thermal case.", These can thermalize faster and have a less relativistic equation of state that is closer to the `harder' thermal case.225 We note that this range of values for the spectral slope is consistent with observational findings for the electron population in FRI sources. especially considering voung systems (e.g. 77)..," We note that this range of values for the spectral slope is consistent with observational findings for the electron population in FRI sources, especially considering young systems \citep[e.g.][]{Birzan2004, Dunn2005}."226 Similarly to the case in which Clis are produced. by supernovae (27) we establish the injection cut-oll ging below which the CR. energy is instantly thermalized., Similarly to the case in which CRs are produced by supernovae \citep{Jubelgas2007} we establish the injection cut-off $q_{\rm inj}$ below which the CR energy is instantly thermalized.227 Equating the injection and loss time scale. we solve for the injection cut-olf (iuj using equations (18) and (19) from 7). and by assuming an initial value of the intrinsic injection cut-olf dini~1 for simplicity.," Equating the injection and loss time scale, we solve for the injection cut-off $q_{\rm inj}$ using equations $(18)$ and $(19)$ from \citet{Jubelgas2007} and by assuming an initial value of the intrinsic injection cut-off $q_{\rm init} \sim 1$ for simplicity."228 Our results do not depend on a particular choice [or (fiui provided. diuil since Coulomb losses rapidly remove the low energy. part of the Cl spectrum. which gets almost instantly. thermalized.," Our results do not depend on a particular choice for $q_{\rm init}$, provided $q_{\rm init} \le 1$ since Coulomb losses rapidly remove the low energy part of the CR spectrum, which gets almost instantly thermalized."229" Finally. at a fixed mechanical feedback. efficiency. we can choose whether to fill the AC:N-inwlated bubbles with relativistic gas exclusively, or to allow some of the hot thermal gas to permeate then as well. by regulating the parameter for the energy fraction &oing into CRs. for."," Finally, at a fixed mechanical feedback efficiency, we can choose whether to fill the AGN-inflated bubbles with relativistic gas exclusively, or to allow some of the hot thermal gas to permeate them as well, by regulating the parameter for the energy fraction going into CRs, $f_{\rm CR}$ ."230northwestwards anc well outside the main nebula. while a possible southeastern counterpart i8 superimposed. by a field star.,"northwestwards and well outside the main nebula, while a possible southeastern counterpart is superimposed by a field star."231 Remarkably. the northwestern knot can. be identified in POSS red. plates of the Digitized Sky Surveys.," Remarkably, the northwestern knot can be identified in POSS red plates of the Digitized Sky Surveys."232 In this respect. 11-2 constitutes a rare case (together with 717009 and S8) because knots/collimated outLows in PNe usually are weak and/or located close to the much brighter main nebula. which do not favor their detection in POSS plates.," In this respect, 1-2 constitutes a rare case (together with 7009 and 8) because knots/collimated outflows in PNe usually are weak and/or located close to the much brighter main nebula, which do not favor their detection in POSS plates."233 Morcover. the Hà and. i]] emission. lines are bv far the dominant emissions from. knots/collimatec outllows in PNe in the optical (e.g. Balick 1993. 1994). as it is the case of the northwestern knot of 11-32.," Moreover, the $\alpha$ and ] emission lines are by far the dominant emissions from knots/collimated outflows in PNe in the optical (e.g., Balick 1993, 1994), as it is the case of the northwestern knot of 1-2."234 In consequence. the emission from the northwestern knot. of 11-2 detected in the POSS red. plates can be attributes to these two emission lines.," In consequence, the emission from the northwestern knot of 1-2 detected in the POSS red plates can be attributed to these two emission lines."235 Vherefore. Hul1-2 ollers an excellent opportunity to attempt a proper motion analysis of knots/collimated outllows in PNe by combining POSS rec plates with modern Ho i1]] imagery.," Therefore, 1-2 offers an excellent opportunity to attempt a proper motion analysis of knots/collimated outflows in PNe by combining POSS red plates with modern $\alpha$ ] imagery."236 In this paper we present a new La Ni] image of 11-2 obtained under subarsecond conditions. and a hieh resolution. long-slit spectrum that allow us to identify the southeastern counterpart of the northwestern knot and to establish that these two knots constitute a high velocity. collimatecl bipolar outflow.," In this paper we present a new $\alpha$ ] image of 1-2 obtained under subarsecond conditions, and a high resolution, long-slit spectrum that allow us to identify the southeastern counterpart of the northwestern knot and to establish that these two knots constitute a high velocity, collimated bipolar outflow."237 In addition. we carry out an analysis of five images obtained at different epochs. including three images from the POSS. to measure the proper motion of the northwestern knot and to constrain the clistance to 11-2.," In addition, we carry out an analysis of five images obtained at different epochs, including three images from the POSS, to measure the proper motion of the northwestern knot and to constrain the distance to 1-2."238 The five images of 11-2 analvzed in this paper are the Following: The images were registered. with routines within the AMLDAS package. using the 2008.67 image as reference. by means of 11 faint Geld stars that do not show noticeable proper motions in the ~ 57 wr time baseline.," The five images of 1-2 analyzed in this paper are the following: The images were registered with routines within the MIDAS package, using the 2008.67 image as reference, by means of 11 faint field stars that do not show noticeable proper motions in the $\simeq$ 57 yr time baseline."239 After the registering process. the positions of the Ll fiducial stars (defined by their centroid) in the 2008.67 epoch are within « ΕΤ their positions in the 1951.51 and. 1953.68. epochs and within « 000 their positions in the 1987.56 and 1994.54 epochs.," After the registering process, the positions of the 11 fiducial stars (defined by their centroid) in the 2008.67 epoch are within $<$ $\farcs$ 1 their positions in the 1951.51 and 1953.68 epochs and within $<$ $\farcs$ 06 their positions in the 1987.56 and 1994.54 epochs."240 The resulting intrinsical error in the proper motion between the dillerent epochs (< + vr1 } is negligible and does not alleet the measurement of nebular proper motions., The resulting intrinsical error in the proper motion between the different epochs $<$ $\pm$ $^{-1}$ ) is negligible and does not affect the measurement of nebular proper motions.241Our assunied. parametric Form for the surface brightness profile is the class of models knows as the »-models.,Our assumed parametric form for the surface brightness profile is the class of models knows as the $\beta$ -models.242 These models parameterize the surface brightness as which. if the gas is isothermal and bas a constant metallicity. corresponds (o a density distribution of the form These models provide σου [its to hot eas around elliptical galaxies (Forman. Jones. and Tucker 1935) as well as the hot σας in galaxy groups ancl clusters (Sarazin 1986).," These models parameterize the surface brightness as which, if the gas is isothermal and has a constant metallicity, corresponds to a density distribution of the form These models provide good fits to hot gas around elliptical galaxies (Forman, Jones, and Tucker 1985) as well as the hot gas in galaxy groups and clusters (Sarazin 1986)."243 We quantified fits to the janodels using \?-minimization and we binned the data to have at least 20 photons per radial bin., We quantified fits to the $\beta$ -models using $\chi^2$ -minimization and we binned the data to have at least 20 photons per radial bin.244 Using the radial surface brightness profiles. we attempt to exclude specific choices of »-model. and the best-fit models are (he profiles which can be excluded al the lowest confidence.," Using the radial surface brightness profiles, we attempt to exclude specific choices of $\beta$ -model, and the best-fit models are the profiles which can be excluded at the lowest confidence."245 We want to be able to exclude at less than confidence for the model to be considered statistically. acceptable., We want to be able to exclude at less than confidence for the model to be considered statistically acceptable.246 We fit the surface brightness profiles to the 2-profiles aud solved [or Sp. ry. aud ;2 using o minimization.," We fit the surface brightness profiles to the $\beta$ -profiles and solved for $S_0$, $r_0$, and $\beta$ using $\chi^2$ minimization."247 We include annuli extending out to 370 arcsec in our fit. since (his radius appears to enclose all (he excess emission visible in the surface brightness prolile (see Figure 3).," We include annuli extending out to 370 arcsec in our fit, since this radius appears to enclose all the excess emission visible in the surface brightness profile (see Figure 3)."248 However. varving this radius does not affect (he result much.," However, varying this radius does not affect the result much."249 We also require a core radius of al least 1 kpc., We also require a core radius of at least 1 kpc.250 Ho would be better if we did not have to coustrain (he core radius at all. but we have no observations within the core radius so an observational constraint is difficult.," It would be better if we did not have to constrain the core radius at all, but we have no observations within the core radius so an observational constraint is difficult."251 A 1 kpe core radius is very small for a hot gaseous halo around a galaxy of this size. so our constraint is at least still somewhat conservative.," A 1 kpc core radius is very small for a hot gaseous halo around a galaxy of this size, so our constraint is at least still somewhat conservative."252 We fit all four proliles simultaneously ancl to find a single set of parameters that worked [or all [our observations., We fit all four profiles simultaneously and to find a single set of parameters that worked for all four observations.253 The best-fit parameters were Sy=9.77x107? count | ? 3 - ≀↕↴↕⋅≺⋱∖⊽≼↲≺∢−⋅∣⋮∣∣∶−⋡⋅∪∩↳↽↕↽≻≺∢⋅↽≳↾∶∩⋅∔↙⋅≀⋯≼⇂⊔∐↲↓∏∐↕⋅≀↕↴∐↖≺↽↔↴≼↲∪↓≀↧↴≺∢≺∢≼↲↕↽≻↥≀↕↴∣↽≻↥≼↲⋯⋟∖⊽↕⋟∖⊽∐≀↧↴↕⋅↕⋅∪∖∖⇁↥⋡∖↽≺∢↥∏⋟∖⊽∩↲↕⋅≼↲≼⇂ ∙⋅ around (hese values (see Figure 3).," The best-fit parameters were $S_0 =9.77\times10^{-8}$ count $^{-1}$ $^{-2}$ $^{-2}$, $r_0 = 1.00$ kpc, $\beta = 0.47$, and the full range of acceptable fits is narrowly clustered around these values (see Figure 3)."254 While we had at least 20 source photons in each radial bin. in (he inner annuli where the galaxy is brighter (han the backeround (here are fewer (han 20 background photons per bin.," While we had at least 20 source photons in each radial bin, in the inner annuli where the galaxy is brighter than the background there are fewer than 20 background photons per bin."255 AcdiGionally. from the size of the radial background. variations at large radii. we can," Additionally, from the size of the radial background variations at large radii, we can"256 ~AL. ~10 (New2009).. (AuderssouTXokkotas1998).," $\sim M_\odot$ $\sim 10$ \citep{Sathyaprakash2009}, \citep{New2003,Ott2009}, \citep{Andersson1998}."257. Andersson(2010) 10277 (Abbottetal.2009) (Acerneseetal.2008).. (Abbott2005.2007.2010).. (Nu2003.2009).," \cite{Andersson2010} $10^{2\sim 3}$ \citep{Abbott2009} \citep{Acernese2008}. \citep{Abbott2005,Abbott2007,Abbott2010}. \citep{Xu2003,Xu2009}."258.. Ushomirskyetal.(2000) clastic deforming neutron stars., \cite{Ushomirsky2000} elastic deforming neutron stars.259" Their estimation of the niaxinmni quadrupole moment of the normal neutron stars is δες1075 ccn, which has been updated by Owen(2005). via redefining the shear modulus."," Their estimation of the maximum quadrupole moment of the normal neutron stars is $2.4\times 10^{38}$ $\cdot$ $^2$, which has been updated by \cite{Owen2005} via redefining the shear modulus."260 They also eive a general equation to calculate the quadrupole moment Induced by shear modulus which can be used to other stars such as solid quark stars. aud Owen(2005) estimates the quadrupole moment of the solid quark stars to be 2.8«10H. ecm.," They also give a general equation to calculate the quadrupole moment induced by shear modulus which can be used to other stars such as solid quark stars, and \cite{Owen2005} estimates the quadrupole moment of the solid quark stars to be $2.8\times26110^{41}$ $\cdot$ $^2$."262 The quadipole moment is also calculated in other stellar models such as Uvbrid crystalline clour-3unperconducting star (INuippel&Se-dvakian2009:IIaskelletal.2007:Liu2007). aud Uvbrid ixd meson condensate stars (Owen2005).," The quadrupole moment is also calculated in other stellar models, such as Hybrid crystalline clour-superconducting star \citep{Knippel2009,Haskell2007,Lin2007}263 and Hybrid and meson condensate stars \citep{Owen2005}."264. srovides a good review on these., \cite{Pitkin2011} provides a good review on these.265 However. all these stucies asstune that the equilibrium structure of the neutron stars is almost sphericallv svinmnetric.," However, all these studies assume that the equilibrium structure of the neutron stars is almost spherically symmetric."266 Certainly. some solidified mouutaius would also be possible ou the surfaces of sold quark stars.," Certainly, some solidified mountains would also be possible on the surfaces of sold quark stars."267 Unlike shear-miodulus-uduced: mountains (clastic mountains). we sugecst here lateut-heat-induced mountains (solidified -j0uutaius) there.," Unlike shear-modulus-induced mountains (elastic mountains), we suggest here latent-heat-induced mountains (solidified mountains) there."268 Under this coucition. instead of the shear anodulus and the breaking strain. lateut heat »erforim an important role that determine the height of 16 Mountains.," Under this condition, instead of the shear modulus and the breaking strain, latent heat perform an important role that determine the height of the mountains."269 From this poiut of view. our model is oulv one paraleter (.e.. latent heat) depeudent. rather than iu two paraneter (.c.. shear modulus aud breaking strain) depeudenut m case of clastic 1iountaius.," From this point of view, our model is only one parameter (i.e., latent heat) dependent, rather than than two parameter (i.e., shear modulus and breaking strain) dependent in case of elastic mountains."270 After estimating the maximum height of the uountaius. we find that if the mass of solid quark stars is sinall chough that the height is of the same order with he radius of the star. the star may be “potato-like”.," After estimating the maximum height of the mountains, we find that if the mass of solid quark stars is small enough that the height is of the same order with the radius of the star, the star may be “potato-like”."271 The critical mass for potato-like solid quark stars is cxtimatec o be ~10°°?A£.. which agrees with the mutually independent study of Nu(2010).," The critical mass for potato-like solid quark stars is estimated to be $\sim 10^{-3\sim -2}M_\odot$, which agrees with the mutually independent study of \cite{Xu2010}."272. Also it is found. that. in reality. the actual CAV amplitudeof a pulsar would ο too sinall tobedetected withLIGOnow since the uaxiuuni CAV amplitude requires a star to defoi iuto a particular distribution of mountains.," Also it is found that, in reality, the actual GW amplitudeof a pulsar would be too small tobedetected withLIGOnow since the maximum GW amplitude requires a star to deform into a particular distribution of mountains."273SRON Netherlands Institute for Space Research. Landleven 12.9747 AD Groningen. The Netherlands,"SRON Netherlands Institute for Space Research, Landleven 12, 9747 AD Groningen, The Netherlands"274trigecrOO gravitational instability aud subsequent SF bursts.,trigger gravitational instability and subsequent SF bursts.275 Tn particular. tidal generation of shocks iu gaseous disk according to Icke (1985)) iiechanisii cau be responsible for observed SF bursts (sec c.g. Pustiluik et al. (20003) ," In particular, tidal generation of shocks in gaseous disk according to Icke \cite{Icke85}) ) mechanism can be responsible for observed SF bursts (see e.g. Pustilnik et al. \cite{Pustilnik00}) )"276for the estimates of tidal effect iu simular situation)., for the estimates of tidal effect in similar situation).277 This galaxy was considered as a candiate dwarf galaxy (Mp 15:235 ) due to its catalog radial velocity V. = 13395 kins + (RCS. de Vaucouleurs et al. (1991)).," This galaxy was considered as a candidate dwarf galaxy $_{B}$ = $-15\fm5$ ) due to its catalog radial velocity V = 395 km $^{-1}$ (RC3, de Vaucouleurs et al. \cite{deVaucouleurs91}) ),"278 cited also in both LEDA aud NED. aud origiwally obtained by Arkhipova Exipov (19793).," cited also in both LEDA and NED, and originally obtained by Arkhipova Esipov \cite{Arkhipova79}) ))."279 However colour iudices of this object are rather typical of eiaut E galaxies thai for dbhr sxstelus (Zasov Arkhipova 2000)., However colour indices of this object are rather typical of giant E galaxies than for dIrr systems (Zasov Arkhipova 2000).280 According to our ¢observations. if is evideut that there was soe misprint in he original work. caused the catalog velocity of this galaxy to be in error by the factor of teu.," According to our observations, it is evident that there was some misprint in the original work, caused the catalog velocity of this galaxy to be in error by the factor of ten."281 Its real velocity. 1ieasured from our spectrum of chussion-line region ou the western periphery (hereafter VV 5I3W) is 11100 kin 1," Its real velocity, measured from our spectrum of emission-line region on the western periphery (hereafter VV 543W) is 100 km $^{-1}$."282 Iu fac. the spectrum of the central bright region of Us galaxy shows. that we have in this case an optical air in projection.," In fact, the spectrum of the central bright region of this galaxy shows, that we have in this case an optical pair in projection."283 Iudee the central part shows only the absorptioi Hines. typical Q: elliptical galaxy. (c.g. Pickles (1988))). n its radial velocity is 16204120 kins ! lower hau that for the eiissioline galaxy.," Indeed the central part shows only the absorption lines, typical of elliptical galaxy (e.g. Pickles \cite{Pickles88}) )), but its radial velocity is $\pm$ 120 km $^{-1}$ lower than that for the emission-line galaxy."284 Its huuinositv Mp 209 evidences that tus ealaxy falls to the class of rormal οἱiicals., Its luminosity $_{B}$ = $-20\fm9$ evidences that this galaxy falls to the class of normal ellipticals.285" The apparent magnitude of VV 5SW js zc 2755 αλα (D ~-- li) tiui that of VV 513E (this estimae folows from he comparison of the fis. Lear A LEIOQO in both ealaxies) what leads o Mp 1s""."," The apparent magnitude of VV 543W is $\approx$ 5 fainter (B $\approx 17\fm7$ ) than that of VV 543E (this estimate follows from the comparison of the flux near $\lambda$ 4400 in both galaxies), what leads to $_{B} \sim$ $-18\fm7$."286 Its linear size aone he major axis ~ 13 kpe is quite mioest. and. owing to 1ο typical spcC60 of Tarveeion. this western coniponcut can be cousiccred as a bright due ealaxyv.," Its linear size along the major axis $\sim$ 13 kpc is quite modest, and, owing to the typical spectrum of -region, this western component can be considered as a bright blue galaxy."287" The conrIAC object wing at about 20"" to NE from t16 absorptioline| galaxy is a foreground star.", The compact object lying at about ${\arcsec}$ to NE from the absorption-line galaxy is a foreground star.288" T1ο extent Ila enulsso oug the nuüuor :WIS ds trace| within 5"".", The extent of $\alpha$ emission along the minor axis is traced within ${\arcsec}$.289 Even after tI iuning iu [| pixels (which corresponds to the seciug of hne veocity curve does not 1idicate clear egradieut., Even after the binning in 4 pixels (which corresponds to the seeing of ${\arcsec}$ ) the velocity curve does not indicate clear gradient.290" T ""ull raise of the radial velocity is about SNO kins | with he mean vaue of 023530 Xii 1", The full range of the radial velocity is about 80 km $^{-1}$ with the mean value of $\pm$ 30 km $^{-1}$.291 According to NED. VV 5BW Ws a preobable conpaiion eaaxv NODP9 F32108038 Goat 5.s! wih the radia velocity 66994 E126 kn 1 and B 1668.," According to NED, VV 543W has a probable companion galaxy NGP9 F324–0303806 at $^{\prime}$ with the radial velocity $\pm$ 126 km $^{-1}$ and B = $16\fm68$ ."292 Corresponding projectio1 dista1ος D10 kpe and ve‘locity difference 1012130 kins ! ave in the range typical of wide pairs of binary galaxies (see e.g. the sicy by Cherealur et al. (1993)), Corresponding projection distance $\approx$ 300 kpc and velocity difference $\pm$ 130 km $^{-1}$ are in the range typical of wide pairs of binary galaxies (see e.g. the study by Chengalur et al. \cite{Chengalur93}) )293 and Norderen ct al. (1998)))., and Nordgren et al. \cite{Nordgren98}) )).294 Some weak tidal action from this galaxy cau be responsible for the eulauced SE iu VV 513W (sce c.g. Reshetuikov Combes (19973). aud Rudnick Ris (1998))).," Some weak tidal action from this galaxy can be responsible for the enhanced SF in VV 543W (see e.g. Reshetnikov Combes \cite{Reshet97}) ), and Rudnick Rix \cite{Rudnick98}) ))."295 This dwart galaxy consists of two clearly separated regions ubedded iito the «ώμο. envelope of low surface brightness., This dwarf galaxy consists of two clearly separated regions embedded into the common envelope of low surface brightness.296" The brighter SW com»neut has full size of aout 15"" and the fainter NE cau be traced down to about a (zs (kN aid O.L kpe respectively).", The brighter SW component has full size of about ${\arcsec}$ and the fainter NE can be traced down to about ${\arcsec}$ $\approx$ 0.8 and 0.4 kpc respectively).297 Both regious show chussiou-line specruni (see Fig., Both regions show emission-line spectrum (see Fig.298" 3b ο),", \ref{VV747_fig}b b).299 The high excitation spectrun Wih the' observed On] ine À L1363 of he SW Cuponeit allows to determiue ONVeCL ukance dsine the direct ieastποιοι of T.., The high excitation spectrum with the observed ] line $\lambda$ 4363 of the SW component allows to determine oxygen abundance using the direct measurement of $T_e$.300 Our ο »uudauice 19 121og(O‘TD) 7.8540.05 compared to the ukance 7OF cleπΊνος x Izotov Thuan (1999))., Our O abundance is 12+log(O/H) = $\pm$ 0.05 compared to the abundance 7.97 derived by Izotov Thuan \cite{Izotov99}) ).301 This ow inetalliciVds lot unvpical for DCCis., This low metallicity is not untypical for BCGs.302" Siuooth velocivocu rve along f1ο slit shows a small mt clear slo)6 across f1ο SW component iu the region of lig1 S/N ratio of Πα with tιο total extent ofabout 15"" aid the volocitv rauge from 510 to 630 kia 1 COlSÜISeut with the maximal roation velocitv of about 5 kn 1 acl meal Laclal velocitv of 585 kn 1"," Smooth velocity curve along the slit shows a small but clear slope across the SW component in the region of high S/N ratio of $\alpha$ with the total extent ofabout ${\arcsec}$ and the velocity range from 540 to 630 km $^{-1}$, consistent with the maximal rotation velocity of about 45 km $^{-1}$ and mean radial velocity of 585 km $^{-1}$."303 The ealaxve body is well elongated. so the iucination COYICCiou does not seen f) he arecr than 20:5.," The galaxy body is well elongated, so the inclination correction does not seem to be larger than $\div$."304 Iu the NE component the veocitv can be measur.«d only in two independent points. showing siguificaut scaterus. COUSISeut with their iuterval oducertaitics.," In the NE component the velocity can be measured only in two independent points, showing significant scattering, consistent with their internal uncertainties."305 The mean velocity of NE componcut. aking from these two points. is about 69027 12 kii 1," The mean velocity of NE component, taking from these two points, is about $\pm$ 42 km $^{-1}$."306 Ihchra et al. (1995)), Huchra et al. \cite{Huchra95}) )307 presented hne values of the observed velocities for two commpoucuts of this galaxy. designated as SW aud NE. but their coordinates eiven in the oper. are the same for both of hem.," presented the values of the observed velocities for two components of this galaxy, designated as SW and NE, but their coordinates given in the paper, are the same for both of them."308 If we accept that they observed the same componcuts. our restIts are consistent with thems (V(SW) = 621432 aud V(NE) = 665411 kin 1j within the cited uncertainties.," If we accept that they observed the same components, our results are consistent with theirs (V(SW) = $\pm$ 32 and V(NE) = $\pm$ 44 km $^{-1}$ ) within the cited uncertainties."309 Since the two separate velocity poiuts for fιο NE COMPOrent do not show auv clear graient. which would indicate its iudependent rotation. aud the mean velocity of the NE component natches well the continuaion of the veocity curve for he SW componcut. there is no reason to consider this svstem as two clifferen ealaxies iu lision.," Since the two separate velocity points for the NE component do not show any clear gradient, which would indicate its independent rotation, and the mean velocity of the NE component matches well the continuation of the velocity curve for the SW component, there is no reason to consider this system as two different galaxies in collision."310 The current daa favour the interpretation of this svete as a single ealaxs swith two super-giaut Ilircesious iu differeut excitation stages., The current data favour the interpretation of this system as a single galaxy with two super-giant -regions in different excitation stages.311 Iu this case f1C SVstenic velociv of this sinele eaaxy is about G20 kins 1 with the fu] velocity range of 510 to 710 kins 1|, In this case the systemic velocity of this single galaxy is about 620 km $^{-1}$ with the full velocity range of 540 to 710 km $^{-1}$.312 Both these values are enite well consisteut with the parameters of Hi-profile of VV TIT cescrihed iux shown in section 3.2.., Both these values are quite well consistent with the parameters of -profile of VV 747 described and shown in section \ref{HI_res}.313 The latter fu] velocity rauge correspos to the maximal rotatioial veociv of 85 lans 1, The latter full velocity range corresponds to the maximal rotational velocity of 85 km $^{-1}$.314 The better knowledge of the veocity curve in the region of the NE compoue dois necessary to exchde COupletely the lhiypothesis of merecr o two dwarf ealaxies., The better knowledge of the velocity curve in the region of the NE component is necessary to exclude completely the hypothesis of merger of two dwarf galaxies.315 At least one indirect argumen favours this interpretaticni., At least one indirect argument favours this interpretation.316 If TF relation holds for this galaxy. 1s mass ancl bue DIuuinositv are more consistewt with the narrower with (Wyse = 7080 lau 4). thanwith he observed one iu," If TF relation holds for this galaxy, its mass and blue luminosity are more consistent with the narrower width $_{0.2}$ = 70–80 km $^{-1}$ ), thanwith the observed one in"317indication that small 8 values doesn’t follow our relation as strictly as for large 6 values.,indication that small $\beta$ values doesn't follow our relation as strictly as for large $\beta$ values.318" This is probably a consequence of comparing the two subdominant terms in the new Jeans equation with one another, which as mentioned doesn't make relation (20)) as strong as the relation between the mass and the bulk rotation."," This is probably a consequence of comparing the two subdominant terms in the new Jeans equation with one another, which as mentioned doesn't make relation \ref{eq:vbeta}) ) as strong as the relation between the mass and the bulk rotation."319 In the figure we have re-binned the data to reduce scatter and cut off the structures where £ was no longer a (roughly) monotonically increasing function of radius., In the figure we have re-binned the data to reduce scatter and cut off the structures where $\beta$ was no longer a (roughly) monotonically increasing function of radius.320 Plotting the structures without making an outer cut doesn't change the picture but only enhances the overall scatter., Plotting the structures without making an outer cut doesn't change the picture but only enhances the overall scatter.321" We see that the rotation term goes to 0 as ϐ goes to 0, exactly as suggested."," We see that the rotation term goes to 0 as $\beta$ goes to 0, exactly as suggested."322" In fact, if we plot the fraction of the kinetic energy in rotation, i.e., [n/o3, we see that it drops from 107? in the outskirts of the structure, down below 1074 for the inner-most bins."," In fact, if we plot the fraction of the kinetic energy in rotation, i.e., $\vrot^2/\sigma_\phi^2$, we see that it drops from $10^{-2}$ in the outskirts of the structure, down below $10^{-4}$ for the inner-most bins."323" Since f is monotonically increasing as a function of radius, the fact that the rotation becomes so small in the inner parts of the structure supports our suggested relation of the rotation term going towards 0 for small f."," Since $\beta$ is monotonically increasing as a function of radius, the fact that the rotation becomes so small in the inner parts of the structure supports our suggested relation of the rotation term going towards 0 for small $\beta$."324 In Figs., In Figs.325" 3 and 4 the only free parameter in our relations, 7, have been fitted for each structure."," \ref{fig:vmall} and \ref{fig:vbeta} the only free parameter in our relations, $\eta$, have been fitted for each structure."326 These values of 7 corresponding to the relations in Eqs. (19)), These values of $\eta$ corresponding to the relations in Eqs. \ref{eq:vm}) )327 and (20)) represents the unknown magnitude of the angular momentum and are shown together with the estimated errors in Table 1.., and \ref{eq:vbeta}) ) represents the unknown magnitude of the angular momentum and are shown together with the estimated errors in Table \ref{tab:eta}.328 Plotting the 7 values and their errors gives Fig. 5.., Plotting the $\eta$ values and their errors gives Fig. \ref{fig:etaeta}.329 Here we see a tendency of nass being larger than ng., Here we see a tendency of $\eta_{\mathrm{mass}}$ being larger than $\eta_\beta$.330 Since the triangles and the cross are cluster like structures and the rest are galaxy like structures we notice that there might be a connection between 7 and the mass of the structures., Since the triangles and the cross are cluster like structures and the rest are galaxy like structures we notice that there might be a connection between $\eta$ and the mass of the structures.331 In Fig., In Fig.332" 6 we plot it has the smallest error bars, percentage-wise) against7g (sincethe estimated virial mass of each structure (see Table 1)), and see that our free parameter anti-correlates slightly with the mass of the structure."," \ref{fig:etam} we plot $\eta_\beta$ (since it has the smallest error bars, percentage-wise) against the estimated virial mass of each structure (see Table \ref{tab:eta}) ), and see that our free parameter anti-correlates slightly with the mass of the structure."333 So according to our suggested relations the effect an added bulk rotation has on a system is correlated with the virial mass of that system., So according to our suggested relations the effect an added bulk rotation has on a system is anti-correlated with the virial mass of that system.334" After having tested our suggested relations from the previous section with the simulations from Maccióetal. (2007), we also held them up against the recent high resolution numerical simulation 'Via Lactea’ by"," After having tested our suggested relations from the previous section with the simulations from \cite{mac07}, , we also held them up against the recent high resolution numerical simulation 'Via Lactea' by"335"For a magnetar (Ee)of age 10* yr, crustal currents from the initial field should still be present. [","For a magnetar of age $10^4$ yr, crustal currents from the initial field should still be present. ["336"We note that the Tong was smaller early in the star's life, since the temperature and resisitivity were higher.]","We note that the $\tau_{\rm ohm}$ was smaller early in the star's life, since the temperature and resisitivity were higher.]"337" Hall drift creates small scale magnetic structures in the crust over the Hall timescale (?),, given by where πε is the electron density and B is the magnetic field strength."," Hall drift creates small scale magnetic structures in the crust over the Hall timescale \citep{ponsgeppert}, given by where $n_e$ is the electron density and $B$ is the magnetic field strength."338 A typical value for the outer crust is Hall drift can concentrate currents in the crust., A typical value for the outer crust is Hall drift can concentrate currents in the crust.339" The induction equation, neglecting ohmic dissipation, is To illustrate how Hall drift may affect the magnetic field, consider a magnetic field in cylindrical coordinates, with only an azimuthal component which depends on r, Eq. ("," The induction equation, neglecting ohmic dissipation, is To illustrate how Hall drift may affect the magnetic field, consider a magnetic field in cylindrical coordinates, with only an azimuthal component which depends on $r$, Eq. ("340"4) becomes Since the magnetic field has only r dependence, and the quantity inside the parenthesis is in the f direction, the curl is zero, and the field is stationary.","4) becomes Since the magnetic field has only $r$ dependence, and the quantity inside the parenthesis is in the $\hat r$ direction, the curl is zero, and the field is stationary."341 Outward drift of the field can replenish currents in the outer crust that are decaying through ohmic diffusion., Outward drift of the field can replenish currents in the outer crust that are decaying through ohmic diffusion.342" In order to get an outward drift of the field, the field must have z-dependence, as considered by (?).."," In order to get an outward drift of the field, the field must have z-dependence, as considered by \citep{ponsgeppert}."343 This would correspond to a field strength that varies from the magnetic pole to the magnetic equator., This would correspond to a field strength that varies from the magnetic pole to the magnetic equator.344 The induction equation for the ¢-component of the field gives, The induction equation for the $\phi$ -component of the field gives345where the epievelic Irequencey. & and the related vorticity frequency ¢ are defined by Finally. from equations (14). (15). and (17). a wave equation can be derived [or the quantity HV=ru: This is the fundamental equation for the model considered in this paper.,"where the epicyclic frequency $\kappa$ and the related vorticity frequency $\zeta$ are defined by Finally, from equations ), ), and ), a wave equation can be derived for the quantity $W\equiv ru$: This is the fundamental equation for the model considered in this paper."346 The mode frequency w is an eigenvalue5 of Chis second. order differential equation aud is determined bv solving5 the equation anc applvingHAS the boundary conditions., The mode frequency $\omega$ is an eigenvalue of this second order differential equation and is determined by solving the equation and applying the boundary conditions.347 Any eigenvalue5 w with a positive imaginary part represen(s an unstable mode., Any eigenvalue $\omega$ with a positive imaginary part represents an unstable mode.348 We focus on such modes in (he rest of the paper., We focus on such modes in the rest of the paper.349 It is possible to derive a necessary condition for the existence of instability. as shown in AppendixA. but we do not use that condition in the main paper.," It is possible to derive a necessary condition for the existence of instability, as shown in Appendix, but we do not use that condition in the main paper."350 Once the eigenvalue w and the eigenfunction Wo=ru are obtained. we may solve for the other perturbed quantities by going back to the linear perturbation equations.," Once the eigenvalue $\omega$ and the eigenfunction $W\equiv ru$ are obtained, we may solve for the other perturbed quantities by going back to the linear perturbation equations."351 Thus. equation (14) gives the perturbed azimuthal velocity ο). and equation (15) gives the perturbed density οι].," Thus, equation ) gives the perturbed azimuthal velocity $v(r)$ , and equation ) gives the perturbed density $\rho_1(r)$."352 To calculate the perturbed total pressure (0). we use the azimuthal component of the first order perturbation of the momentum equation (2). The perturbed magnetic field By can be calculated from the first order perturbation of the induction equation (3). ∖∖⇁∐≼↲↕⋅≼↲≼↲≺⇂∏≀↧↴∐∪∐≼⊥⊥⋝↥⋯⋟∖⊽∣↽≻≼↲≼↲∐," To calculate the perturbed total pressure $p_{t1}(r)$, we use the azimuthal component of the first order perturbation of the momentum equation ), The perturbed magnetic field $B_1$ can be calculated from the first order perturbation of the induction equation ), where equation ) has been substituted."353⋟∖⊽∏∣↽≻⋟∖⊽⋯⋯≼↲≺⇂⋅⊡∐≀↧↴∐⋡∖↽⋅⊔∐↲↕↽≻≼↲↕⋅⊓∐⋅∣↽≻≼↲≼⇂↖⊂↽↔↴≀↧⊍∖⊽↕↽≻↕⋅≼↲⋟∖⊽⋟∖⊽⋯⋅≼↲∣↗↓≺∢≀↧↴∐∣↽≻≼↲ ≺∢≀↕↴↥≺∢∏↥≀↧↴∩↲≺⇂↓⋟↕⋅∪∐⊔↲≺⇂∏≀↧↴∐∪∐⋟∖⊽⋖↜∃↭≀↕↴," Finally, the perturbed gas pressure $p_1$ can be calculated from equations ) and ), by making use of $p_1 = p_{t1}354- B_0 B_1/4\pi$."355"∐≼⊔∃↓↕⋝⋅∣↽≻⋡∖↽∐↓≀↧↴↳↽↕∐↖≺↽↔↴∏⋟∖⊽≼↲∪↓⋟∣↗↓∶∣↗∕↓−∐∣∣∐↓∕∕∕∔⊼⋅ since (he equilibrium model has a discontinuity al r=r,,. where the accretion disk meets (he magnetosphlere. the solution must satisIv certainjunction conditions at this boundary."," Since the equilibrium model has a discontinuity at $r = r_m$, where the accretion disk meets the magnetosphere, the solution must satisfy certainjunction conditions at this boundary."356The uncertainties quoted in this expression are formal ones derived by taking into account the confidence range in each aand mmeasurement.,The uncertainties quoted in this expression are formal ones derived by taking into account the confidence range in each and measurement.357 These uncertainties are much smaller than the intrinsic scatter of the relation (about 0.5 dex in A/c)., These uncertainties are much smaller than the intrinsic scatter of the relation (about 0.5 dex in ).358 Equation (9) can thus be used to estimate the ‘typical’ dust mass in a galaxy. based on the star formation rate.," Equation \ref{equ1}) ) can thus be used to estimate the `typical' dust mass in a galaxy, based on the star formation rate."359 To our knowledge it is the first time that such an expression is calibrated for a large sample of galaxies., To our knowledge it is the first time that such an expression is calibrated for a large sample of galaxies.360 We have investigated the extent to which the SDSS. aand selections of our sample may introduce a bias in the relation between star formation rate and dust mass derived from Fig. 5..," We have investigated the extent to which the SDSS, and selections of our sample may introduce a bias in the relation between star formation rate and dust mass derived from Fig. \ref{fig:dust5}."361 We used for this the library of stochastic models described in Section 3.2.1.., We used for this the library of stochastic models described in Section \ref{library}.362 Since these models are normalised to total stellar mass (2)... we assigned a random stellar mass cand scaled dust mass and star formation rate) to each model in the library.," Since these models are normalised to total stellar mass \citep{daCunha2008}, we assigned a random stellar mass (and scaled dust mass and star formation rate) to each model in the library."363 We drew the stellar masses uniformly in log(M./A.;) between 8.5 and 11.5. to be consistent with the distribution of galaxy stellar masses in our sample.," We drew the stellar masses uniformly in $\log(\mstar/\msun)$ between 8.5 and 11.5, to be consistent with the distribution of galaxy stellar masses in our sample."364 For each model in the library. we computed the expectedGALEX.. SDSS and mmagnitudes in different redshift bins from 2=θ to 2 0.20.," For each model in the library, we computed the expected, SDSS and magnitudes in different redshift bins from $z=0$ to $z=0.20$ ."365 Then. we applied the same selection criteria as used for our observed sample to the model library.," Then, we applied the same selection criteria as used for our observed sample to the model library."366 These selection criteria introduce minimum detectable stellar mass. dust mass and star formation rate.," These selection criteria introduce minimum detectable stellar mass, dust mass and star formation rate."367 We find that. for example. at the low-redshift end of our sample (2= 0.0025). the fflux limit tends to exclude galaxies with log(AlyfAds)«4.5.," We find that, for example, at the low-redshift end of our sample $z=0.0025$ ), the flux limit tends to exclude galaxies with $\log(\mdust/\msun) < 4.5$."368 At the typical redshift of our sample. ;=0.05. the combination of SDSS and sselections sets a minimum detectable dust mass of about 10 aand a minimum star formation rate of about 0.0]. vr1 Gt also introduces serious incompleteness for galaxies with star formation rates less than | yr. y.," At the typical redshift of our sample, $z=0.05$, the combination of SDSS and selections sets a minimum detectable dust mass of about $10^7$ and a minimum star formation rate of about $0.01$ $^{-1}$ (it also introduces serious incompleteness for galaxies with star formation rates less than 1 $^{-1}$ )."369 We have checked that these selection effects do not affect significantly the empirical relation between the star formation rate and dust mass derived from Fig. 5..," We have checked that these selection effects do not affect significantly the empirical relation between the star formation rate and dust mass derived from Fig. \ref{fig:dust5},"370 which is dominated by more massive galaxies (including only salaxies with c>LAL: yr| and Aly10'AL; leaves the derived slope unchanged in equation 9).," which is dominated by more massive galaxies (including only galaxies with $\psi>1\,$ $^{-1}$ and $\mdust>10^7\msun$ leaves the derived slope unchanged in equation \ref{equ1}) )."371 In Fig. 5..," In Fig. \ref{fig:dust5},"372 we also plot for comparison the dust masses and star formation rates derived by ?. for the SINGS galaxies (orange symbols)., we also plot for comparison the dust masses and star formation rates derived by \citet{daCunha2008} for the SINGS galaxies (orange symbols).373 These nearby galaxies follow the same relation as the galaxies in the matched ssumple studied here and extend to slightly lower dust masses and star formationrates”., These nearby galaxies follow the same relation as the galaxies in the matched sample studied here and extend to slightly lower dust masses and star formation.374.. We note that. at fixed star formation rate. the SINGS galaxies tend to have slightly larger dust masses than the galaxies in our sample.," We note that, at fixed star formation rate, the SINGS galaxies tend to have slightly larger dust masses than the galaxies in our sample."375 This is likely to result from the different selection criteria of the SINGS sample., This is likely to result from the different selection criteria of the SINGS sample.376 The typical error bars in aand aare smaller for the SINGS galaxies than for the sample studied here. because a wider collection of observational constraints (especially in the mid-infrared) were available to 2..," The typical error bars in and are smaller for the SINGS galaxies than for the sample studied here, because a wider collection of observational constraints (especially in the mid-infrared) were available to \citet{daCunha2008}."377 In an attempt to understand which observations set the main constraints on dust mass. we have investigated how the likelihood estimates of ccorrelate with a wide range of galaxy colours.," In an attempt to understand which observations set the main constraints on dust mass, we have investigated how the median-likelihood estimates of correlate with a wide range of galaxy colours."378" We find that ecorrelates most strongly with the £1/7? colour. where £41"" is the flux density in the bband and , that in the SDSS g band."," We find that correlates most strongly with the $F_\nu^{\,100}/F_\nu^{\,g}$ colour, where $F_\nu^{\,100}$ is the flux density in the band and $F_\nu^{\,g}$ that in the SDSS $g$ band."379 The Spearman rank coefficient for this correlation is rs=0.56. indicating a positive correlation at the 237 level for this sample size (we note that the correlation is not improved by the inclusion of an ultraviolet band such as FFUV).," The Spearman rank coefficient for this correlation is $r_S=0.56$, indicating a positive correlation at the $23\sigma$ level for this sample size (we note that the correlation is not improved by the inclusion of an ultraviolet band such as FUV)."380" The reason for this correlation is that 1,2/7 traces the primary contributor toAz: cold dust in the diffuse ISM GUP! in eq. 79."," The reason for this correlation is that $F_\nu^{\,100}/F_\nu^{\,g}$ traces the primary contributor to: cold dust in the diffuse ISM $M_\mathrm{C}^{\,\mathrm{ISM}}$ in eq. \ref{eq:mdust}) )."381 This component is also mainly responsible for the attenuation of the emission from stars older than 10. vr. which dominate the SDSS g-band light. and it is the main contributor to the emission at 100 (a more detailed discussion of the set of observables necessary to constrain ccan be found in Section 3.2.2 of 25.," This component is also mainly responsible for the attenuation of the emission from stars older than $10^7$ yr, which dominate the SDSS $g$ -band light, and it is the main contributor to the emission at 100 (a more detailed discussion of the set of observables necessary to constrain can be found in Section 3.2.2 of \citealt{daCunha2008}) )."382 In Fig. 6..," In Fig. \ref{fig:dust6},"383" we explore the relations between specific star formation rate aand three particularly interesting physical properties of the galaxies in our sample: the dust-to-stellar mass ratio AliM.. the ratio of dust mass to star formation rate AZ,/c. and the fraction fj of the total infrared luminosity ccontributed by dust in the diffuse ISM."," we explore the relations between specific star formation rate and three particularly interesting physical properties of the galaxies in our sample: the dust-to-stellar mass ratio $\mdust/\mstar$, the ratio of dust mass to star formation rate $\mdust/\sfr$, and the fraction $f_\mu$ of the total infrared luminosity contributed by dust in the diffuse ISM."384 As in Fig. 5..," As in Fig. \ref{fig:dust5},"385 grey contours show the relations for the full sample of 3258 galaxies. while individual points show the relations for the 1658 galaxies with highest-S/N photometry.," grey contours show the relations for the full sample of 3258 galaxies, while individual points show the relations for the 1658 galaxies with highest-S/N photometry."386 The top panels of Fig., The top panels of Fig.387" 6 indicate that Aa/M Mac and fj, are all strongly correlated withc3: the Spearman rank coefficients for the full sample are rs=0.5. 0.60 and. —0.66. respectively. indicating that the correlations are significant at more than 20 level for this sample size (similar results are obtained when using only the high-S/N subsample)."," \ref{fig:dust6} indicate that $\mdust/\mstar$, $\mdust/\sfr$ and $f_\mu$ are all strongly correlated with: the Spearman rank coefficients for the full sample are $r_{S} = 0.84$, $-0.60$ and $-0.66$, respectively, indicating that the correlations are significant at more than $20\sigma$ level for this sample size (similar results are obtained when using only the high-S/N subsample)."388 It is important to check that stellar mass is not the main driver for these strong correlations., It is important to check that stellar mass is not the main driver for these strong correlations.389 To verify this. in the bottom panels of Fig. 6..," To verify this, in the bottom panels of Fig. \ref{fig:dust6},"390 we show differences in the same quantities as in the top panelsfor pairs of galaxies closely matched in stellar mass (we have included all possible galaxy pairs for any stellar mass iin the full sample)., we show differences in the same quantities as in the top panelsfor pairs of galaxies closely matched in stellar mass (we have included all possible galaxy pairs for any stellar mass in the full sample).391" Specifically. for each galaxy pair. we plot the difference in specific star formation rate between the two galaxies. [Xοσοννε 13]. against the difference in dust-mass to stellar-mass ratio. [AAlog(M4/M. )]. the difference in ratio of dust mass to star formation rate. [Alog(M4/ 0)]. and the difference in Traction of total infrared luminosity contributed by the diffuse ISM ANf, ]."," Specifically, for each galaxy pair, we plot the difference in specific star formation rate between the two galaxies, $\Delta \log (\ssfr/ \mathrm{yr}^{-1})$ ], against the difference in dust-mass to stellar-mass ratio, $\Delta 392\log(\mdust/\mstar)$ ], the difference in ratio of dust mass to star formation rate, $\Delta \log (\mdust/ \sfr )$ ], and the difference in fraction of total infrared luminosity contributed by the diffuse ISM $\Delta f_\mu$ ]."393 The fact that the strong correlations subsist from the top to he bottom panels of Fig., The fact that the strong correlations subsist from the top to the bottom panels of Fig.394 6 demonstrates that stellar mass isnot he main driver of these correlations., \ref{fig:dust6} demonstrates that stellar mass isnot the main driver of these correlations.395 It is of interest to check the extent to which the properties of galaxies in Fig., It is of interest to check the extent to which the properties of galaxies in Fig.396 6 actually depend on stellar mass., \ref{fig:dust6} actually depend on stellar mass.397" Several studies iive shown that the star formation activity of a galaxy tends to ""ecreuse with increasing stellar mass (e.g.. 23)."," Several studies have shown that the star formation activity of a galaxy tends to decrease with increasing stellar mass (e.g., \citealt{Brinchmann2004}) )."398 In Fig. 7..," In Fig. \ref{fig:dust7},"399" we plot AlifAls. Mac and f, as a function of for 3 different stellar-mass ranges chosen to contain roughly P2imilar numbers of galaxies."," we plot $\mdust/\mstar$, $\mdust/\sfr$ and $f_\mu$ as a function of for 3 different stellar-mass ranges chosen to contain roughly similar numbers of galaxies."400 The distributions in the various quantities on the y-axis and their median values are displayed in the right-hand panels., The distributions in the various quantities on the $y$ -axis and their median values are displayed in the right-hand panels.401 Fig., Fig.402 7. shows that the relation between A4/M. and ddepends little on stellar mass. with only a slight tendency for the less massive galaxies to have somewhat higher AZ4/À..," \ref{fig:dust7} shows that the relation between $\mdust/403\mstar$ and depends little on stellar mass, with only a slight tendency for the less massive galaxies to have somewhat higher $\mdust/\mstar$ ."404" Also. the cuantity 3,4/ c. which traces the dust-to-gas ratio. tends to increase Pallightly with stellar mass."," Also, the quantity $\mdust/\sfr$ , which traces the dust-to-gas ratio, tends to increase slightly with stellar mass."405" The quantity displaying the strongest ""ependence on stellar mass in Fig.", The quantity displaying the strongest dependence on stellar mass in Fig.406" 7 is the fraction /,, of the", \ref{fig:dust7} is the fraction $f_\mu$ of the407The calibrated visibility of the shortest baseline (UT2-UT3) remains almost. constant αἱ 0.95 over the whole wavelength range ancl the source is only marginally resolved.,The calibrated visibility of the shortest baseline (UT2-UT3) remains almost constant at $\approx$ 0.95 over the whole wavelength range and the source is only marginally resolved.408 As expected. for the longest baseline (UT2-UT4) the lowest visibility is observed ranging from κ.τὸ al 8.3j0n to 70.6 at 1350n.. For the intermediate baseline (UT3-UTA) the visibility shows a slight increase from 20.73. al 8.34 to 220.85 at 125m. The fact that the object is Clearly resolved with (wo baselines in the MIR supports the argument of that we are observing an extended circumstellar structure. ie. a disk. aud not only the stellar photosphere (Herbieetal.2003).," As expected, for the longest baseline (UT2-UT4) the lowest visibility is observed ranging from $\approx$ 0.73 at $\mu$ m to $\approx$ 0.6 at $\mu$ m. For the intermediate baseline (UT3-UT4) the visibility shows a slight increase from $\approx$ 0.73 at $\mu$ m to $\approx$ 0.85 at $\mu$ m. The fact that the object is clearly resolved with two baselines in the MIR supports the argument of \citet{malbet} that we are observing an extended circumstellar structure, i.e. a disk, and not only the stellar photosphere \citep{herbig}."409. For the two baselines UT2-UT3 and UT2-UT4 the observations are consistent. with expectations [from thermal disk emission as despite the decreasing resolution for longer wavelengths the visibilities indicate larger sizes lor the emitting regions (see also section 5.3.)., For the two baselines UT2-UT3 and UT2-UT4 the observations are consistent with expectations from thermal disk emission as despite the decreasing resolution for longer wavelengths the visibilities indicate larger sizes for the emitting regions (see also section 5.3.).410 The observed increase in visibility for the UT2-UT4 baseline implies that for this baseline. however. the object appears smaller at μη (han at jn. This seems difficult io imagine in the context of a circumstellar disk as emitting source and certainly a second observation [or this baseline configuration seems eligible.," The observed increase in visibility for the UT3-UT4 baseline implies that for this baseline, however, the object appears smaller at $\mu$ m than at $\mu$ m. This seems difficult to imagine in the context of a circumstellar disk as emitting source and certainly a second observation for this baseline configuration seems eligible."411 Theoretically it is possible that (he photometric measurements carried out directly alter (he interferometric observations are corrupted due to technical problems or different weather conditions., Theoretically it is possible that the photometric measurements carried out directly after the interferometric observations are corrupted due to technical problems or different weather conditions.412 This in turn might then lead to a change in the visibility function., This in turn might then lead to a change in the visibility function.413 However. the calibrators observed at this night cid nol show anv sign of poor photometric measurements and their (ausler function was very stable over the whole night.," However, the calibrators observed at this night did not show any sign of poor photometric measurements and their transfer function was very stable over the whole night."414 In addition. also other YSOs with circumstellar disks showed an increasing visibilitv lor certain baselines when observed with MIDI.," In addition, also other YSOs with circumstellar disks showed an increasing visibility for certain baselines when observed with MIDI."415 Thus. since we do not lind any evidence for excluding this dataset due to bad quality we decided to keep it in our analvses.," Thus, since we do not find any evidence for excluding this dataset due to bad quality we decided to keep it in our analyses."416 As thus far no MIDI visibilities for TTanri stars have been published we are limited to a comparison between FU Ori and circumstellar disks around Ierbig Ae/Be stars (ILAeDes)., As thus far no MIDI visibilities for TTauri stars have been published we are limited to a comparison between FU Ori and circumstellar disks around Herbig Ae/Be stars (HAeBes).417 It shows that these stars as well as models applied to them normally show a prominent drop in the visibility between San and LOjau from where the curve remains almost constant (Leinertetal.2004).., It shows that these stars as well as models applied to them normally show a prominent drop in the visibility between $\mu$ m and $\mu$ m from where the curve remains almost constant \citep{leinert}.418 Qualitatively. Chis drop results from the intensity. distribution of the passive disks around the ILXeDes: At the short wavelength end the hot inner rim of the disks provides an overproportional contribution to the flux and is at the same tme confined to a small spatial region leading to a high visibility.," Qualitatively, this drop results from the intensity distribution of the passive disks around the HAeBes: At the short wavelength end the hot inner rim of the disks provides an overproportional contribution to the flux and is at the same time confined to a small spatial region leading to a high visibility."419 Most of the rest of the MIB. emission originates [rom a large area of the hot. illuminated surface laver of the f[Iared. cireiumstellar," Most of the rest of the MIR emission originates from a large area of the hot, illuminated surface layer of the flared circumstellar"420"where yec252p, ancl yec252p,.","where $\nu_{a,<}^{\rm{IC}}\approx 2\gamma_{c}^2\nu_{a,<}$ and $\nu_{a,>}^{\rm{IC}}\approx 2\gamma_{c}^2\nu_{a,>}$."421 Inserting equations (8)). (16)). (25)) and (26)) into the above equation. we obtain while the expression for vi is As we can see. p is below the X-ray [frequency v~LO Hz for typical parameters in most times curing the [ast-cooling phase.," Inserting equations \ref{eqn:fc:gc}) ), \ref{eqn:gamma_cm-2}) ), \ref{eqn:fc:nu_a<}) ) and \ref{eqn:fc:nu_a>}) ) into the above equation, we obtain while the expression for $\nu_{a,>}^{\rm{IC}}$ is As we can see, $\nu_{a}^{\rm{IC}}$ is below the X-ray frequency $\nu\sim10^{18}$ Hz for typical parameters in most times during the fast-cooling phase."422 For simplicity. we do not consider Chis lrequency for our estimation of the IC component in (he X-ray light curve.," For simplicity, we do not consider this frequency for our estimation of the IC component in the X-ray light curve."423 The SSC frequency v1C ⋯≼↲≺⇂∏≀↧⊥∖∩⊔∕∖∖↥∐↲∐∕∕↿⋅⋯⋅↕⋅≼↲⋅↗∣∕⋮↓⋅≺≡−≻↶↵−⋡↿⋯≚≺≺∪⊓∐∐⋃↥∪ ↴∙⋅↽≽," The SSC frequency $\nu_{m}^{\rm{IC}}$ equals to $\nu_{c}^{\rm{IC}}$ when $t=t_{cm}$, i.e. $\nu_{cm}^{\rm{IC}}\equiv 2\gamma_{e,cm}^2\nu_{cm}$."424 equations (15)) and (17)). we obtain which ean be further reduced numerically as The characteristic SSC frequencies p and pF evolve with time as The peak flux density of the SSC spectrum. £16... is roughly the product of the peak [ιν densitv of the svnchrotron spectrum by the Thomson optical depth.," According to equations \ref{eqn:gamma_cm-1}) ) and \ref{eqn:nu_0-1}) ), we obtain which can be further reduced numerically as The characteristic SSC frequencies $\nu_{c}^{\rm{IC}}$ and $\nu_{m}^{\rm{IC}}$ evolve with time as The peak flux density of the SSC spectrum, $F_{\nu,\rm{max}}^{\rm{IC}}$, is roughly the product of the peak flux density of the synchrotron spectrum by the Thomson optical depth."425 Considering some nunmerical [actors of order unitv. (he exact expression is (Sari Esin 2001)," Considering some numerical factors of order unity, the exact expression is (Sari Esin 2001)"426[ield amplified by helical kinematic diamo action are determined by both bound (localized) and unbound (nonlocalized) growing eigenmodes.,field amplified by helical kinematic dynamo action are determined by both bound (localized) and unbound (nonlocalized) growing eigenmodes.427 In particular. the large-scale component ol the field is defined bv the unbound eigenmodes and by the shallow bound. eigenmocles.," In particular, the large-scale component of the field is defined by the unbound eigenmodes and by the shallow bound eigenmodes."428 Because these shallow hound eigenmocles have growth rates higher than those of all unbound eigenmocdes. al any given scale (he former may rapidly become dominant over (he latter.," Because these shallow bound eigenmodes have growth rates higher than those of all unbound eigenmodes, at any given scale the former may rapidly become dominant over the latter."429 In practical applications. (his means that the shallow bound modes. rather (han the unbound modes. are likely to become essential in (he large-scale magnetic field configurations in astrophysical svstems.," In practical applications, this means that the shallow bound modes, rather than the unbound modes, are likely to become essential in the large-scale magnetic field configurations in astrophysical systems."430 In. (his case (he conventional a-clvuamo model (Steenbeck.Ixrause&Radler1966:Moffatt1978:Nulsrud2005). gives an inadequate description of the magnetic field even at the kinematic stage of dvnamo action.," In this case the conventional $\alpha$ -dynamo model \citep{skr,moffatt78,kulsrud1} gives an inadequate description of the large-scale magnetic field even at the kinematic stage of dynamo action."431 The a-model becomes inapplicable in tliis case because il uses a critical assumption that small-scale (hietuations of the velocity and magnetic fields are much weaker and concentrated al the scales much smaller than the seales of the growing large-scale field., The $\alpha$ -model becomes inapplicable in this case because it uses a critical assumption that small-scale fluctuations of the velocity and magnetic fields are much weaker and concentrated at the scales much smaller than the scales of the growing large-scale field.432 Under. this assumption the a-moclel is obtained by averaging the induction Equation (1)) over these small-scale [Iuctuations to obtain a linear and. homogeneous dillerential equation for the large-scale mean magnetic Thus. the a-moclel misses all growing bound magnetic eigenmodes. including the essential shallow bound. eigenmodes that determine the eventual large-scale configuration of the magnetic field.," Under this assumption the $\alpha$ -model is obtained by averaging the induction Equation \ref{induction}) ) over these small-scale fluctuations to obtain a linear and homogeneous differential equation for the large-scale mean magnetic Thus, the $\alpha$ -model misses all growing bound magnetic eigenmodes, including the essential shallow bound eigenmodes that determine the eventual large-scale configuration of the magnetic field."433 We thank Fausto Cattaneo lor many useful and stimulating discussions., We thank Fausto Cattaneo for many useful and stimulating discussions.434 This work was supported by the NSF Center for Magnetie Sell-Organization in Laboratory and Astrophysical Plasmas at (he Universities of Chicago and Wisconsin-Macdison., This work was supported by the NSF Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas at the Universities of Chicago and Wisconsin-Madison.435 5.D. is supported by the U.S. Department of Energy under (he grant no., S.B. is supported by the U.S. Department of Energy under the grant no.436 DE-EGO2-07121354932., DE-FG02-07ER54932.437setting it equal to zero as has been done in this paper ane in the analytic derivations of Paper In this paper we continue our study of the viability. and properties of weakly ionized protostellar accretion disces that transport their excess angular momentum vertically through the surfaces by means of centrifugallv driven winds.,setting it equal to zero as has been done in this paper and in the analytic derivations of Paper In this paper we continue our study of the viability and properties of weakly ionized protostellar accretion discs that transport their excess angular momentum vertically through the surfaces by means of centrifugally driven winds.438 In view of the suggestive evidence that this situation is realized in at least some protostellar svstems (e.g.Rayetal.2007).. and vet mindful of the fact that the total racial extent of such wincd-driving disc regions is still unknown. we consider racially localized. disc configurations (which. however. are joined. to a global wind model).," In view of the suggestive evidence that this situation is realized in at least some protostellar systems \citep[e.g.][]{Ray07}, and yet mindful of the fact that the total radial extent of such wind-driving disc regions is still unknown, we consider radially localized disc configurations (which, however, are joined to a global wind model)."439 We employ the formulation evised by WIX93 for modelling steady. geometrically thin. Pvertically isothermal and. nearly. Weplerian cliscs in. which magnetic dillusivitv counters the shearing and advection of 1e magnetic field.," We employ the formulation devised by WK93 for modelling steady, geometrically thin, vertically isothermal and nearly Keplerian discs in which magnetic diffusivity counters the shearing and advection of the magnetic field."440 WIN93 assumed that the charge carriers were singly-charecd ions and electrons. ancl focussed on 1f ambipolar dillusivity regime., WK93 assumed that the charge carriers were singly-charged ions and electrons and focussed on the ambipolar diffusivity regime.441 In Paper I we extended us model to the Hall and Ohm diffusivity regimes using 16 conductivitv-tensor. formalism. although we reverted to using the multilluid approach emploved bv WIN93 [or deriving parameter constraints on physically viable solutions in these regimes.," In Paper I we extended this model to the Hall and Ohm diffusivity regimes using the conductivity-tensor formalism, although we reverted to using the multifluid approach employed by WK93 for deriving parameter constraints on physically viable solutions in these regimes."442 This derivation generalized. the corresponding results of WIX93 for the ambipolar cilfusivity regime and was similarly. carried out in the context. of the hvdrostatic approximation. in which the vertical velocity component is neglected. inside the disc (which. results in several of the dilferential equations for the dise structure simplifving to algebraic relations).," This derivation generalized the corresponding results of WK93 for the ambipolar diffusivity regime and was similarly carried out in the context of the hydrostatic approximation, in which the vertical velocity component is neglected inside the disc (which results in several of the differential equations for the disc structure simplifying to algebraic relations)."443 The hydrostatic analysis of paper Lincdicated that viable wind-driving dise solutions correspond. to. four. parameter, The hydrostatic analysis of paper I indicated that viable wind-driving disc solutions correspond to four parameter444in contradiction with our present understanding of LSS formation. since it partly arises from Nbody simulations of the structure formation process which capture multistreaming effects. and hence are not coustrained by the analvtical approximation to dust which. iu its simplest realizations (c.e.. Zeldovichs approximation (ZeVdovich 1970)). features imunecdiate decay of structures iter their formation.,"in contradiction with our present understanding of LSS formation, since it partly arises from N–body simulations of the structure formation process which capture multi--streaming effects, and hence are not constrained by the analytical approximation to dust which, in its simplest realizations (e.g., Zel'dovich's approximation (Zel'dovich 1970)), features immediate decay of structures after their formation."445 We also consider an exteusion of the model to include effects., We also consider an extension of the model to include effects.446" This ""stochasticitv arises from the effect on the dvuauuical evolution of plivsical processes Occurnues on tie and/or lenethscales much smaller han those directly associate with LSS formation. thus allowing to mode them by means of a stochastic source (a 10186)."," This “stochasticity” arises from the effect on the dynamical evolution of physical processes occurring on time– and/or length–scales much smaller than those directly associated with LSS formation, thus allowing to model them by means of a stochastic source (a noise)."447 Possible sources are deviations from the mean field approximation. fluctuations inherent to the lycrocwuamic (Le. coarseerained) description. aud nongravitational orocesses m barvonic matter.," Possible sources are deviations from the mean field approximation, fluctuations inherent to the hydrodynamic (i.e., coarse–grained) description, and non–gravitational processes in baryonic matter."448 We shal use the simplest uodel of a Gaussiandistributed forcing on the coarse-erained evolution., We shall use the simplest model of a Gaussian–distributed forcing on the coarse-grained evolution.449 As with pressurelike forces. we just want to stress tha a noisy forcing could be relevant ο LSS formation. but a detailed consideration of its origin and propertics is bevoud the scope of the preseut paper.," As with pressure–like forces, we just want to stress that a noisy forcing could be relevant to LSS formation, but a detailed consideration of its origin and properties is beyond the scope of the present paper."450 Iu fact. application ofthe Renormalization Group shows that noise is relevant In nonexceptional coucitious (Barbero ct al.," In fact, application of the Renormalization Group shows that noise is relevant in non–exceptional conditions (Barbero et al."451 1997: ngeuez et al., 1997; nguez et al.452 1999). inuplviug that even if it is very weak (apparently negligible). its effects are amplified and can have anonucelieible effect ou the dvuamical evolution.," 1999), implying that even if it is very weak (apparently negligible), its effects are amplified and can have a non–negligible effect on the dynamical evolution."453 This paper is structured as follows: in Sect., This paper is structured as follows: in Sect.454 2. we beein bv preseutiug the basic svstei of equations in the Newtomian reeiuc. aud then proceed to a discussion of restrictive assumptions for the weakly nonlinear regime.," \ref{basic_equations} we begin by presenting the basic system of equations in the Newtonian regime, and then proceed to a discussion of restrictive assumptions for the weakly nonlinear regime."455 lu Sect., In Sect.456 3. we discuss the role of the pressure.Bike force for sole particular choices of the equation of state p=νο) aud the connection with Dureers equation., \ref{pressure} we discuss the role of the pressure–like force for some particular choices of the equation of state $p=p(\varrho)$ and the connection with Burgers' equation.457 In Sect., In Sect.458 1 we consider the role of noise and provide a detailed description of he relatiouship between the cosiological equations and the NardarParisiZhane UsPZ) equation., \ref{KPZ} we consider the role of noise and provide a detailed description of the relationship between the cosmological equations and the Kardar–Parisi–Zhang (KPZ) equation.459 Iu Sect., In Sect.460 5. we study the iuecar regine in1 the presence of pressure and noise., \ref{linear_regime} we study the linear regime in the presence of pressure and noise.461 We finally conclude in Sect. 6.., We finally conclude in Sect. \ref{conclusions}.462 Some techinicalities have been left for two appendices. one devoted to the exploration of the validity of what we call insect.," Some technicalities have been left for two appendices, one devoted to the exploration of the validity of what we call in Sect."463 L the vadiahatic approximation”. aud another to aanore detailed discussion of the linear regine.," \ref{KPZ} the “adiabatic approximation”, and another to a more detailed discussion of the linear regime."464 We are interested in discussing LSS formation iu the nonrelativistic regine and therefore cousicer the οποία cosmological equations for a selferavitating fluid iun a standard tre (FL) cosmological backeround dominated bv uourelativistic matter (Peebles 1980)., We are interested in discussing LSS formation in the non--relativistic regime and therefore consider the Newtonian cosmological equations for a self–gravitating fluid in a standard tre (FL) cosmological background dominated by non--relativistic matter (Peebles 1980).465 The cosmological background is characterized by the cosmic expuiuusiou factor ασ) and the homogeneous background matter density oí). which obey (IIlubbles function is defined as If=fa) where the coustaut A deteriuues the sien of the spatial curvature (treated as an iuteeration constant in the Newtomian framework considered throughout this paper). oy is the background deusitv at some time fy when e(fy)=l. and A is the cosimological constant.," The cosmological background is characterized by the cosmic expansion factor $a(t)$ and the homogeneous background matter density $\varrho_{b}(t)$, which obey (Hubble's function is defined as $H =466\dot{a} / a$ ) where the constant $K$ determines the sign of the spatial curvature (treated as an integration constant in the Newtonian framework considered throughout this paper), $\varrho_{0}$ is the background density at some time $t_{0}$ when $a(t_{0})=1$ , and $\Lambda$ is the cosmological constant."467 Without loss of eeneralitv. oue can choose ty to correspond to the present epoch.," Without loss of generality, one can choose $t_{0}$ to correspond to the present epoch."468" It is convenient to work iu comoving coordinates x= ly, where r mro the standard nonrotating Eulerian coordinates."," It is convenient to work in comoving coordinates ${\bf x} \equiv469a^{-1}{\bf r}$ , where $\bf {r}$ are the standard non–rotating Eulerian coordinates."470" The ""udaineutal fields will be as follows: the density ο (or equivaleutlv. the deusitv contrast d:—Cofon)l ) the peculiarvelocity UW=μηνIv. where Ujays is the physical velocity aud Ir i$ the IIubble flow. aud the gravitational peculiaracceleration ΕΞδη.|i(1xGpi,A)r. where Zphys is the plysical eravitational acceleration. aud i(1xGo,Ajr is the Newtoman counterpart of the gravitational acceleration opposing tothe backeround expiusiou."," The fundamental fields will be as follows: the density $\varrho$ (or equivalently, the density contrast $\delta :=471(\varrho / \varrho_{b}) - 1$ ), the peculiar–velocity ${\bf u} \equiv472{\bf u}_{phys} - H {\bf r}$, where ${\bf u}_{phys}$ is the physical velocity and $H {\bf r}$ is the Hubble flow, and the gravitational peculiar–acceleration ${\bf g} = {\bf g}_{phys} + \frac{1}{3}\left(4473 \pi G \rho_{b} - \Lambda \right) {\bf r}$, where ${\bf g}_{phys}$ is the physical gravitational acceleration and $-\frac{1}{3}\left( 4 \pi474 G \varrho_{b} - \Lambda \right) {\bf r}$ is the Newtonian counterpart of the gravitational acceleration opposing tothe background expansion."475" We subject o. u aud g to periodic boundary conditious on some large scale to assure uniqueness of the cosmiological solutions. in which case of, is equal to the spatially averaged density (sce Elilers Buchert 1997)."," We subject $\varrho$, ${\bf u}$ and ${\bf g}$ to periodic boundary conditions on some large scale to assure uniqueness of the cosmological solutions, in which case $\varrho_{b}$ is equal to the spatially averaged density (see Ehlers Buchert 1997)."476 The fields ο. u obey a set of hydrodynamic equations expressing the conservation of mass and momentuni iu an expanding background.," The fields $\varrho$, ${\bf u}$ obey a set of hydrodynamic equations expressing the conservation of mass and momentum in an expanding background."477 These equatious are quite simular to those of the standard dust model (Peebles 1980). except for two forcing terius m Eulers equatiou that inodel the unltistreamine and stochastic effects discussed- in. the IutroductionH +: e Continuity equation: e Euler's equation: e Nowtonian field equations: We emphasize that the integral curves of the peculiar ficll u are not associated to trajectories of," These equations are quite similar to those of the standard dust model (Peebles 1980), except for two forcing terms in Euler's equation that model the multi-streaming and stochastic effects discussed in the Introduction : $\bullet$ Continuity equation: $\bullet$ Euler's equation: $\bullet$ Newtonian field equations: We emphasize that the integral curves of the peculiar--velocity field ${\bf u}$ are not associated to trajectories of"478eedge in the ASCA (Brinkmann et al. 1996)),edge in the ASCA (Brinkmann et al. \cite{wpb96}) )479 is exactly the expected signature of dust within à warm absorber (cf., is exactly the expected signature of dust within a warm absorber (cf.480 Fig. 4))., Fig. \ref{wa-dwa}) ).481 The structure in the spectrum around 0.65 keV was modeled as an aabsorption edge by Brandt et al. (1997)), The structure in the spectrum around 0.65 keV was modeled as an absorption edge by Brandt et al. \cite{brandt97}) )482 and as an isolated emission line by Brinkmann et al. (1996))., and as an isolated emission line by Brinkmann et al. \cite{wpb96}) ).483 In fact. even both features may be present and overlapping.," In fact, even both features may be present and overlapping."484 We note that also an instrumental emission feature hàs been reported around 0.6 keV (see 22.1 of Otant et al. 1996))., We note that also an instrumental emission feature has been reported around 0.6 keV (see 2.1 of Otani et al. \cite{otani}) ).485 The major problem with dusty warm absorber models for Ilies in the fact that they are. at most. marginally consistent with the ROSAT PSPC data.," The major problem with dusty warm absorber models for lies in the fact that they are, at most, marginally consistent with the ROSAT PSPC data."486 Even if one accepts the reduced quality of the fit Ον% 1.7). a temporal change of the intrinsic continuum of ATz0.50.7 between the ROSAT and the ASCA observation has to be explained.," Even if one accepts the reduced quality of the fit $\chi^2_{\rm red} \approx 1.7$ ), a temporal change of the intrinsic continuum of $\Delta\Gamma \approx 0.5-0.7$ between the ROSAT and the ASCA observation has to be explained."487 The difference in the quality of the fit between the dust-free and the dusty warm absorbers is due to the clear indication of an aabsorption edge in the ROSAT data (see also Table | of BFP96). which should be much weaker if the warm gas Is dusty.," The difference in the quality of the fit between the dust-free and the dusty warm absorbers is due to the clear indication of an absorption edge in the ROSAT data (see also Table 1 of BFP96), which should be much weaker if the warm gas is dusty."488 In principle. it is possible to introduce increased aabsorption also 1n the case of a dusty warm absorber. for example by increasing the gas-phase oxygen abundance (which is depletec in the models to account for the binding of metals into dust).," In principle, it is possible to introduce increased absorption also in the case of a dusty warm absorber, for example by increasing the gas-phase oxygen abundance (which is depleted in the models to account for the binding of metals into dust)."489 However. the limited spectral resolution of ROSAT certainly does not warrant this kind of fine-tuning to achieve optimal fits and the improved spectral capabilities of future X-ray missions are be needed to study in detail the elemental abundances of the warm absorber as well as the properties of the any dust in13349+2438.," However, the limited spectral resolution of ROSAT certainly does not warrant this kind of fine-tuning to achieve optimal fits and the improved spectral capabilities of future X-ray missions are be needed to study in detail the elemental abundances of the warm absorber as well as the properties of the any dust in."490. As far as the change in the intrinsic continuum. is concerned. one might speculate about various explanations. including a ‘real’ change in the spectrum and instrumental effects.," As far as the change in the intrinsic continuum is concerned, one might speculate about various explanations, including a 'real' change in the spectrum and instrumental effects."491 The X-ray continuum spectrum might indeed have varied by AT=0.5(.7 between the ROSAT and the ASCA observations. which are separated by about three years.," The X-ray continuum spectrum might indeed have varied by $\Delta\Gamma\approx 0.5-0.7$ between the ROSAT and the ASCA observations, which are separated by about three years."492 This possibility of course cannot be ruled out and in fact spectral changes have previously been observed in narrow-line Seyfert I galaxies (e.g. Mrk 766; Leighly et al., This possibility of course cannot be ruled out and in fact spectral changes have previously been observed in narrow-line Seyfert 1 galaxies (e.g. Mrk 766; Leighly et al.493 1996)., 1996).494 However. we consider it unlikely for im view of the fact that no spectral variations have been observed between as well as within the individual PSPC and ASCA observations.," However, we consider it unlikely for in view of the fact that no spectral variations have been observed between as well as within the individual PSPC and ASCA observations."495 In particular. the spectra observed in the two PSPC observations seem to be consistent despite a dramatic increase in flux by a factor of four.," In particular, the spectra observed in the two PSPC observations seem to be consistent despite a dramatic increase in flux by a factor of four."496 Furthermore. no spectral variations have been detected within the ASCA observation (e.g. Brinkmann et al. 1996)).," Furthermore, no spectral variations have been detected within the ASCA observation (e.g. Brinkmann et al. \cite{wpb96}) )."497 Systematic differences between ASCA and ROSAT spectra have been reported for various simultaneous observations in the past (e.g. NGC 5548; Iwasawa et al. (1999)), Systematic differences between ASCA and ROSAT spectra have been reported for various simultaneous observations in the past (e.g. NGC 5548; Iwasawa et al. \cite{iwasawa}) )498 and references therein)., and references therein).499 In particular. the photon index tends to be steeper by AT=0.1 in these PSPC observations as compared to ASCA.," In particular, the photon index tends to be steeper by $\Delta\Gamma\approx 0.4$ in these PSPC observations as compared to ASCA."500 On the other hand there are also observations. where the ASCA and ROSAT spectra do agree reasonably well (e.g. Miyaji et al. 1998::," On the other hand there are also observations, where the ASCA and ROSAT spectra do agree reasonably well (e.g. Miyaji et al. \cite{miyaji};"501 Brinkmann et al. 1998::, Brinkmann et al. \cite{brinkmann98};502 Cappi et al. 1997))., Cappi et al. \cite{cappi}) ).503 Although these observations were not done simultaneously. it seems unlikely that spectral changes occured in all these sources which exactly compensate for any putative calibration uncertainties.," Although these observations were not done simultaneously, it seems unlikely that spectral changes occured in all these sources which exactly compensate for any putative calibration uncertainties."504 The ASCA/ROSAT discrepancies definitely need to be further investigated., The ASCA/ROSAT discrepancies definitely need to be further investigated.505 This is. however. beyond the scope of this paper.," This is, however, beyond the scope of this paper."506 We conclude that it cannot be excluded that the observed difference between. the ROSAT and ASCA power law continuum spectrum of lis at least partly due to instrumental effects., We conclude that it cannot be excluded that the observed difference between the ROSAT and ASCA power law continuum spectrum of is at least partly due to instrumental effects.507 We note. however. that even if we allow for the steeper PSPC spectrum in the dusty warm absorber model (and only in this model a systematically steeper continuum ts required for the ROSAT data). the fit is still only marginally acceptable.," We note, however, that even if we allow for the steeper PSPC spectrum in the dusty warm absorber model (and only in this model a systematically steeper continuum is required for the ROSAT data), the fit is still only marginally acceptable."508 In the previous section we discussed the possibility of a variable dust-free warm absorber., In the previous section we discussed the possibility of a variable dust-free warm absorber.509 In order to preserve the dusty warm absorber hypothesis. and hence to obtain a physical model to explain all X-rayaad the optical properties consistently. we might also speculate about more complicated warm absorber models.," In order to preserve the dusty warm absorber hypothesis, and hence to obtain a physical model to explain all X-ray the optical properties consistently, we might also speculate about more complicated warm absorber models."510 For example. à two-zone warm absorber has been proposed for the Seyfert 1 galaxy 30-15 (Otani et al. 1996)).," For example, a two-zone warm absorber has been proposed for the Seyfert 1 galaxy MCG--6--30--15 (Otani et al. \cite{otani}) ),"511 re. a variable inner warm absorber responsible for the aabsorption edge and an outer warm absorber in a lower ionization state and thus mainly imprinting the eedge., i.e. a variable inner warm absorber responsible for the absorption edge and an outer warm absorber in a lower ionization state and thus mainly imprinting the edge.512" mmight be a similar case: the inner warm absorber varied between the ROSAT and the ASCA observation. either. by changes in the ionization state and/or by a variation in N,-. whereas the outer warm absorber is present in. both observations."," might be a similar case: the inner warm absorber varied between the ROSAT and the ASCA observation either by changes in the ionization state and/or by a variation in $_{\rm w}$, whereas the outer warm absorber is present in both observations."513 We presented new ROSAT HRI data for aand a re-analysis of the ROSAT PSPC and ASCA spectra in terms of a warm absorber. but self-consistently including the effects of dust on the soft X-ray spectrum.," We presented new ROSAT HRI data for and a re-analysis of the ROSAT PSPC and ASCA spectra in terms of a warm absorber, but self-consistently including the effects of dust on the soft X-ray spectrum."514 The HRI light curve of cconfirms the rapid and large amplitude variability already noted in the ASCA data (Brinkmann et al. 1996))., The HRI light curve of confirms the rapid and large amplitude variability already noted in the ASCA data (Brinkmann et al. \cite{wpb96}) ).515 We observed a factor of two change in count rate within one day and variability within about three hours., We observed a factor of two change in count rate within one day and variability within about three hours.516 These rapid variations of the soft X-ray flux rule out a significant contribution of scattered X-rays to the total flux., These rapid variations of the soft X-ray flux rule out a significant contribution of scattered X-rays to the total flux.517 The analysis of the measured ROSAT PSPC and ASCA spectra gives contradictory results., The analysis of the measured ROSAT PSPC and ASCA spectra gives contradictory results.518 The PSPC data are best fit by a dust-free warm absorber. but large changes in the column density of the ionized material and the tonization state are required to describe the ASCA data with this model.," The PSPC data are best fit by a dust-free warm absorber, but large changes in the column density of the ionized material and the ionization state are required to describe the ASCA data with this model."519 And finally it cannot explain the discrepancy between the optical reddening and the absence of cold X-ray absorption., And finally it cannot explain the discrepancy between the optical reddening and the absence of cold X-ray absorption.520 On the, On the521representative.,representative.522 ud. therefore. the interpretation of results for distant extragalactic PNe are. at least in a statistical sense. not as seriously alfected by the lack of spatial resolution.," And, therefore, the interpretation of results for distant extragalactic PNe are, at least in a statistical sense, not as seriously affected by the lack of spatial resolution."523 We would like to dedicate this paper to the memory of llugo E. Schwarz. the observer of the cata used here.," We would like to dedicate this paper to the memory of Hugo E. Schwarz, the observer of the data used here."524 We also thank John Danziger. the referee. for his revision of the paper with suggestions that. helped. to. improved it.," We also thank John Danziger, the referee, for his revision of the paper with suggestions that helped to improved it."525 Three Brazilian agencies gave us partial support for this work., Three Brazilian agencies gave us partial support for this work.526 So MLLE. DRG and. LAL would like to thank CAPES. FAPIEBJs E-26/110.107/2008 grant and EAPIESP (2003/00692-0 erant). respectively.," So MLLF, DRG and HM would like to thank CAPES, FAPERJ's E-26/110.107/2008 grant and FAPESP (2003/09692-0 grant), respectively."527analysis of igh quality erouud-based transit observations.,analysis of high quality ground-based transit observations.528 We judge that we lose little information by our adopted restrictions. but the subsequent restriction in the fitted paralucters helps to increase the usefulness of the erouud-based data.," We judge that we lose little information by our adopted restrictions, but the subsequent restriction in the fitted parameters helps to increase the usefulness of the ground-based data."529 Iu the case of the the D-baud transit data. we are primarily interested iu the cousisteucy between the retrieved linear lnib-darkeniug coefficient aud the model atmosphere prediction.," In the case of the the B-band transit data, we are primarily interested in the consistency between the retrieved linear limb-darkening coefficient and the model atmosphere prediction."530" So iu that case. we fix both the orbital inelination aud the value of a/R, to their best-fit Kepler values. aud we fit ouly for the linear Biub-darkeuiug cocfiicient. as well as ΠΠ aud coutral transit tine."," So in that case, we fix both the orbital inclination and the value of $a/R_s$ to their best-fit Kepler values, and we fit only for the linear limb-darkening coefficient, as well as $R_p/R_s$ and central transit time."531 As regards the linear limb darkening cocficieut. we mipose the restriction that the AICAIC chains cannot step to values excecding unitv. since those values produce maplysical reeative) disk iutensities.," As regards the linear limb darkening coefficient, we impose the restriction that the MCMC chains cannot step to values exceeding unity, since those values produce unphysical (negative) disk intensities."532 Our first exploratory MCMC chains for the J-baud fit showed a strong degeneracy between orbital inclination and a/R., Our first exploratory MCMC chains for the J-band fit showed a strong degeneracy between orbital inclination and $a/R_s$.533 This is not surprising. since we have previously lüehliehted this degeneracy for small plancts (Sada 2010)..," This is not surprising, since we have previously highlighted this degeneracy for small planets \citep{sada}."534 In the limit of a small planet transiting a uniform stellar disk. the transit curve approaches an inverse square-wave function where the duration of the transit nieasures oulv the total leneth of the chord across the stellar disk.," In the limit of a small planet transiting a uniform stellar disk, the transit curve approaches an inverse square-wave function where the duration of the transit measures only the total length of the chord across the stellar disk."535 Iu that case. the mipact parameter G.c.. orbital inclination) iid stellar radius cau trade-off freely.," In that case, the impact parameter (i.e., orbital inclination) and stellar radius can trade-off freely."536 Hence. iu the J-baud we fix the orbital iuclinatiou at the I&epler value (89.117. Table 1). aud. we solve for a/Ry.," Hence, in the J-band we fix the orbital inclination at the Kepler value $89.41^{\circ}$, Table 1), and we solve for $a/R_s$."537 Results from the J- and D-baud ft procedures are included in Table 1. and best-fit transit curves are overplotted on Figure 1.," Results from the J- and B-band fit procedures are included in Table 1, and best-fit transit curves are overplotted on Figure 1."538 A useful by-product of our transit analyses is that we can update the transit ephemeris for this svstem., A useful by-product of our transit analyses is that we can update the transit ephemeris for this system.539 We include transits at the two epochs reported by DIO. as well as trausits from Iirauoetal.(2011) and Dittinanuetal. (2009).. and the Kepler transits.," We include transits at the two epochs reported by B10, as well as transits from \citet{hirano} and \citet{dittmann}, and the Kepler transits."540 Table 2 gives the ceutral transit times and errors for the Ikepler transits. using our bisector method.," Table 2 gives the central transit times and errors for the Kepler transits, using our bisector method."541 The precision of the updated ephemeris is donuuuated by the Kepler transits. that each have a timing precision of order LO seconds.," The precision of the updated ephemeris is dominated by the Kepler transits, that each have a timing precision of order 10 seconds."542 An error-woeiehted linear least-squares solution for the ephemeris vields Jy=2151605.89155+ 0.00013. in a harveeutric TDB frame (Eastmanetal.2010).. and P=L8SSTSOdlS41.6«10 days.," An error-weighted linear least-squares solution for the ephemeris yields $T_0=2454605.89155\pm0.00013$ , in a barycentric TDB frame \citep{eastman}, and $P=4.8878018\pm 1.6 \times 10^{-6}$ days."543 We consider this to be a provisional update. because many additional values for transit ceuter times will be possible with future IKepler data.," We consider this to be a provisional update, because many additional values for transit center times will be possible with future Kepler data."544 Figure 7 shows residuals for the times of iudividual transits. after removing the best-fit ephemeris.," Figure 7 shows residuals for the times of individual transits, after removing the best-fit ephemeris."545 As noted iu Sec., As noted in Sec.546 2.1. we omit our 2010 J- aud D-baud trausits from the eplicmeris solution. but we include their residuals ou Figure 7 where they individually lic off the best-fit ephemeris. but agree with it on average.," 2.1, we omit our 2010 J- and B-band transits from the ephemeris solution, but we include their residuals on Figure 7 where they individually lie off the best-fit ephemeris, but agree with it on average."547 Iu the case where multiple hieh quality transit lelt curves are available for a planet that transits at an oblique anele to the stellar equator. we can correct the derived planetary radius for the effect of star spots that arenot crossed by the planet during transit.," In the case where multiple high quality transit light curves are available for a planet that transits at an oblique angle to the stellar equator, we can correct the derived planetary radius for the effect of star spots that are crossed by the planet during transit."548 The method we describe here assumes that the distribution of star spots is not correlated with the transits., The method we describe here assumes that the distribution of star spots is not correlated with the transits.549 We argue that lis method has advantages over inferences based ou the rotational light curve of the star (Czeslaetal.2009). vecause star spot effects in the rotational light cuve cau )o reduced when iuiultiple spots are distributed wnitormiy over longitudo.," We argue that this method has advantages over inferences based on the rotational light curve of the star \citep{czesla}, because star spot effects in the rotational light curve can be reduced when multiple spots are distributed uniformly over longitude."550 The foxiidisii of our star spot correction has two woad steps., The formalism of our star spot correction has two broad steps.551 First. we integrate over the path crossed w the planet. aud average over all observed transits. to calculate the average flux deficit due to star spots on the ih of the planet.," First, we integrate over the path crossed by the planet, and average over all observed transits, to calculate the average flux deficit due to star spots on the path of the planet."552 The orbit of ILXT-P-I1b is essentially serpendicular (within the errors) to the stellar equator (Winnetal.2010:ITHixauo2011).," The orbit of HAT-P-11b is essentially perpendicular (within the errors) to the stellar equator \citep{winn, hirano}."553. We find (Table 1) hat the orbital iuclination is very close to 90-degrees. aud herefore the impact paranieter is near zero.," We find (Table 1) that the orbital inclination is very close to 90-degrees, and therefore the impact parameter is near zero."554 Moreover. the stellar active latitudes are not far from the stellar equator.," Moreover, the stellar active latitudes are not far from the stellar equator."555 Therefore the flux deficit that we calculate in this first step will he characteristic of regions near the ceuter of the stellar disk., Therefore the flux deficit that we calculate in this first step will be characteristic of regions near the center of the stellar disk.556 The second broad step will extend the fiux deficit calculated over the transit path of the planet. to estimate the total spot coverage over the cutire facing hemisphere of the star.," The second broad step will extend the flux deficit calculated over the transit path of the planet, to estimate the total spot coverage over the entire Earth-facing hemisphere of the star."557 Figure 8 shows a cartoon of the transit ecometiy., Figure 8 shows a cartoon of the transit geometry.558 Near disk ceuter. the planet subteuds au approximately constaut range of longitude as it transits (iudicated by blue meridians of longitude on Figure 8).," Near disk center, the planet subtends an approximately constant range of longitude as it transits (indicated by blue meridians of longitude on Figure 8)."559 This approxination of course breaks down near the poles because meridians of longitude converge. but we expect few if any star spots at the poles.," This approximation of course breaks down near the poles because meridians of longitude converge, but we expect few if any star spots at the poles."560" Ποσο, by integrating over the path of the planet we are essentially defining the spot coverage in the ranec of longitude defined by the aneular exteut of the planet."," Hence, by integrating over the path of the planet we are essentially defining the spot coverage in the range of longitude defined by the angular extent of the planet."561 Consider a highly simplified situation where the planet transits a very sinall star spot present on a star without limb darkeuiug., Consider a highly simplified situation where the planet transits a very small star spot present on a star without limb darkening.562 Let Fy be the flux from theunspotted star. and let 6F be the stellar fux deficit caused by the small star spot.," Let $F_0$ be the flux from the star, and let $\delta F$ be the stellar flux deficit caused by the small star spot."563" In transit. before the star spot is crossed. the observed flux Poa. is FyFut OF. where R,, aud Rare the radii of the planet audD A"")star respectively."," In transit, before the star spot is crossed, the observed flux $F_{obs}$ is $F_0-F_0(R_p^2/R_s^2)-\delta F$ , where $R_p$ and $R_s$ are the radii of the planet and star respectively."564" When the planet crosses the star spot. the 6F term: vanishes. so the flux becomes £54,=Fo(lRz). which is the usual expression for the iu-trausit flux τῇof a star neglecting limb darkening."," When the planet crosses the star spot, the $\delta F$ term vanishes, so the flux becomes $F_{obs}=F_0(1-R_p^2/R_s^2)$, which is the usual expression for the in-transit flux of a star neglecting limb darkening."565 The effect of the star spot will be seen in the transit curve as an inverted square wave of amplitude 6F. lasting for a crossing time (measured in phase units) ἐν. (," The effect of the star spot will be seen in the transit curve as an inverted square wave of amplitude $\delta F$, lasting for a crossing time (measured in phase units) $t_{\phi}$. ("566Note that we use orbital pliase as a time variable. not an anele.),"Note that we use orbital phase as a time variable, not an angle.)"567" Avery sinall star spot would create a simple square-wave type signature iu the transit curve, but real star spots are comparable to the size of the planet itself. their intensity varies from the outer pemuubra to their unbral core. aud they often occur in eroups."," A very small star spot would create a simple square-wave type signature in the transit curve, but real star spots are comparable to the size of the planet itself, their intensity varies from the outer penumbra to their umbral core, and they often occur in groups."568 Therefore their signature im transit light curves can be complex. not a simple square wave.," Therefore their signature in transit light curves can be complex, not a simple square wave."569 Nevertheless. we can derive the total star spot fiux deficit crossed by the plauet duriug a transit. OF}. as: where àE(o) is the amplitude of the deviation seen in the transit curve at phase o. and the integral is taken over the path of the planct. literally over the transit curve.," Nevertheless, we can derive the total star spot flux deficit crossed by the planet during a transit, $\delta F_t$, as: where $\delta F(\phi)$ is the amplitude of the deviation seen in the transit curve at phase $\phi$, and the integral is taken over the path of the planet, literally over the transit curve."570 We ποσα uot explicitly cousicer the intensity eradicutacross a star spot. we can derive the total flux deficit from the above integral. iudependeut of star spot morphology.," We need not explicitly consider the intensity gradientacross a star spot, we can derive the total flux deficit from the above integral, independent of star spot morphology."571 Moreover.," Moreover,"572The count rates are converted into {lixes using the conversion [actors for a white dwarf. as recommended by the OAL calibration manual.,"The count rates are converted into fluxes using the conversion factors for a white dwarf, as recommended by the OM calibration manual."573 Using the extinction curve of Carclelli et al. (, Using the extinction curve of Cardelli et al. (5741989) and the extinction parameters of £4=3.1 and Ay=0.102. we correct the fluxes with the extinction coefficient at the effective wavelength of each filter.,"1989) and the extinction parameters of $R_V=3.1$ and $A_V=0.102$, we correct the fluxes with the extinction coefficient at the effective wavelength of each filter."575 The value of Ay: is taken [rom NED. which was obtained by following Appendix D of Schlegel et al. (," The value of $A_V$ is taken from NED, which was obtained by following Appendix B of Schlegel et al. ("5761998).,1998).577 The OM light curves alter extinction correction are shown in the top panel of Figure 16. with filler name indicated., The OM light curves after extinction correction are shown in the top panel of Figure \ref{fig:om} with filter name indicated.578 The fluxes gathered. with different. fillers can not be used to do a straightlorwared comparison will the X-rav light curve for the whole observational leneth., The fluxes gathered with different filters can not be used to do a straightforward comparison with the X-ray light curve for the whole observational length.579 We thus scale all the V. U and UWVAI2 [fIuxes to the fhixes al the effective wavelength of the UVWI filter (A=291 nm).," We thus scale all the V, U and UVM2 fluxes to the fluxes at the effective wavelength of the UVW1 filter $\lambda580= 291$ nm)."581 We assume a power law spectrum between anv pair ol fillers. whose spectral index is caleulated with the average fluxes at the two filters.," We assume a power law spectrum between any pair of filters, whose spectral index is calculated with the average fluxes at the two filters."582 The sealed UVW1 light curve is shown in the middle panel of Figure 16.., The scaled UVW1 light curve is shown in the middle panel of Figure \ref{fig:om}.583 By adopting a constant spectral index to scale (he fluxes from one filler to UVWI. the scaled UVWI light curve keep (hie same shape as the original one.," By adopting a constant spectral index to scale the fluxes from one filter to UVW1, the scaled UVW1 light curve keep the same shape as the original one."584 For each filter. our sealing law changes its flix level only.," For each filter, our scaling law changes its flux level only."585 The 0.510 keV light curve is also shown in the bottom panel of Figure 16. [or a visual comparison with the scaled UVW1 light curve.," The 0.5–10 keV light curve is also shown in the bottom panel of Figure \ref{fig:om}586 for a visual comparison with the scaled UVW1 light curve."587 It is important to emphasize that the scaled UVWI light curve is just used to make a general comparison rather (han to build strict correlation with the X-ray light curve. since the scaled UVWHI fluxes might be sufficiently different from the true UVWI fluxes due to the known spectral variability of the source in (he optical-UV range.," It is important to emphasize that the scaled UVW1 light curve is just used to make a general comparison rather than to build strict correlation with the X-ray light curve, since the scaled UVW1 fluxes might be sufficiently different from the true UVW1 fluxes due to the known spectral variability of the source in the optical-UV range."588 The sealed UVWI light. curve does not closely track the N-rav. one throughout. the observation., The scaled UVW1 light curve does not closely track the X-ray one throughout the observation.589 The most significant difference might be the sharp transition from the last scaled flux to the first UVWH Πας. whieh does not have a correspondence in the N-rav light curve.," The most significant difference might be the sharp transition from the last U-to-UVW1 scaled flux to the first UVW1 flux, which does not have a correspondence in the X-ray light curve."590 Nevertheless. it is certain that (he. variability. amplitude is significantly smaller in the UVWI band than in the X-ray band.," Nevertheless, it is certain that the variability amplitude is significantly smaller in the UVW1 band than in the X-ray band."591 It is also possible to compare (he OM lieht curves in different filters with the X-ray light curve over the same time intervals. respectively.," It is also possible to compare the OM light curves in different filters with the X-ray light curve over the same time intervals, respectively."592 It is clear Chat (he V. UVW1 and UVM?2 light curves do not follow the X-ray light curve.," It is clear that the V, UVW1 and UVM2 light curves do not follow the X-ray light curve."593 The decay of ~8 ks long in the X-ray light curve is nol seen in the V. band light cuve., The decay of $\sim 8$ ks long in the X-ray light curve is not seen in the V band light curve.594 Instead. the V. light eurve seems to show a well-defined micro-f[lare.," Instead, the V light curve seems to show a well-defined micro-flare."595 The UVWI light curve displays a rise of ~6 ks long. which is nol clear in (he corresponding N-rax light curve.," The UVW1 light curve displays a rise of $\sim 6$ ks long, which is not clear in the corresponding X-ray light curve."596 The UVM? liesht curve shows a decay followed bv a rise. whereas (he N-ray. lieht curve exhibits a rapid decay lollowed by a slow deca.," The UVM2 light curve shows a decay followed by a rise, whereas the X-ray light curve exhibits a rapid decay followed by a slow decay."597 llowever. the U Leht curve appears to track the X-ray. light curve. where the peaks in the U light curve show a delay of ~2 ks with respect to the ones in the X-ray light curve.," However, the U light curve appears to track the X-ray light curve, where the peaks in the U light curve show a delay of $\sim 2$ ks with respect to the ones in the X-ray light curve."598 The OM data also extend the svnchrotron SED of the source to the optical-UV range. where the svnchrotron emission may peak around.," The OM data also extend the synchrotron SED of the source to the optical-UV range, where the synchrotron emission may peak around."599 Figure 17. plots the average, Figure \ref{fig:omsed} plots the average600"In this case the likelihood function for the data D=[5,.53.....53;] is where Baves’s theorem may be stated as where P(o.5|D) is the joint posterior distribution for σ and 5. and P(o) and P(3) are (he prior distributions lor the (wo parameters.","In this case the likelihood function for the data $D=\{s_1,s_2,...,s_M\}$ is where Bayes's theorem may be stated as where $P(\sigma, \gamma |D )$ is the joint posterior distribution for $\sigma$ and $\gamma$, and $P(\sigma )$ and $P(\gamma )$ are the prior distributions for the two parameters."601 Following (he approach for the simple power law. we choose a uniform prior for . given by equation (À5)).," Following the approach for the simple power law, we choose a uniform prior for $\gamma$, given by equation \ref{eq:pl_prior}) )."602 However. the rollover σ appears in equation (D1)) as à scale factor. in which case it is appropriate to use a JelIrevs prior (Jeffrevs 1961: Javnes 2003): With (his choice ancl with the uniform prior for 5 (he joint posterior distribution evaluates to where E is a normalisation constant. which may be determined by numerical integration. musing (he (rapezoicdal rule (Press et 11992).," However, the rollover $\sigma$ appears in equation \ref{eq:PS_plr_rep}) ) as a scale factor, in which case it is appropriate to use a Jeffreys prior (Jeffreys 1961; Jaynes 2003): With this choice and with the uniform prior for $\gamma$ the joint posterior distribution evaluates to where $E$ is a normalisation constant, which may be determined by numerical integration, using the trapezoidal rule (Press et 1992)."603 Posterior distributions for the individual parameters are obtained by marginalization. namely integrating over the unwanted parameters.," Posterior distributions for the individual parameters are obtained by marginalization, namely integrating over the unwanted parameters."604 For example. the marginal posterior distribution for the power-law index is given by Parameter estimates are (hen obtained by taking moments of the marginal posterior distributions.," For example, the marginal posterior distribution for the power-law index is given by Parameter estimates are then obtained by taking moments of the marginal posterior distributions."605 Bavesian model comparison involves taking ratios of the posterior probabilities lor models., Bayesian model comparison involves taking ratios of the posterior probabilities for models.606 The likelihood terms for the models are expanded as integrals over all possible choices, The likelihood terms for the models are expanded as integrals over all possible choices607Figure 8. shows cumulative histograms of the Gime periods over which the field changes occur. zn.+. for the X-class and. M-class [Ires separately and [or all of the flares combined.,"Figure \ref{cumhist} shows cumulative histograms of the time periods over which the field changes occur, $\pi n^{-1}$, for the X-class and M-class flares separately and for all of the flares combined."608 Because the temporal resolution of the data is 1 minute. where zi!<1.0 in the fit to the data. we reset wn+ to 1.0 in constructing these histograms.," Because the temporal resolution of the data is 1 minute, where $\pi n^{-1} < 1.0$ in the fit to the data, we reset $\pi n^{-1}$ to 1.0 in constructing these histograms."609 This occurs in about of our cases compared to in SII05., This occurs in about of our cases compared to in SH05.610 The difference is due to the inclusion of slower field changes in this work. up to 40 minutes. compared to the upper limit of 20 minutes in SILOS.," The difference is due to the inclusion of slower field changes in this work, up to 40 minutes, compared to the upper limit of 20 minutes in SH05."611 The time periods over which the field changes occur do not differ significantly between. X- and M-class flares., The time periods over which the field changes occur do not differ significantly between X- and M-class flares.612 The median value for the A-class [Lares is 13 minutes whereas (he median value for the M-class flares is 15 minutes. (, The median value for the X-class flares is 13 minutes whereas the median value for the M-class flares is 15 minutes. (613The median value for all flares is 1H minutes.),The median value for all flares is 14 minutes.)614 The second plot of Figure 8. shows cumulative histograms of the differences between the GOES start times of the flares and (he start (mes of the corresponding magnetic field change for X-class aud M-class flares separately aud for all of the flares combined., The second plot of Figure \ref{cumhist} shows cumulative histograms of the differences between the GOES start times of the flares and the start times of the corresponding magnetic field change for X-class and M-class flares separately and for all of the flares combined.615" The start time. /,. of the field change is derived [rom the fit parameters. and the time delay. /;. is the time lag between the GOES X-ray start time of the flare (given in Tables 1. and 2)) and the start time of the field change. /.."," The start time, $t_{s}$, of the field change is derived from the fit parameters, and the time delay, $t_d$, is the time lag between the GOES X-ray start time of the flare (given in Tables \ref{mtable} and \ref{xtable}) ) and the start time of the field change, $t_s$."616 In about one third of the cases. (he (ime delays are negative. so it appears (hat (he magnetic field begins to change before the flare occurs.," In about one third of the cases, the time delays are negative, so it appears that the magnetic field begins to change before the flare occurs."617 We emphasize again that Equation (1)) does not represent a physical model., We emphasize again that Equation \ref{atancurve}) ) does not represent a physical model.618 We do not believe that the negative time delays in the second plot in Figure 5 are meaninghul., We do not believe that the negative time delays in the second plot in Figure \ref{cumhist} are meaningful.619 The start (me of the field change. defined by Equation (4)). corresponds to the first point of maximum curvature in the step function fit to the data.," The start time of the field change, defined by Equation \ref{tstart}) ), corresponds to the first point of maximum curvature in the step function fit to the data."620 The longer the time period over which the field change occurs. the shallower (he maximum curvature. and the less certain we can be about the time al which the magnetic field begins to change (see Figure 6. for (wo contrasting examples).," The longer the time period over which the field change occurs, the shallower the maximum curvature, and the less certain we can be about the time at which the magnetic field begins to change (see Figure \ref{strongcols} for two contrasting examples)."621 Moreover. Equation (1)) can represent some measured field changes better than others.," Moreover, Equation \ref{atancurve}) ) can represent some measured field changes better than others."622 For example. if a field echange has instantaneous transilions Irom a constant field (o a steady elige (straight. sloping graph) to a constant field again. then Equation (1)) is doomed to overestimate the field change duration and the estimated start (me. /;. is too early.," For example, if a field change has instantaneous transitions from a constant field to a steady change (straight, sloping graph) to a constant field again, then Equation \ref{atancurve}) ) is doomed to overestimate the field change duration and the estimated start time, $t_s$, is too early."623 This (vpe of error can occur for both abrupt aud gradual field changes but is generally larger for gradual changes., This type of error can occur for both abrupt and gradual field changes but is generally larger for gradual changes.624" In other words. the uneertainty in /, is proportional to the field change duration z»+."," In other words, the uncertainty in $t_s$ is proportional to the field change duration $\pi n^{-1}$."625 Indeed. in our caleulations the error in 1. is dominated by the error in nt. whose 1-0. value is often on the order of a few minutes.," Indeed, in our calculations the error in $t_{s}$ is dominated by the error in $n^{-1}$, whose $\sigma$ value is often on the order of a few minutes."626 The third plot in Figure 8. shows the time period over which the field change occurs. zn.!. against the time delay. /;.," The third plot in Figure \ref{cumhist} shows the time period over which the field change occurs, $\pi n^{-1}$, against the time delay, $t_d$."627 The vertical line separates the field changes that appear to start belore the GOES X-ray signature (iy« 0). at least according to the fit of Equation (1)) to the data. and the field changes that start after the GOES X-ray. signature (/;22 0).," The vertical line separates the field changes that appear to start before the GOES X-ray signature $(t_d < 0$ ), at least according to the fit of Equation \ref{atancurve}) ) to the data, and the field changes that start after the GOES X-ray signature $t_d > 0$ )."628 The, The629It has been suggested by anonymous referee (hat the higher order Fourier amplitudes shown in Figure 3 5 are correlated wilh the first order Fourier amplitude (21) in the same bands (the Fourier intrarelations).,It has been suggested by anonymous referee that the higher order Fourier amplitudes shown in Figure \ref{fig:fig3} \ref{fig:fig5} are correlated with the first order Fourier amplitude $A_1$ ) in the same bands (the Fourier intrarelations).630 These have been examined. [ον example. by 1987). and in the appendix.," These have been examined, for example, by \citep{ant87} and in the appendix."631 However. the Fourier intrarelations are less preferable (han Fourier interrelations for reconstructing the Cepheicl light curves.," However, the Fourier intrarelations are less preferable than Fourier interrelations for reconstructing the Cepheid light curves."632 The reasons are discussed in following examples and in Appendix., The reasons are discussed in following examples and in Appendix.633 Ilere. we reexamine the results of Antonelloetal.(1987). with our data sets and compare them to the Fourier interrelations.," Here, we reexamine the results of \citet{ant87} with our data sets and compare them to the Fourier interrelations."634" We used all “calibrating set Cepheids and pick only the ""good"" OGLE LMC Cepheids (crosses) Irom Figure 3..", We used all “calibrating set” Cepheids and pick only the “good” OGLE LMC Cepheids (crosses) from Figure \ref{fig:fig3}.635" Then we re-plot the ly—sly Fourier intrarelations and the A4,(V)—Ay(/) Fourier interrelation in Figure 20..", Then we re-plot the $A_1-A_2$ Fourier intrarelations and the $A_1(V)-A_1(I)$ Fourier interrelation in Figure \ref{fig:fig20}.636 The ~Calibrating set Cepheids and OGLE LAIC Cepheids are in left ancl right panels. respectively.," The “Calibrating set” Cepheids and OGLE LMC Cepheids are in left and right panels, respectively."637 In the ligure. we distinguished Cepheids with different period ranges: crosses are for Cepheids with periods shorter than 8 days (short-period Cepheid): triangles are for Cepheids with period in between ὃ {ο 14 days (bump Cepheid): aud filled circles are for Cepheids with periods longer than 14 davs (long-period Cepheid).," In the figure, we distinguished Cepheids with different period ranges: crosses are for Cepheids with periods shorter than 8 days (short-period Cepheid); triangles are for Cepheids with period in between 8 to 14 days (bump Cepheid); and filled circles are for Cepheids with periods longer than 14 days (long-period Cepheid)."638 Error bars for each data point are omitted in (he ligure for clarity., Error bars for each data point are omitted in the figure for clarity.639" The top two panels in Figure 20. are Fourier intrarelations in V aud 1 band respectively. and the bottom panel is the Fourier interrelations of 44,(V) and A)."," The top two panels in Figure \ref{fig:fig20} are Fourier intrarelations in V and I band respectively, and the bottom panel is the Fourier interrelations of $A_1(V)$ and $A_1(I)$."640 lt is clear from the figure that the scatter of “ly—As intrarelations are larger than the scatter of A4(V)—M) interrelations., It is clear from the figure that the scatter of $A_1-A_2$ intrarelations are larger than the scatter of $A_1(V)-A_1(I)$ interrelations.641 Furthermore. (he short-period. bump and long-period Cepheids populate different regions in the plots of intrarelations. as is also seen in (1987).," Furthermore, the short-period, bump and long-period Cepheids populate different regions in the plots of intrarelations, as is also seen in \citet{ant87}."642. In contrast. The tightness of correlations in the Fourier interrelations is clear. and less dependent on period distribution.," In contrast, The tightness of correlations in the Fourier interrelations is clear, and less dependent on period distribution."643 These two properties make Fourier interrelations more applicable in reconstructing the light curves than Fourier intrarelations., These two properties make Fourier interrelations more applicable in reconstructing the light curves than Fourier intrarelations.644 The relatively large ranges of the Fourier amplitudes for Cepheids with periods less than 10 days (orlog(P)< 1.0) is one reason lor using the Fourier techniques to reconstruct the Cepheid light curves., The relatively large ranges of the Fourier amplitudes for Cepheids with periods less than 10 days (or$\log(P)<1.0$ ) is one reason for using the Fourier techniques to reconstruct the Cepheid light curves.645 From Figure 3. to 5.. il can be seen that the distribution of the Fourier amplitudes at periods longer than 10 days (or log(/?)> 1.0) show certain trends. which can be used to construct templates light curves as a function of period.," From Figure \ref{fig:fig3} to \ref{fig:fig5}, it can be seen that the distribution of the Fourier amplitudes at periods longer than 10 days (or $\log(P) > 1.0$ ) show certain trends, which can be used to construct templates light curves as a function of period."646 IIowever. the Fourier amplitudes for Cepheids with period less (han LO davs do not show any obvious trends but scalter around certain ranges (as given in Table 1)).," However, the Fourier amplitudes for Cepheids with period less than 10 days do not show any obvious trends but scatter around certain ranges (as given in Table \ref{tab1}) )."647 For example. al a given short. period. AOT) may occupy the range from ~0.1 to ~ 0.4.," For example, at a given short period, $A_1(V)$ may occupy the range from $\sim 0.1$ to $\sim 0.4$ ."648 Therefore. extra care has to be taken," Therefore, extra care has to be taken"649is in the corresponding fori. Le. clustered ito iuini-halos. or eutirely muachistered aud he calculated contributions are in this sense uutuallv exclusive.,"is in the corresponding form – i.e. clustered into mini-halos, or entirely unclustered – and the calculated contributions are in this sense mutually exclusive."650 Towever. recognising that (4) he wninihalos are made up of individual clouds. (i) the mnminihalos are unbiased tracers of the nean deusitv. and (d) the mniüinihalos iutroduce onlv a simall modulation around the mean sky xiehtnuess. we see that in practice the predicted xoperties of the ~mulli-arcsecoud fluctuation veal are larecly independent of whether or not he clouds ire clustered iuto nünibalos.," However, recognising that (i) the minihalos are made up of individual clouds, (ii) the minihalos are unbiased tracers of the mean density, and (iii) the minihalos introduce only a small modulation around the mean sky brightness, we see that in practice the predicted properties of the $\sim$ milli-arcsecond fluctuation peak are largely independent of whether or not the clouds are clustered into minihalos."651 If all the clouds are clustered iuto iumnibhalos. then there would. however. be many fewer clouds very local o the Sun. aud so the low-frequency (1.0. stall fy) power from individual clouds would be much reduced.," If all the clouds are clustered into minihalos, then there would, however, be many fewer clouds very local to the Sun, and so the low-frequency (i.e. small $l$ ) power from individual clouds would be much reduced."652 Ilow do our predictions compare with existing data?, How do our predictions compare with existing data?653 We do not cousider. here. the low-order imltipoles (/= 10) which were measured by CODE (S1uoot et al 1992). because the calculations we have uudertaken are valid onlv for /||.," We do not consider, here, the low-order multipoles $l\la10$ ) which were measured by COBE (Smoot et al 1992), because the calculations we have undertaken are valid only for $l\gg1$."654 TheCODE doetectious at siall ? did. however. create ercat interest in measuring the higher order multipoles. and after much effort expended ou special-purpose experiments there are now several clear detectious of anisotropies on degree scales (e.g. de Bernardis et al 2000: Tlanauy et al 2000: Pivke et al 2002: it ct al 2002).," TheCOBE detections at small $l$ did, however, create great interest in measuring the higher order multipoles, and after much effort expended on special-purpose experiments there are now several clear detections of anisotropies on degree scales (e.g. de Bernardis et al 2000; Hanany et al 2000; Pryke et al 2002; t et al 2002)."655" The peak of the observed signa OT,zT0μ]ν at 1.2200 is roughly 20 times larger hau the model predictions at the same angular scale. for high-latitude fields. aud for ταν o»urposes this small contribution to the observed rower (about )) can be neglected."," The peak of the observed signal – $\delta T_b\simeq70\;656{\rm\mu K}$ at $l\simeq200$ – is roughly 20 times larger than the model predictions at the same angular scale, for high-latitude fields, and for many purposes this small contribution to the observed power (about ) can be neglected."657 However. it nay still be possible to detect the predicted minuiialo anisotropies against the backerouud of the douunant CAB fluctuations. if we select the data appropriately.," However, it may still be possible to detect the predicted mini-halo anisotropies against the background of the dominant CMB fluctuations, if we select the data appropriately."658 In particular the CAIB anisotropies all to 230pls at multipoles /~50. near the peak of the predicted spectrum. wlile the latter attains a value z8ply at |b]=307.," In particular the CMB anisotropies fall to $\simeq30\;{\rm\mu K}$ at multipoles $l\sim50$, near the peak of the predicted spectrum, while the latter attains a value $\simeq8\;{\rm\mu K}$ at $|b|=30^\circ$."659 Data collected by the MAP should be able to reveal this Galactic foreground. provided that the spectrua is close to the assumed ereyv-body form (see 855 and figure 5).," Data collected by the MAP should be able to reveal this Galactic foreground, provided that the spectrum is close to the assumed grey-body form (see 5 and figure 5)."660 To date there has beeu only limited iuterest in the arcnünute-scale anisotropies. because Silk damping is expected to stronglv supress aly primary cosmological anisotropy on these scales (Silk 1968).," To date there has been only limited interest in the arcminute-scale anisotropies, because Silk damping is expected to strongly supress any primary cosmological anisotropy on these scales (Silk 1968)."661 Consequently there is at present oulv a limited amount of data in the region 105z|€10 (Subraluuauvan et al 1997: Dawson ct al 2001: Masou et al 2002)., Consequently there is at present only a limited amount of data in the region $10^3\la l\la10^4$ (Subrahmanyan et al 1997; Dawson et al 2001; Mason et al 2002).662 ere again the observed sigual is large m comparison with the model: 25pls at /~2500 (Mason ct al 2002): roughly an order of magnitude larger than the anisotropies predicted by the present model., Here again the observed signal is large in comparison with the model: $25\;{\rm\mu K}$ at $l\sim2500$ (Mason et al 2002); roughly an order of magnitude larger than the anisotropies predicted by the present model.663 Consequently data at these very high multipoles do not vet provide strong constraints ou the model we have presented., Consequently data at these very high multipoles do not yet provide strong constraints on the model we have presented.664 Moreover these angular scales are below the resolution of the instrumentation carried by MAD. so there is no inuniediate prospect of a major improvement iu sensitivity.," Moreover these angular scales are below the resolution of the instrumentation carried by MAP, so there is no immediate prospect of a major improvement in sensitivity."665 It would. however. be useful to obtain rther imeasurcments of the powoer-spoectrui using eround-based interferoueters. particularly with a view to coustrainiug its latitude dependence. vocause the origin of the observed high-frequency oower (Mason et al 2002) is not clear at present and it remains possible that it is a Galactic signal.," It would, however, be useful to obtain further measurements of the power-spectrum using ground-based interferometers, particularly with a view to constraining its latitude dependence, because the origin of the observed high-frequency power (Mason et al 2002) is not clear at present and it remains possible that it is a Galactic signal."666 For !z910 the anisotropies predicted by our nodel are dominated by the individual clouds. anc nore specifically the closest examples within the area under study: cousequenutlv for these angular scales the miodel predicts ταν little latitude dependence in the power-spectrum.," For $l\gg10^4$ the anisotropies predicted by our model are dominated by the individual clouds, and more specifically the closest examples within the area under study; consequently for these angular scales the model predicts very little latitude dependence in the power-spectrum."667 The comeain of large / is also techuically challenging. in that the sensitivity of an interferometer to surface brightness fluctuations worsens i proportion to 7.," The domain of large $l$ is also technically challenging, in that the sensitivity of an interferometer to surface brightness fluctuations worsens in proportion to $l$."668 Thus the predicted uulli-Nelvwin peak on mulli-caresecond scales is not imunediately opeu to experimental scrutiny., Thus the predicted milli-Kelvin peak on milli-arcsecond scales is not immediately open to experimental scrutiny.669 Fortunately the model predictions can be put to the test in another wav: rather than attempting to measure the anisotropies per se we can simply study the bright source counts., Fortunately the model predictions can be put to the test in another way: rather than attempting to measure the anisotropies per se we can simply study the bright source counts.670 At low frequencies the fux from cach cloud iucreases. as »v7. or faster.. whereas the flux from non-thermal (svuclrotrou) radio sources vpicallv declines with increasing frequency.," At low frequencies the flux from each cloud increases as $\nu^2$, or faster, whereas the flux from non-thermal (synchrotron) radio sources typically declines with increasing frequency."671 Thus ii a shvsurvev for compact sources at high requencies the predicted population should staud out., Thus in a sky-survey for compact sources at high frequencies the predicted population should stand out.672 For the purposes of testing the model. the ideal approach is to make a survey of a large raction of the sky. with sufficient seusitivitv to detect sources having fiux πιο less than Fy.," For the purposes of testing the model, the ideal approach is to make a survey of a large fraction of the sky, with sufficient sensitivity to detect sources having flux much less than $F_{max}$ ."673 The model then predicts that mamy sources with hermal spectra should be detected. and any such," The model then predicts that many sources with thermal spectra should be detected, and any such"674the bottom pancls of Fieure 5..,the bottom panels of Figure \ref{fig:Fig8MillHODerr}.675 The error bars in the SAMs denote the 1o scatter around the mean., The error bars in the SAMs denote the $1\sigma$ scatter around the mean.676 Note that this discrepancy could be less dramatic. as there might be ~25% underestimation in the ZCZÜT calculation of the stellar mass at :~1 due to DEEP? red ealaxy incompleteness (see ZCZO? for details).," Note that this discrepancy could be less dramatic, as there might be $\sim 25\%$ underestimation in the ZCZ07 calculation of the stellar mass at $z\sim 1$ due to DEEP2 red galaxy incompleteness (see ZCZ07 for details)."677 This effect is shown bv the dotted lines in the bottoni panels., This effect is shown by the dotted lines in the bottom panels.678 Even with this potential correction. the discrepaucy is sienificaut.," Even with this potential correction, the discrepancy is significant."679 We note that these discrepancies are present at roughly the same level for SANs. indicating that their cause is of a amore fundamental origin not reflected iu the differences between the two models.," We note that these discrepancies are present at roughly the same level for SAMs, indicating that their cause is of a more fundamental origin not reflected in the differences between the two models."680 It is also worth mentioning that the major diserepaucy between the SAMs and ZCZO7T predictions for the stellar mass erowtli appears to be preseut already at redshift 2., It is also worth mentioning that the major discrepancy between the SAMs and ZCZ07 predictions for the stellar mass growth appears to be present already at redshift 2.681 Frou the results presented i 832.L. we soe that the amount of stars in place in central galaxies by 2~ predicted by the MPA SAM is of the order of the phenomenological results for the amount of stars in place by :~] ," From the results presented in 3.4, we see that the amount of stars in place in central galaxies by $z \sim 2$ predicted by the MPA SAM is of the order of the phenomenological results for the amount of stars in place by $z \sim 1$ ."682The top pancls of Figure 6 compare the predictions of the SAM (solid lines) to the ZCZO7 results for thetotal stellar mass acquired through mereie of sinaller central and satellite galaxies on top of that already in place at +~ 1l. normalized by the final stellar mass at Do0.," The top panels of Figure \ref{fig:Fig9MillHOD} compare the predictions of the SAMs (solid lines) to the ZCZ07 results for the stellar mass acquired through merging of smaller central and satellite galaxies on top of that already in place at $z\sim 1$ , normalized by the final stellar mass at $z\sim 0$."683" For 26201, we plot both the standard estimation (dashed line iu cach panel) aud the couscrvative estimate including the possible correction of the stellar mass at 2~1 (dotted liue)."," For ZCZ07, we plot both the standard estimation (dashed line in each panel) and the conservative estimate including the possible correction of the stellar mass at $z \sim 1$ (dotted line)."684 Here the agreement is better. especially at high halo masses.," Here the agreement is better, especially at high halo masses."685The difference between,The difference between68624 Galactic globular clusters covering tlie wide metallicity range from -2.12 to -0.49 dex was used (equations 1 and 2).,24 Galactic globular clusters covering the wide metallicity range from -2.12 to -0.49 dex was used (equations 1 and 2).687 It was demonstrated by these authors that these calibrations agree verv well with the predictions from theoretical models., It was demonstrated by these authors that these calibrations agree very well with the predictions from theoretical models.688 ΜΠΟΡΩ5567—0.31x[Fe/1I] ΜΟΙ—6.980.58x[Fe/1I] Adopting the metallicities and reddenings listed in Table 2. and our measured TRGB magnitudes. (he following true distaunce moduli were calculated from these calibration equations: Carina: 20.09 + 0.03 (J band). 20.13 + 0.04 (IX. Fornax: 20.84 + 0.03 (J band). 20.84 + 0.04 (IN. banc) For both galaxies. the respective distances from the J and Ix bands agree within the statistical uncertainties of the TRGB magnitudes.," ${\rm {M}_{J}^{TRGB} = -5.67 - 0.31 \times [Fe/H]}$ ${\rm {M}_{K}^{TRGB} = -6.98 - 0.58 \times [Fe/H]}$ Adopting the metallicities and reddenings listed in Table 2, and our measured TRGB magnitudes, the following true distance moduli were calculated from these calibration equations: Carina: 20.09 $\pm$ 0.03 (J band), 20.13 $\pm$ 0.04 (K Fornax: 20.84 $\pm$ 0.03 (J band), 20.84 $\pm$ 0.04 (K band) For both galaxies, the respective distances from the J and K bands agree within the statistical uncertainties of the TRGB magnitudes."689 With the assumed uncertainty of the photometric J and IX band zero points of 0.02 mag. an estimated error associated to the extinction determinations of 0.02 mag. and an assumed uncertaintv in the adopted metallicities of 0.2 dex we calculate the total svstematic uncertainties of our distance moduli determinations for Carina and Formax (o be of 0.12 mag and 0.14 for the J and Ix band fillers. respectively. for both galaxies.," With the assumed uncertainty of the photometric J and K band zero points of 0.02 mag, an estimated error associated to the extinction determinations of 0.02 mag, and an assumed uncertainty in the adopted metallicities of 0.2 dex we calculate the total systematic uncertainties of our distance moduli determinations for Carina and Formax to be of 0.12 mag and 0.14 for the J and K band filters, respectively, for both galaxies."690 The dominant part in the svstematie uncertainties of the current infrared TRGB distances to Carina and Fornax comes from the assumed uncertainties on (he appropriate metallicities of (he red eiant branch lip stars., The dominant part in the systematic uncertainties of the current infrared TRGB distances to Carina and Fornax comes from the assumed uncertainties on the appropriate metallicities of the red giant branch tip stars.691 Their effect on the distance has been estimated [rom the metallicity coefficients in equations 1 and 2., Their effect on the distance has been estimated from the metallicity coefficients in equations 1 and 2.692 It should be noted here that we did not take into account any contribution from possible svstematic errors in the coefficients themselves in the calibration of Valenti. Ferraro. and Origlia (2004).," It should be noted here that we did not take into account any contribution from possible systematic errors in the coefficients themselves in the calibration of Valenti, Ferraro, and Origlia (2004)."693 As our final distance results. we adopt a (rue distance modulus of (20.11 4 0.13) mag for the Carina dSph galaxy. and (20.84 + 0.15) mag lor the Fornax dSph galaxy.," As our final distance results, we adopt a true distance modulus of (20.11 $\pm$ 0.13) mag for the Carina dSph galaxy, and (20.84 $\pm$ 0.15) mag for the Fornax dSph galaxy."694 Results of previous distance determinations to the Fornax and Carina galaxies [rou different methods reported in the literature are eiven in Table 3., Results of previous distance determinations to the Fornax and Carina galaxies from different methods reported in the literature are given in Table 3.695 Pietrzviisski. Gieren and," Pietrzyńsski, Gieren and"6961996 September pancl)) for the spectral regiou enconipassiug Al656 (it has to be kept in nünd that because of the paucity of the photoimoetric data. the streusth of the spectral lines in these coutinuuni-normalized spectra has not been corrected for the varving continuun fux level).,"1996 September ) for the spectral region encompassing $\lambda$ 4686 (it has to be kept in mind that because of the paucity of the photometric data, the strength of the spectral lines in these continuum-normalized spectra has not been corrected for the varying continuum flux level)."697 The Temporal Variance Spectr (TVS: Fullertonctal. 1996)) has been used to assess the level of spectral variability as a function of wavoleusth., The Temporal Variance Spectrum (TVS; \cite{Fullertontvs}) ) has been used to assess the level of spectral variability as a function of wavelength.698 The (square root of the) TVS. eiving the typical Usze of the deviations from a template-weighted mean spectrum (expressed iu percentage of the contiuuua flux) is shown. along with the 09.0 confidence levelfor variability. iu Figure L..," The (square root of the) TVS, giving the typical “size” of the deviations from a template-weighted mean spectrum (expressed in percentage of the continuum flux) is shown, along with the 99.0 confidence levelfor variability, in Figure \ref{f4}."699 As can be seen. lughly sienificant variability affects the emission lines. with the notable exception of A 1915 for which oulv little evidence for variability is found.," As can be seen, highly significant variability affects the emission lines, with the notable exception of $\lambda$ 4945 for which only little evidence for variability is found."700" Abu peaks (ic. locatious of ""preferential variability) can be distinguished in the TVS."," Many peaks (i.e., locations of “preferential” variability) can be distinguished in the TVS."701 The locations of these peaks (in terms of the projected velocity referred to the laboratory rest waveleneth of the spectral feature iu are quoted in Table 3., The locations of these peaks (in terms of the projected velocity referred to the laboratory rest wavelength of the spectral feature in question) are quoted in Table 3.702 This investigation shows that: ANN»a) the variability often extends to velocitics conrparable the wind terminal velocity ος 2: 2135 kan Hl: Rochowiez&Niedzielski 19953). eg. c0 1790 kin ον the relatively uubleuded line A 1859: (b) the TVS structure iade up of several subpeaks presents sole situilarities for the various catures.," This investigation shows that: (a) the variability often extends to velocities comparable to the wind terminal velocity $v_{\infty}$ $\approx$ 2135 km $^{-1}$; \cite{Rocho}) ), e.g., $v$ $\approx$ – 1790 km $^{-1}$ for the relatively unblended line $\lambda$ 4859; (b) the TVS structure — made up of several subpeaks — presents some similarities for the various features."703 However. the velocities quoted in Table 3 are certainly entached of considerable unucertaimties (ec... because of blending of TVS subpeaks) making dificult a clear statement as fo whether the variability takes place at the same characteristic velocities im differcut lines.," However, the velocities quoted in Table 3 are certainly entached of considerable uncertainties (e.g., because of blending of TVS subpeaks) making difficult a clear statement as to whether the variability takes place at the same characteristic velocities in different lines."704 The TVS analysis alsoreveals substantial variability at the location of the P. Cyeui absorption component of ALGOL L))., The TVS analysis alsoreveals substantial variability at the location of the P Cygni absorption component of $\lambda$ 4604 \ref{f4}) ).705 This mainly results from the transition of the ALGOL feature from) a pure enussiou iu 1995 October to à P. Cveui line-profile in 1996 September (Fis.5))., This mainly results from the transition of the $\lambda$ 4604 feature from a pure emission in 1995 October to a P Cygni line-profile in 1996 September \ref{f5}) ).706 Noc car variations iu the streneth of this absorption trough on a daily timescale are observed., No clear variations in the strength of this absorption trough on a daily timescale are observed.707 An eulhauced peak in the TVS cau also be found at thelocation where the carbon triplet ADSOG and A5876 meree lj)., An enhanced peak in the TVS can also be found at thelocation where the carbon triplet $\lambda$ 5806 and $\lambda$ 5876 merge \ref{f4})).708 The large daily changes affecting AS5SO6 and/or AbSTG iu October 1995 and September 1996 are illustrated in Figure 6 (this phenomenon is no observed in 1996 Novoniber)., The large daily changes affecting $\lambda$ 5806 and/or $\lambda$ 5876 in October 1995 and September 1996 are illustrated in Figure \ref{f6} (this phenomenon is not observed in 1996 November).709 The high level of variability observed at this particular location is likely due to the superpositiou of two distinct type of variabilitv: (a) red-wing variability of ADSOG as observed in other spectral features (e.g.Herthe AlG86: ly): (b) variations in the strength of IB Creni absorption component of A5876.? theThe latter interpretation is supported bv the fact that projected velocity of the peak in the TVS (ez 1980 kins |. referred to the rest laboratory wavelength) matches fairly well the wind terminal velocity (ος. m 2135 luu sty .," The high level of variability observed at this particular location is likely due to the superposition of two distinct type of variability: (a) red-wing variability of $\lambda$ 5806 as observed in other spectral features (e.g., $\lambda$ 4686; \ref{f4}) ); (b) variations in the strength of the P Cygni absorption component of $\lambda$ The latter interpretation is supported by the fact that the projected velocity of the peak in the TVS $v$ $\approx$ – 1980 km $^{-1}$, referred to the rest laboratory wavelength) matches fairly well the wind terminal velocity $v_{\infty}$ $\approx$ 2135 km $^{-1}$ )."710 Considering the relatively modest level of variability affecting the red-wing part of the line profiles in l)). it is likely that changes in the streueth of the P Cyeni absorption componcut of the feature contribute to the observed changes.," Considering the relatively modest level of variability affecting the red-wing part of the line profiles in \ref{f4}) ), it is likely that changes in the strength of the P Cygni absorption component of the feature contribute to the observed changes."711 A possible correlated pattern of variability in two differcut spectral features has been investigated by calculating the Spearman rauk-order correlation matrices (sce. c.g. Johus&Basri 1995)). whose elements r(4j) vield the deeree of correlation between the liue iutensity variations at pixels / aud j in cach line profile. respectively.," A possible correlated pattern of variability in two different spectral features has been investigated by calculating the Spearman rank-order correlation matrices (see, e.g., \cite{Johnsbasri}) ), whose elements $r(i,j)$ yield the degree of correlation between the line intensity variations at pixels $i$ and $j$ in each line profile, respectively."712 Tn the case of perfectly. positively correlate varlations. a matrix unity is obtained.," In the case of perfectly, positively correlated variations, a matrix unity is obtained."713 The correlation matrices of A5 112 with AL6s86.Πο ALS59. aud “ALOIS are shown iu Figure 7 in the form of contour plots. where the lowest contour indicates a sigenificaut positive (or negative) correlation at the 99.5 confidence leve (the other specrallimes were uot covered chough to be included iun the analysis).," The correlation matrices of $\lambda$ 5412 with $\lambda$ 4686, $\lambda$ 4859, and $\lambda$ 4945 are shown in Figure \ref{f7} in the form of contour plots, where the lowest contour indicates a significant positive (or negative) correlation at the 99.5 confidence level (the other spectrallines were not covered enough to be included in the analysis)."714 These matrices are displaved in the projected velocity frame (πο. to the line laboratory rest waveleneth)., These matrices are displayed in the projected velocity frame (referred to the line laboratory rest wavelength).715 A senificaut positive correlation is ecucrally found between the pattern of variability of A5112 ancl A L686, A significant positive correlation is generally found between the pattern of variability of $\lambda$ 5412 and $\lambda$ 4686.716 The same conclusion. however restricted to the velocity range € 1000. | 1000) kin LO holds for the variations affecting A5112 and A1859.," The same conclusion, however restricted to the velocity range (– 1000, + 1000) km $^{-1}$, holds for the variations affecting $\lambda$ 5412 and $\lambda$ 4859."717" Tn contrast. the (veal) variations of ALOLS are apparently not linked to those of A5112 (the same is true for ASS06 and λοδτο),"," In contrast, the (weak) variations of $\lambda$ 4945 are apparently not linked to those of $\lambda$ 5412 (the same is true for $\lambda$ 5806 and $\lambda$ 5876)."718 Various actors are susceptible to mask, Various factors are susceptible to mask719 Various actors are susceptible to mask., Various factors are susceptible to mask720Ndtars initiative. administered by JPL. Pasadena. CA.,"NStars initiative, administered by JPL, Pasadena, CA."721 D.IET. acknowledges support. [rom NASA through a Space Telescope Science Institute grant to Gary Bernstein., D.E.T. acknowledges support from NASA through a Space Telescope Science Institute grant to Gary Bernstein.722 Thanks to Adam Burrows for making his models available for our use and for answering our questions about ihem., Thanks to Adam Burrows for making his models available for our use and for answering our questions about them.723 PRA. thanks Nelle Cruz for her help in perfecting the plots in this paper., P.R.A. thanks Kelle Cruz for her help in perfecting the plots in this paper.724 The authors would also like to thank the releree for his/her valuable comments and quick response. as well as our editor. Paula Szkocly. for her timeliness and excellent choice of releree.," The authors would also like to thank the referee for his/her valuable comments and quick response, as well as our editor, Paula Szkody, for her timeliness and excellent choice of referee."725The orbital model provides ouly the (a.¢.7) distribution of the NEO population aud we expect that the eccentricity of the Earth's orbit is a small correction to the impactor clistribution. so for what follows we have modeled the Earth's heliocentric orbit as perfectly. circular.,"The orbital model provides only the $(a,e,i)$ distribution of the NEO population and we expect that the eccentricity of the Earth's orbit is a small correction to the impactor distribution, so for what follows we have modeled the Earth's heliocentric orbit as perfectly circular."726 As a result we can. without loss of generality. take all encounters to occur at (1 AU.0.0) in heliocentric coordinates. where we have lost knowledge of the day of the vear of the encounters (although we can easily average over the year bypos/-facto selecting a random azimuth for the Earth's spin pole at the time of a projectile’s arrival at the top of the atinosphere).," As a result we can, without loss of generality, take all encounters to occur at (1 AU,0,0) in heliocentric coordinates, where we have lost knowledge of the day of the year of the encounters (although we can easily average over the year by selecting a random azimuth for the Earth's spin pole at the time of a projectile's arrival at the top of the atmosphere)."727 With this restriction. each Eartli-crossiug orbit cau lave an encounter in one of four geometries cepeudiug on the argument oL pericenter w and the true anomaly f. which must satisly: By construction. the encounter must occur at either the ascending or desceudiug uode aloug the a-axis. and so the longitude of ascending node is Q=0 or s.," With this restriction, each Earth-crossing orbit can have an encounter in one of four geometries depending on the argument of pericenter $\omega$ and the true anomaly $f$, which must satisfy: By construction, the encounter must occur at either the ascending or descending node along the $x$ -axis, and so the longitude of ascending node is $\Omega$ =0 or $\pi$."728 Taking f and w in [0.22). for ascending encounters. f=2x—w for either encounters with pericenters above (&=[0.3)) or below (eo= [1.22)) the ecliptic.," Taking $f$ and $\omega$ in $[0,2\pi)$, for ascending encounters, $f=2\pi-\omega$ for either encounters with pericenters above $\omega=[0,\pi)$ ) or below $\omega=[\pi,2\pi)$ ) the ecliptic."729 If the encounter occurs at the descending node. f=x—w for post-pericenter eucounters and f=3$—w lor pre-pericenter eucounters.," If the encounter occurs at the descending node, $f = \pi - \omega$ for post-pericenter encounters and $f = 3\pi - \omega$ for pre-pericenter encounters."730 With this in miud. we effectively quadruple the number of initial conditions to 65228.," With this in mind, we effectively quadruple the number of initial conditions to 65228."731 With the longitude of asceudiug uode fixed Ge., With the longitude of ascending node fixed (ie.732 Q=0or x). we then coustruct a plethora of incoming initial couditious based ou the orbital elements from the cdebiased NEO mocel converte to Cartesian coordinates.," $\Omega = 0733\mathrm{\ or\ }\pi$ ), we then construct a plethora of incoming initial conditions based on the orbital elements from the debiased NEO model converted to Cartesian coordinates."734 For each initial orbit. all four of the encounter geometries are equally likely.," For each initial orbit, all four of the encounter geometries are equally likely."735" We randomly choose a particle for a flyby based on its eucounter probability with the Eartl as judged by an Oppik collision probability calculation (Donesefal,1999).", We randomly choose a particle for a flyby based on its encounter probability with the Earth as judged by an Öppik collision probability calculation \citep{dones99}.736. Gravitational focusing by the Earth wasnof included iu the encounter probability estimate as an increased frequency of Earth deliveries will occur uaturally duriug the flyby phase if the Earth's gravity is iniportant., Gravitational focusing by the Earth was included in the encounter probability estimate as an increased frequency of Earth deliveries will occur naturally during the flyby phase if the Earth's gravity is important.737 Both Earth aud a test particle (TP) are then placed at the nodal intersection aud. movec backwards on their respective orbits until the separation between the NEO aud the Earth is 0.02 AU., Both Earth and a test particle (TP) are then placed at the nodal intersection and moved backwards on their respective orbits until the separation between the NEO and the Earth is 0.02 AU.738 At this point. we create a disk of 10? non-interacting test particles. meant to represent asteroids or Comets. centered on the chosen orbit.," At this point, we create a disk of $10^5$ non-interacting test particles, meant to represent potentially-impacting asteroids or comets, centered on the chosen orbit."739 A short numerical integration is run for each of the 65228 initial coucitious aud oue TP trajectory that results in au arrival at the Earth in each flyby is placed into a table of new initial conditions., A short numerical integration is run for each of the 65228 initial conditions and one TP trajectory that results in an arrival at the Earth in each flyby is placed into a table of new initial conditions.740" This procedure is performed because curing the ""backup phase” to separate the Earth aud TP by 0.02 AU. gravitational focusing was not accounted for."," This procedure is performed because during the “backup phase” to separate the Earth and TP by 0.02 AU, gravitational focusing was not accounted for."741 The omission could result in the particle missing the Earth iu a forward integration. as the Eartli's gravity would be present. modifying the chosen trajectory.," The omission could result in the particle missing the Earth in a forward integration, as the Earth's gravity would be present, modifying the chosen trajectory."742 This gives us a fiual set oL 65228 initial trajectories that strike the Earth when a forward integration is performed., This gives us a final set of 65228 initial trajectories that strike the Earth when a forward integration is performed.743 For convenieuce we then convert [roi heliocentric coordinates to a geocentric [rame of refereuce., For convenience we then convert from heliocentric coordinates to a geocentric frame of reference.744 For our simulations. oue of the new initial couclitious is raucomly chosen based ou a newly," For our simulations, one of the new initial conditions is randomly chosen based on a newly"745"For an isothermal plasma in hydrostatic equilibrium, the gas mass fraction. fi... is calculated as the ratio of the mass of the gas and of the total gravitating mass. Adio. within the radius. Z?4. at which the given mean overdensity of the total mass within cluster. A. with respect to the background value. Quipo. is reached: where Ry=06di, is the physical radius. @ is the angular separation. dau. is the angular diameter distance.Zi... 1s the ICM temperature. & is the Boltzmann constant. j£ is the mean molecular weight in a.m.u.","For an isothermal plasma in hydrostatic equilibrium, the gas mass fraction, $f_{\rm gas}$, is calculated as the ratio of the mass of the gas and of the total gravitating mass, $M_{\rm grav}$, within the radius, $R_{\Delta}$, at which the given mean overdensity of the total mass within cluster, $\Delta$, with respect to the background value, $\Omega_{\rm m}\rho_{\rm c}$, is reached: where $R_{\Delta} = \theta \ d_{\rm ang}$ is the physical radius, $\theta$ is the angular separation, $d_{\rm ang}$ is the angular diameter distance,$T_{\rm gas}$ is the ICM temperature, $k$ is the Boltzmann constant, $\mu$ is the mean molecular weight in a.m.u."746" (~ 0.6). C is the gravitational constant and 7, is the proton mass."," $\sim 0.6$ ), $G$ is the gravitational constant and $m_{\rm p}$ is the proton mass."747 The surface brightness. (8) is given by the integral along the line of sight: Hence. the gas density. fox. iS proportional to diat.," The surface brightness, $S(\theta)$ is given by the integral along the line of sight: Hence, the gas density, $\rho_{\rm gas}$ is proportional to $d_{\rm748ang}^{-0.5}$."749 Combining this with the other dependence in Eq. Al..," Combining this with the other dependence in Eq. \ref{eqn:fgas},"750" For £4,=0. d, can be written as The mean overdensity. A. for Oj-2 0 is given by (e.g. Kitayama Suto 1996: Henry 2000) where(Q,.1)2(Q4.—DG|zu)."," For $\Omega_{\rm k}=0$, $d_{\rm ang}$ can be written as The mean overdensity, $\Delta$, for $\Omega_{\rm k}$ = 0 is given by (e.g. Kitayama Suto 1996; Henry 2000) where $(\Omega_{{\rm m},z}^{-1} -1) =(\Omega_{\rm m}^{-1}-1)/(1+z)^3$."751 The observed mass profile is calculated as and is proportional to 7?4 for a virialised system so that Lahav (2000) (see also Bridle 2000. Lahav 20012 2001b). generalised the standard procedure of combining likelihoods using the “Hyper-Parameters’ approach.," The observed mass profile is calculated as and is proportional to $R_{\Delta}$ for a virialised system so that Lahav (2000) (see also Bridle 2000, Lahav 2001a 2001b), generalised the standard procedure of combining likelihoods using the 'Hyper-Parameters' approach."752 The conventional way of combining likelihood functions of different data sets is either to give all the sets the same statistical weight or to assign weights in an ad-hoc way., The conventional way of combining likelihood functions of different data sets is either to give all the sets the same statistical weight or to assign weights in an ad-hoc way.753" The ""Hyper-Parameters? method generalises this approach by assigning each data a relative weight.", The `Hyper-Parameters' method generalises this approach by assigning each data a relative weight.754 Given two independent data sets Dy and Dg (with Noy and Ne data points respectively). our approach is to combine the 47s in the following manner: where o and 2 are “Hyper-Parameters(HPs).," Given two independent data sets $D_{A}$ and $D_{B}$ (with $N_{A}$ and $N_{B}$ data points respectively), our approach is to combine the $\chi^{2}$ s in the following manner: where $\alpha$ and $\beta$ are `Hyper-Parameters'(HPs)."755 The maximum likelihood of a given model is estimated by minimising the above quantity., The maximum likelihood of a given model is estimated by minimising the above quantity.756" We calculate the \7s using the equation below: where the sum is over the number of measurements. c; is the error for each data point and w is the vector of free parameters we wish to determine (e.g. Qu, and /7)."," We calculate the $\chi^2$ s using the equation below: where the sum is over the number of measurements, $\sigma_{i}$ is the error for each data point and $\bfw$ is the vector of free parameters we wish to determine (e.g. $\Omega_{\rm m}$ and $h$ )."757 The HPs are eliminated by marginalisation over à and 3: In order to evaluate the above integral. we use Bayes” theorem to write the following relations: and We ulso assume the following: and We take the prior probabilities in Eq.," The HPs are eliminated by marginalisation over $\alpha$ and $\beta$ : In order to evaluate the above integral, we use Bayes' theorem to write the following relations: and We also assume the following: and We take the prior probabilities in Eq."758 BS as Jeffreys” uniform priors in the log. (Ina)=P(In3j)I.," \ref{eqn:prior} as Jeffreys` uniform priors in the log, $P(\ln \alpha) = P(\ln \beta) =1$."759 Assuming Gaussianity. we write P(Di[w.a)xQnexp(5VÀ) and similarly for Dg. It then follows that the probability for the parameters w given the data sets is: To find the best fit parameters w requires us to minimise the above probability in the w space.," Assuming Gaussianity, we write $P(D_{A} | \bfw, \alpha) \; \propto \;760\alpha^{N_{A}/2}\; \exp (-{\alpha \over 2} \chi_{A}^{2} )$ and similarly for $D_{B}$ It then follows that the probability for the parameters $\bfw$ given the data sets is: To find the best fit parameters $\bfw$ requires us to minimise the above probability in the $\bfw$ space."761 It is as easy to calculate this statistic as the standard X7. and it can be generalized for any number of data sets., It is as easy to calculate this statistic as the standard $\chi^2$ and it can be generalized for any number of data sets.762 Since a and ;; have been eliminated from the analysis by marginalisation they do not haveparticular values that ean be quoted., Since $\alpha$ and $\beta$ have been eliminated from the analysis by marginalisation they do not haveparticular values that can be quoted.763Rather. each value of à. ,"Rather, each value of $\alpha$ "764As we have shown that tropical overestimation only composed a relatively small fraction in (he sample. the setup of Figure 11 amore or less represents (he situation of mid-to-high latitude area.,"As we have shown that tropical overestimation only composed a relatively small fraction in the sample, the setup of Figure \ref{fig11} more or less represents the situation of mid-to-high latitude area."765 This is affirmed by the FBI value which lies way below 1. suggesting a global underestimation of convective clou.," This is affirmed by the FBI value which lies way below 1, suggesting a global underestimation of convective cloud."766" The PPF varies around 0.6 and creates a decent picture of the forecast ability. but the rare occurrence of convective eloud in most areas will lead (o a significant fraction of PPF being contributed [rom ""Z events (not-Iorecasted and not-observed events). so we must take POD and FAR into account for a unbiased view."," The PPF varies around 0.6 and creates a decent picture of the forecast ability, but the rare occurrence of convective cloud in most areas will lead to a significant fraction of PPF being contributed from “Z” events (not-forecasted and not-observed events), so we must take POD and FAR into account for a unbiased view."767 From POD we notice that only slightly less than half of the convective cloud can be detected by the model., From POD we notice that only slightly less than half of the convective cloud can be detected by the model.768 Since convective cloud is most commonly seen in tropical area. the POD for mid-to-high latitude area must be lower.," Since convective cloud is most commonly seen in tropical area, the POD for mid-to-high latitude area must be lower."769 IIowever. globally speaking. the model is still well skilled as the FAR. is about 2 times lower than the POD.," However, globally speaking, the model is still well skilled as the FAR is about 2 times lower than the POD."770 To study the reliability of cloud forecast from the GES model as a relerence of astronomical, To study the reliability of cloud forecast from the GFS model as a reference of astronomical771"In this paper we presented a new NLTE radiation transport code, which can be used to calculate synthetic spectra for all types of SNe at intermediate and late epochs.","In this paper we presented a new NLTE radiation transport code, which can be used to calculate synthetic spectra for all types of SNe at intermediate and late epochs."772 Our treatment of intermediate epochs opens a new window for SN spectral analysis., Our treatment of intermediate epochs opens a new window for SN spectral analysis.773" Currently, is working in spherical symmetry, but a three-dimensional version may be available in the future."," Currently, is working in spherical symmetry, but a three-dimensional version may be available in the future."774 In its one-dimensional version the code can be used for spectral modelling of observed SN spectra or for calculating synthetic spectra of (approximately) spherically symmetric SN explosion models., In its one-dimensional version the code can be used for spectral modelling of observed SN spectra or for calculating synthetic spectra of (approximately) spherically symmetric SN explosion models.775Type [a supernovae (SNe Ia) are generally believed to be the thermonuclear explosions of carbon-oxygen white dwarfs (CO WDs) in binaries (for a review see Nomotoetal. 1997)).,Type Ia supernovae (SNe Ia) are generally believed to be the thermonuclear explosions of carbon-oxygen white dwarfs (CO WDs) in binaries (for a review see \cite{nom97}) ).776 Because of an uniform luminosity. SNe [a are used as the standard candlelight to determine the cosmological distances. and estimate the cosmological parameters © and A (eg. Riessetal.1906.Perlmutteretal. 1999)).," Because of an uniform luminosity, SNe Ia are used as the standard candlelight to determine the cosmological distances, and estimate the cosmological parameters $\Omega$ and $\Lambda$ (e.g. \cite{ries98,perl99}) )."777 However some key issues including the properties of their progenitors and the physical mechanisms of the explosion are still. poorly known by astrophysicists (Hillebrandt&Niemeyer2000.RópkeHillebrandt2005.Wangetal.2008.Podsiadlowski 2008)).," However, some key issues including the properties of their progenitors and the physical mechanisms of the explosion are still poorly known by astrophysicists \cite{hill00,rop05,wang08,pod08}) )."778 At present. there exist two progenitor models of SNe la. r e single-degenerate model (Whelan&Iban1973.Nomoto 1982)) and double-degenerate model (Iben&Tutukov1984.Webbink 1984)).," At present, there exist two progenitor models of SNe Ia, i. e. single-degenerate model \cite{whel73,nom82}) ) and double-degenerate model \cite{iben84,webb84}) )."779 Over the past decade. many groups have widely investigated the single-degenerate model. in which the CO WD accretes H/He-rich material from a non-degenerate companion star.," Over the past decade, many groups have widely investigated the single-degenerate model, in which the CO WD accretes H/He-rich material from a non-degenerate companion star."780 In this scenario. the donor star of WD may be a main-sequence star. a subgiant star or a red-giant star (see Hachisu et al.," In this scenario, the donor star of WD may be a main-sequence star, a subgiant star or a red-giant star (see Hachisu et al."781 1996: Li van den Heuvel 1997; Hachisu et al., 1996; Li van den Heuvel 1997; Hachisu et al.782 1999a.b: Langer et al.," 1999a,b; Langer et al."783 2000: Han Podsiadlowski 2004. 2006. Chen Li 2007. Han 2008. Chen Li 2009. Meng et al.," 2000; Han Podsiadlowski 2004, 2006, Chen Li 2007, Han 2008, Chen Li 2009, Meng et al."784 2009. Lü et al.," 2009, Lü et al."785 2009. Wang et al.," 2009, Wang et al."786 2010a. Meng Yang 2010a.b).," 2010a, Meng Yang 2010a,b)."787 Limongi&Tornambe(1991) have firstly studied. the evolution of the binary consisting of a CO WD and a He star. In which the CO WD accretes He matter from the He star and grows its mass to the canonical Chandrasekhar limit of 14M...," \cite{limo91} have firstly studied the evolution of the binary consisting of a CO WD and a He star, in which the CO WD accretes He matter from the He star and grows its mass to the canonical Chandrasekhar limit of $1.4M_{\odot}$."788 Yoon Langer (2003) also found that CO WD + He star systems can form a reliable channel producing SNe la. Recently. Wangetal.(2009a) systematically explored the evolution of 2600 close WD binaries including a He MS star or He subgiant. and obtained the parameter spaces for the progenitor of SNe Ia. Using a detailed binary population synthesis approach. Wang et al. (," Yoon Langer (2003) also found that CO WD + He star systems can form a reliable channel producing SNe Ia. Recently, \cite{wang09a} systematically explored the evolution of 2600 close WD binaries including a He MS star or He subgiant, and obtained the parameter spaces for the progenitor of SNe Ia. Using a detailed binary population synthesis approach, Wang et al. ("7892009b) suggested that this channel can contribute a SN Ia birthrate of 3x107yr! in the Galaxy. and can result in the short delay times (<100Mvr) between the formation of the progenitor systems and the explosions.,"2009b) suggested that this channel can contribute a SN Ia birthrate of $3\times 10^{-4}~\rm yr^{-1}$ in the Galaxy, and can result in the short delay times $\la100\rm Myr$ ) between the formation of the progenitor systems and the explosions."790 Recently. overluminous SN Ia 2003fe has been detected (Astieretal. 2006)). and its explosive mass was estimated to be ~2.1M. (Howelletal.2006)) |," Recently, overluminous SN Ia 2003fg has been detected \cite{asti06}) ), and its explosive mass was estimated to be $\sim7912.1~M_{\odot}$ \cite{how06}) )."792 Later several possible overluminous SNe la 200657. 20071. and 2009de were also discovered (Hickenetal.2007.YuanTanaka2010.Scalzoetal.2010.Silverman 2010)).," Later, several possible overluminous SNe Ia 2006gz, 2007if, and 2009dc were also discovered \cite{hick07,yuan07,tana10,scal10,silv10}) )."793 The. differential rotation may support these massive WDs (Yoonetal.2004.Yoon&Langer2004. 2005)). which may also result. from. the merger. of two massive WDs (Tutukov&Yungelson1994.Howell2001.Piersantietal. 2003).," The differential rotation may support these massive WDs \cite{yoon04a,yoon04b,yoon05}) ), which may also result from the merger of two massive WDs \cite{tutu94,how01,pier03}) )."794 Based. on the single degenerate model and the assumption that the WD differentially rotate. Chen Li (2009) have explored the evolution of close binaries consisting of a WD and a H main sequence star.," Based on the single degenerate model and the assumption that the WD differentially rotate, Chen Li (2009) have explored the evolution of close binaries consisting of a WD and a H main sequence star."795 Their results indicate that. for an initial massive WD with 1.2M. the maximum explosive mass of the WDs is 1.76Mis.," Their results indicate that, for an initial massive WD with $1.2~M_{\odot}$, the maximum explosive mass of the WDs is $1.76~M_{\odot}$."796 It is an interesting issue to explore the progenitors of overluminous SNe Ia based on the single-degenerate model., It is an interesting issue to explore the progenitors of overluminous SNe Ia based on the single-degenerate model.797 In this paper. we attempt to explore whether the WD + He star systems can produce overluminous SNe la. To obtain the distribution of the initial He star mass and the initial orbital period. of the progenitor binaries. we have calculated the evolution of 1000 WD binaries including a He star and a rotating CO WD.," In this paper, we attempt to explore whether the WD + He star systems can produce overluminous SNe Ia. To obtain the distribution of the initial He star mass and the initial orbital period of the progenitor binaries, we have calculated the evolution of 1000 WD binaries including a He star and a rotating CO WD."798 In section 2. we give a detailed description of input physics including the formation of WD + He star systems and the binary evolution code.," In section 2, we give a detailed description of input physics including the formation of WD + He star systems and the binary evolution code."799 In section 3 we present the calculated results., In section 3 we present the calculated results.800" Finally. a brief discussion and summary are presented,"," Finally, a brief discussion and summary are presented."801node in a reference frame defined by the total angular momentum vector.,node in a reference frame defined by the total angular momentum vector.802" ForJ1903+0327, we obtain a maximum value of ὡς=Jox7.910° ""/ century."," For, we obtain a maximum value of $\dot{\omega}_s = J_2\,\times \, 7.9 \times 10^{5}$ / century."803" As we have shown in 23.1, the companion star has a mass, age and temperature similar to that of the Sun."," As we have shown in \ref{sec:oresults}, the companion star has a mass, age and temperature similar to that of the Sun."804 Such stars should rotate slowly like the Sun ?;; the latter has a rotational velocity of voto= 2kkmss~'.," Such stars should rotate slowly like the Sun \cite{iab+09}; the latter has a rotational velocity of $v_\mathrm{rot, \odot} =8052$ $^{-1}$."806" This should result in a quadrupolar moment similar to that of the Sun, Joo~1.7x1077."," This should result in a quadrupolar moment similar to that of the Sun, $J_{2, \odot} \sim 1.7 \times 10^{-7}$."807" For this value of Jo we get ws~07013/century, about seven times smaller than the measurement uncertainty of wo."," For this value of $J_2$ we get $\dot{\omega}_s\,\sim \,0\farcs013/ \rm808century$, about seven times smaller than the measurement uncertainty of $\dot{\omega}_o$."809" However, because the companion's rotation is not well constrained by the optical measurements (which indicate UrotSiniz« l40kkmss ὃ-σ, see 2.1)), we can use the agreement between ha, ¢ !,and w, to constrain ws assuming that GR is the correct theory of gravity."," However, because the companion's rotation is not well constrained by the optical measurements (which indicate $v_\mathrm{rot}\sin i_* <810140$ $^{-1}$ , $\sigma$, see \ref{sec:optical}) ), we can use the agreement between $h_3$, $\varsigma$ and $\dot{\omega}_r$ to constrain $\dot{\omega}_s$ assuming that GR is the correct theory of gravity."811 The minimum total mass compatible (at the 1-c level) with ha and ¢ is 2.59Mo., The minimum total mass compatible (at the $\sigma$ level) with $h_3$ and $\varsigma$ is $2.59 M_{\odot}$.812" The corresponding minimum w, (84.1"" /century) can then be used to derive a 1-o limit of ὡς=Wo—Wr,min<2.3""/century (here we are assuming a median expected value of 0 for wx)."," The corresponding minimum $\dot{\omega}_r$ $84.1 \asec/ \rm century $ ) can then be used to derive a $\sigma$ limit of $\dot{\omega}_s =813\dot{\omega}_o - \dot{\omega}_{r, \rm min} \,<\,2.3 \asec/ \rm814century$ (here we are assuming a median expected value of $0$ for $\dot{\omega}_k$ )."815 Future optical/near infrared measurements might be able to better constrain vrot., Future optical/near infrared measurements might be able to better constrain $v_\mathrm{rot}$.816 If this is small then the agreement of the 3 different PK parameters can be used directly as a test of general relativity., If this is small then the agreement of the 3 different PK parameters can be used directly as a test of general relativity.817" To calculate ὧς, we use eq."," To calculate $\dot{x}_s$, we use eq."818" 81 of ? to derive Using the parameters above, we obtain |z,/z|«2.2x10 !, which is one order of magnitude below the measurement55s error."," 81 of \cite{wex98} to derive Using the parameters above, we obtain $|\dot{x}_s/x| < 2.2 \times 10^{-18}\rm\,s^{-1}$ , which is one order of magnitude below the measurement error."819" Therefore, an improved measurement of $ will likely improve the determination of the orbital orientation."," Therefore, an improved measurement of $\dot{x}$ will likely improve the determination of the orbital orientation."820" From the 3-D map, we obtain the following parameters: i=(7747+0.15)? or (102.53+0.15)? (1-0), M,=(2.697+0.029) Mo, me=(1.029+0.008)Mo, m,=(1.667+0.021)Mc and R=1.620+0.008."," From the 3-D map, we obtain the following parameters: $i\,=\,(77.47 \pm 0.15)^\circ$ or $(102.53 \pm 0.15)^\circ$ $\sigma$ ), $M_t\,=\,(2.697 \pm 0.029)\,M_{\odot}$ , $m_c\,=\,(1.029 \pm 0.008)\,M_{\odot}$, $m_p\,=\,(1.667 \pm 0.021)\,M_{\odot}$ and $R\,=\,1.620 \pm 0.008$."821" The underlying probability distribution functions for these parameters have a shape that is very different from a Gaussiancurve (see Fig. 8)),"," The underlying probability distribution functions for these parameters have a shape that is very different from a Gaussiancurve (see Fig. \ref{fig:masses}) ),"822 therefore it is not very meaningful to refer to c limits., therefore it is not very meaningful to refer to $\sigma$ limits.823 For all the previous values we indicated instead confidence limits., For all the previous values we indicated instead confidence limits.824 These values and their uncertainties can, These values and their uncertainties can825The 2004 December 27 flare from the Soft-y-ray Repeater SGR 1806-20 was a major event in astronomy in a number of ways.,The 2004 December 27 flare from the $\gamma$ -ray Repeater SGR 1806-20 was a major event in astronomy in a number of ways.826 First of all by the energy of the explosion: the brightest flash of radiation from beyond our solar system ever recorded., First of all by the energy of the explosion: the brightest flash of radiation from beyond our solar system ever recorded.827 This is how it caught the attention of a larger audience., This is how it caught the attention of a larger audience.828 Secondly. because the flare provided new observational data about a known class of objects: magnetars. Le.. strongly magnetized neutron stars (see.e.g..?)..," Secondly, because the flare provided new observational data about a known class of objects: magnetars, i.e., strongly magnetized neutron stars \citep[see, e.g.,][]{Hurley2005}."829 Also. it led to speculation about a possible link with y-ray bursts (GRBs) (see.e.g..?)..," Also, it led to speculation about a possible link with $\gamma$ -ray bursts (GRBs) \citep[see, e.g.,][]{Tanvir2005}."830 Theorists investigated the connection between the magnetic field and the explosion (see.e.g.?)..," Theorists investigated the connection between the magnetic field and the explosion \citep[see, e.g.][]{Blandford2005}."831 Other focused on modeling the fireball and the afterglow (see.e.g..???)..," Other focused on modeling the fireball and the afterglow \citep[see, e.g.,][]{Nakar2005,Dai2005,Wang2005}."832 Astronomers performed a number of follow-up observations at various wavelengths (2??22)..," Astronomers performed a number of follow-up observations at various wavelengths \citep{Rea2005,Israel2005,Palmer2005,Schwartz2005,Fender2006}."833 In particular. the flux from the radio nebula produced by the explosion (2???) was measured very frequently in 2005 January.," In particular, the flux from the radio nebula produced by the explosion \citep{Gaensler2005a,Cameron2005, Taylor2005} was measured very frequently in 2005 January."834 These observations focused on total intensity measurements at various radio wavelengths and on polarimetry at 8.5 GHz., These observations focused on total intensity measurements at various radio wavelengths and on polarimetry at 8.5 GHz.835 Some polarimetry was done at lower frequencies. but without the proper correction for the leakages (?)..," Some polarimetry was done at lower frequencies, but without the proper correction for the leakages \citep{Gaensler2005b}."836 We have performed accurate polarimetry at 350. 850 and 1300 MHz.," We have performed accurate polarimetry at 350, 850 and 1300 MHz."837 Also. we were able to measure the Stokes I flux from the radio nebula at 350 and 850 MHz more precisely by observing the same field again in 2005 April/May.," Also, we were able to measure the Stokes I flux from the radio nebula at 350 and 850 MHz more precisely by observing the same field again in 2005 April/May."838 In this way. we could properly subtract the background sources from the (u. v) data of the 2005 January observations.," In this way, we could properly subtract the background sources from the (u, v) data of the 2005 January observations."839 We compare our measurements with those at nearby frequencies., We compare our measurements with those at nearby frequencies.840 A total of 19 observations were performed in January. April and May of 2005.," A total of 19 observations were performed in January, April and May of 2005."841 Four of these. on January 16. 20. 23 and 29 were alternating between 350 and 850 MHz.," Four of these, on January 16, 20, 23 and 29 were alternating between 350 and 850 MHz."842 On January 7 and 10 scans at 1300 MHz were also included., On January 7 and 10 scans at 1300 MHz were also included.843 On January 4 we observed at 350. 650 and 1300 MHz. but the 650 MHz data was not used.," On January 4 we observed at 350, 650 and 1300 MHz, but the 650 MHz data was not used."844 A summary ts shown in table 1., A summary is shown in table \ref{tab:Obs}.845 We used AIPS (?) and ParselTongue (?) scripts for the reduction of all 19 datasets., We used AIPS \citep{Greisen2003} and ParselTongue \citep{Kettenis} scripts for the reduction of all 19 datasets.846 The Westerbork Synthesis Radio Telescope (WSRT) was used for all observations., The Westerbork Synthesis Radio Telescope (WSRT) was used for all observations.847 The WSRT is a linear array with I4 equatorially mounted 25-m dishes equipped with linear feeds., The WSRT is a linear array with 14 equatorially mounted 25-m dishes equipped with linear feeds.848 Its maximum baseline ts 2.7 km., Its maximum baseline is 2.7 km.849 All datasets recorded four polarization products with 8. IFs., All datasets recorded four polarization products with 8 IFs.850 3C286 was observed before the target and 3C48 after., 3C286 was observed before the target and 3C48 after.851 RFI was excised from the spectral line data using the AIPS task Calibration was done in four steps., RFI was excised from the spectral line data using the AIPS task Calibration was done in four steps.852 First we determined the variation in system temperature as a function of time (and therefore also as a function of position on the sky).," First we determined the variation in system temperature as a function of time (and therefore also as a function of position on the sky),"853"This leads (to an equation for the radius r(x.v) at which the slr intensity is x in a galaxy of mass v. where Ix(x) is given by The simple requirement that (he radius r(x.v) be greater (han or equal to O puts a lower limit on the mass v of a galaxy that can contribute (ο a star formation intensitv x. That minimum mass y, is given bv A given star formation intensity interval Aw corresponds to a radius interval Ar in a 5ealaxv equal to diAr.","This leads to an equation for the radius r(x,y) at which the sfr intensity is x in a galaxy of mass y. where K(x) is given by The simple requirement that the radius r(x,y) be greater than or equal to 0 puts a lower limit on the mass y of a galaxy that can contribute to a star formation intensity x. That minimum mass $y_m$ is given by A given star formation intensity interval $\Delta x$ corresponds to a radius interval $\Delta r$ in a galaxy equal to $\Delta x854\frac{dr}{dx}$."855" The 0.25 logarithmic5 intervals of x used in fig5 1 correspond. to an interval of 0.584x which is a Ar of 994,4, "," The 0.25 logarithmic intervals of x used in fig \ref{fig:hx} correspond to an interval of 0.584x which is a $\Delta856r$ of $\frac{0.584}{1.4} r_e$."857The area corresponding to intensity interval is simplv 2zr(zx.y)r.," The area corresponding to intensity interval is simply $2 \pi r(x,y) \Delta r$."858 The total area for the intensity interval is obtained by integrating over all masses v weighted by the probability of galaxies will that mass given by eqn. 2.., The total area for the intensity interval is obtained by integrating over all masses y weighted by the probability of galaxies with that mass given by eqn. \ref{eqn:shc}.859 Integration of the second term of equ., Integration of the second term of eqn.860" 11. vields I(x) times the incomplete gamma function Pla+1+7.y,,))."," \ref{eqn:area} yields K(x) times the incomplete gamma function $\Gamma(\alpha +1+\frac{2}{n},y_m))$."861 The integration of the first term was performed numerically with Mathematica., The integration of the first term was performed numerically with Mathematica.862 The area is then Equation 12. is appropriate for a galaxy viewed [ace on but the observations include ealaxies at all inclinations., The area is then Equation \ref{eqn:ar} is appropriate for a galaxy viewed face on but the observations include galaxies at all inclinations.863 Inclination of a galaxy by an angle 8 to the line of sight increases, Inclination of a galaxy by an angle $\theta$ to the line of sight increases864Table 1. which is based on data compiled in Sandage Tamunann (1981) and van den Bergh (2002). shows that EO and Sa galaxies are. on average. about twice as Iuminous as SO galaxies.,"Table 1, which is based on data compiled in Sandage Tammann (1981) and van den Bergh (2002), shows that E0 and Sa galaxies are, on average, about twice as luminous as S0 galaxies."865 This difference is found to hold in all environments., This difference is found to hold in all environments.866 A Ilxolmogorov-9Smirnov test performed on (he data listed in this table shows that the probability of E and SO galaxies having been drawn [rom the same parent Inminosity distribution is0.2%... and respectively. in clusters. groups and the field.," A Kolmogorov-Smirnov test performed on the data listed in this table shows that the probability of E and S0 galaxies having been drawn from the same parent luminosity distribution is, and respectively, in clusters, groups and the field."867 In other words. elliptical galaxies are more luminous (han lenticulars in all environments. ," In other words, elliptical galaxies are more luminous than lenticulars in all environments. ["868The S0 galaxies in the particularly rich Virgo cluster are also fainter than those of types E and Sa. but (because of their small number) not at a respectable level of statistical significance.],"The S0 galaxies in the particularly rich Virgo cluster are also fainter than those of types E and Sa, but (because of their small number) not at a respectable level of statistical significance.]"869 Furthermore the data in Table 1 also show that the probabilities of SO and Sa galaxies in clusters. groups and in the field. having been drawn [rom the same parent huminositv. distribution are only8... not meaningful and3%.. respectively.," Furthermore the data in Table 1 also show that the probabilities of S0 and Sa galaxies in clusters, groups and in the field, having been drawn from the same parent luminosity distribution are only, not meaningful and, respectively."870 It is noted in passing that the luminosity distributions of οί) and SBO galaxies in Sandage Tammann (1981) do not differ significantly., It is noted in passing that the luminosity distributions of S0 and SB0 galaxies in Sandage Tammann (1981) do not differ significantly.871 By the same token no significant difference is Found between the Iuminositv. distributions of Sa and SBa. ealaxies., By the same token no significant difference is found between the luminosity distributions of Sa and SBa galaxies.872 Recently Nair (2009. p.76) has shown that. among 13575 Sloan Digital Skv Survey ealaxies. objects of (vpe SQ are also lainter than are those of morphological tvpes E and Sa.," Recently Nair (2009, p.76) has shown that, among 13575 Sloan Digital Sky Survey galaxies, objects of type S0 are also fainter than are those of morphological types E and Sa."873 The conclusion that the Iuminosities of SO galaxies are not intermediate between those of ivpes E and Sa therefore isn't just a quirk of the relatively small Shaplev-Ames sample., The conclusion that the luminosities of S0 galaxies are not intermediate between those of types E and Sa therefore isn't just a quirk of the relatively small Shapley-Ames sample.874 Burstein et al. (, Burstein et al. (8752005) have also found that elliptical galaxies are more luminous (han lenticulars from Ix-band. photometry of E ancl SO galaxies in the Third Reference Catalogue of Bright Galaxies by de Vaucouleurs οἱ al. (,2005) have also found that elliptical galaxies are more luminous than lenticulars from K-band photometry of E and S0 galaxies in the Third Reference Catalogue of Bright Galaxies by de Vaucouleurs et al. (8761991).,1991).877 This observed luminosity difference between E and SO galaxies cannot be blamed on evolutionary effects., This observed luminosity difference between E and S0 galaxies cannot be blamed on evolutionary effects.878 This is so because the intrinsic colors of E and SO galaxies are observationally indistinguishable., This is so because the intrinsic colors of E and S0 galaxies are observationally indistinguishable.879 Sandage Visvanathan (1973) find that the fully corrected mean colors of field + cluster galaxies are <usr>=28340.01 and <--τος2.85240.01 respectively. for SO and E galaxies.," Sandage Visvanathan (1978) find that the fully corrected mean colors of field + cluster galaxies are $<u - r> = 2.83 \pm 0.01$ and $<u - r> = 2.85 \pm 0.01$ respectively, for S0 and E galaxies."880 s-ravs are detected from many galactic and extragalactic sources. including pulsars. supernova remnants. eamma rav bursts and blazars.,"$\gamma$ -rays are detected from many galactic and extragalactic sources, including pulsars, supernova remnants, gamma ray bursts and blazars."881 Ht ds believed that multiwavelength enussion of the latest (wpe of the mentioned objects is due to small scale highly relativistic jets. which are formed. near active galactic nuclei of host galaxies and are inclined at small angles to the line of sight (e.g..Bregman1990).," It is believed that multiwavelength emission of the latest type of the mentioned objects is due to small scale highly relativistic jets, which are formed near active galactic nuclei of host galaxies and are inclined at small angles to the line of sight \citep[e.g.,][]{bre90}."882. Iligh observed bolometric luminosities of blazars (0vpicallv 104!—1075 erg/s) are often dominated by 5-rav emission. what enabled to observe many of them byEGRET in z;~0.1—10 GeV energy range (vonMontignyοἱHartimanetal. 1999).," High observed bolometric luminosities of blazars (typically $10^{44} - 10^{48}$ erg/s) are often dominated by $\gamma$ -ray emission, what enabled to observe many of them by in $\varepsilon_{\gamma} \sim 0.1 - 10$ GeV energy range \citep{mon95,har99}."883. Some nearby low-Inminositv blazars. like the best known Mick 421 and Mrk 501. are also confirmed to be sources of very high energy (VIIE) 5-ravs with ος>100 GeV (Punchetal.1992:Quinn1996.respectively)...," Some nearby low-luminosity blazars, like the best known Mrk 421 and Mrk 501, are also confirmed to be sources of very high energy (VHE) $\gamma$ -rays with $\varepsilon_{\gamma} > 100$ GeV \citep[respectively]{pun92,qui96}."884 Detection of such VIE radiation by ground-based instruments was possible due (o development. of imagine atmospheric Cherenkov telescopes. (see.e.g..Aharonian1998;Volk2003).," Detection of such VHE radiation by ground-based instruments was possible due to development of imaging atmospheric Cherenkov telescopes, \citep[see, e.g.,][]{aha98,vol03}."885. The observed broad-band blazar emission allows one to determine physical parameters ol nuclear AGN jets., The observed broad-band blazar emission allows one to determine physical parameters of nuclear AGN jets.886 5-rav observations are crucial in (his respect. providing important constraints on the involved particle acceleration processes. or on (he characteristic spatial scales for the blazar phenomenon (e.g..SikoraandAlaclejski2002:Iinoetal.2002).," $\gamma$ -ray observations are crucial in this respect, providing important constraints on the involved particle acceleration processes, or on the characteristic spatial scales for the blazar phenomenon \citep[e.g.,][]{sik02,kin02}."887. Llowever. observations al VIIE range are complicated because propagation effects are important for the hieh energv photons created at cosmologieal distances (Nikishov1962:Gouldand1966:Steckerοἱal. 1992)... and also. obviously. because of a low photon statistics in 5-rav telescopes.," However, observations at VHE range are complicated because propagation effects are important for the high energy photons created at cosmological distances \citep{nik62,gou66,ste92}, and also, obviously, because of a low photon statistics in $\gamma$ -ray telescopes."888" Among the other issues. one should mention here a case of VILE emission [rom Alrk 501. which extends up to energies £4,>10 TeV. which seems to be in conflict with some models of cosmic infrared background (CIB) radiation (see.e.g..ProtheroeanclAharonian 2001)."," Among the other issues, one should mention here a case of VHE emission from Mrk 501, which extends up to energies $\varepsilon_{\gamma}> 10$ TeV, which seems to be in conflict with some models of cosmic infrared background (CIB) radiation \citep[see, e.g.,][]{pro00, aha01}."889. Detailed studies of cosmic background photon fields aud their interactions with 5-ravs during their propagation. as well as future 5-ray missions. will possibly answer some of (he questions connected with production of VIIE radiation in blazars.," Detailed studies of cosmic background photon fields and their interactions with $\gamma$ -rays during their propagation, as well as future $\gamma$ -ray missions, will possibly answer some of the questions connected with production of VHE radiation in blazars."890 Contrary (to blazar parsec-scale jets. their large scale counterparts extending from a few to a few hundreds of kiloparsecs Lom active galactic nuclei were usually studied only at radio frequencies (DridleandPerley1984).," Contrary to blazar parsec-scale jets, their large scale counterparts extending from a few to a few hundreds of kiloparsecs from active galactic nuclei were usually studied only at radio frequencies \citep{bri84}."891. Recently. however. (UST) and telescopes gathered. new information about optical ancl X-rav emission of some of these objects.," Recently, however, ) and telescopes gathered new information about optical and X-ray emission of some of these objects."892 For several hundreds of known radio jets. only about 20 are observed al optical," For several hundreds of known radio jets, only about 20 are observed at optical"893deprojection of X-ray surface brightness and spatially resolved tSZ data. testing its performance against idealized spherical clusters and full cosmological hydrodynamical simulations.,"deprojection of X–ray surface brightness and spatially resolved tSZ data, testing its performance against idealized spherical clusters and full cosmological hydrodynamical simulations."894 This method is based on the assumption of spherical symmetry. but do not assume any specific model for the gas density and temperature profiles.," This method is based on the assumption of spherical symmetry, but do not assume any specific model for the gas density and temperature profiles."895 We will deseribe two different implementations., We will describe two different implementations.896" The first one is analogous to that already applied to deproject spectroscopic X-ray data (e.g...2) and is based on assuming a onion-like structure of the cluster. in which projected data of X-ray and tSZ ""fluxes"" are used to recover gas density and temperature in the external layers and then propagated to the internal layers in a iterative way."," The first one is analogous to that already applied to deproject spectroscopic X–ray data \citep[e.g.,897][]{1983ApJ...272..439K} and is based on assuming a onion–like structure of the cluster, in which projected data of X–ray and tSZ “fluxes” are used to recover gas density and temperature in the external layers and then propagated to the internal layers in a iterative way."898 The second implementation is based instead on a multi-parametric fitting procedure. in which the fitting parameters are the values of gas density and temperature within different three-dimensional radial bins.," The second implementation is based instead on a multi–parametric fitting procedure, in which the fitting parameters are the values of gas density and temperature within different three–dimensional radial bins."899 The values of these parameters are then obtained through a Monte Carlo Markov Chain maximum likelihood fitting by comparing the resulting projected X-ray and tSZ profiles to those obtained from the maps., The values of these parameters are then obtained through a Monte Carlo Markov Chain maximum likelihood fitting by comparing the resulting projected X–ray and tSZ profiles to those obtained from the maps.900 As we shall discuss in detail. this second method naturally provides the error correlation matrix. which fully accounts for the covariance between error estimates at different radii and among different (ie. gas density and temperature) profiles.," As we shall discuss in detail, this second method naturally provides the error correlation matrix, which fully accounts for the covariance between error estimates at different radii and among different (i.e. gas density and temperature) profiles."901 The quality of the X—ray data required by our methods are basically already available with the current generation of X-ray telescopes., The quality of the X--ray data required by our methods are basically already available with the current generation of X–ray telescopes.902 As for the tSZ data. exploiting the full potentiality of the deprojection requires spatially resolved data.," As for the tSZ data, exploiting the full potentiality of the deprojection requires spatially resolved data."903 For illustrative purposes. we will assume the forecast observing conditions and sensitivity of the CCAT ΙΟ.Ol] -ceat-feasibility.pdf).. although our computations can be easily repeated for other telescopes.," For illustrative purposes, we will assume the forecast observing conditions and sensitivity of the CCAT \citep[][see also904http://www.submm.caltech.edu/$\sim$sradford/ccat/doc/2006-01-ccat-feasibility.pdf]905{2006SPIE.6267E..75S}, although our computations can be easily repeated for other telescopes."906 The plan of the paper is as follows., The plan of the paper is as follows.907 In Section 2 we describe the two implementations of the deprojection method. while we describe in Section 3 their application on a spherical polytropic i-model.," In Section 2 we describe the two implementations of the deprojection method, while we describe in Section 3 their application on a spherical polytropic $\beta$ –model."908 Section 4 presents the results of the analysis on the hydrodynamical simulations of clusters., Section 4 presents the results of the analysis on the hydrodynamical simulations of clusters.909 The main conclusions of our analysis are summarized in Section 5., The main conclusions of our analysis are summarized in Section 5.910 The first method that we apply to recover the three-dimensional profiles of temperature and gas density is based on a geometrical technique originally introduced by ?.. and subsequently adopted by (e.g.???) to deproject X-ray images and spectra of galaxy clusters.," The first method that we apply to recover the three–dimensional profiles of temperature and gas density is based on a geometrical technique originally introduced by \cite{1983ApJ...272..439K}, and subsequently adopted by \citep[e.g.,][]{2000ApJ...539..172B,9112002A&A...391..841E, 2007MNRAS.tmp..541M} to deproject X–ray images and spectra of galaxy clusters."912 This method of geometrical deprojection is fully non—parametric and allows to reconstruct the 3-dimensional profile of a given quantity from its 2-dimensional observed projection. under the assumption of spherical symmetry.," This method of geometrical deprojection is fully non--parametric and allows to reconstruct the 3-dimensional profile of a given quantity from its 2-dimensional observed projection, under the assumption of spherical symmetry."913 Following ?.. the cluster is assumed to have a onion-like structure (see Figure 1). with NW concentric spherical shells. each characterized by uniform gas density and temperature within it.," Following \cite{1983ApJ...272..439K}, the cluster is assumed to have a onion–like structure (see Figure \ref{fi:shells}) ), with $N$ concentric spherical shells, each characterized by uniform gas density and temperature within it."914 Therefore. the cluster image in projection is divided into rings. which are generally assumed to have the same radii of the 3D spherical shells.," Therefore, the cluster image in projection is divided into rings, which are generally assumed to have the same radii of the 3D spherical shells."915 Let us detine c; as the signal to be recovered from he deprojection method within the ;-th shell., Let us define $\epsilon_i$ as the signal to be recovered from the deprojection method within the $i$ -th shell.916 In our analysis c; will be proportional to either »..2;. for the tSZ signal. or to 02.A(17) for he X-ray emissivity.," In our analysis $\epsilon_i$ will be proportional to either $n_eT_e$ for the tSZ signal, or to $n_e^2 \Lambda(T)$ for the X–ray emissivity."917" In this way. the contribution of the ;-th shell o the surface in the ring j of the image will be given by 8),=6;Vif. where the matrix V; has as entries the values of the volume of the shell / which is projected on the ring). whose area is ;1;."," In this way, the contribution of the $i$ -th shell to the surface in the ring $j$ of the image will be given by $s_{i,j}=\epsilon_i \cdot V_{i,j} /918A_j$ , where the matrix $V_{i,j}$ has as entries the values of the volume of the shell $i$ which is projected on the ring $j$, whose area is $A_j$."919" By definition. 5;,;=0 for j=7."," By definition, $s_{i,j}=0$ for $j > i$."920 Accordingly. he surface brightness s in the ring j can be obtained by summing up the contributions from all the shells. Sy =tSο”... where the sums extend over the AN’ radial bins.," Accordingly, the surface brightness $S'_j$ in the ring $j$ can be obtained by summing up the contributions from all the shells, S'_j = = _i, where the sums extend over the $N$ radial bins."921 The deprojection amounts to invert the above equation. i.e. to recover the values of c; from the observed projected signal s;," The deprojection amounts to invert the above equation, i.e. to recover the values of $\epsilon_i$ from the observed projected signal $S'_j$."922 We refer to Figure |. to illustrate how this deprojection is performed in practice., We refer to Figure \ref{fi:shells} to illustrate how this deprojection is performed in practice.923" Let the shell 7. limited by 7; andr; ,. be the outermost one."," Let the shell $i$, limited by $r_{i}$ and $r_{i+1}$, be the outermost one."924 Then. from the surface brightness $f in the ring 7 (limited by 72; and 22;1). one can directly compute the emissivity of the shell ¢ simply by knowing the volume of the region (a) and the area of the ring.," Then, from the surface brightness $S'_i$ in the ring $i$ (limited by $R_i$ and $R_{i+1}$ ), one can directly compute the emissivity of the shell $i$ simply by knowing the volume of the region (a) and the area of the ring."925 In this case. the sum in eq.," In this case, the sum in eq."926 | has only the term j=7ΑΝ., \ref{eq:deproj} has only the term $j=i=N$.927" The adjacent inner ring. having index /.—1 and limited by 7/?;,and /?;. takes instead a contribution from both the 71 and ? shells."," The adjacent inner ring, having index $i-1$ and limited by $R_{i-1}$and $R_{i}$, takes instead a contribution from both the $i-1$ and $i$ shells."928 The former is computed by multiplying the emissivity of that shell by the volume of the region (b)., The former is computed by multiplying the emissivity of that shell by the volume of the region (b).929" After subtracting it. the only remaining contribution is that of the sell ; from which the emissivity ¢;, Is computed."," After subtracting it, the only remaining contribution is that of the sell $i-1$ from which the emissivity $\epsilon_{i-1}$ is computed."930 This procedure is then repeated from ring to ring down to the center of the cluster., This procedure is then repeated from ring to ring down to the center of the cluster.931 For this simple scheme to be applied. one requires to have images extended out to the true external edge of the cluster. i.e. out to the radius where the surface brightness goes virtually to zero.," For this simple scheme to be applied, one requires to have images extended out to the true external edge of the cluster, i.e. out to the radius where the surface brightness goes virtually to zero."932 Clearly. this situation is never attained in practical applications for at least two reasons.," Clearly, this situation is never attained in practical applications for at least two reasons."933 First. clusters are always embedded in a large-scale cosmic web. which makes it difficult to define a sharp outer boundary.," First, clusters are always embedded in a large–scale cosmic web, which makes it difficult to define a sharp outer boundary."934 Second. and more important. both instrumental and cosmic backgrounds often dominate the genuine signal from the cluster well before its virial boundary is reached.," Second, and more important, both instrumental and cosmic backgrounds often dominate the genuine signal from the cluster well before its virial boundary is reached."935" To overcome this problem, it is then necessary to take into account the emission from the gas. which extends outside the A’- shell."," To overcome this problem, it is then necessary to take into account the emission from the gas, which extends outside the $N$ -th shell."936 This emission does not have a corresponding ring in the image butcan give a non-negligible contribution to the surface brightness in all rings., This emission does not have a corresponding ring in the image butcan give a non–negligible contribution to the surface brightness in all rings.937" To account for this contribution. we follow the approach of ?.. who modeled the volume emission from the gas beyond the last observable annulus as a power law. e(r)xr"" "," To account for this contribution, we follow the approach of \cite{1999AJ....117.2398M}, , who modeled the volume emission from the gas beyond the last observable annulus as a power law, $\epsilon(r) \propto r^{-\alpha}$ "938"(ST&: 9 yam: L1"" /pix).",(ST8; 9 $\micron$ ; $\arcsec$ /pix).939 All frames were bias subtracted and flat fielded., All frames were bias subtracted and flat fielded.940 CCD frames obtained with (he 50/70 cm Schmidt telescope were also corrected Lor dark counts., CCD frames obtained with the 50/70 cm Schmidt telescope were also corrected for dark counts.941 Twilight flat fields in each filter were obtained on each night., Twilight flat fields in each filter were obtained on each night.942 All frames were taken through a standard Johnson- set of fillers., All frames were taken through a standard Johnson-Cousins set of filters.943 Aperture photometry was performed using DAOPIIOT routines., Aperture photometry was performed using DAOPHOT routines.944 The tvpical exposure limes are 60-120 sec for I. 120-180 sec for Ro and. 180-300 sec for the V filter.," The typical exposure times are 60-120 sec for I, 120-180 sec for R and 180-300 sec for the V filter."945 There is generally excellent agreement between the data obtained at VVO and at the Enropean observatories., There is generally excellent agreement between the data obtained at VVO and at the European observatories.946 The results of our previous study of IIAIW 15. based on data obtained over the first five vears of the monitoring program and reported in Paper 1. documented an apparent eclipse. unremarkable but [or its extremely lone duration.," The results of our previous study of HMW 15, based on data obtained over the first five years of the monitoring program and reported in Paper I, documented an apparent eclipse, unremarkable but for its extremely long duration."947 Relatively stable im the first season. the star faded. by approximately 0.7 mag over the following season ancl remained stably al the fainter magnitude for the 2000-2001 season belore recovering steadilv to its original brightness throughout. 2001-2002 and stabilizing during the 4th season.," Relatively stable in the first season, the star faded by approximately 0.7 mag over the following season and remained stably at the fainter magnitude for the 2000-2001 season before recovering steadily to its original brightness throughout 2001-2002 and stabilizing during the 4th season."948 Although a lew previous observations by Trullols&Jordi(1997) and Herbie(L998) indicated the possibility of recurrence. the 2002-2003 season of data showed unexpected variation ancl no clear continuing pattern.," Although a few previous observations by \citet{tj} and \citet{h98} indicated the possibility of recurrence, the 2002-2003 season of data showed unexpected variation and no clear continuing pattern."949 However. the recently reduced data from the 2004-2006. seasons. plotted with the prior VVO observations in Figure 1.. show a striking recurrence of nearly identical eclipsing behavior: the star [ades steadily throughout the 2004-2005 season al nearly (he same ingress slope observed in the 1999-2000 season. Chen. alter (assumecdly) remaining stable al the fainter magnitude lor the summer of 2005. begins to brighten (o its magnitude in the 2005-2006 season. again with a slope similar to that observed in the earlier egress.," However, the recently reduced data from the 2004-2006 seasons, plotted with the prior VVO observations in Figure \ref{lightcurve}, show a striking recurrence of nearly identical eclipsing behavior: the star fades steadily throughout the 2004-2005 season at nearly the same ingress slope observed in the 1999-2000 season, then, after (assumedly) remaining stable at the fainter magnitude for the summer of 2005, begins to brighten to its out-of-eclipse magnitude in the 2005-2006 season, again with a slope similar to that observed in the earlier egress."950 Given (he evident recurrence of the eclipse. the period of recurrence was estimated by visual examination of phased light curves of different (rial periods.," Given the evident recurrence of the eclipse, the period of recurrence was estimated by visual examination of phased light curves of different trial periods."951 Our “best fit phased lieht curve from (his process is shown in Fig.," Our “best fit"" phased light curve from this process is shown in Fig."952 2. and is for a period of 4.7 v (1717 d)., \ref{phase} and is for a period of 4.7 y (1717 d).953 In addition to the recent data from VVO and Europe. we have included five earlier measurements bv llerbig(1998) and Trullols&Jordi(1997).. obtained in the early to mid-1990s.," In addition to the recent data from VVO and Europe, we have included five earlier measurements by \citet{h98} and \citet{tj}, obtained in the early to mid-1990's."954 These data were reported in Paper I and thev are shown on the plot as open squares., These data were reported in Paper I and they are shown on the plot as open squares.955 They. probe one or lwo cycles earlier in (he light curve aud are. therefore. particularly important for period determination.," They probe one or two cycles earlier in the light curve and are, therefore, particularly important for period determination."956 As can be seen. our adopted period fits all of the data on this star well except for the very first measurement. which is from Trullols&Jordi(1997). aud obtained on 24 October 1992.," As can be seen, our adopted period fits all of the data on this star well except for the very first measurement, which is from \citet{tj} and obtained on 24 October 1992."957 We can adjust the periodsomewhat aud obtain a better fit for that one datum. but," We can adjust the periodsomewhat and obtain a better fit for that one datum, but"958AIuch work has been done ou the deteruination of power spectra of the diffuse Colactie svuchrotron backgrouud. because the Galactic svuchrotron radiation is a foreground contanünator in Cosmic Microwave Background Radiation (CAIBR) polarization ineasuremienuts at hnieh frequeucies νzz 30 - 100 CIIz.,"Much work has been done on the determination of power spectra of the diffuse Galactic synchrotron background, because the Galactic synchrotron radiation is a foreground contaminator in Cosmic Microwave Background Radiation (CMBR) polarization measurements at high frequencies $\nu \approx$ 30 - 100 GHz."959 Power spectra of the diffuse polarized svuchrotron background iuteusitv have been determuned from several radio surveys at frequencies from LOS MIIZ to 2.7 CGIIz. iu many parts of the sky (Tucci et 22000. 2002. Daccigalupi ct 22001. αταπιο et 22002. Bruscoli et 22002).," Power spectra of the diffuse polarized synchrotron background intensity have been determined from several radio surveys at frequencies from 408 MHz to 2.7 GHz, in many parts of the sky (Tucci et 2000, 2002, Baccigalupi et 2001, Giardino et 2002, Bruscoli et 2002)."960 These power spectra studies are based ou the following survevs of polarized radiation: Power spectra of total intensity Fo and poluized intensity P were derived in these surveys for multipoles over a range of (zz10 to GOO," These power spectra studies are based on the following surveys of polarized radiation: Power spectra of total intensity $I$ and polarized intensity $P$ were derived in these surveys for multipoles over a range of $\ell \approx96110$ to 6000."962 Fie., Fig.963 12 shows the variation of ap with Calactic longitude. latitude aux frequency. using the available data as detailed iui Table 3..," \ref{f9:lit} shows the variation of $\alpha_P$ with Galactic longitude, latitude and frequency, using the available data as detailed in Table \ref{t9:lit}."964 In the left plots. the lines show ranecs in longitude (top) and latitude (bottoni) OVCT which àp was computed.," In the left plots, the lines show ranges in longitude (top) and latitude (bottom) over which $\alpha_P$ was computed."965 Solid lines give Ligh uniltipole uumnbers (100<f 6000). dashec-dotted lines denote an intermediate multipole rauge (30<( 200) aud the dotted lines give sinall imultipoles (10<€ 80).," Solid lines give high multipole numbers $100 < \ell <9666000$ ), dashed-dotted lines denote an intermediate multipole range $30 < \ell < 200$ ) and the dotted lines give small multipoles $10 <967\ell < 80$ )."968 The WSRT data from the Auriga. Horologiunn ena WENSS," The WSRT data from the Auriga, Horologium en WENSS"969"basis of the color criteria ofOuchietal.(2004a),, i.e., B—R»12, R-i'«0.7, and B—R»1.6(R—1.9, which were determined with the results of spectroscopyi!)4- and Monte-Carlo simulations.","basis of the color criteria of\citet{ouchi2004a}, i.e., $B-R>1.2$, $R-i'<0.7$, and $B-R>1.6(R-i')+1.9$, which were determined with the results of spectroscopy and Monte-Carlo simulations."970 We visually inspect all the candidates and mask areas contaminated with halos of bright stars and CCD blooming., We visually inspect all the candidates and mask areas contaminated with halos of bright stars and CCD blooming.971" Our final catalog includes 16,920 LBGs in a 1.00 deg? area (Table 1))."," Our final catalog includes 16,920 LBGs in a 1.00 $^2$ area (Table \ref{tab:results}) )."972 Figure 1 shows the sky distribution of our LBGs.," Figure \ref{fig:dist_BRiLBG}973 shows the sky distribution of our LBGs."974" Our spectroscopic follow-up observations show that 60 out of 63 identified candidates are real LBGs at z—3.54.5; ie., 17 out of 17 and 43 out of 46 are LBGs in the SXDF (Akiyama M. in preparation) and in the Subaru Deep Field, respectively, where the latter LBG sample is made with the same color criteria as ours (Yoshida 2005)."," Our spectroscopic follow-up observations show that 60 out of 63 identified candidates are real LBGs at $z=3.5-4.5$; i.e., 17 out of 17 and 43 out of 46 are LBGs in the SXDF (Akiyama M. in preparation) and in the Subaru Deep Field, respectively, where the latter LBG sample is made with the same color criteria as ours \citep{yoshida2005}."975". Thus, the contamination rate of our LBG sample is estimated to be (63—60)/63=5%."," Thus, the contamination rate of our LBG sample is estimated to be $(63-60)/63 = 5$."976". We derive the ACF, ω(θ), by the formula of Landy&Szalay(1993) with random samples composed of 200,000 sources, and estimate bootstrap errors (Lingetal.1986)."," We derive the ACF, $\omega(\theta)$, by the formula of \cite{landy1993} with random samples composed of 200,000 sources, and estimate bootstrap errors \citep{ling1986}."977". Since clustering properties of our contaminants are not clear, we do not apply a correction for contaminants with the assumption of random distribution (c.f. Ouchietal. 2004b))."," Since clustering properties of our contaminants are not clear, we do not apply a correction for contaminants with the assumption of random distribution (c.f. \citealt{ouchi2004b}) )."978" However, this correction changes ω(0) and bias only by 1096 or less."," However, this correction changes $\omega(\theta)$ and bias only by $10$ or less."979" Figure 2 presents the ACF of LBGs (top panel), residuals of a power-law fit (middle panel), and galaxy-dark matter bias (bottom defined as 0(0)= where vam(0) is the panel)ACF predicted by the non-linear \/w(@)/wam(@),model of Peacock&Dodds (1996)."," Figure \ref{fig:acorr_BRiLBG_all} presents the ACF of LBGs (top panel), residuals of a power-law fit (middle panel), and galaxy-dark matter bias (bottom panel) defined as $980b(\theta)981 \equiv982 \sqrt{\omega(\theta)/\omega_{\rm dm}(\theta)}983$, where $\omega_{\rm dm}(\theta)$ is the ACF predicted by the non-linear model of \cite{peacock1996}."984". In the top and middle panels of Figure 2 the ACF of LBGs shows significant excess on small scale, and indicates that a apower law, A,,0~°, does not fit the data."," In the top and middle panels of Figure \ref{fig:acorr_BRiLBG_all}985 the ACF of LBGs shows a significant excess on small scale, and indicates that a power law, $A_\omega \theta^{-\beta}$, does not fit the data."986 This is the definitive identification of the departure from a power law for the ACF of LBGs at z=4., This is the definitive identification of the departure from a power law for the ACF of LBGs at $z=4$.987" With a visual inspection, we confirm that all close-pairs of LBGs are not false detections."," With a visual inspection, we confirm that all close-pairs of LBGs are not false detections."988 We also plot histogram of galaxy sizes for LBG pairs., We also plot histogram of galaxy sizes for LBG pairs.989" We find that most of our LBGs have FWHM~1” for pairs with any separations down to, at least,2"", and that extended LBGs do not boost small-scale ACF by producing false pairs."," We find that most of our LBGs have $\simeq 1''$ for pairs with any separations down to, at least,$\simeq 2''$, and that extended LBGs do not boost small-scale ACF by producing false pairs."990" Uncertainties in source deblending and photometry can hardly account for the small-scale excess at 2"".", Uncertainties in source deblending and photometry can hardly account for the small-scale excess at $\gtrsim 2''$.991" In fact, a similar small-scale excess of ACF for z>=4—5 LBGs is also found by a recent study on high-resolution (~ 0.1) HST images (Leeetal.2005)."," In fact, a similar small-scale excess of ACF for $z=4-5$ LBGs is also found by a recent study on high-resolution $\sim 0''.1$ ) HST images \citep{lee2005}."992". Comparing our ACF with the one of dark matter, we find that the small-scale excess extends up to ~ 7”, ie. 0.24h7) Mpe, which is comparable to virial radius, r290, of dark halos with a mass of 10!1-1?M5 (see the"," Comparing our ACF with the one of dark matter, we find that the small-scale excess extends up to $\simeq 7''$ i.e. $0.24 h_{70}^{-1}$ Mpc, which is comparable to virial radius, $r_{200}$ , of dark halos with a mass of $10^{11-12}M_\odot$ (see the"993The core growth during the TP-AGB phase is a strict lower limit on the mass of nuclear burning products in TP-AGB stars and the requisite contribution to stellar populations’ bolometric luminosity.,The core growth during the TP-AGB phase is a strict lower limit on the mass of nuclear burning products in TP-AGB stars and the requisite contribution to stellar populations' bolometric luminosity.994" In Figure 2., we illustrate the fraction of the final core mass grown during the phase as a function of initial mass."," In Figure \ref{fig:frac}, we illustrate the fraction of the final core mass grown during the TP-AGB phase as a function of initial mass."995 We define this fractional mass as Mywhere üsthediff erencebetweenthe finalremnantmassandthecoremassattheonseto ftheT P—AGBphase., We define this fractional mass as $=\delmc / \mf$ where is the difference between the final remnant mass and the core mass at the onset of the TP-AGB phase.996T hed ata po, The data points are made using the weighted mean initial and final masses for each cluster.997intsa uusingevolutionarvtracksbothwithandwithoutovershooting., As mentioned in Section \ref{sec:methods} we compute the progenitor mass and using evolutionary tracks both with and without overshooting.998Filledsquaresrepresentmeasses found withmodel sana phas, Filled squares represent masses found with models and cluster ages incorporating overshoot; open squares are masses that do not take overshooting into account.999ea, Dashed lines connect the results of these two cases for each cluster.1000nd initialmass.res pectively.," The error bars, calculated according to Sections \ref{sec:m1tp} and \ref{sec:mi}, represent one sigma errors in fractional core mass gained during the TP-AGB phase and initial mass, respectively."1001T heredlinesconnectthemoving weightedmeano f eachdatapoinutt," The red lines connect the moving weighted mean of each data point type, illustrating the overall trends in the figure."1002ype.illusi ((οιι pomtsareonlyaveragedwiththeclosestdatapoint).," At every filled or open point, we calculate the weighted mean of itself and its closest neighbor in both directions of (end points are only averaged with the closest data point)."1003T hesolidredlineconnectstheaverageso f the filleddata poi, The solid red line connects the averages of the filled data points (OS); the dashed red line connects the open square (nOS) averages.1004 These moving averages highlight the large increase in fractional core mass growth during the TP-AGB phase between 2 and ~3M. (up to 4M.. in the no overshooting case)., These moving averages highlight the large increase in fractional core mass growth during the TP-AGB phase between $2$ and $\sim3 M_{\odot}$ (up to $4 M_{\odot}$ in the no overshooting case).1005 In the case where convective overshooting is considered (OS). the weighted mean tp-acp=0.20+£0.01 when 1.9XM;<3.6 and drops by a factor of two to 0.08£0.02 elsewhere.," In the case where convective overshooting is considered (OS), the weighted mean $= 0.20 \pm 0.01$ when $1.9 \leq\mi\leq 3.6$ and drops by a factor of two to $0.08\pm 0.02$ elsewhere."1006 This broad peak in aabove the remainder of the sample is significant at the 3.5σ level., This broad peak in above the remainder of the sample is significant at the $3.5 \sigma$ level.1007 For progenitor masses calculated with models and cluster ages that do not include convective overshooting (NOS). iis generally smaller than its OS counterpart and the fraction of core mass gained in the TP-AGB phase peaks at a slightly higher progenitor mass (3.5M. versus 3M. ).," For progenitor masses calculated with models and cluster ages that do not include convective overshooting (nOS), is generally smaller than its OS counterpart and the fraction of core mass gained in the TP-AGB phase peaks at a slightly higher progenitor mass $3.5 M_{\odot}$ versus $3 M_{\odot}$ )."1008 These shifts are a natural consequence of the inclusion or absence of convective overshooting in evolutionary models and isochrones., These shifts are a natural consequence of the inclusion or absence of convective overshooting in evolutionary models and isochrones.1009 Convective overshooting models predict a larger He core and longer lifetime along the main sequence compared to nOS models., Convective overshooting models predict a larger He core and longer lifetime along the main sequence compared to nOS models.1010" Due to these larger cores, iis larger for a given wwhen overshooting is considered."," Due to these larger cores, is larger for a given when overshooting is considered."1011 Η the initial masses calculated with and without convective overshooting were the same. wwould be larger in the nOS case.," If the initial masses calculated with and without convective overshooting were the same, would be larger in the nOS case."1012" However, OS isochrones assign older cluster ages (and subsequently smaller M;)) than nOS isochrones given the same cluster CMD."," However, OS isochrones assign older cluster ages (and subsequently smaller ) than nOS isochrones given the same cluster CMD."1013 The -- rrelation is monotonically increasing and thus the nOS iis higher than its OS counterpart in the same cluster when Mi5M.. (the -- rrelation flattens slightly at higherMi; nOS aare similar to the OS iin this mass range)., The - relation is monotonically increasing and thus the nOS is higher than its OS counterpart in the same cluster when $\leq 5 \msol$ (the - relation flattens slightly at higher; nOS are similar to the OS in this mass range).1014" Still, the nOS average curve shows the same shape às that composed of OS progenitor masses."," Still, the nOS average curve shows the same shape as that composed of OS progenitor masses."1015" On a cluster by cluster basis, the OS and nOS core growth fractions are"," On a cluster by cluster basis, the OS and nOS core growth fractions are"1016variability. consistent with it being a member of the Je/N-rav binary group of sources - though its spectral classification is unusually carly (Negueruela. 1998).,variability consistent with it being a member of the Be/X-ray binary group of sources - though its spectral classification is unusually early (Negueruela 1998).1017 Further optical observations by Schmidtke. ct al (1996). revealed evidence for small photometric changes up to a few tenths ofa magnitude., Further optical observations by Schmidtke et al (1996) revealed evidence for small photometric changes up to a few tenths of a magnitude.1018 The Optical Gravitational Lensing Experiment (OGLE) is a long term observational program with the main goal of searching for dark. unseen matter using the microlensing phenomenon (Ucdalski et al.," The Optical Gravitational Lensing Experiment (OGLE) is a long term observational program with the main goal of searching for dark, unseen matter using the microlensing phenomenon (Udalski et al."1019 1992)., 1992).1020 In general the OGLE data cover the period June 1997 to February 2000 ancl primarily consist ofL band observations. though some observations were also taken in the V. band.," In general the OGLE data cover the period June 1997 to February 2000 and primarily consist of I band observations, though some observations were also taken in the V band."1021 The optical counterparts were identified in the OGLE data base and all the photometric measurements extracted., The optical counterparts were identified in the OGLE data base and all the photometric measurements extracted.1022 ligure 1 (top panel) shows the optical lighteurve for. RX J0544.1-7100 obtained from the OGLE E band data., Figure 1 (top panel) shows the optical lightcurve for RX J0544.1-7100 obtained from the OGLE I band data.1023 The OGLE data of tX. J0520.5-6932 are shown in Figure 2., The OGLE data of RX J0520.5-6932 are shown in Figure 2.1024 Figure 3 shows the power spectrum of RA JO544.1-7100 obtained using the Lomb-Scarele technique on 219 E band data points obtained over the period 5 Oct 1997 - 27 March 2000., Figure 3 shows the power spectrum of RX J0544.1-7100 obtained using the Lomb-Scargle technique on 219 I band data points obtained over the period 5 Oct 1997 - 27 March 2000.1025 Periods in the range LO - 500 days were investigated., Periods in the range 10 - 500 days were investigated.1026 The largest. peak shown in Figure 3 corresponds to a period of 286d and undoubtably arises from. the variability on several long timescales evident in Figure 1., The largest peak shown in Figure 3 corresponds to a period of 286d and undoubtably arises from the variability on several long timescales evident in Figure 1.1027 ligure 4 shows the Lomb-Scarele power spectrum. obtained for WN JO520.5-6932 using the same search parameters as those used for RX JO544.17100., Figure 4 shows the Lomb-Scargle power spectrum obtained for RX J0520.5-6932 using the same search parameters as those used for RX J0544.1–7100.1028 In this case there is a very clear ancl strong peak corresponding to a period of 24.45d., In this case there is a very clear and strong peak corresponding to a period of 24.45d.1029 The lower panel in Figure 2 shows the average folded lighteurve compared to the first. ancl most," The lower panel in Figure 2 shows the average folded lightcurve compared to the first, and most"1030have estimated that about 7C of UC and LIC regions observed at two epochs separated by about LO vears should have detectable Hux increments. and that about 38% should have detectable decrements.,"have estimated that about $7~\%$ of UC and HC regions observed at two epochs separated by about 10 years should have detectable flux increments, and that about $3~\%$ should have detectable decrements."1031 In total. ~10% of regions should have detectable Hux variations in a period of 10 vears.," In total, $\sim10~\%$ of regions should have detectable flux variations in a period of 10 years."1032 Dedicated: observations of as many. sources as possible are now needed to test this model., Dedicated observations of as many sources as possible are now needed to test this model.1033 Our long timescale data can only be constrained by observational surveys. not by time monitoring.," Our long timescale data can only be constrained by observational surveys, not by time monitoring."1034 In Section 3.5 we have shown that the racio luminosities (1.6.. cistance-corrected flux) in the long-term evolution of the simulated regions are consistent with major surveys. except. [or the most luminous regions. in which likely accretion has stopped. and which therefore do not. correspond: with our data.," In Section 3.3 we have shown that the radio luminosities (i.e., distance-corrected flux) in the long-term evolution of the simulated regions are consistent with major surveys, except for the most luminous regions, in which likely accretion has stopped and which therefore do not correspond with our data."1035 The hypothesis that a considerable. fraction. of observed UC and LIC regions may harbor stars that are still accreting material still needs more convincing evidence in addition to matching the model here presented., The hypothesis that a considerable fraction of observed UC and HC regions may harbor stars that are still accreting material still needs more convincing evidence in addition to matching the model here presented.1036 For mos cases the dynamics of the surrounding molecular gas. aux of the ionizecl gas have not been studied at high. angular resolution. and such studies in many sources are key to test this idea.," For most cases the dynamics of the surrounding molecular gas and of the ionized gas have not been studied at high angular resolution, and such studies in many sources are key to test this idea."1037" From available observations. almost all of the massive star formation regions with signatures of active accretion and in which the mass of the protostar is estimate from dynamics to be AZ,z20M. havea relatively bright region (withatleast~LOOmyshortemwavelenghts.e.g..Beltranetal.2007:Galván-Maclrid 2009)."," From available observations, almost all of the massive star formation regions with signatures of active accretion and in which the mass of the protostar is estimated from dynamics to be $M_\star>20~\Msun$ have a relatively bright region \citep[with at least $\sim 100$ mJy at short cm wavelenghts, e.g.,][]{Beltran07,GM09}."1038". To our knowledge. the only clear exception is the recent report by Zapataetal.(2009) of an accreting protostar in W51 N with an estimated. mass of M,~60AZ. and only 17 mv at 7 mm."," To our knowledge, the only clear exception is the recent report by \cite{Zap09} of an accreting protostar in W51 N with an estimated mass of $M_\star\sim 60 ~ \Msun$ and only 17 mJy at 7 mm."1039 This object can be understood in the context. of our simulations if it is in a quenched. faint state as currently observed.," This object can be understood in the context of our simulations if it is in a quenched, faint state as currently observed."1040 As mentioned in Papers LH. and HE. the simulations here presented do not include the elfects of stellar winds and magnetically-driven jets originating from within 100 AU. which would produce outflows that are more powerful than the purely. pressure-driven outllows that appear in Rus A and D (Paper 1).," As mentioned in Papers I, II, and III, the simulations here presented do not include the effects of stellar winds and magnetically-driven jets originating from within 100 AU, which would produce outflows that are more powerful than the purely pressure-driven outflows that appear in Runs A and B (Paper I)."1041 The inclusion of stellar winds ancl jets may allect the results presented in this paper only quantitatively., The inclusion of stellar winds and jets may affect the results presented in this paper only quantitatively.1042 Petersetal.(2011). have shown that magnetically driven outLows vor radii bevond 100 AU do not stop aceretion and even channel more material to the central most massive ootostars., \cite{Peters11} have shown that magnetically driven outflows from radii beyond 100 AU do not stop accretion and even channel more material to the central most massive protostars.1043 The simulations of Wangctal.(2010) also indicate. that collimated outflows may be an important regulator of star formation by slowing the accretion rate rut without impeding accretion., The simulations of \cite{Wang10} also indicate that collimated outflows may be an important regulator of star formation by slowing the accretion rate but without impeding accretion.1044 Observationally. molecular outllows tend to be less eollimated for the more massive O-ype protostars capable of producing regions than for D-tvpe protostars (Arceetal.2007).," Observationally, molecular outflows tend to be less collimated for the more massive O-type protostars capable of producing regions than for B-type protostars \citep{Arce07}."1045.. Reearding the radio-continuum. it is unknown if the free-free emission from the »hotoionized regions produced by O-type protostars can coexist with the frec-free emission from (partially) ionized. magnetically driven jets.," Regarding the radio-continuum, it is unknown if the free-free emission from the photoionized regions produced by O-type protostars can coexist with the free-free emission from (partially) ionized, magnetically driven jets."1046 Before the appearance of an region. these jets are detected. in protostars less massive than 15M. (ασ.Carrasco-Gonzalezetal.2010)... and even though their radio emission also appears to be variable2006).. their twvpical centimeter Hux is ~1 nilv. one to two orders of magnitude fainter than the tvpical Hux of UC and HIC regions (exceptmaybefor2003).," Before the appearance of an region, these jets are detected in protostars less massive than $\sim 15~\Msun$ \citep[e.g.,][]{Carrasco10}, and even though their radio emission also appears to be variable, their typical centimeter flux is $\sim 1$ mJy, one to two orders of magnitude fainter than the typical flux of UC and HC regions \citep[except maybe for the youngest gravitationally-trapped \HII regions, see][]{Keto03}."1047. Therefore. the relative ellect of any variation in a hypothetical radio jet should be small compared: with the variations in the region Dux.," Therefore, the relative effect of any variation in a hypothetical radio jet should be small compared with the variations in the region flux."1048 A further limitation of this study is that aceretion onto the protostars is not well resolved. since the maximum cell resolution (98 AW) corresponds to a scale of the order of the inner accretion disk. (see also Paper 1).," A further limitation of this study is that accretion onto the protostars is not well resolved, since the maximum cell resolution (98 AU) corresponds to a scale of the order of the inner accretion disk (see also Paper I)."1049 We performed. an analysis of the /radio-continuum variability in regions that appear in the racdiation-hvdrodvnamüc simulations of massive-star— formation presented in Paper L The ultimate late of ultracompac ancl hypercompact regions is to expand. but. during their evolution they Hicker due to the complex interplay of the inner ionized gas and the outer neutral gas.," We performed an analysis of the radio-continuum variability in regions that appear in the radiation-hydrodynamic simulations of massive-star formation presented in Paper I. The ultimate fate of ultracompact and hypercompact regions is to expand, but during their evolution they flicker due to the complex interplay of the inner ionized gas and the outer neutral gas."1050 The radio-luminosities of the regions formed by the accreting protostars in our simulations are in agreement with those of observational radio surveys. except for the most. luminous of the observed. regions.," The radio-luminosities of the regions formed by the accreting protostars in our simulations are in agreement with those of observational radio surveys, except for the most luminous of the observed regions."1051 We show that regions are highly variable in all timescales from. 10 to 107 vr. ane estimate that at least 10 οἳ observed. ultracompact anc hypercompact regions should. exhibit (lux variations larger than 10% for time intervals longer than about LO ve.," We show that regions are highly variable in all timescales from 10 to $10^4$ yr, and estimate that at least $10 ~\%$ of observed ultracompact and hypercompact regions should exhibit flux variations larger than $10 ~\%$ for time intervals longer than about 10 yr."1052 The authors acknowledge the referee for a report that helped. to. clarify. the main aspects of this paper., The authors acknowledge the referee for a report that helped to clarify the main aspects of this paper.1053 lL.G.M. thanks Luis EF. Hodrígguez for comments on a draft of the paper., R.G.M. thanks Luis F. Rodrígguez for comments on a draft of the paper.1054 RC.ΔΙ acknowledges support from the SAO and ASLAA through an SALA predoctoral fellowship., R.G.M. acknowledges support from the SAO and ASIAA through an SMA predoctoral fellowship.1055 TPL ds a bellow of the Bacden-Wirrttembere Stiftung unded by their program International. Collaboration LL (crant P-LS-SPIL/18)., T.P. is a Fellow of the Baden-Würrttemberg Stiftung funded by their program International Collaboration II (grant P-LS-SPII/18).1056 T.P. also. acknowledges support rom an Annette |xade Fellowship for his visit to the AAINIL and ao Visiting Scientist Award of the SAO., T.P. also acknowledges support from an Annette Kade Fellowship for his visit to the AMNH and a Visiting Scientist Award of the SAO.1057 aacknowledges financial support. from. the Daden-Württemberg Stiftung via. their program. International Collaboration 11 (erant P-LS-SPLIEIS) and from the German Dundesministerium. ftir Bildung und. Forschung. via. the ASTRONET project SPAR. FORALAT (grant. O5AQOVILA).," acknowledges financial support from the Baden-W\""{u}rrttemberg Stiftung via their program International Collaboration II (grant P-LS-SPII/18) and from the German Bundesministerium fürr Bildung und Forschung via the ASTRONET project STAR FORMAT (grant 05A09VHA)."1058 LS. furthermore gives. thanks for subsidies Lrom the Deutsche Forsehunesgemeimschalt (DEG) under grants WAL 1358/1. KL 1358/4. INL. 1359/5. KL 1358/10. and Wh 1358/11. as well as from a Frontier grant of Heidelberg University sponsored by the German IExcellence Initiative.," R.S.K. furthermore gives thanks for subsidies from the Deutsche Forschungsgemeinschaft (DFG) under grants KL 1358/1, KL 1358/4, KL 1359/5, KL 1358/10, and KL 1358/11, as well as from a Frontier grant of Heidelberg University sponsored by the German Excellence Initiative."1059 AL-ALALL. was partly supported ον NSE erant AST. 08-351734., M.-M.M.L. was partly supported by NSF grant AST 08-35734.1060 ROB. is funded by the DEG. via the Emmv-Noether erant. DX 3706/1-1., R.B. is funded by the DFG via the Emmy-Noether grant BA 3706/1-1.1061 We acknowledge computing time at the Leibniz-Itechenzentrum in. Garching (Germany). the NSE- Texas Advanced. Computing Center (USA). and at Jtillich Supercomputing Centre (Germany).," We acknowledge computing time at the Leibniz-Rechenzentrum in Garching (Germany), the NSF-supported Texas Advanced Computing Center (USA), and at Jüllich Supercomputing Centre (Germany)."1062 The ELASIE code was in part developed by the DOI-supported Alliances, The FLASH code was in part developed by the DOE-supported Alliances1063turbulent velocity in the models that include the shear layer exhibit a bump where the velocity gradient is located.,turbulent velocity in the models that include the shear layer exhibit a bump where the velocity gradient is located.1064" This feature does not appear in non-shearing models (see dotted line), suggesting that turbulent motions are developing in this regions."," This feature does not appear in non-shearing models (see dotted line), suggesting that turbulent motions are developing in this regions."1065 The bump is more pronunced in models with larger Sh which indicates that this turbulent motions are probably due to the KH instability., The bump is more pronunced in models with larger $\Sh$ which indicates that this turbulent motions are probably due to the KH instability.1066 This difference in u;ms reflects in the value of the equipartition magnetic field (Eq. 13)), This difference in $\urms$ reflects in the value of the equipartition magnetic field (Eq. \ref{equ:Beq}) )1067 which differs from model to model., which differs from model to model.1068 We find that the amplitude of the magnetic energy increases for deeper tachoclines., We find that the amplitude of the magnetic energy increases for deeper tachoclines.1069 This is an expected result since below the convection zone the magnetic diffusivity has smaller values which allows a larger storage., This is an expected result since below the convection zone the magnetic diffusivity has smaller values which allows a larger storage.1070 The vertical distribution of the toroidal component of the magnetic energy σὺ peaks roughly at the center of the shear layer., The vertical distribution of the toroidal component of the magnetic energy $\mean{B}_y^2$ ) peaks roughly at the center of the shear layer.1071 The tail of this curve towards the convection zone may hint how buoyant the magnetic field is on each model., The tail of this curve towards the convection zone may hint how buoyant the magnetic field is on each model.1072 We expect that the larger the magnetic field (Run D04) the more magnetic flux becomes buoyant and rises into the upper layers., We expect that the larger the magnetic field (Run D04) the more magnetic flux becomes buoyant and rises into the upper layers.1073 The time evolution of the magnetic field of the runs in Set D are shown in the middle panel of Fig. 2.., The time evolution of the magnetic field of the runs in Set D are shown in the middle panel of Fig. \ref{fig:b-t}.1074" We find that the growth rate of the magnetic field, A—dlnBrms/dt, decreases slightly as the shear layer is moved deeper."," We find that the growth rate of the magnetic field, $\lambda={\rm d}\ln1075\brms/{\rm d}t$, decreases slightly as the shear layer is moved deeper."1076 This is not very clear in Table 1. since the error of this quantity is of the same order as the difference between different runs., This is not very clear in Table \ref{tab:1} since the error of this quantity is of the same order as the difference between different runs.1077" However, it is clear from both, the figure and the table, that the volume averaged magnetic field increases with the tachocline depth."," However, it is clear from both, the figure and the table, that the volume averaged magnetic field increases with the tachocline depth."1078" In the third group of simulations (Runs TO1-TO4), we increase the width of the shear layer gradually from d;=0.05d in Run TOI to d;=0.11d in Run T04."," In the third group of simulations (Runs T01–T04), we increase the width of the shear layer gradually from $d_z=0.05d$ in Run T01 to $d_z=0.11d$ in Run T04."1079" This change implies lower values of the shear parameter Sh (Eq. 12)),"," This change implies lower values of the shear parameter $\Sh$ (Eq. \ref{equ:Sh}) ),"1080 but also larger fraction of the tachocline in the turbulent and stable layers., but also larger fraction of the tachocline in the turbulent and stable layers.1081" The results, presented in Table 1 and depicted in Figs."," The results, presented in Table \ref{tab:1} and depicted in Figs."1082" 1 and 2 (see legends), indicate that smaller values of the shear, Shz3, are still able to excite the dynamo at the price of a lower growth rate."," \ref{fig:strat} and \ref{fig:b-t} (see legends), indicate that smaller values of the shear, $\Sh\approx3$, are still able to excite the dynamo at the price of a lower growth rate."1083 We notice that the growth rate depends on the magnetic Reynolds number (compare Runs T04 and T04b)., We notice that the growth rate depends on the magnetic Reynolds number (compare Runs T04 and T04b).1084 The fact that a smaller shear generates a larger magnetic field is a counter-intuitive result and does not agree with previous mean-field studies on the thickness of the solar tachocline (?).., The fact that a smaller shear generates a larger magnetic field is a counter-intuitive result and does not agree with previous mean-field studies on the thickness of the solar tachocline \citep{gue07a}.1085" However, as it will be explained below, the important fact is that this configuration seems to be favorable to a longer storage of magnetic field in the stably stratified layer, with the advantage that here the effects of the shear on the thermal properties of the fluid are less important than in the previous sets of simulations."," However, as it will be explained below, the important fact is that this configuration seems to be favorable to a longer storage of magnetic field in the stably stratified layer, with the advantage that here the effects of the shear on the thermal properties of the fluid are less important than in the previous sets of simulations."1086 With the settings of Run T04 we find that the critical magnetic Reynolds number is between 20.8 (Run T0409) and 26.3 (Run T0409)., With the settings of Run T04 we find that the critical magnetic Reynolds number is between $20.8$ (Run $_0$ ) and $26.3$ (Run $_0$ ).1087" Based on the results above, we perform another series of simulations whose parameters and results are summarized in Table 2.."," Based on the results above, we perform another series of simulations whose parameters and results are summarized in Table \ref{tab:2}."1088" Runs ΑΚΟΙ and ARO2 correspond to Run T04 but with aspect ratios (Lz,Ly,L;)=(8,4,2)d and (4,8,2)d, respectively."," Runs AR01 and AR02 correspond to Run T04 but with aspect ratios $(L_x,L_y,L_z)=(8,4,2)d$ and $(4,8,2)d$, respectively."1089" Runs D03b, and T04a to T04c have essentially the same configuration than Runs D03 and T04 with 256? grid points resolution."," Runs D03b, and T04a to T04c have essentially the same configuration than Runs D03 and T04 with $256^3$ grid points resolution."1090 The values of v and K have been modified in order to obtain different Reynolds and Prandtl numbers., The values of $\nu$ and $K$ have been modified in order to obtain different Reynolds and Prandtl numbers.1091 The model with larger extent perpendicular to the direction of the shear does not show differences with respect to the reference case., The model with larger extent perpendicular to the direction of the shear does not show differences with respect to the reference case.1092" On the other hand, the model with larger extent in the direction of the shear results in a reduced growth rate"," On the other hand, the model with larger extent in the direction of the shear results in a reduced growth rate"1093different frou the value uormally given.,different from the value normally given.1094" Since we assmnie a raucous oricutation. o, represcuts tle standard deviation i the intrinsic distribution of the real part of the complex ellipticitv. a tei which has an expected mean of zero."," Since we assume a random orientation, $\sigma_{\chi}$ represents the standard deviation in the intrinsic distribution of the real part of the complex ellipticity, a term which has an expected mean of zero."1095" The intrinsic variation in the octopole moments iu the octopoles are labeled 07,5. aud 0:,,2:."," The intrinsic variation in the octopole moments in the octopoles are labeled $\sigma_{\langle1096x^3\rangle}$ , and $\sigma_{\langle xy^2\rangle}$."1097 These terms represeut the standard deviation iu the following dimensionless fori: with a similar form for the other octopole., These terms represent the standard deviation in the following dimensionless form: with a similar form for the other octopole.1098 We again assiuunue no covariance., We again assume no covariance.1099 To simplity the analysis. we assume that the halt-lieht radius. Πρι aud the characteristic radius is known with perfect certainty. as is the integrated fux.," To simplify the analysis, we assume that the half-light radius, $R_e$, and the characteristic radius is known with perfect certainty, as is the integrated flux."1100 Since these terms are dominant uear the ceuter of the image. their errors will be considerably smaller than the higher order moments.," Since these terms are dominant near the center of the image, their errors will be considerably smaller than the higher order moments."1101 Finally. we consider the uncertainty in the shear from the measurement of the quadrupoles of a single galaxy.," Finally, we consider the uncertainty in the shear from the measurement of the quadrupoles of a single galaxy."1102" Iu the limit of weak lensing. the reduced shear may be approximated as: Since the orientation of the tutriusic ellipticity. yv; is random. σε,=7,v2."," In the limit of weak lensing, the reduced shear may be approximated as: Since the orientation of the intrinsic ellipticity, $\chi_{\beta}$ is random, $\sigma_{\chi_1}=\sigma_{\chi}/\sqrt{2}$."1103 Ebbels et al. (, Ebbels et al. (11042000) derive a probability distribution function for the observed ellipticity distribution for galaxies of different morphological types from the Medimu Deep Survey.,2000) derive a probability distribution function for the observed ellipticity distribution for galaxies of different morphological types from the Medium Deep Survey.1105" Adapting this. we find a reasonable value of o,=0.30."," Adapting this, we find a reasonable value of $\sigma_\chi=0.30$."1106 Thus. the variance in the estimate of g from the ellipticity is: Iu most instances. this uncertainty will be dominated by the spread in the intrinsic galaxy cllipticitics.," Thus, the variance in the estimate of $g$ from the ellipticity is: In most instances, this uncertainty will be dominated by the spread in the intrinsic galaxy ellipticities."1107 The details of parameter estimation from the octopole moments are sliehtly more involved., The details of parameter estimation from the octopole moments are slightly more involved.1108 We may beeiu by simplifving the terms in equs., We may begin by simplifying the terms in eqns.1109 (21. and 25)) which are fictions of g., \ref{eq:octx3} and \ref{eq:octxy2}) ) which are functions of $g$ .1110 For snall g. we may sav: We then simplify equs.," For small $g$, we may say: We then simplify eqns."1111 (21. and 25)) to the following expressions: and where the terms. can be derived by inspection. aud thei uucertaiuties can be determined by the staudiid propagation of errors.," \ref{eq:octx3} and \ref{eq:octxy2}) ) to the following expressions: and where the terms, $u_{ij}$, can be derived by inspection, and their uncertainties can be determined by the standard propagation of errors."1112 πιWe reiterate here that this analysis assumes that the errors are Gaussian and uncorrelated. which is certainly not the case.," We reiterate here that this analysis assumes that the errors are Gaussian and uncorrelated, which is certainly not the case."1113 Tuverting these expressions vields: and Since the expectation value of the intrinsic octopoles is zero. estimating the parameters from these equatious is straightforward.," Inverting these expressions yields: and Since the expectation value of the intrinsic octopoles is zero, estimating the parameters from these equations is straightforward."1114 Finally. fom the form above. calculation of the variance aud covarianceof g aud rg’ is a straightforward but tedious exercise in propagation oferrors.," Finally, from the form above, calculation of the variance and covarianceof $g$ and $r \ g'$ is a straightforward but tedious exercise in propagation oferrors."1115due to prompt and afterglow phases of GRBs which is 10? GeV cm? s! sr!.,due to prompt and afterglow phases of GRBs which is $\sim$ $^{-9}$ GeV $^{-2}$ $^{-1}$ $^{-1}$.1116" On the other hand, in the same energy range, EGRET measured the EGB flux to be 10? GeV cm? s! sr!1998).."," On the other hand, in the same energy range, EGRET measured the EGB flux to be $10^{-5}$ GeV $^{-2}$ $^{-1}$ $^{-1}$."1117" Therefore, GRBs that were detected by BATSE but were not detected as point sources by EGRET contribute to the EGB at least ~0.01%."," Therefore, GRBs that were detected by BATSE but were not detected as point sources by EGRET contribute to the EGB at least $\sim$."1118". Again, we note that the estimates for the prompt phase are those of synchrotron component."," Again, we note that the estimates for the prompt phase are those of synchrotron component."1119" We thus need to take the predicted IC contribution into account, which is represented by a correction factor 1+ηις/ in Table 2.."," We thus need to take the predicted IC contribution into account, which is represented by a correction factor $1+\eta_{\rm IC} / \eta_{\rm syn}$ in Table \ref{table:result}."1120" Since this factor could be as large as ~10 accordingενα to the discussion in 3,, EGB flux due to prompt phase of GRBs could also becomes ~10 times larger, which makes GRB contribution as large as ~0.1% of the observations above  GeV. In any case, the contributions from other sources such as blazars are expected to be more significant astrophysicalthan GRBstherein)."," Since this factor could be as large as $\sim$ 10 according to the discussion in \ref{sec:Constraint on high-energy emission with1121EGRET}, EGB flux due to prompt phase of GRBs could also becomes $\sim$ 10 times larger, which makes GRB contribution as large as $\sim$ of the observations above $\sim$ GeV. In any case, the contributions from other astrophysical sources such as blazars are expected to be more significant than GRBs."1122. Additional contribution to EGB is expected from large number of GRBs that away from us and thereforea would not have been detectedpoint with BATSE., Additional contribution to EGB is expected from a large number of GRBs that point away from us and therefore would not have been detected with BATSE.1123 The emission from these bursts points towards us once the external shock decelerates1997)., The emission from these bursts points towards us once the external shock decelerates.1124" Since the total GeV energy emitted every decade of time during the afterglow is roughly constant, the contribution of these GRBs to EGB can be estimated by the GeV emission of the bursts that were detected by BATSE."," Since the total GeV energy emitted every decade of time during the afterglow is roughly constant, the contribution of these GRBs to EGB can be estimated by the GeV emission of the bursts that were detected by BATSE."1125" Similar contribution is expected from bursts that points towards us but that are too faint to be detected by BATSE, if the GRB luminosity function behaves as #(L)cL? as suggested by the universal structured jet model"," Similar contribution is expected from bursts that points towards us but that are too faint to be detected by BATSE, if the GRB luminosity function behaves as $\phi(L) \propto L^{-2}$ as suggested by the universal structured jet model."1126" Therefore the contribution of bursts that were not detected by BATSE to EGB can be estimated by the afterglow fluence of the detected bursts, assuming no contribution from bursts with only an upper limit."," Therefore the contribution of bursts that were not detected by BATSE to EGB can be estimated by the afterglow fluence of the detected bursts, assuming no contribution from bursts with only an upper limit."1127 This is a reasonable estimate since the GeV flux is dominated by the few brightest bursts in GeV which are the most likely to be detected., This is a reasonable estimate since the GeV flux is dominated by the few brightest bursts in GeV which are the most likely to be detected.1128" Taking the fluence of the detected GeV bursts as the logarithmic mean of these upper and lower limits implies Jggg~5x10? GeV cm? s! !, a GRB contribution being ~0.1% of the EGB."," Taking the fluence of the detected GeV bursts as the logarithmic mean of these upper and lower limits implies $I_{\rm1129EGB} \sim 5 \times 10^{-9}$ GeV $^{-2}$ $^{-1}$ $^{-1}$, a GRB contribution being $\sim$ of the EGB."1130" Finally, we note that there is a big uncertainty in removing the Galactic foreground contamination from the total diffuse flux2004)."," Finally, we note that there is a big uncertainty in removing the Galactic foreground contamination from the total diffuse flux."1131". Additionally, EGRET observations do not constrain TeV emission that cascades down into the GeV range for GRBs at cosmological distances2007).."," Additionally, EGRET observations do not constrain TeV emission that cascades down into the GeV range for GRBs at cosmological distances."1132" Thus, if the foreground subtraction was indeed underestimated or if GRB TeV emission is not negligible, then GRB contribution might be much more significant than the estimates here."," Thus, if the foreground subtraction was indeed underestimated or if GRB TeV emission is not negligible, then GRB contribution might be much more significant than the estimates here."1133 TheGLAST satellite would enable us to test emission mechanisms of GRBs., The satellite would enable us to test high-energy emission mechanisms of GRBs.1134" If this emissionhigh-energy will be found to be consistent with SSC then its observations would constrain physical parameters such as c,/eg ratio and the bulk Lorentz factor of the jet, I'5."," If this emission will be found to be consistent with SSC then its observations would constrain physical parameters such as $\epsilon_{e}/\epsilon_B$ ratio and the bulk Lorentz factor of the jet, $\Gamma_{b}$."1135" The EGRET instrument on boardCGRO, while less sensitive than the GLAST-LAT detector, identified several BATSE GRBs with GeV photons."," The EGRET instrument on board, while less sensitive than the -LAT detector, identified several BATSE GRBs with GeV photons."1136" In addition, stringent upper limits for ~100 GRBs were put on fluences in the GeV band by analyzing the EGRET data2005)."," In addition, stringent upper limits for $\sim$ 100 GRBs were put on fluences in the GeV band by analyzing the EGRET data."1137". In this paper, we further extended this EGRET result, comparing with the SSC emission model."," In this paper, we further extended this EGRET result, comparing with the SSC emission model."1138" theoretical models of SSC, we assumed that there Followingis a linear correlation between fluences in BATSE and EGRET energy bands, and that the proportionality coefficient η follows a log-normal distribution."," Following theoretical models of SSC, we assumed that there is a linear correlation between fluences in BATSE and EGRET energy bands, and that the proportionality coefficient $\eta$ follows a log-normal distribution."1139 We found that the predictions from the SSC model using canonical parameter values is fully consistent with EGRET fluence measurements and upper limits for both the prompt and afterglow phases., We found that the predictions from the SSC model using canonical parameter values is fully consistent with EGRET fluence measurements and upper limits for both the prompt and afterglow phases.1140" During the course of showing this result, we properly took the Klein-Nishina feedback effect into account in the theoretical calculation."," During the course of showing this result, we properly took the Klein-Nishina feedback effect into account in the theoretical calculation."1141" The best-fit value of the coefficient was log~—1.5 for both the prompt and afterglow emissions, and it is already stringent enough to test the SSC scenario."," The best-fit value of the coefficient was $\log \eta \simeq -1.5$ for both the prompt and afterglow emissions, and it is already stringent enough to test the SSC scenario."1142" The limits for the prompt emission phase are for the synchrotron radiation, and thus if we consider the IC component as well, the value of could be by to one order of magnitude."," The limits for the prompt emission phase are for the synchrotron radiation, and thus if we consider the IC component as well, the value of $\eta$ could be larger by up to one order of magnitude."1143" The obtainedη 7 distribution,larger uptogether with the BATSE fluence distribution, gives the expected fluence distribution in the GeV band, which is shown in Figure 4.."," The obtained $\eta$ distribution, together with the BATSE fluence distribution, gives the expected fluence distribution in the GeV band, which is shown in Figure \ref{fig:dndf_egret}."1144" As the GLAST-LAT detector covers EGRET energy band, we can predict the detectable number of GRBs withGLAST from the distribution of Fgcrer, given the GLAST-LAT sensitivity."," As the -LAT detector covers EGRET energy band, we can predict the detectable number of GRBs with from the distribution of $F_{\rm EGRET}$, given the -LAT sensitivity."1145 Our conservative estimate using the five-photon criterion is that about ~20 GRBs among those detected with GBM would be detected with GLAST-LAT each year., Our conservative estimate using the five-photon criterion is that about $\sim$ 20 GRBs among those detected with GBM would be detected with -LAT each year.1146 This number could be even larger if we use fewer-photon criteria., This number could be even larger if we use fewer-photon criteria.1147 The fluence distribution can also be used to estimate the GRB contribution to the EGB intensity., The fluence distribution can also be used to estimate the GRB contribution to the EGB intensity.1148 We found that the contribution would be at least ~0.01% but is likely to be as large as ~0.1%.., We found that the contribution would be at least $\sim$ but is likely to be as large as $\sim$.1149" We are grateful to B. L. Dingus and M. M. Gonzallez 2005)mainBodyCitationEnd5186]LipunovO1,Rossi02,ZhangO2,PerBáafiOBez for very helpful comments and discussions.", We are grateful to B. L. Dingus and M. M. Gonzállez Sánnchez for very helpful comments and discussions.1150 We thank the referee for useful comments., We thank the referee for useful comments.1151" This work was supported by Sherman Fairchild Foundation (SA and EN),"," This work was supported by Sherman Fairchild Foundation (SA and EN),"1152the survey of the COSMOS field vields a space desity of only 107?Mpc? at z==44 whilst the model predicts a value that is four times higher.,"the survey of the COSMOS field yields a space density of only $10^{-6}\,\rm{Mpc}^{-3}$ at 4 whilst the model predicts a value that is four times higher."1153 Therefore we propose to use the IFRS population to complement the number of X-ray-unidentified AGN in the Universe?)., Therefore we propose to use the IFRS population to complement the number of X-ray-unidentified AGN in the Universe.1154. We stress that comparing our results to other surveys must be done with exceptional care because the IFRS sample presented here may be biased. e.g. towards dusty sources.," We stress that comparing our results to other surveys must be done with exceptional care because the IFRS sample presented here may be biased, e.g. towards dusty sources."1155 Further observations of a subsample of IFRS with the Space Observatory will clarify the dust content of these extreme objects., Further observations of a subsample of IFRS with the Space Observatory will clarify the dust content of these extreme objects.1156 For AGN at even higher redshifts (z>4). give a lower limit on the surface density of AGN of 44ος”.," For AGN at even higher redshifts $>$ 4), give a lower limit on the surface density of AGN of $^{-2}$."1157 This value is on the same order of magnitude as our estimate of the fAGN surface density of ~ 3310ddeg7 (ten times the IFRS surface density)., This value is on the same order of magnitude as our estimate of the fAGN surface density of $\sim$ $^{-2}$ (ten times the IFRS surface density).1158 Considering that approximately half of these objects are likely to be situated at such highredshifts*.. our estimates are in good agreement with the value.," Considering that approximately half of these objects are likely to be situated at such high, our estimates are in good agreement with the value."1159 Since no IFRS in the ELAIS-SIfield is detected as discrete X- source by the corresponding survey carried out by?.. the question arises where their X-ray radiation goes.," Since no IFRS in the ELAIS-S1field is detected as discrete X-ray source by the corresponding survey carried out by, the question arises where their X-ray radiation goes."1160 We propose that the X-ray emission contributes to the cosmic X-ray background (CXB)., We propose that the X-ray emission contributes to the cosmic X-ray background (CXB).1161 Given the surface density of FAGN of - ddeg. and an average mass of their central SMBHs of 105 Mc one can calculate their contribution.," Given the surface density of fAGN of $\sim$ $^{-2}$, and an average mass of their central SMBHs of $10^8\,$ $_{\sun}$ one can calculate their contribution."1162 Following?.. an SMBH at its Eddington limit emits a flux density in. the observer kkeV band of: Here fy denotes the fraction of theA total energy radiated in the observer 0.5-2.0kkeV band. its value of 0.03 is taken from the template spectrum of and will be adopted for all further calculations.," Following, an SMBH at its Eddington limit emits a flux density in the observer keV band of: Here $f_X$ denotes the fraction of the total energy radiated in the observer keV band, its value of 0.03 is taken from the template spectrum of and will be adopted for all further calculations."1163 For the fAGN population this implies a contribution of CXByagx=9-107 mm ddeg while assuming an average redshift of pica=4.," For the fAGN population this implies a contribution of $CXB_{fAGN}\,=\,9\cdot116410^{-16}$ $^{-2}$ $^{-2}$ while assuming an average redshift of $z_{fAGN}\,=\,4$."1165 This is 1n reasonable agreement with the CXB measurements by?.. who give a total soft 2.0kkeV) CXB of 75.3- 1077 ddeg? with a 3.5.1075 mm ddeg7 component for by either point sources. diffuse emission. or scattering.," This is in reasonable agreement with the CXB measurements by, who give a total soft keV) CXB of $75.3\cdot 10^{-16}$ $^{-2}$ $^{-2}$ with a $3.5\cdot116610^{-16}$ $^{-2}$ $^{-2}$ component for by either point sources, diffuse emission, or scattering."1167" We note that CXB,4cs is an upper limit for the contribution of TAGN to the CXB.", We note that $CXB_{fAGN}$ is an upper limit for the contribution of fAGN to the CXB.1168 First. because the adopted mass of their central SMBH is an upper limit. and second. no dust extinction of the X-ray emission (predominantly affecting the soft band) was considered. which would result in the absorption of X-ray flux and re-emission at longer wavelengths.," First, because the adopted mass of their central SMBH is an upper limit, and second, no dust extinction of the X-ray emission (predominantly affecting the soft band) was considered, which would result in the absorption of X-ray flux and re-emission at longer wavelengths."1169 To calculate the contribution of fAGN to the hard CXB. one first needs to integrate the template spectrum in the observer's frame 2.0-IOkkeV range to obtain a fraction for the amount of energy radiated at these wavelengths.," To calculate the contribution of fAGN to the hard CXB, one first needs to integrate the template spectrum in the observer's frame keV range to obtain a fraction for the amount of energy radiated at these wavelengths."1170 We derived a fraction of fy=0.1 which we then used in Eqn.," We derived a fraction of $f_X\,=\,0.1$ which we then used in Eqn."1171 5 to calculate the hard band X-ray flux in the same manner as done above for the soft band., \ref{eq:SSMBH} to calculate the hard band X-ray flux in the same manner as done above for the soft band.1172 This results in a contribution of fAGN to the 2.0-lOkkeV region of the CXB of 3-107 mm ddeg. which is about of the total value in this band given by?.," This results in a contribution of fAGN to the keV region of the CXB of $3\cdot117310^{-15}$ $^{-2}$ $^{-2}$, which is about of the total value in this band given by."1174. These authors also give as the fraction of resolved point-like and extended sources contributing to the hard fraction of the CXB. implying an unresolved component of11.," These authors also give as the fraction of resolved point-like and extended sources contributing to the hard fraction of the CXB, implying an unresolved component of."11752%... So also in the hard band does the fAGN population nicely account for the unresolved fraction of the CXB., So also in the hard band does the fAGN population nicely account for the unresolved fraction of the CXB.1176 However. even though our estimates match other observations and predictions. these calculations should be understood only as a rough estimate of the IFRS number densities and hence fAGN population contributing to the CXB.," However, even though our estimates match other observations and predictions, these calculations should be understood only as a rough estimate of the IFRS number densities and hence fAGN population contributing to the CXB."1177" The presence of a population of AGN-driven objects of which at least a fraction. (up to 500) is likely to be located at very high redshifts (z, 55) putsseveralconstraintsonthe formationscenarioo FS MBHsshortl ", The presence of a population of AGN-driven objects of which at least a fraction (up to ) is likely to be located at very high redshifts $>$ 5) puts several constraints on the formation scenario of SMBHs shortly after the Big Bang.1178cosmology. contains only one massive (Mpay—poto=5.5.107 Mo) halo at z==66.2 which is a candidate for a quasar sufficiently bright to be observed by the SDSS.," The Millennium Simulation, to date the largest cosmological simulation probing $\Lambda$ CDM cosmology, contains only one massive $M_{DM-halo}\,=\,5.5\cdot 10^{12}\,$ $_{\sun}$ ) halo at 6.2 which is a candidate for a quasar sufficiently bright to be observed by the SDSS."1179 The SMBH mass density at z==66 of ~1077 MM5 MMpc? derived from this simulation is therefore several orders of magnitude lower than the mass density we extrapolate from our fAGN (Eq. 4)).," The SMBH mass density at 6 of $\sim\,10^{-9}$ $_{\sun}$ $^{-3}$ derived from this simulation is therefore several orders of magnitude lower than the mass density we extrapolate from our fAGN (Eq. \ref{fAGN}) )."1180" We note. however. that bright. quasars are still very rare objects which can be treated às statistical ""spikes"" in the primordial density profile and thus do not very much affect current theories concerning. structure. formation."," We note, however, that bright quasars are still very rare objects which can be treated as statistical “spikes” in the primordial density profile and thus do not very much affect current theories concerning structure formation."1181 Given the very small number density of such bright SDSS quasarsdeg. or the powerful high redshift radio sources?).. we point out that IFRS resp.," Given the very small number density of such bright SDSS quasars, or the powerful high redshift radio sources, we point out that IFRS resp."1182 fAGN can play an important role just because of their abundance of several tens to several hundred per square degree., fAGN can play an important role just because of their abundance of several tens to several hundred per square degree.1183 One can also compare the mass densities to models of SMBH formation., One can also compare the mass densities to models of SMBH formation.1184 assert that major mergers account for most of the high-z SMBHs., assert that major mergers account for most of the high-z SMBHs.1185 Their approach yields a close match to our mass density. in. particular when their simulation scenario G is considered. where the probability of forming a seed black hole during à merger event is less than unity and the fraction of halo gas accreted onto the black hole is constant.," Their approach yields a close match to our mass density, in particular when their simulation scenario G is considered, where the probability of forming a seed black hole during a merger event is less than unity and the fraction of halo gas accreted onto the black hole is constant."1186 This scenario yields a mass density of ~10 MMco ΜΜΡΟ when SMBHs with 10* MM at 66 are considered., This scenario yields a mass density of $\sim 10^3$ $_{\sun}$ $^{-3}$ when SMBHs with $10^8$ $_{\sun}$ at 6 are considered.1187 Since not all fAGN are likely to be located at such high redshifts. their model variant B. in which the halo gas acecretion. fraction is proportional to the halo virial velocity squared. is also promising. and yields à mass density of ~5-107 MMe MMpe™.," Since not all fAGN are likely to be located at such high redshifts, their model variant B, in which the halo gas accretion fraction is proportional to the halo virial velocity squared, is also promising, and yields a mass density of $\sim 5\cdot 10^2$ $_{\sun}$ $^{-3}$ ."1188 Another attempt to model SMBH, Another attempt to model SMBH1189The surge of activity. over the past decade or so in the fields of supernovae ancl οἱ eamnin-ray bursts and their afterglows has led to renewed investigation into the behavior of strong shocks.,The surge of activity over the past decade or so in the fields of supernovae and of gamma-ray bursts and their afterglows has led to renewed investigation into the behavior of strong shocks.1190 Much of the analvtic work on strong shock propagation to date has focused on self-similar solutions to the hydrodynamic equations., Much of the analytic work on strong shock propagation to date has focused on self-similar solutions to the hydrodynamic equations.1191 Ii these solutions. the profiles of the hvdrodyvnamic variables as Functions of position have constant overall shapes whose time evolution consists simply of scalings in amplitude and position.," In these solutions, the profiles of the hydrodynamic variables as functions of position have constant overall shapes whose time evolution consists simply of scalings in amplitude and position."1192 As a result. self-similarity allows us to reduce the nominal svstem of 6wo-dimensional partial differential hydrodyvnamic," As a result, self-similarity allows us to reduce the nominal system of two-dimensional partial differential hydrodynamic"1193present cannot be completely ruled out.,present cannot be completely ruled out.1194" The best-fit companion would have a flux ratio of 3.0x10? and would be located at (E: mmas, N: mmas) from tau Cet."," The best-fit companion would have a flux ratio of $3.0\times10^{-3}$ and would be located at (E: mas, N: mas) from tau Cet."1195" This potential companion would, however, not be bright enough to explain the K-band excess found by ?.."," This potential companion would, however, not be bright enough to explain the K-band excess found by \citet{DiFolco07}."1196" This A3 main sequence star, located at 49+4 ppc, is a known astrometric binary with poorly constrained orbital parameters (?).."," This A3 main sequence star, located at $49\pm4$ pc, is a known astrometric binary with poorly constrained orbital parameters \citep{Goldin07}."1197" ? shows that its radial velocity is variable and also identifies it as a binary, but fails to constrain the orbit of the companion due to the small time span of their observations («400 ddays)."," \citet{Lagrange09b} shows that its radial velocity is variable and also identifies it as a binary, but fails to constrain the orbit of the companion due to the small time span of their observations $<400$ days)."1198" With our PIONIER observations, we directly detect the companion for the first time, although with some ambiguity on its position."," With our PIONIER observations, we directly detect the companion for the first time, although with some ambiguity on its position."1199" The orbital parameters cannot be refined based on this sole measurement, and would require the binary to be observed again at several phases along its orbit."," The orbital parameters cannot be refined based on this sole measurement, and would require the binary to be observed again at several phases along its orbit."1200" However, with this single snapshot, we can readily estimate the spectral type of the companion."," However, with this single snapshot, we can readily estimate the spectral type of the companion."

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