ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 The foregoing considerations are specific to ie anisotropy power spectrum. but it may be yossible to detect microwave cussion from the wini-halos in other wavs.," The foregoing considerations are specific to the anisotropy power spectrum, but it may be possible to detect microwave emission from the mini-halos in other ways."3 In particular we note iat the brightest muni-halos may be detectable as iudividual sources., In particular we note that the brightest mini-halos may be detectable as individual sources.4 In this case those sources should also be bright a eamuna-ravs. and a sensible strategy is therefore to search for microwave counterparts to the Unidentified ECRET sources (Walker. Mori and Olishi 2003).," In this case those sources should also be bright in gamma-rays, and a sensible strategy is therefore to search for microwave counterparts to the Unidentified EGRET sources (Walker, Mori and Ohishi 2003)."5 We also note the possibility of detecting the predicted microwave foreground component via its mean intensity which. as noted earlier. is much larger than the anisotropy level.," We also note the possibility of detecting the predicted microwave foreground component via its mean intensity which, as noted earlier, is much larger than the anisotropy level."6 For erev-body cussion the mca intensity is roughly 30/|sinb|As in the Rayleigh-Jeans regine.," For grey-body emission the mean intensity is roughly $30/|\sin\,b|\;{\rm\mu K}$ in the Rayleigh-Jeans regime."7 The fact tha the present model naturally vields a deeree-scale anisotropy peak. in the form of low-temperature thermal radiation. sugecsts that it nuelt ο possible to construct a model in which the observed microwave anisotropies are interpreted cutively im terms of cussion from muni-halos.," The fact that the present model naturally yields a degree-scale anisotropy peak, in the form of low-temperature thermal radiation, suggests that it might be possible to construct a model in which the observed microwave anisotropies are interpreted entirely in terms of emission from mini-halos."8 In support of this idea we note that (i) the frequency dependence of the auisotropies would be quite simall (assuming ai grev-body spectra at 12 Ν see fieure 5). aud (41) the reating rate of the clouds might be rather larger han our estimate. either because of a very large »pulatiou of low-enerev cosnüc-cravs (see the discussion in ll). or because there are other reat) sources which are more muportant than οδόπαν».," In support of this idea we note that (i) the frequency dependence of the anisotropies would be quite small (assuming a grey-body spectrum at 4.2 K – see figure 5), and (ii) the heating rate of the clouds might be rather larger than our estimate, either because of a very large population of low-energy cosmic-rays (see the discussion in 4.1), or because there are other heat sources which are more important than cosmic-rays."9 However. a generic prediction of any such model is a strong latitude dependence of he peak power. aud this is at odds with existing constraints on any latitude dependence (Cariffitls," However, a generic prediction of any such model is a strong latitude dependence of the peak power, and this is at odds with existing constraints on any latitude dependence (Griffiths"10least two subcomponents are emerging [from the stationary subcomponent in the eastern. end of LIST-1 at. times shown by arrows in Fig.,least two subcomponents are emerging from the stationary subcomponent in the eastern end of HST-1 at times shown by arrows in Fig.11 Baa (Cheungetal.2007).. which implies that the newly emerging subcomponent(s) has a relatively steep. spectrum. ancl hence changes the hardness of the overall spectrum of LIST-1 during the outburst assuming that the spectrum keeps constant for the stationary subcomponent.," \ref{fig2}a a \citep{che07}, which implies that the newly emerging subcomponent(s) has a relatively steep spectrum, and hence changes the hardness of the overall spectrum of HST-1 during the outburst assuming that the spectrum keeps constant for the stationary subcomponent."12 Note that the bright components of the radio jet appear to accelerate with distance from core to LIST-1 with subluminal speeds. whereas several knots placed further out from the core (0.8-6.3 aresec) move superluminallvs: down the jet (Stawarzctal.2006).," Note that the bright components of the radio jet appear to accelerate with distance from core to HST-1 with subluminal speeds, whereas several knots placed further out from the core (0.8-6.3 arcsec) move superluminally down the jet \citep{sta06}."13.. In. particular. multi-epoch optical ancl Very Long Baseline Array (WLBA) observations all showed. that the unresolved stationary feature at. the upstream edee of the LIST-1 knot seems to emit various subcomponents down the jet with relativistic speed (Direttaetal.1999:Cheungοἱ 2007).," In particular, multi-epoch optical and Very Long Baseline Array (VLBA) observations all showed that the unresolved stationary feature at the upstream edge of the HST-1 knot seems to emit various subcomponents down the jet with relativistic speed \citep{bir99, che07}."14.. Phat is to καν. except for the stationary subcomponent which is special cluc to either standing shock or optical opacity there. all other subcomponents may well be accelerated. and electrons are energized in this region.," That is to say, except for the stationary subcomponent which is special due to either standing shock or optical opacity there, all other subcomponents may well be accelerated, and electrons are energized in this region."15 On the other hand. a major Dare of HIST-1 occurred during the period. of 2003 to 2007. accompanied by two subcomponents emerging from. the stationary one in the rising stage (Cheungetal.2007:Llar-risetal.2009).," On the other hand, a major flare of HST-1 occurred during the period of 2003 to 2007, accompanied by two subcomponents emerging from the stationary one in the rising stage \citep{che07,har09}."16.. Acliabatic compression at least should. no be the dominant mechanism for energizing the racdiating electrons. or else the spectra would be hardening in the rising stage (Llarrisetal.2003). which is contrary to the observec results.," Adiabatic compression at least should not be the dominant mechanism for energizing the radiating electrons, or else the spectra would be hardening in the rising stage \citep{har03}, which is contrary to the observed results."17 Lt is more likely that. as suggested by Llarrisetal.(2003).. the increased. intensity arises from the injection of new radiating particles that are energized in the region of HIS'T-1 due to the fact that no significant. emission. [rom radio to X-ray are detected immediately upstream of LIST- even in the outburst period.," It is more likely that, as suggested by \cite{har03}, the increased intensity arises from the injection of new radiating particles that are energized in the region of HST-1 due to the fact that no significant emission from radio to X-ray are detected immediately upstream of HST-1 even in the outburst period."18 Hence. there must be a way or mechanism. for example. a helical magnetic field. that plays a role in feature acceleration ancl particle energizing in the major outburst. which will be further discussed bellow.," Hence, there must be a way or mechanism, for example, a helical magnetic field, that plays a role in feature acceleration and particle energizing in the major outburst, which will be further discussed bellow."19 According to theoretical models (e.g... Meierctal.2001). jets in AGN are. propelled ancl collimatecl by magnetic iclds twisted by differential rotation of the black holejs accretion disk or inertial-Lrame- dragging ergosphere. aud he primary observational indicator of magnetic collimation requiring a helical magnetic field in the spine of the jet is he evolution of the polarization. which manifests as ΕΝΑ rotation as a feature accelerates and focuses along its spiral xüh (Alarseheretal.2008).," According to theoretical models (e.g., \citealt{mei01}) ), jets in AGN are propelled and collimated by magnetic fields twisted by differential rotation of the black hole¡¯s accretion disk or inertial-frame- dragging ergosphere, and the primary observational indicator of magnetic collimation requiring a helical magnetic field in the spine of the jet is the evolution of the polarization, which manifests as EVPA rotation as a feature accelerates and focuses along its spiral path \citep{mar08}."20. The EVPA rotation has been detected in the monitoring of EVPA to the sources BL Lac and PIS 1510-089 (Marscherctal.2008.2010).," The EVPA rotation has been detected in the monitoring of EVPA to the sources BL Lac and PKS 1510-089 \citep{mar08,mar10}."21. Through multi-epoch. polarized VLA observations at. 3. wavebancs over 3 vears. we find a similar case with the feature HST-1 in AIST jet.," Through multi-epoch polarized VLA observations at 3 wavebands over 3 years, we find a similar case with the feature HST-1 in M87 jet."22 The intrinsic ΜΟΝΟΛΑ changes with time in a regular wav. as is shown in the top panel of Fig. 3..," The intrinsic EVPA changes with time in a regular way, as is shown in the top panel of Fig. \ref{fig3}."23 In this map. the Faraday rotation elfect. which will give rise to EVPA change by Ay=ΗΛΙΑΣ. has been eliminated at all the epochs.," In this map, the Faraday rotation effect, which will give rise to EVPA change by $\rm{\triangle\chi =24RM\lambda^2}$, has been eliminated at all the epochs."25 Here. RAL is obtained through fits of EVPA to the wavelength square A7.," Here, RM is obtained through fits of EVPA to the wavelength square $\lambda^2$."26 Except for the epoch 2007 Aug. 10. at which the observational EVDPAs of calibrator 3€ 286. and hence. AIST at 22 Cllz are not available. the resultant RAL-corrected EWPA shows a roughly monotonous variation from 90° to ~0," Except for the epoch 2007 Aug. 10, at which the observational EVPAs of calibrator 3C 286, and hence M87 at 22 GHz are not available, the resultant RM-corrected EVPA shows a roughly monotonous variation from $\sim-90^\circ$ to $\sim0^\circ$."27 Although the monotonous variation of EVPA may be also interpreted as a random. walk of the resultant. polarization vector direction as simulation cells with random. magnetic field orientations enter and then exit the emission region. the probability is supposed to be very low (Marscherοἱal. 2010)..," Although the monotonous variation of EVPA may be also interpreted as a random walk of the resultant polarization vector direction as simulation cells with random magnetic field orientations enter and then exit the emission region, the probability is supposed to be very low \citep{mar10}. ."28 It is more likely that the observed long-term IVIA variation is dictated by the magnetic geometry. as suggested bv Marscherctal.(2008).," It is more likely that the observed long-term EVPA variation is dictated by the magnetic geometry, as suggested by \cite{mar08}."29. Another point is that as mentioned above. the emission features may well be accelerated in HST-1 region. which is also supported by the fact that almost all subcomponents within HIS'T-1 move superluminally (Cheungetal.2007).. and acceleration. obviously occurs. for LIST-1 itself. over he whole major outhurst period (Ciovanninietal.2011).. whereas all components upstream of LIST-1 are subluminal (Stzwarzetal.2006).," Another point is that as mentioned above, the emission features may well be accelerated in HST-1 region, which is also supported by the fact that almost all subcomponents within HST-1 move superluminally \citep{che07}, and acceleration obviously occurs for HST-1 itself over the whole major outburst period \citep{gio11}, whereas all components upstream of HST-1 are subluminal \citep{sta06}."30. Jased on the model proposed. by Alarscheretal.(2008).. the emission. features will move ollowing a spiral path if a helical magnetic field exists. and cilferent features may follow cifferent subset. of streamlines hrough the acceleration andcollimation zone.," Based on the model proposed by \cite{mar08}, the emission features will move following a spiral path if a helical magnetic field exists, and different features may follow different subset of streamlines through the acceleration andcollimation zone."31 This scenario i been definitely detected. by the multi-epoch. VLBA, This scenario has been definitely detected by the multi-epoch VLBA32reflection. each of unit radius.,"reflection, each of unit radius."33 The function 7f endows each point in the sky with a complex phase., The function ${\cal H}$ endows each point in the sky with a complex phase.34 In correspondence with the Fourier shift theorem aa phase shift corresponds to a spatial shift) this point is then moved in to the third dimension of power-spectrum which corresponds to the w-direction of theionosphere’., In correspondence with the Fourier shift theorem a phase shift corresponds to a spatial shift) this point is then moved in to the third dimension of power-spectrum which corresponds to the $w$ -direction of the.35 Realistic interferometers neither observe the full sky. nor sample the electric field in the full plane of the array.," Realistic interferometers neither observe the full sky, nor sample the electric field in the full plane of the array."36" If we define the complex electric field beam pattern as B(s,,.ο) and the sampling function of the electric field on the plane of the interferometer uusually delta functions at the positions of the antennae) as Ptr.v) and its Fourier transform as διs,). then Eqn.(23)) for incoherent emitters can be rewritten as: where we suppressed the explicitly dependence of the functions on the (s,.5.δις) Or (1.v.Ww)."," If we define the complex electric field beam pattern as ${B}(s_{u},s_{v})$ and the sampling function of the electric field on the plane of the interferometer usually delta functions at the positions of the antennae) as ${P}(u,v)$ and its Fourier transform as $\tilde{P}(s_{u},s_{v})$, then \ref{eqn:powerspectrum}) ) for incoherent emitters can be rewritten as: where we suppressed the explicitly dependence of the functions on the $(s_{u},s_{v},s_{w})$ or $(u,v,w)$."37 The equation holds for each given w., The equation holds for each given $w$.38 The usual two dimensional array point spread function ddirty beam) is denoted by [PF and its Fourier transform is the visibility sampling function in the av plane., The usual two dimensional array point spread function dirty beam) is denoted by $|\tilde{P}|^{2}$ and its Fourier transform is the visibility sampling function in the $uv$ plane.39 Similarly. [Ε|- is the usual two dimensional antenna beam pattern.," Similarly, $|B|^{2}$ is the usual two dimensional antenna beam pattern."40 This equation shows clearly that the visibilities of the incident intensity field are both multiplied with the Fourier transforms of power-spectrum of the ionosphere and that of the «v sampling function. respectively.," This equation shows clearly that the visibilities of the incident intensity field are both multiplied with the Fourier transforms of power-spectrum of the ionosphere and that of the $uv$ sampling function, respectively."41 The resulting field is then convolved with the Fourier. transform of the rescaled beam pattern. which to first order (1f the beam is much smaller than the sky) is the aperture gain pattern of the antennae.," The resulting field is then convolved with the Fourier transform of the rescaled beam pattern, which to first order (if the beam is much smaller than the full sky) is the aperture gain pattern of the antennae."42 To derive fullΦ/Γ} from this equation thus requires deconvolution of the observed visibilities of the scattered intensity field., To derive $|\tilde{\Phi} |^{2})$ from this equation thus requires deconvolution of the observed visibilities of the scattered intensity field.43 This could be difficult in principle were it not for the fact that the beam size in general is much larger than the extent of the the dirty beam., This could be difficult in principle were it not for the fact that the beam size in general is much larger than the extent of the and the dirty beam.44 In that case the scale over which Tb)παπά.TOP.) varies is very large compared to. the convolution kernel and the latter can be neglected for modes much smaller than the field of view., In that case the scale over which ${\cal F}(|\tilde{\Phi} |^{2})\times {\cal F}(|\tilde{P}|^{2})$ varies is very large compared to the convolution kernel and the latter can be neglected for modes much smaller than the field of view.45 Hence in practice it is expected that the deconvolution is not really required to obtain an accurate evaluation of the power-spectrum —d[)., Hence in practice it is expected that the deconvolution is not really required to obtain an accurate evaluation of the power-spectrum $|\tilde{\Phi} |^{2}$ ).46 Whereas in this paper we started our discussion from the Born approximation and derived the scattered field. this is only a valid approach in the weak scattering scattering or weak scintillating regime.," Whereas in this paper we started our discussion from the Born approximation and derived the scattered field, this is only a valid approach in the weak scattering scattering or weak scintillating regime."47 Despite this approximation. it is remarkably accurate up to intensity fluctuations very close to unity.," Despite this approximation, it is remarkably accurate up to intensity fluctuations very close to unity."48 However. there are other ways to solve for the scattered electric field in the weak scattering regime that are closely connected to the formalism as introduced above and to the phase-screen approach.," However, there are other ways to solve for the scattered electric field in the weak scattering regime that are closely connected to the formalism as introduced above and to the phase-screen approach."49 Instead of looking at every point of the medium as à source of a single scattering (as is done in the Born approximation). one can also assume that the medium does not modify the amplitude of the incident wave to first order and that light rays travel on a straight line through the medium.," Instead of looking at every point of the medium as a source of a single scattering (as is done in the Born approximation), one can also assume that the medium does not modify the amplitude of the incident wave to first order and that light rays travel on a straight line through the medium."50 In that case. since the medium does not absorb or amplify the wave. only a phase shift occurs between different points in the medium when a plane wave enters the ionosphere.," In that case, since the medium does not absorb or amplify the wave, only a phase shift occurs between different points in the medium when a plane wave enters the ionosphere."51 We can again describe this in terms of the refractive index or electron density as follows., We can again describe this in terms of the refractive index or electron density as follows.52 A phase shift of Ow=k[δηds is introduced between a wave traveling in a medium with refractive index |+on(r) and unity. respectively. where the integral is carried out along a straight line through the medium1971).," A phase shift of $\delta \psi \approx 53k \int \delta n(\vc{r})\, ds$ is introduced between a wave traveling in a medium with refractive index $1+\delta n(\vc{r})$ and unity, respectively, where the integral is carried out along a straight line through the medium."54. A plane wave of a source with unit amplitude entering medium exits as a wave with a “wrinkled” phase-front due to varying refractive indices along different paths1972)., A plane wave of a source with unit amplitude entering medium exits as a wave with a “wrinkled” phase-front due to varying refractive indices along different paths.55. The auto-correlation of this “phase-screen™ is the function with which the visibilities of that source are multiplied in the wv-plane and its Fourier transform is the aas we discussed it before., The auto-correlation of this “phase-screen” is the function with which the visibilities of that source are multiplied in the $uv$ -plane and its Fourier transform is the as we discussed it before.56 This allows us to directly connect the previous analysis with that of the phase-sereen through the so-called Radon transform. which ts related to the Fourier projection-slice theorem.," This allows us to directly connect the previous analysis with that of the phase-screen through the so-called Radon transform, which is related to the Fourier projection-slice theorem."57 The Fourier projection-slice theorem1986).. in our context. states that the two-dimensional Fourier transform of the Radon projection 1983).. along straight lines. of a three-dimensional medium equals a two-dimensional slice (perpendicular to the projection direction) through the three-dimensional Fourier transform of the object.," The Fourier projection-slice theorem, in our context, states that the two-dimensional Fourier transform of the Radon projection , along straight lines, of a three-dimensional medium equals a two-dimensional slice (perpendicular to the projection direction) through the three-dimensional Fourier transform of the object."58 We now note that the phase-screen. up to a constant. is in fact a two-dimensional projection of the refractive index ón(r) in three dimensions.," We now note that the phase-screen, up to a constant, is in fact a two-dimensional projection of the refractive index $\delta n(\vc{r})$ in three dimensions."59 Hence the Fourier transform of the phase-screen is simply a two-dimensional slice through the three-dimensional Fourier transform of the refractive index ón(r) of the medium., Hence the Fourier transform of the phase-screen is simply a two-dimensional slice through the three-dimensional Fourier transform of the refractive index $\delta n(\vc{r})$ of the medium.60 The autocorrelation of the phase-screen as measured in the in plane is then a slice through the three dimensional power spectrum of the refractive index. hence that of the electron density distribution.," The autocorrelation of the phase-screen as measured in the $uv$ -plane is then a slice through the three dimensional power spectrum of the refractive index, hence that of the electron density distribution."61 We immediately see the connection to the discussion in Section 5 and how this connects to Eqn.(11))., We immediately see the connection to the discussion in Section 5 and how this connects to \ref{eqn:scattering_psf}) ).62 Since point-sources in different directions project the three dimensional power-spectrum differently on the in plane. they probe different slices through the power-spectrum.," Since point-sources in different directions project the three dimensional power-spectrum differently on the $uv$ -plane, they probe different slices through the power-spectrum."63 Disregarding the geometric curvature terms. this slice is the tangent plane to the Ewald sphere of influence at the point s— which for small vectorial differences are all slices through S—Sy=(0.0.0). which ts exactly the Fourier projection-slice theorem.," Disregarding the geometric curvature terms, this slice is the tangent plane to the Ewald sphere of influence at the point $\vc{s}-\vc{s}_{0}$ which for small vectorial differences are all slices through $\vc{s}-\vc{s}_{0} =(0,0,0)$, which is exactly the Fourier projection-slice theorem."64 Observing over à wide field of view allows one to build of a three-dimensional electron density power-spectrum from these different slices., Observing over a wide field of view allows one to build of a three-dimensional electron density power-spectrum from these different slices.65 Obviously the measured auto-correlation of the phases are the result of many point sources and need to be disentangled., Obviously the measured auto-correlation of the phases are the result of many point sources and need to be disentangled.66" This was discussed in Section 5 in detail and is identical in the current situation,", This was discussed in Section 5 in detail and is identical in the current situation.67 Thence. the phase-sereen approach extended to three dimensions is completely identical to the approach taken in this paper.," Thence, the phase-screen approach extended to three dimensions is completely identical to the approach taken in this paper."68 A tomographic method has been introduced that allows to quantify the three-dimensional power-spectrum of the ionospheric electron-density fluctuations. based on. radio- observations by à two-dimensional planararray., A tomographic method has been introduced that allows to quantify the three-dimensional power-spectrum of the ionospheric electron-density fluctuations based on radio-interferometric observations by a two-dimensional planararray.69 The goal has been to provide a more complete and, The goal has been to provide a more complete and70facts at hand.,facts at hand.71 Demanding that the coefficient of the 7? term vanish requires C1 − ∕∣∣∣⊻⋤≹∐∶∣∣ JE ασ) EX, Demanding that the coefficient of the $T^2$ term vanish requires C - D = _0^2 A_0 ] 3.084 T_0^2.72"E The lattice calculations of [33] found that 260.24 GeV?,", The lattice calculations of \cite{HotQCD} found that $2C \approx 0.24$ $^2$ .73 This translates into Czz3.3770 usinge their value of Tyzz190 MeV. There are no calculations of the j? term in the pressure. but (his analvsis suggests (hat D is very small: we shall take it to be zero for simplicity of exposition.," This translates into $C \approx 3.3 T_0^2$ using their value of $T_0 \approx 190$ MeV. There are no calculations of the $\mu^2$ term in the pressure, but this analysis suggests that $D$ is very small; we shall take it to be zero for simplicity of exposition."74 With even larger uncertainties Ref., With even larger uncertainties Ref.75 [33]. found that Bo~Tj., \cite{HotQCD} found that $B \sim T_0^4$.76 For a reasonable interpolation of the lattice results near ancl just above the crossover reelon we take (he coellicient to be 0.8., For a reasonable interpolation of the lattice results near and just above the crossover region we take the coefficient to be 0.8.77 The parameterization is therefore P = E losgsll212 QOIS 1 ONT Ti gars da , The parameterization is therefore P = T^4 + ^2 T^2 + ^4 - 3.084 T_0^2 T^2 - 0.8 T_0^4 s = T^3 + ^2 T - 6.168 T_0^2 T n = T^2 + ^3 = - P +Ts + n .78The critical pressure is computed [rom this to be D.=0.74971., The critical pressure is computed from this to be $P_c = 0.749 T_0^4$.79 The critical entropy densitv. s. barvon density. ο. and energy density e. of course depend on the choice of 7; and therefore µ..," The critical entropy density $s_c$, baryon density $n_c$ , and energy density $\epsilon_c$ of course depend on the choice of $T_c$ and therefore $\mu_c$."80 All that remains is (o specify An al T—0 and [ο, All that remains is to specify $\Delta n$ at $T=0$ and $f_{\sigma}$.81" Since f, is assumed to be constant. itis natural that it be proportional to D."," Since $f_{\sigma}$ is assumed to be constant, it is natural that it be proportional to $P_c$."82" For definiteness we shall take f,=5D.22512 /Im? and An=n,/3.", For definiteness we shall take $f_{\sigma} = 5P_c \approx 512$ $^3$ and $\Delta n = n_c/3$.83" In what follows we shalluse all of the aboveparameterizations and only vary 7,(o see what effect it might have on heavy ion collisions.", In what follows we shalluse all of the aboveparameterizations and only vary $T_c$to see what effect it might have on heavy ion collisions.84subsamples is a little. lower than that of the full A- sample. by about LO per cent. which corresponds to 32 per cent in the ων.,"subsamples is a little lower than that of the full $K$ -limited sample, by about 19 per cent, which corresponds to 32 per cent in the $A_{\omega}$."85 The reason lor this is that photometric redshifts are not always accurate and thus the low and highin] redshift subsamples will both experience some contamination [rom galaxies in the other redshift range. which are not correlated with the correctly selected galaxies and dilute the observable clustering.," The reason for this is that photometric redshifts are not always accurate and thus the low and high redshift subsamples will both experience some contamination from galaxies in the other redshift range, which are not correlated with the correctly selected galaxies and dilute the observable clustering."86 HE for example. the true w(8) of the lower redshift ERGs is cl) and of the high τν. and we examine a Low phot SUbsample with a contamination a. the wf) we calculate will casscCLou|aou.," If, for example, the true $\omega(\theta)$ of the lower redshift ERGs is $A_{l}$ and of the high $A_{h}$, and we examine a low $z_{phot}$ subsample with a contamination $\alpha$, the $\omega(\theta)$ we calculate will be $A_{obs}\simeq (1-\alpha)^2 A_{l} + \alpha^2 A_{h}$."87 ‘The observed. shortfall could » accounted for by a2 0.20., The observed shortfall could be accounted for by $\alpha\simeq 0.20$ .88 We have not attempted to correct. for this is deriving a roy. and thus the low and high redshift roy will both be slight underestimates. (by similar amounts. as here the two subsamples have similar size anc clustering).," We have not attempted to correct for this is deriving a $r_{c0}$, and thus the low and high redshift $r_{c0}$ will both be slight underestimates, (by similar amounts, as here the two subsamples have similar size and clustering)."89 Secondly. it Cah be SCCDL that the higher. redshift subsamples have a comoving ro similar to or even a little. ereater than the lower redshift ERGs.," Secondly, it can be seem that the higher redshift subsamples have a comoving $r_0$ similar to or even a little greater than the lower redshift ERGs."90 This is clearly more consistent with comoving clustering rather than stable clustering., This is clearly more consistent with comoving clustering rather than stable clustering.91 The slight increase in rg with redshift. if real could. rellect a stronger clustering for more massive/luminous ERGs.," The slight increase in $r_{c0}$ with redshift, if real could reflect a stronger clustering for more massive/luminous ERGs."92 Comoving clustering of ry~192 * Alpe is CONSIS~CHL witi the clustering. of both shallower (Dacleli et al., Comoving clustering of $r_0\simeq 12$ $13 h^{-1}$ Mpc is consistent with the clustering of both shallower (Daddi et al.93 2000) and deeper ERG samples. e.g. Daceli et al (2004) estimate ry0 17h+ Apc at Ly<2«2.y 3.," 2000) and deeper ERG samples, e.g. Daddi et al (2004) estimate $r_0=9$ $17 h^{-1}$ Mpc at $1.7<z<2.3$ ."94 Extrapolateck to. lower redshifts. this model would overpredict the clustering of local passive galaxies of all unminositles. ty=T.2h Mpe (Alacdewiek et al.," Extrapolated to lower redshifts, this model would overpredict the clustering of local passive galaxies of all luminosities, $r_0=7.2 h^{-1}$ Mpc (Madgwick et al."95 2003) nut be consisten with the clustering of the most luminous (Alp< ) earlv-tvpes at 0:32<0.9. rg11.2x1.0h x: comoving (Brown et al.," 2003), but be consistent with the clustering of the most luminous $M_R<-22.27$ ) early-types at $0.3<z<0.9$, $r_0=11.2\pm 1.0 h^{-1}$ Mpc comoving (Brown et al."96 20)3)., 2003).97 This can 2€ CX.Xained i£ (1) many of the zz1 ERGs undergo further mereing to become very massive ellipticals. (ii) only some (~ yall) of he mocderate-Iuminosity E/SOs found locally have evolved ¢irectIy from 2>1 ERGs and the others are formed at z1 from mergers of less strongly clustered spirals. thus cliluting he clustering.," This can be explained if (i) many of the $z>1$ ERGs undergo further merging to become very massive ellipticals, (ii) only some $\sim $ half) of the moderate-luminosity E/S0s found locally have evolved directly from $z>1$ ERGs and the others are formed at $z\leq 1$ from mergers of less strongly clustered spirals, thus diluting the clustering."98 To |Yetter understand. the evolution. of ERGs it will be usefu to compare their clustering. with hat of their their likely progenitors at higher redshifts. suchas sub-mum ealaxies. for which the clustering will be measured in the ongoing SLLADES survey.," To better understand the evolution of ERGs it will be useful to compare their clustering with that of their their likely progenitors at higher redshifts, suchas sub-mm galaxies, for which the clustering will be measured in the ongoing SHADES survey."99 There is already evidence that the most massive Lyman break galaxies at z4 have a similar comoving ry (114225.+ Mpe) tothe z~1 2 ERGs (Allen et al., There is already evidence that the most massive Lyman break galaxies at $z\sim 4$ have a similar comoving $ r_0$ $11.4\pm 2 h^{-1}$ Mpc) to the $z\sim 1$ –2 ERGs (Allen et al.100 2005)., 2005).101 We perform spectroscopic age-dating of the ERGs by fitting their SEDs with passively evolving models (from Jiment ool al., We perform spectroscopic age-dating of the ERGs by fitting their SEDs with passively evolving models (from Jimenez et al.102 2004). and obtain mean stellar ages ranging widely [rom ο 104.5 Cyr. with a mean of 2.10.3 Cor.," 2004), and obtain mean stellar ages ranging widely from 0.6 to 4.5 Gyr, with a mean of $2.1\pm 0.3$ Gyr."103 We can compare these results with similar age-dating analvses performed by other authors. though must be careful to consider the dilferences in how the sample are selected.," We can compare these results with similar age-dating analyses performed by other authors, though must be careful to consider the differences in how the sample are selected."104 Firstly. Dacddi al. (, Firstly Daddi et al. (105"2004) give ages (from. FORS2 spectra) for 9 {ν-selected (IN,< 20) very massive star-forming galaxies at licis2233 note that not all of these are red enough to be called ERGs.",2004) give ages (from FORS2 spectra) for 9 $K$ -selected $K_s<20$ ) very massive star-forming galaxies at $1.7<z<2.3$ – note that not all of these are red enough to be called ERGs.106 Daddi et al. (, Daddi et al. (1072005) give ages [rom low-resolution ACS spectra of 7 ERGs at 1.39.<τς247. of which 5 are passive cllipticals ane » weakly star-forming.,"2005) give ages from low-resolution ACS spectra of 7 ERGs at $1.39<z<2.47$, of which 5 are passive ellipticals and 2 weakly star-forming."108 AleCarthy ct al. (, McCarthy et al. (1092004) using Gemini Deep Deep Survey spectra. give ages for a varied sample of 20 red (£0A7 3.5) ealaxies at. 1.3<z«2.2.,"2004) using Gemini Deep Deep Survey spectra, give ages for a varied sample of 20 red $I-K>3.5$ ) galaxies at $1.3<z<2.2$."110 Finally. Longhetti et al. (," Finally, Longhetti et al. ("1112005) using low-resolution NIIU spectra (observed. with NICS on the La Palma Ελα). estimate mass-weighted ages for10 of the most. bright. CA 16.618.4) ancl massive ECis (Roo- 5.0) present at z~ 1.5.,"2005) using low-resolution NIR spectra (observed with NICS on the La Palma TNG), estimate mass-weighted ages for10 of the most bright $K^{\prime}=16.6$ –18.4) and massive ERGs $R-K^{\prime}>5.0$ ) present at $z\sim 1.5$ ."112 Figure 9 plots stellar age Zp. against spectroscopic redshift) for all these samples. with loci of the redsrifts corresponding to time Zi... before observation.," Figure 9 plots stellar age $T_{pas}$ against spectroscopic redshift for all these samples, with loci of the redshifts corresponding to time $T_{pas}$ before observation."113quadruplets that include the object P; as one of their members.,quadruplets that include the object $P_i$ as one of their members.114" The s;-histograms emphasize the topological ghosts: if ghost images really exist. they show some hills in the large-s; region,"," The $s_i$ -histograms emphasize the topological ghosts: if ghost images really exist, they show some hills in the $s_i$ region."115 We tested the method in catalogs of toy quasars with no observational uncertainties., We tested the method in catalogs of toy quasars with no observational uncertainties.116 We considered the severest cases for each type of holonomies. and any holonomies except for the targeted ones are assumed to be beyond the observed region.," We considered the severest cases for each type of holonomies, and any holonomies except for the targeted ones are assumed to be beyond the observed region."117 The translational distance of each holonomy is fixed with L16 Gpe for which 8=(16/2) Gpe corresponds to z~5. and the shell region is chosen as 7.8 Gpe<r «8.2 Gpe (4.7<z 5.5).," The translational distance of each holonomy is fixed with $L=16$ Gpc for which $8=(16/2)$ Gpc corresponds to $z \sim 5$, and the shell region is chosen as 7.8 $<r<$ 8.2 Gpc $4.7 \lesssim z \lesssim 5.5$ )."118 In this situation. where the space is comparable to the observed region in size. existing crystallography method is no longer valid due to the contamination of false signal.," In this situation, where the space is comparable to the observed region in size, existing crystallography method is no longer valid due to the contamination of false signal."119" It is found that our filters are able to eliminate such contamination, and the existence of topological ghosts is clearly recognized by the 5;-histograms."," It is found that our filters are able to eliminate such contamination, and the existence of topological ghosts is clearly recognized by the $s_i$ -histograms."120 For practical application of our method. more realistic simulations are necessary. and will be carried out in the next paper.," For practical application of our method, more realistic simulations are necessary, and will be carried out in the next paper."121 They will include more realistic characteristics of quasars such às spatial correlations. activity cycles. and anisotropic. morphology.," They will include more realistic characteristics of quasars such as spatial correlations, activity cycles, and anisotropic morphology."122 Technical problems such às nagnitude limits and selection biases will also be considered there., Technical problems such as magnitude limits and selection biases will also be considered there.123 Presently available data in the latest versions of the Vérron-Cetty Vérron quasar catalog (Véllon-Cetty Vérron 2010) and the Sloan Digital Sky Survey (SDSS) quasar catalog (Schneider et al., Presently available data in the latest versions of the V\'erron-Cetty Vérron quasar catalog (Véllon-Cetty Vérron 2010) and the Sloan Digital Sky Survey (SDSS) quasar catalog (Schneider et al.124 2010) will be used to make more precise constraints. when compared with the previous constraints that ignore the lifetime of quasars.," 2010) will be used to make more precise constraints, when compared with the previous constraints that ignore the lifetime of quasars."125 Moreover. future observations that will detect hundreds of quasars with z>6 (e.g.. the Joint Astrophysics Nascent Universe Satellite (JANUS)). will enable us to remove the disagreement in the observational constraints using CMB data: specifically. we will detect or exclude the cubic 3-torus topology with L=3.8£;; mentioned by Aurich (2008).," Moreover, future observations that will detect hundreds of quasars with $z>6$ (e.g., the Joint Astrophysics Nascent Universe Satellite (JANUS)), will enable us to remove the disagreement in the observational constraints using CMB data; specifically, we will detect or exclude the cubic 3-torus topology with $L\simeq 3.8L_H$ mentioned by Aurich (2008)."126 We present the results for all types of holonomies here., We present the results for all types of holonomies here.127 The spatial resolutions used in these simulations are given in Table Al.., The spatial resolutions used in these simulations are given in Table \ref{table5}. .128 &' is defined as the maximum value of εν. ἓν. and &.. and we conservatively substitute (ήο.ο) for & ," $\varepsilon '$ is defined as the maximum value of $\varepsilon _x$, $\varepsilon _y$, and $\varepsilon _z$, and we conservatively substitute $(\varepsilon ', \varepsilon ', \varepsilon ')$ for $\vec \varepsilon$."129Those for glide reflection (type II) were determined in the same way as for half-turn corkserew motion (type II). while the others were determined in the same way as for parallel translation.," Those for glide reflection (type II) were determined in the same way as for half-turn corkscrew motion (type II), while the others were determined in the same way as for parallel translation."130 The reason we did so ts that. for the latter types of holonomies. the deviation of the observer's location from the center always pushes all the faces away. and makes it harder to detect them.," The reason we did so is that, for the latter types of holonomies, the deviation of the observer's location from the center always pushes all the faces away, and makes it harder to detect them."131 We cannot observe any ghosts except for those that stand very close to the faces of our Dirichlet domain., We cannot observe any ghosts except for those that stand very close to the faces of our Dirichlet domain.132 Hence a relative cosmic time between a quasar P; and its ghost y(P;) is very small. which leads to small positional uncertainties (integrated effect) and small spatial resolutions.," Hence a relative cosmic time between a quasar $P_i$ and its ghost $\gamma (P_i)$ is very small, which leads to small positional uncertainties (integrated effect) and small spatial resolutions."133 We located the observer at the center and used the correct coordinate axes., We located the observer at the center and used the correct coordinate axes.134 The situations in which these quantities deviate from them are discussed in section 5.2., The situations in which these quantities deviate from them are discussed in section 5.2.135 The results are given in Table A2 and Figures Al and A2.., The results are given in Table \ref{table6} and Figures \ref{figure7} and \ref{figure8}. .136 Relatively strong signals for half-turn corkserew motion (type II) and glide reflection (type II) stem from the large spatial resolution., Relatively strong signals for half-turn corkscrew motion (type II) and glide reflection (type II) stem from the large spatial resolution.137 The signals for n-th corkscrew motion for n=4.3. and 6 are also strong. since we have to use two filters to detect y and y.," The signals for $n$ -th corkscrew motion for $n=4,3,$ and 6 are also strong, since we have to use two filters to detect $\gamma$ and $\gamma ^{-1}$."138 We can see that the hills always appear. which are constituted by topological ghosts.," We can see that the hills always appear, which are constituted by topological ghosts."139 For a case where the clear distinction between the multiconnected space and the simply connected one is notseen. s;-histograms areindispensable to distinguish them.," For a case where the clear distinction between the multiconnected space and the simply connected one is notseen, $s_i$ -histograms areindispensable to distinguish them."140 Our method is valid for all flat spaces., Our method is valid for all flat spaces.141 As, As142 ≼↛⋜⋯∣⋡∢⋅↿⋖⋅≱∖↿∢⋅∠⇂⋜↧⋏∙≟⋜↧⊲↓⊔⊳∖⇂⇂↓↕∢⊾∺∟⊲∐∖∪⇂⋅⊏↥⊔⋠⊓⋅≱∖≼∙⋖⋅⊔↿≱∖∙∖⇁≱∖↿⋖⋅⊔↓⊳∖∶⋜↧ critical parameter in the model is the binary. separation. which is known for many S-type svmbiotic binaries (where periods are a few vears. typically) but not known for D-type systems (which are thought to be more widely separated and to have periods spanning one or more decades),"can be tested against the SEDs of quiescent systems: a critical parameter in the model is the binary separation, which is known for many S-type symbiotic binaries (where periods are a few years, typically) but not known for D-type systems (which are thought to be more widely separated and to have periods spanning one or more decades)."143 Attempts been made to constrain £4 for several welbstuclicc S-type systems (RW Ίνα Mikolajewska Omont 1998: AG. Pee and Z And Ivison et 11992. 1995) but these studies have usually had to rely on estimates of the optically thin. [ree-free. emission. in. the. sub-mum range derived from optical/ultraviolet (UV) free-free and »ound-free emission measures.," Attempts been made to constrain $\nu_{\rm t}$ for several well-studied S-type systems (RW Hya — ajewska Omont 1998; AG Peg and Z And — Ivison et 1992, 1995) but these studies have usually had to rely on estimates of the optically thin free-free emission in the sub-mm range derived from optical/ultraviolet (UV) free-free and bound-free emission measures."144 The consistency between the data ancl binary models revealed by the aforementioned work is not therefore based. on direct measurements. of he turnover frequency. only on an optically thin emission measure inferred from. optical/UV. spectroscopy.," The consistency between the data and binary models revealed by the aforementioned work is not therefore based on direct measurements of the turnover frequency, only on an optically thin emission measure inferred from optical/UV spectroscopy."145 \We need o sample the mmj/sub-mnm spectral energy. clistribution of S-type symbiotic stars in order to define the turnover requencey in à mocdel-independent manner., We need to sample the mm/sub-mm spectral energy distribution of S-type symbiotic stars in order to define the turnover frequency in a model-independent manner.146 For the investigation reported here. we selected the welstudied S-type system. Cl €vg. a proto-tvpical svmbiotic star with a known orbital period (Pan=S55.6 cle and a well-defined. spectroscopic orbit (Alikolajowska 1997: 3elezvisski οἱ 22000 and references therein).," For the investigation reported here, we selected the well-studied S-type system, CI Cyg, a proto-typical symbiotic star with a known orbital period $P_{\rm orb} = 855.6$ d) and a well-defined spectroscopic orbit ajewska 1997; Belczyńsski et 2000 and references therein)."147" A thorough spectroscopic study of Cl Cvg by Wkenvon et (1991) demonstrated that it consists ofan ΜΟΙ asymptotic branch elant. A,~1.5Mz. anda ~0.5AL: companion separated byAU."," A thorough spectroscopic study of CI Cyg by Kenyon et (1991) demonstrated that it consists of an II asymptotic branch giant, $M_{\rm g} \sim 1.5\, \rm M_{\sun}$, and a $\sim 0.5\, \rm M_{\sun}$ companion separated by."148.. Our objective was to define the shape of the spectral energy. distribution from centimetre (em) to sub-mm. wavelengths. determining ™ and thus quantitatively testing and cdiscriminating between the existing mocdels for svmbiotic binaries.," Our objective was to define the shape of the spectral energy distribution from centimetre (cm) to sub-mm wavelengths, determining $\nu_{\rm t}$ and thus quantitatively testing and discriminating between the existing models for symbiotic binaries."149 In 822. We report our measurements of CL Cve. which we obtained. near-simultancously at wavelengths between sam and Geen during 1998 January ancl February.," In 2, we report our measurements of CI Cyg, which we obtained near-simultaneously at wavelengths between $\mu$ m and cm during 1998 January and February."150 Our interpretation of the resulting spectral energy. distribution is presented in 833., Our interpretation of the resulting spectral energy distribution is presented in 3.151 Observations were carried out during 1998 February 15 ane 20 (ur) with the NRAO Very Large Array (VLA). New Mexico. during a move between the D and A configurations.," Observations were carried out during 1998 February 15 and 20 ) with the NRAO Very Large Array (VLA), New Mexico, during a move between the D and A configurations."152 Around mmin was spent on source at 0.69. 1.33. 2.01. 3.54 and ccm. with measurements of the bright gain/phase calibrator. 2015|311. every IOmmin.," Around min was spent on source at 0.69, 1.33, 2.01, 3.54 and cm, with measurements of the bright gain/phase calibrator, 2015+371, every min."153 The lux density scale was set using observations of 2286 at 2.01. 3.54 anc G.17cenm. and using à variety of bright calibrators at 0.69 and ccm.," The flux density scale was set using observations of 286 at 2.01, 3.54 and cm, and using a variety of bright calibrators at 0.69 and cm."154 We recorded a bandwidth of MMlIz two contiguous 50-MllIz bands. with both right and Left circular »olarizations.," We recorded a bandwidth of MHz – two contiguous 50-MHz bands, with both right and left circular polarizations."155 Calibration of the svnthesis. data followed: standard JUXO. Cookbook oocedures withinAlPS., Calibration of the synthesis data followed standard NRAO Cookbook procedures within.156 A 6.17 and 3.54ccem. the routine was used to make ancl maps. restricting the we coverage to ΚΑ to reject hose antennas which hac alreacky been moved. into A-configuration positions.," At 6.17 and cm, the routine was used to make and maps, restricting the $uv$ coverage to $\lambda$ to reject those antennas which had already been moved into A-configuration positions."157 At shorter wavelengths we utilised xior knowledge of the source position (from a 3.54-cm. map mace using all baselines) to determine the [ux density directlv from the visibility data. again restricting ourselves o short baselines twpical of D configuration.," At shorter wavelengths we utilised prior knowledge of the source position (from a 3.54-cm map made using all baselines) to determine the flux density directly from the visibility data, again restricting ourselves to short baselines typical of D configuration."158 The measured lux densities are listed in Table 1., The measured flux densities are listed in Table 1.159in the corona. Le. more distant from the stellar surface. and. at the same time. over a more extended voluuc. while either maintaining the same total heating rate or doubling it.,"in the corona, i.e. more distant from the stellar surface, and, at the same time, over a more extended volume, while either maintaining the same total heating rate or doubling it."160 Iu order to obtain a significant brieltcnine over the background atmosphere. in all simulatious with Heler base coronal pressure. the heating rate fy is higher han the reference value. since the atmosphere is brighter and also more cficicnt in radiating the additional heat. his ταπιο any smaller heating barely effective.," In order to obtain a significant brightening over the background atmosphere, in all simulations with higher base coronal pressure, the heating rate $H_0$ is higher than the reference value, since the atmosphere is brighter and also more efficient in radiating the additional heat, this making any smaller heating barely effective."161 For most simulations. the duration of the constant reating (the time in which g(t)= 1) is 150 s. but a case of uuch longer heating (£j;=600 3) has also been explored.," For most simulations, the duration of the constant heating (the time in which $g(t) = 1$ ) is 150 s, but a case of much longer heating $t_H =162600$ s) has also been explored."163 The reference simmiation (named ref iu Table 1)) will ve described in more detail iu the following., The reference simulation (named in Table \ref{tab:sim}) ) will be described in more detail in the following.164 With the total reating rate of ~2«1075 ere st. the total heat released is therefore ~3:«107 ere.," With the total heating rate of $\sim 2 \times 10^{28}$ erg $^{-1}$, the total heat released is therefore $\sim 3 \times 10^{30}$ erg."165 The evolution is coniputed for a total time of SOU s. 10. the decay is studied for 650 s. The grid is 800&228 erid «ο».," The evolution is computed for a total time of 800 s, i.e. the decay is studied for 650 s. The grid is $800 \times 228$ grid cells."166 For comparison with the models of flares in non-confined atinospheres. Table 1 shows also the xwanmieters aud results of a model of flare in aconfined coronal loop. labelled withConf.," For comparison with the models of flares in non-confined atmospheres, Table \ref{tab:sim} shows also the parameters and results of a model of flare in a coronal loop, labelled with."167 Tu particular. the paraiieters are those of a fare iu an active region loop of halt-leneth 2«109 cm and initial pressure 6 dine 7 (Peres et al.," In particular, the parameters are those of a flare in an active region loop of half-length $2 \times 10^9$ cm and initial pressure 6 dyne $^{-2}$ (Peres et al."168 1982. Peres et al.," 1982, Peres et al."169 1987)., 1987).170 The heating duration. spatial extent and intensity per unit volume have been choseu identical to those of the refereuce model.," The heating duration, spatial extent and intensity per unit volume have been chosen identical to those of the reference model."171 A loop cross-section area of a2.5«41011T cn?2 has been asstuned. corresponding.5 to a loop aspect. ic. radius divided by halflength. of 0.1.," A loop cross-section area of $2.5 \times 10^{17}$ $^2$ has been assumed, corresponding to a loop aspect, i.e. radius divided by half-length, of 0.1."172 Fig., Fig.173 2 shows distributions of temperature. density. pressure and vertical component of velocity aloug the central Z axis at various times during the phase in which the heating is switched on in the reference simulation.," \ref{fig:hydro1} shows distributions of temperature, density, pressure and vertical component of velocity along the central Z axis at various times during the phase in which the heating is switched on in the reference simulation."174 Fig., Fig.175 9 shows the analogous results of the evolution ὲter the heating has been switched off., \ref{fig:hydro2} shows the analogous results of the evolution after the heating has been switched off.176 Figs., Figs.177 | aud Ὁ respectively show grev-scale nuages of the temperature aud deusitv contrasts Z/T aud »s/ng. where Ty aud Dg are the temperature and density of the unperturbed atmosphere at various times curing the same simulation. including th heating aud decay phase.," \ref{fig:imtemp} and \ref{fig:imdens} respectively show grey-scale images of the temperature and density contrasts $T/T_0$ and $n/n_0$, where $T_0$ and $n_0$ are the temperature and density of the unperturbed atmosphere at various times during the same simulation, including both heating and decay phase."178 Figs. 2..," Figs. \ref{fig:hydro1},"179 E. and 5 clearly show the evolution of the plaza in the heating phase., \ref{fig:imtemp} and \ref{fig:imdens} clearly show the evolution of the plasma in the heating phase.180 Because of the stroug impulsive heating the plasma temperature at he center of the heating release on the Z axis increases rapidlv (iu less than 2 8) from 1.5 to 12 ADS. (and similarly the pressure by a factor 10) and then remains practically constant there., Because of the strong impulsive heating the plasma temperature at the center of the heating release on the $Z$ axis increases rapidly (in less than 2 s) from 1.5 to 12 MK (and similarly the pressure by a factor 10) and then remains practically constant there.181" A thermal couductiou front develops aud propagates spherically aud very rapidly in such a thin corona. taking ~2 s to reach the base of the corona. the ransition region and the chromosphere. aud. on the opposite side. a height Z~5<10"" ο."," A thermal conduction front develops and propagates spherically and very rapidly in such a thin corona, taking $\sim 2$ s to reach the base of the corona, the transition region and the chromosphere, and, on the opposite side, a height $Z \sim 5 \times 10^9$ cm."182 As the conduction front propagates iu corona. expanding from. the heating region. it fades and slows down siguificautly.," As the conduction front propagates in corona, expanding from the heating region, it fades and slows down significantly."183 While a height Z=10219 en is reached by the eni])oratire change after onlv ~15 s. it takes oue munute more to reach Z=2<Lote Cni. ale at the end of the heating +16 conduction frout is only sliehtly üeher than that.," While a height $Z = 10^{10}$ cm is reached by the temperature change after only $\sim 15$ s, it takes one minute more to reach $Z = 2 \times 10^{10}$ cm, and at the end of the heating the conduction front is only slightly higher than that."184 Iu the orthogonal (radial) directiou the couduction front is slower. because the temperature increases wpwards. aud therefore so does the efficiency of thermal conduction. while this does not occur in the radial direction: —1jl cni ix reached only after 50 s since the beeinmineOoC» of the simulation aud at the cud of the heating the distauce of re conduction frout from the Z axis is R=1.5«10/9 a.," In the orthogonal (radial) direction the conduction front is slower, because the temperature increases upwards, and therefore so does the efficiency of thermal conduction, while this does not occur in the radial direction; $R = 10^{10}$ cm is reached only after 50 s since the beginning of the simulation and at the end of the heating the distance of the conduction front from the $Z$ axis is $R = 1.5 \times 10^{10}$ cm."185 To have au idea of the weakening of the expanding conduction front. uote that. at the end of the heating. 1ο feniperature is below 10 MIS farther than 2:&10° cm youn the center of he heating release and below | MES for R>10! cin.," To have an idea of the weakening of the expanding conduction front, note that, at the end of the heating, the temperature is below 10 MK farther than $2186\times 10^9$ cm from the center of the heating release and below 4 MK for $R > 10^{10}$ cm."187 As soon as the chromosphere is hit aud heated by he conduction frout. it expands upwards with a shocked densityfrout!.," As soon as the chromosphere is hit and heated by the conduction front, it expands upwards with a shocked density."188. This is the chromospheric evaporation uodeled iu confined solar coronal flares (6.8. Nagai 1980. Peres ot al.," This is the chromospheric evaporation modeled in confined solar coronal flares (e.g. Nagai 1980, Peres et al."189 1982)., 1982).190 The plasma mnaxiuun speed of the evaporation frout rapidly imereases to ~600 kii/s in about 30 s and then remains between 600 aud 700 kin/s. The pressure of the evaporation frout along the Z axis increases by another actor 5. reaching+ a value ~+10 dyue P7 at the base of the corona.," The plasma maximum speed of the evaporation front rapidly increases to $\sim 600$ km/s in about 30 s and then remains between 600 and 700 km/s. The pressure of the evaporation front along the $Z$ axis increases by another factor 5, reaching a value $\sim 10$ dyne $^{-2}$ at the base of the corona."191" The density front reaches the central position of the heating alone the Z axis in —00 x. and a height Z—101"" eji at the eud of the heating (t = 150 s). corresponding to an average propagation speed of 600 km/s. As a consequence the deusitv in the ceutral post-shock region increases above a factor 3 but practically iu all the coronal region it is «]10?  at any time."," The density front reaches the central position of the heating along the $Z$ axis in $\sim 30$ s, and a height $Z \sim 10^{10}$ cm at the end of the heating (t = 150 s), corresponding to an average propagation speed of $\sim 600$ km/s. As a consequence the density in the central post-shock region increases above a factor 3 but practically in all the coronal region it is $< 10^{9}$ $^{-3}$ at any time."192 Given the lighly localized heating release im a non confined atinosphere. the evaporation front. which mostly determines the soft N-rayv burst. is not plane-parallel: it is practically senuücireubu. strouger along the Z axis and weaker and weaker moving farther and farther from R=0.," Given the highly localized heating release in a non confined atmosphere, the evaporation front, which mostly determines the soft X-ray burst, is not plane-parallel: it is practically semicircular, stronger along the $Z$ axis and weaker and weaker moving farther and farther from $R=0$."193 The reason is that the couduction front arrives at the chromosphere first along the ceutral Z axis. and proeressively later at greater and ereater distances from it.," The reason is that the conduction front arrives at the chromosphere first along the central $Z$ axis, and progressively later at greater and greater distances from it."194 The frout amplitucle ects weaker and weaker aud with a stnaller pitch angle., The front amplitude gets weaker and weaker and with a smaller pitch angle.195 For R>1019 cm the evaporation speed is <100 km/s aud the local density cnhancemen very suall at amy time.," For $R >19610^{10}$ cm the evaporation speed is $< 100$ km/s and the local density enhancement very small at any time."197 The density iu the post-shock region is uot unifon: the plasma behind the shock aoves faster than a the shock and acctuuulates there: the evaporation frou becomes then a bow frout aud a region of low density (a proper depression) ors behiud i., The density in the post-shock region is not uniform: the plasma behind the shock moves faster than at the shock and accumulates there; the evaporation front becomes then a bow front and a region of low density (a proper depression) forms behind it.198 The vow frontfades farther aud farther frou the centra head., The bow frontfades farther and farther from the central head.199 The diameter of, The diameter of200 , 2012 mouths from February 7 till April L the four other epoch observations took ace during inteecr uuuber of consecutive vears witlin 27 days from the same calendar date.,"2 months from February 7 till April 4, the four other epoch observations took place during integer number of consecutive years within 27 days from the same calendar date."202 Overall. the change in position due to trigonometric xuwallax is expected to f of the order of 16 mas at asin for an asstuned distance of ppc (Gnaiulv due to the spread in time of the 1997 observations). and can therefore be neelected for our purpose.," Overall, the change in position due to trigonometric parallax is expected to be of the order of 16 mas at maximum for an assumed distance of pc (mainly due to the spread in time of the 1997 observations), and can therefore be neglected for our purpose."203 As or the photometry we found that fitting 2-D Catssian oxofiles was providing the inost accurate results and oeood estimates of the positional errors., As for the photometry we found that fitting 2-D Gaussian profiles was providing the most accurate results and good estimates of the positional errors.204 Positions from automated processes such as Sextractor or DAOPIIOT ined out to be less reliable in general., Positions from automated processes such as Sextractor or DAOPHOT turned out to be less reliable in general.205 The fixed width of the stellar profiles iun right ascension aud declination were first derived by averaging the values obtained ou a set of relatively bright but nonsaturated stars., The fixed width of the stellar profiles in right ascension and declination were first derived by averaging the values obtained on a set of relatively bright but nonsaturated stars.206 Then the position of a eroup of LO reference stars was measured. together with that of aand of 17 faint test objects.," Then the position of a group of 10 reference stars was measured, together with that of and of 17 faint test objects."207 Refercuce stars are evenly spread within oof aaud are in the ranee of D uaenitude frou 21.8 to 18.5., Reference stars are evenly spread within of and are in the range of B magnitude from 21.8 to 18.8.208 Comparison objects are distributed iu the same sky region as the reference stars and were selected for their stellar-like appearance., Comparison objects are distributed in the same sky region as the reference stars and were selected for their stellar-like appearance.209 Their uaenitudes range from D — 27.0 to 23.5., Their magnitudes range from B $\sim$ 27.0 to 23.5.210 Using a rotation. ranslation and scaling transformation. the 1997. 1999. 2000 January and 2003 positions were then moved to ιο 2000 December FORSL/VLT vetereuce frame which xovides the most accurate positions.," Using a rotation, translation and scaling transformation, the 1997, 1999, 2000 January and 2003 positions were then moved to the 2000 December FORS1/VLT reference frame which provides the most accurate positions."211 Not all the reference stars are «ΟΜΙΛΟΙ to all frames aud the 1997 to December, Not all the reference stars are common to all frames and the 1997 to December212The last decade has witnessed an explosive growth of high-quality. data aid models for supernovae with spectacular results that provided new perspectives lor the use of SNe Ia as cosmological vard sticks and for eoustraining (he physics of supernovae.,The last decade has witnessed an explosive growth of high-quality data and models for supernovae with spectacular results that provided new perspectives for the use of SNe Ia as cosmological yard sticks and for constraining the physics of supernovae.213 SNe Ia have provided new estimates for the value of the IIubble constant (Z9) with 10 uncertainty based on a purelv empirical procedure (Παινetal.1996:Riess.Press.&Ixirshner1996)... and on a comparison of detailed theoretical models with observations (Ilóflich&IXhokhlov.Nugentοἱal. 1997).," SNe Ia have provided new estimates for the value of the Hubble constant $H_0$ ) with 10 uncertainty based on a purely empirical procedure \citep{Hamuy:1996,RiessPK:1996}, and on a comparison of detailed theoretical models with observations \citep{HofKho:1996,Nugent:1997}."214". More recently. (he routine successful detection of supernovae al large redshifts. z (Perlmutteretal.1997:Riess1993).. provided results Chat are consistent with a low matter density in the Universe and. most intriguing of all. vielded hints for a positive cosmological constant. Qa 220.7. and prompted the quest for the nature of the ""dark energv or cosmological equation of state (Perlinutter.Turner.&White1999)."," More recently, the routine successful detection of supernovae at large redshifts, z \citep{Perlmutter:1997,Riess:1998}, provided results that are consistent with a low matter density in the Universe and, most intriguing of all, yielded hints for a positive cosmological constant, $\Omega_\Lambda $ $\approx 0.7$, and prompted the quest for the nature of the “dark energy"" or cosmological equation of state \citep{PerlTurnWhite:1999}."215. To pursue these issues wilh SNe Ia. (he required photometric accuracy has to be better than 2," To pursue these issues with SNe Ia, the required photometric accuracy has to be better than 2"216The Jodrell Bank-Very Large Array (VLA) Astrometric Survey (VAS: Patnaiketal.1992:Browne1998:Wilkinson 1998)) and the Cosmic Lens All-Sky Survey (CLASS: Browneetal.2003:Myers 20031) are the largest. statistically complete searches for gravitationally lensed radio-loud active galactic nuclei (AGN).,"The Jodrell Bank–Very Large Array (VLA) Astrometric Survey (JVAS; \citealt{patnaik92,browne98,wilkinson98}) ) and the Cosmic Lens All-Sky Survey (CLASS; \citealt{browne03,myers03}) ) are the largest, statistically complete searches for gravitationally lensed radio-loud active galactic nuclei (AGN)."217 Together. these two surveys found 22 gravitational lens systems with image separations between 0.3 aresec ZBE 6 aresec. Which corresponds to the galaxy-seale regime of gravitational lensing.," Together, these two surveys found 22 gravitational lens systems with image separations between 0.3 arcsec $\leq \Delta\theta_{\rm sep} \leq$ 6 arcsec, which corresponds to the galaxy-scale regime of gravitational lensing."218 The lens systems discovered by JVAS and CLASS have been used. for example. to determine the mass profile of lensing galaxies (Cohnetal.2001:Wucknitz 2009).. investigate the impact of baryon cooling (Kochanek&White 2001).. quantify the level of low mass-substructure in the lensing haloes (Bradaéetal.2002:Biggs2004: 2010). measure the Hubble constant (Biggsetal.2005:Suyuet2010) and investigate the high redshift Universe (Barvainis&Ivison2002:Impellizzerietal.2008).," The lens systems discovered by JVAS and CLASS have been used, for example, to determine the mass profile of lensing galaxies \citep{cohn01,wucknitz04,suyu09}, investigate the impact of baryon cooling \citep{kochanek01}, quantify the level of low mass-substructure in the lensing haloes \citep{bradac02,biggs04,dalal02,kochanek04,mckean07b,jackson10}, measure the Hubble constant \citep{biggs99,koopmans00,fassnacht02,york05,suyu10} and investigate the high redshift Universe \citep{barvainis02,impellizzeri08}."219. The gravitational lensing statistics from the JVAS and CLASS surveys have also been used to constrain cosmological models (Chaeetal. 2002)., The gravitational lensing statistics from the JVAS and CLASS surveys have also been used to constrain cosmological models \citep{chae02}.220" The JVAS and CLASS surveys targeted flat-spectrum radio sources (et 0.5 where S.x ov""). which typically show compact radio emission on sub-aresec scales."," The JVAS and CLASS surveys targeted flat-spectrum radio sources $\alpha \geq -$ 0.5 where $S_{\nu} \propto \nu^{\alpha}$ ), which typically show compact radio emission on sub-arcsec scales."221 The surveys were carried out with the VLA at 8.46 GHz in A-configuration. which had a beam-size of ~ 200 mas and reached a sensitivity of ~ 200 μὴν in just 30-s of integration.," The surveys were carried out with the VLA at 8.46 GHz in A-configuration, which had a beam-size of $\sim$ 200 mas and reached a sensitivity of $\sim$ 200 $\mu$ Jy in just 30-s of integration."222 During the course of TVAS and CLASS. over ~15 0000 radio sources were observed with the VLA.," During the course of JVAS and CLASS, over $\sim$ 000 radio sources were observed with the VLA."223" However. using the NVSS (National Radio Astronomy Observatory VLA Sky Survey: Condonetal. 1998)) catalogue at I.4 GHz and the GB6 (Greenbank 6 em: Gregoryetal. 1996)) catalogue at 4.85 GHz. a complete sample of 6685 flat-spectrum radio sources with 94,scgz2 30 mJy was detined."," However, using the NVSS (National Radio Astronomy Observatory VLA Sky Survey; \citealt{condon98}) ) catalogue at 1.4 GHz and the GB6 (Greenbank 6 cm; \citealt{gregory96}) ) catalogue at 4.85 GHz, a complete sample of 685 flat-spectrum radio sources with $S_{\rm 4.85~GHz} \geq\,$ 30 mJy was defined."224 The observing set-up used for the JVAS and CLASS surveys made it possible to also search for examples of gravitational lensing by groups of galaxies and galaxy clusters., The observing set-up used for the JVAS and CLASS surveys made it possible to also search for examples of gravitational lensing by groups of galaxies and galaxy clusters.225 Lensing by more massive haloes like these would result in a larger separation between the lensed images., Lensing by more massive haloes like these would result in a larger separation between the lensed images.226" Phillipsetal.(2001). carried out such a search by inspecting all of the images produced during the JVAS and CLASS VLA observations and found thirteen gravitational lensing candidates with image separations between 6 arcsec <AG, 15 arcsec.", \cite{phillips01} carried out such a search by inspecting all of the images produced during the JVAS and CLASS VLA observations and found thirteen gravitational lensing candidates with image separations between 6 arcsec $\leq \Delta\theta_{\rm sep} \leq$ 15 arcsec.227 The upper-limit of this lens search was set to reduce the number of random alignments and limit the possibility of variability. coupled with a large lensing time-delay. changing the observed properties of the candidate lensed images.," The upper-limit of this lens search was set to reduce the number of random alignments and limit the possibility of variability, coupled with a large lensing time-delay, changing the observed properties of the candidate lensed images."228 These lens candidates were re-observed using the VLA and observed with MERLIN (Multi-Element Radio Linked Interferometric Network) between |.4 and 15 GHz to investigate the radio spectral energy distributions. polarization and morphology of the radio sources.," These lens candidates were re-observed using the VLA and observed with MERLIN (Multi-Element Radio Linked Interferometric Network) between 1.4 and 15 GHz to investigate the radio spectral energy distributions, polarization and morphology of the radio sources."229— Optical spectroscopy was also carried out to determine the redshifts. in some cases.," Optical spectroscopy was also carried out to determine the redshifts, in some cases."230 From these observations 12. of the candidates were rejected as gravitational lens systems with wide image separations., From these observations 12 of the candidates were rejected as gravitational lens systems with wide image separations.231 The one, The one232and [M/H]«0.3.,and $<0.3$.233" For higher temperatures the H50-K2 index saturates, where the saturation Tig depends on "," For higher temperatures the $\rm H_2O$ -K2 index saturates, where the saturation $T_{\rm eff}$ depends on [M/H]."234"For stars with H2O-K2 near the saturation, a slightly[M/H]. higher H2O-K2 index converts to a large increase in the measured Τομ."," For stars with $\rm H_2O$ -K2 near the saturation, a slightly higher $\rm H_2O$ -K2 index converts to a large increase in the measured $T_{\rm eff}$."235 We accommodate this by providing asymmetric uncertainty estimates in Τομ using a Monte Carlo approach described in Section ??.., We accommodate this by providing asymmetric uncertainty estimates in $T_{\rm eff}$ using a Monte Carlo approach described in Section \ref{errors}.236" KOI 904 and KOI 956 had H20-K2 outside of the calculated surface, and are therefore not included in our results."," KOI 904 and KOI 956 had $\rm H_2O$ -K2 outside of the calculated surface, and are therefore not included in our results."237 We place the low-mass KOIs on a grid of physical parameters based on the Dartmouth stellar evolution models (Dotteretal.2008;Feiden2011).," 	 We place the low-mass KOIs on a grid of physical parameters based on the Dartmouth stellar evolution models \citep{Dotter2008, Feiden2011}."238". These models are in generally good agreement with OLBI observations (see Figure 2)), but there may well be systematic offsets in mass, radius or effective temperature, so these inferred physical parameters should be used with caution."," These models are in generally good agreement with OLBI observations (see Figure \ref{fig:models}) ), but there may well be systematic offsets in mass, radius or effective temperature, so these inferred physical parameters should be used with caution."239" We do not use the BCAH evolution models, as they are only available in two metallicities, [M/H] = 0.0 and [M/H] = -0.5, and a comprehensive metallicity grid is required for reliable interpolation of our measurements."," We do not use the BCAH evolution models, as they are only available in two metallicities, [M/H] = 0.0 and [M/H] = -0.5, and a comprehensive metallicity grid is required for reliable interpolation of our measurements."240" All but one of the stars in our sample are treated homogeneously, so the relative radii, masses and"," All but one of the stars in our sample are treated homogeneously, so the relative radii, masses and"241"10"", 15"" and 20"" respectively.","$10\arcsec$ , $15\arcsec$ and $20\arcsec$ respectively."242 The middle right panel shows the variation of electric current J!=uyVxB)! with r. where the dots give the values of J! and the double-shelled curve shows the mean value of J! with a bin of 1” in r.," The middle right panel shows the variation of electric current $J_{z}^1=\mu_0 (\bigtriangledown \times \textbf{\emph{B}})_{z}^1$ with $r$, where the dots give the values of $J_{z}^1$ and the double-shelled curve shows the mean value of $J_{z}^1$ with a bin of $\arcsec$ in $r$."243 Similarly. the bottom left and right panels respectively show the A!=J!B' and à! values and their averages with a bin of 1” in r.," Similarly, the bottom left and right panels respectively show the $h_{c}^1=J_z^1 B_{z}^1$ and $\alpha_{z}^1$ values and their averages with a bin of $''$ in $r$."244" We see clearly here that the inner most fields (where r<5”) have a positive average value of /! or a! and the average value becomes negative when r>5""", We see clearly here that the inner most fields (where $r < 5 ''$ ) have a positive average value of $h_c^1$ or $\alpha_z^1 $ and the average value becomes negative when $r > 5 ''$.245" The mean value of |B.| in the central umbra (7€5"") is 2976 G, and is 970 G for fields in 5""«r<20""."," The mean value of $|B_z|$ in the central umbra $r\leq5\arcsec) $ is 2976 G, and is 970 G for fields in $5\arcsec<r\leq20\arcsec $."246" The mean value of a! inr €5"" is 5.033x107r! and is -0.717«107° for regions in 5""«r<20"".", The mean value of $\alpha_{z}^1$ in $r\leq5\arcsec$ is $\times10^{-8}m^{-1}$ and is $\times10^{-8}m^{-1}$ for regions in $5\arcsec<r\leq20\arcsec$.247" The mean value of A! in r€5"" is 3.942x100Η and is -0.543x107Gm! for regions in 5""«r€20"".", The mean value of $h_{c}^1$ in $r\leq5\arcsec$ is $\times10^{-2}G^{2}m^{-1}$ and is $\times 10^{-2}G^{2}m^{-1}$ for regions in $5\arcsec<r\leq20\arcsec$.248" For the whole active region, with |B.|> 100G, al=-3.274x10?m! and aj,=—1.332x107m!"," For the whole active region, with $|B_{z}| > $ 100 G, $\alpha^1_{z}=-3.274\times 10^{-9}m^{-1}$ and $\alpha^1_{hc}=-1.332\times 10^{-8}m^{-1}$."249 This means that the sign of the whole AR is dominated by the sign of weak field (penumbra). as also pointed out in Zhang (2006).," This means that the sign of the whole AR is dominated by the sign of weak field (penumbra), as also pointed out in Zhang (2006)."250" Figure 5 gives another example. NOAA 11084, observed on July 2, 2010 of the solar cycle 24."," Figure 5 gives another example, NOAA 11084, observed on July 2, 2010 of the solar cycle 24."251" As in Figure 4, the top two panels present the continuum image of the sunspot and the corresponding electric current distribution."," As in Figure 4, the top two panels present the continuum image of the sunspot and the corresponding electric current distribution."252" Here the circles represent where ris 5"", 10"" and 15” respectively."," Here the circles represent where $r$ is $5\arcsec$ , $10\arcsec$ and $15\arcsec$ respectively."253 Similar trend as that in Figure 4 can be seen from the bottom panels of //! and a., Similar trend as that in Figure 4 can be seen from the bottom panels of $h_{c}^1$ and $\alpha_{z}^1$.254" Here the average A! or a! values change their sign at about 4"".", Here the average $h_{c}^1$ or $\alpha_{z}^1$ values change their sign at about $4\arcsec$ .255" The mean value of |B.| in r€5"" is 2382 G. and is 713 Gin 5""«r< 20""region."," The mean value of $|B_z|$ in $r\leq5\arcsec$ is 2382 G, and is 713 G in $5\arcsec<r\leq20\arcsec$ region."256" The mean value of a! in r€5"" is -1.300x105r! and is 2.950x107r! in 5""«r< 20""region.", The mean value of $\alpha_{z}^1$ in $r\leq5\arcsec$ is $\times10^{-8}m^{-1}$ and is $\times10^{-8}m^{-1}$ in $5\arcsec<r\leq20\arcsec$ region.257" The mean value of A! in r€5"" is -0.901 x10-7Gnm! and is 0.315x107G?n! in 5”<r€20"".", The mean value of $h_{c}^1$ in $r\leq5\arcsec$ is -0.901 $\times 10^{-2}G^{2}m^{-1}$ and is $\times10^{-2}G^{2}m^{-1}$ in $5\arcsec<r\leq20\arcsec$.258" For the whole AR, a!=3.599x107m and qi.=1.910xIO?nr with [B.|> 100 G. We see here again thatthe inner umbra and outer penumbra has the opposite helicity sign and the helicity sign of the whole AR is dominated by the sign in penumbra."," For the whole AR, $\alpha^1_{z}=3.599\times10^{-8}m^{-1}$ and $\alpha^1_{hc}=1.910\times10^{-8}m^{-1}$ with $|B_{z}| > $ 100 G. We see here again thatthe inner umbra and outer penumbra has the opposite helicity sign and the helicity sign of the whole AR is dominated by the sign in penumbra."259 Note that Chatterjee et al. (, Note that Chatterjee et al. (2602006) modeled the penetration of a poloidal field into atoroidal rising flux tube through turbulence diffusion.,2006) modeled the penetration of a poloidal field into atoroidal rising flux tube through turbulence diffusion.261 One important prediction of their model is the, One important prediction of their model is the262"where A4,4(£) is a modified Bessel function. with £'=£(124-5707?ES 2GFalGL fL. and where the + signs correspond (o emission in the forward (defined for uf> 0) and backward direction.","where $K_{1/3}(\xi)$ is a modified Bessel function, with $\xi'_\pm=\xi'_{c\pm}(1+\gamma'^2_\pm\theta'^2)^{3/2}$, $\xi'_{c\pm}=(\pi/\sqrt{2})(\omega'/\omega'_{c\pm})(\gamma'_\pm/\gamma'_{\rm max})^{1/2}$ and where the $\pm$ signs correspond to emission in the forward (defined for $u'_0>0$ ) and backward direction."263 The characteristic properties of LAE implied by (4.2)) are discussed in paper 2., The characteristic properties of LAE implied by \ref{emissivity}) ) are discussed in paper 2.264 Let ο) be the number density of one speciesof particle. electrons say. with initial (al phase \= 0) 4-velocity in the range aj to uf+duty.," Let $g'(u'_0)\rmd u'_0$ be the number density of one speciesof particle, electrons say, with initial (at phase $\chi=0$ ) 4-velocity in the range $u'_0$ to $u'_0+\rmd u'_0$."265 The volume emissivity is fdutg'Cuni(e.0).," The volume emissivity is $\int\rmd u'_0g'(u'_0)\eta'_\pm(\omega',\theta')$."266 The absorption coelficient can be related to the eniissivity (4.2)) by an argument using detailed balance (Twiss1958:Wild.Smerd&Weiss1963).," The absorption coefficient can be related to the emissivity \ref{emissivity}) ) by an argument using detailed balance \citep{T58,WSW63}."267". In the one-dimensional case of relevance here this gives with cos@zz+1 such that the signs of cos9 and uj, are the same."," In the one-dimensional case of relevance here this gives, with $\cos\theta'\approx\pm1$ such that the signs of $\cos\theta'$ and $u'_0$ are the same."268 Maser emission corresponds (o negative absorption.requiring I(ω”.0')« 0.," Maser emission corresponds to negative absorption,requiring $\Gamma'_\pm(\omega',\theta')<0$ ."269 We comment below on the possibility of maser emission al low [requencies., We comment below on the possibility of maser emission at low frequencies.270to the hotspot region. impacts simultaneously into various locations across the hotspot generating a complex shocker region that defines an arc-shaped structure.,"to the hotspot region, impacts simultaneously into various locations across the hotspot generating a complex shocked region that defines an arc-shaped structure."271 Phis. combine with projection ellects may explain a wide (projected) emitting region. (," This, combined with projection effects may explain a wide (projected) emitting region. ("2722) Another possibility is a narrow jet tha impacts into the hotspot in a small region where electrons are accelerated at à strong shock.,2) Another possibility is a narrow jet that impacts into the hotspot in a small region where electrons are accelerated at a strong shock.273 In this case the accelerate particles are then transported upstream in. the. hotspo volume where they are continuously re-acecleratecl by stochastic mechanisms. likely ciue to turbulence generate by the jet and shock itself. (," In this case the accelerated particles are then transported upstream in the hotspot volume where they are continuously re-accelerated by stochastic mechanisms, likely due to turbulence generated by the jet and shock itself. ("274"3) Finally. extended emission mav be explained by the ""dentists απ scenario. in which the jet impacts into the hotspot region in dilferent locations at clillerent times.","3) Finally, extended emission may be explained by the “dentist's drill” scenario, in which the jet impacts into the hotspot region in different locations at different times."275 The peculiar morphology and the rather high Nllt/optical luminosity of 1105. South and. 4445 South. makes these hotspots ideal targets to investigate the nature of extended dilfuse emission.," The peculiar morphology and the rather high NIR/optical luminosity of 105 South and 445 South, makes these hotspots ideal targets to investigate the nature of extended diffuse emission."276 In 1105 South. the detection of optical emission in both primary and secondary hotspots implies that in these regions there is a continuous re-acceleration. of particles.," In 105 South, the detection of optical emission in both primary and secondary hotspots implies that in these regions there is a continuous re-acceleration of particles."277 The secondary hotspot. 83. could. be interpreted as a splatter-spot from material accelerated in the primary one. S2 (Williams&Cull1985).," The secondary hotspot S3 could be interpreted as a splatter-spot from material accelerated in the primary one, S2 \citep{williams85}."278. Both the alignment ancl the distance between these components exclude the jet drilling scenario: the light. time between the (vo components is more than 107 vears. Le. much longer than their radiative time (lable 3). suggesting that acceleration is taking place in both $2 and 83 simultaneously.," Both the alignment and the distance between these components exclude the jet drilling scenario: the light time between the two components is more than $^{4}$ years, i.e. much longer than their radiative time (Table 3), suggesting that acceleration is taking place in both S2 and S3 simultaneously."279 The secondary. hotspot $3 shows some elongation. always in the same cirection. in all the radio and optical images with adequate spatial resolution.," The secondary hotspot S3 shows some elongation, always in the same direction, in all the radio and optical images with adequate spatial resolution."280 “This elongation is expected. in a splatter-spot and it follows the structure of the shock generated by the impact of the outllow from the primary upon the cocoon wall., This elongation is expected in a splatter-spot and it follows the structure of the shock generated by the impact of the outflow from the primary upon the cocoon wall.281 This scenario. able to explain the presence of optical emission [rom two bright and. distant. components. fails in reproducing the clilfuse optical emission. enshroucing the main features. and the extended tail," This scenario, able to explain the presence of optical emission from two bright and distant components, fails in reproducing the diffuse optical emission enshrouding the main features, and the extended tail."282 In. this case. an additional contribution from. stochastic mechanisms caused by turbulence in the downstream region is necessary.," In this case, an additional contribution from stochastic mechanisms caused by turbulence in the downstream region is necessary."283 Although this acceleration mechanism is in general less ellicient than Fermi-l processes. the (radiative) energy Losses of particles are smaller in the presence of low magnetic fields. such as those in between S2 ancl S3. (potentially) allowing stochastic mechanisms to maintain electrons at high energies.," Although this acceleration mechanism is in general less efficient than Fermi-I processes, the (radiative) energy losses of particles are smaller in the presence of low magnetic fields, such as those in between S2 and S3, (potentially) allowing stochastic mechanisms to maintain electrons at high energies."284 In 3€ 445 South the observational picture is complex., In 3C 445 South the observational picture is complex.285 The optical images of 3€ 445 South show a spectacular 10-κρο arc-shape structure., The optical images of 3C 445 South show a spectacular 10-kpc arc-shape structure.286 High resolution HIST. images allow a further step since they resolve this structure in two elongated. components enshrouded by dilfuse emission., High resolution HST images allow a further step since they resolve this structure in two elongated components enshrouded by diffuse emission.287" These components may mark the regions where a ""dentists drill jet impacts on the ambient medium. representing the most recent episode of shock acceleration. due to the jet impact."," These components may mark the regions where a “dentist's drill” jet impacts on the ambient medium, representing the most recent episode of shock acceleration due to the jet impact."288 On the other hand. they could. simply trace the locations of higher particle-acceleration cllicieney [rom a wide/complex interaction between the jet and the ambient ΠΙΟΜΗ.," On the other hand, they could simply trace the locations of higher particle-acceleration efficiency from a wide/complex interaction between the jet and the ambient medium."289 However. the transverse extension. about 1 kpe. of the two elongated components is much larger than what is derived if the relativistie particles. accelerated at the shock. age in the downstream region (provided that the hotspot advances at typical speeds of 0.05-0.16).," However, the transverse extension, about 1 kpc, of the two elongated components is much larger than what is derived if the relativistic particles, accelerated at the shock, age in the downstream region (provided that the hotspot advances at typical speeds of $c$ )."290 Furthermore. the diffuse optical emission on larger scale suggests the presence of additional. complex. acceleration mechanisms. such as stochastic processes. able to keep particle re-acceleration ongoing in the hotspot region.," Furthermore, the diffuse optical emission on larger scale suggests the presence of additional, complex, acceleration mechanisms, such as stochastic processes, able to keep particle re-acceleration ongoing in the hotspot region."291 “Phe detection. of X-ray emission. with adds a new grade. of complexity., The detection of X-ray emission with adds a new grade of complexity.292 This emission and its displacement. are interpreted by Porlmanetal.(2010) as due to LC-CAIB originating in he fast part of the decelerating How., This emission and its displacement are interpreted by \citet{perlman10} as due to IC-CMB originating in the fast part of the decelerating flow.293 Ελα model requires hat the angle between the jet velocity ancl the observer's ine of sight is small., Their model requires that the angle between the jet velocity and the observer's line of sight is small.294 Llowever. 4445 is a classical double radio galaxy and the jet should. form a large angle. with he line of sight. (see also Perlman et al.," However, 445 is a classical double radio galaxy and the jet should form a large angle with the line of sight (see also Perlman et al."295 2010)., 2010).296 On the other hand. we suggest that the X-ray/optical olfset might ος the outcome of ongoing ellicient particle acceleration occurring in the hotspot region.," On the other hand, we suggest that the X-ray/optical offset might be the outcome of ongoing efficient particle acceleration occurring in the hotspot region."297 An evidence supporting his interpretation mav reside on the faint and. diffuse blob seen in U- ancl D-bands (labelled SC in Fig. 2)), An evidence supporting this interpretation may reside on the faint and diffuse blob seen in U- and B-bands (labelled SC in Fig. \ref{fig_3c445}) )298" just about 1"" downstream the X-ray peak.", just about $^{\prime\prime}$ downstream the X-ray peak.299 The surface brightness of this component decreases. rapidly as the frequency decreases. as it is shown in Fig. 2:," The surface brightness of this component decreases rapidly as the frequency decreases, as it is shown in Fig. \ref{fig_3c445}:"300 well-detected in U- and D-bands. marginally visible in I-band. and absent at NI and radio wavelengths.," well-detected in U- and B-bands, marginally visible in I-band, and absent at NIR and radio wavelengths."301" The SED of the diffuse hotspot emission (including SC component ancl excluding SW. and SE) is consistent with svnchrotron emission. with a break at high [requencies. 107 Hz « νι, 107"" Hz. and may significantly contribute to the observed. X-ray flux."," The SED of the diffuse hotspot emission (including SC component and excluding SW and SE) is consistent with synchrotron emission with a break at high frequencies, $^{15}$ Hz $<$ $\nu_{b}$ $\leq$ $\times$ $^{16}$ Hz, and may significantly contribute to the observed X-ray flux."302" Such a hard spectrum is in agreement with (i) à very recent episode of particle acceleration. (the radiative cooling time of the emitting particles being 107-10"" sr): (i) ellicient spatially-clistributecd acceleration processes. similar to the scenario. proposed. for the western. hotspot. of. Pictor A Clingav ct al."," Such a hard spectrum is in agreement with (i) a very recent episode of particle acceleration (the radiative cooling time of the emitting particles being $^{2}$ $^{3}$ yr); (ii) efficient spatially-distributed acceleration processes, similar to the scenario proposed for the western hotspot of Pictor A (Tingay et al."303 2008. see their Fig.5).," 2008, see their Fig.5)."304 We presented a multi-band. high spatial resolution study of the hotspot regions in two nearby radio galaxies. namely 1105 South and 4445 South. on the basis. of racio VLA. Nllt/optical WLP and HIST. ancl X-ray observations.," We presented a multi-band, high spatial resolution study of the hotspot regions in two nearby radio galaxies, namely 105 South and 445 South, on the basis of radio VLA, NIR/optical VLT and HST, and X-ray observations."305 At the sub-aresee resolution achieved at racio and optical wavelengths. both hotspots. display multiple resolved Components connected by dilfuse emission detected also in optical.," At the sub-arcsec resolution achieved at radio and optical wavelengths, both hotspots display multiple resolved components connected by diffuse emission detected also in optical."306 The hotspot region in 1105 resolves in hree major components: a primary hotspot. unresolved and aligned. with the jet direction. and a secondary hotspot. elongated in shape. and interpreted as a splatter-spot arising rom continuous outflow of particles from the primary.," The hotspot region in 105 resolves in three major components: a primary hotspot, unresolved and aligned with the jet direction, and a secondary hotspot, elongated in shape, and interpreted as a splatter-spot arising from continuous outflow of particles from the primary."307 Such a feature. together with the extremely short radiative ages of the electron populations emitting in the optical. indicates hat the jet has been impacting almost in the same position or a long period. making the drilling jet scenario unrealistic.," Such a feature, together with the extremely short radiative ages of the electron populations emitting in the optical, indicates that the jet has been impacting almost in the same position for a long period, making the drilling jet scenario unrealistic."308 Vhe detection of an excess of X-ray emission from the northern component of 1105 South suggests that this region is likely a relativistic knot in the jet rather than a genuine hotspot feature., The detection of an excess of X-ray emission from the northern component of 105 South suggests that this region is likely a relativistic knot in the jet rather than a genuine hotspot feature.309 The optical clilfuse emission, The optical diffuse emission310"ratio of the two axes of the ellipse 2,/2»=0.00013 describes the fact that the particle motion is mainly due to the Ed in the cc-direction. and that the polarization drift in the direction of the wave-veetor (the g-direction) is negligible.","ratio of the two axes of the ellipse $\varepsilon_1/\varepsilon_2=0.00013$ describes the fact that the particle motion is mainly due to the $\vec E\times311\vec B$ -drift in the $x$ -direction, and that the polarization drift in the direction of the wave-vector (the $y$ -direction) is negligible."312 Performing the same plot. for. electrons. vields the same ce» as expected (the E B-dvilt is independent. on mass). while c; becomes reduced. by the. factor. mom; (the polarization erift. separates charges and it is mass dependent).," Performing the same plot for electrons yields the same $\epsilon_2$ as expected (the $\vec E\times \vec B$ -drift is independent on mass), while $\epsilon_1$ becomes reduced by the factor $m_e/m_i$ (the polarization drift separates charges and it is mass dependent)."313" On the other hand. taking a time-varving potential Ó,() due to the above demonstrated. αρ wave instability. and restricting the time interval to relatively short values (below the onset time of the stochastic heating). vields a spiral trajectory in the vw. g-plane."," On the other hand, taking a time-varying potential $\phi_1(t)$ due to the above demonstrated drift wave instability, and restricting the time interval to relatively short values (below the onset time of the stochastic heating), yields a spiral trajectory in the $x, y$ -plane."314 One example of this is presented in Fig., One example of this is presented in Fig.315 2., 2.316" Here. the starting value for the potential is the same as above eó4,(0)/(82;)=0.01. and the same holds for the particle position."," Here, the starting value for the potential is the same as above $e \phi_1(0)/(\kappa T_i)=0.01$, and the same holds for the particle position."317 The other parameters are the same as in Pig., The other parameters are the same as in Fig.318 1., 1.319" With the same normalization the potential is given by ó,(/)=oóexp(s1/O;). >=026, c,=254 111. oO=(0)."," With the same normalization the potential is given by $\phi_1(t)=\widehat{\phi}\exp(\gamma t/\Omega_i)$, $\gamma=0.26 \omega_r$, $\omega_r=254\;$ Hz, $\widehat{\phi}=\phi_1(0)$."320 The maximum time in physical units here is 0.04 s. and in this moment the potential has reached. the value of 17 V. Comparing with Fig.," The maximum time in physical units here is $0.04\;$ s, and in this moment the potential has reached the value of $17\;$ V. Comparing with Fig."321 1. one observes that the displacement in the y-direction due to the polarization drift is now increased bv a factor 20.," 1, one observes that the displacement in the $y$ -direction due to the polarization drift is now increased by a factor 20."322 ]t is interesting to compare the Ieading perpendicular E B-cvilt velocity οι and the parallel velocity ος (along the magnetic field vector).," It is interesting to compare the leading perpendicular $\vec E\times \vec B$ -drift velocity $v_x$, and the parallel velocity $v_z$ (along the magnetic field vector)."323 The parametric plot in Fig., The parametric plot in Fig.324 3 shows that for these potential amplitudes the parallel velocity ο remains about one order of magnitude smaller., 3 shows that for these potential amplitudes the parallel velocity $v_z$ remains about one order of magnitude smaller.325 In order to see what happens for larger amplitudes of the electrostatic drift wave when the stochastic heating is supposed. to be in action. Eqs. (7))-(9))," In order to see what happens for larger amplitudes of the electrostatic drift wave when the stochastic heating is supposed to be in action, Eqs. \ref{e6}) \ref{e8}) )"326 are solved. by allowing a slightly [larger time range., are solved by allowing a slightly larger time range.327 One of the results is shown in Fig., One of the results is shown in Fig.328" 4 for the kinetic energy of a particle with unit mass E(l)/m—v,(Y|PEUoypee 2. with normalized velocities as above."," 4 for the kinetic energy of a particle with unit mass $E(t)/m=[v_x(t)^2+v_y(t)^2 +329v_z(t)^2]/2$ , with normalized velocities as above."330 “Phe other parameters are the same as in he previous text and figures., The other parameters are the same as in the previous text and figures.331 Here. the stochastic heating akes place after around. 0.078 s. in the moment when the growing wave amplitude reaches the value of around. 150 V. ote that this is by about a factor 2.5 larger than the value obtained from the condition (6)) which. in fact. follows rom an approximative procedure as explained earlier.," Here, the stochastic heating takes place after around $0.078\;$ s, in the moment when the growing wave amplitude reaches the value of around $150\;$ V. Note that this is by about a factor $2.5$ larger than the value obtained from the condition \ref{a}) ) which, in fact, follows from an approximative procedure as explained earlier."332 Thus. a higher necessary threshold. for the stochastic heating is expected.," Thus, a higher necessary threshold for the stochastic heating is expected."333 However. a plasma can support multiple waves in he same time.," However, a plasma can support multiple waves in the same time."334 The drift wave spectrum described by I5qs. (1.. 2))," The drift wave spectrum described by Eqs. \ref{k1}, \ref{k2}) )"335 in realistic situations imply the presence of more waves rather than a single one., in realistic situations imply the presence of more waves rather than a single one.336 The analysis presented in a recent study (Shengetal.2009) shows that in such cases the instability threshold can be considerably reciuced., The analysis presented in a recent study \citep{sheng} shows that in such cases the instability threshold can be considerably reduced.337 Therefore. 1e ion heating by the mechanism which we discuss here will be even more efficient.," Therefore, the ion heating by the mechanism which we discuss here will be even more efficient."338 The corresponding plot. of the displacement. in the direction. of the wave y(f). which is in fact also equal to the velocity ον) see Eq. (9))]," The corresponding plot of the displacement in the direction of the wave $y(t)$, which is in fact also equal to the velocity $v_x(t)$ [see Eq. \ref{e8}) )]"339 is shown in Fig., is shown in Fig.340 5., 5.341" The plot of the velocity ¢,(7) (hat is not. given here) reveals the amplitude that is completely. negligible until ΟΕ becomes close to S-107: after that it is very stochastic and with the amplitude equal to that of the velocity ος", The plot of the velocity $v_y(t)$ (that is not given here) reveals the amplitude that is completely negligible until $\Omega_i t$ becomes close to $8\cdot 10^4$; after that it is very stochastic and with the amplitude equal to that of the velocity $v_x(t)$.342 Thus we are in the range of parameters in which the expansion procedure used. previously is not. valid any longer because the polarization and διD drifts are of the sume order. and thestochastic heating is fully in action.," Thus we are in the range of parameters in which the expansion procedure used previously is not valid any longer because the polarization and $\vec343E\times \vec B$ drifts are of the same order, and thestochastic heating is fully in action."344 Note that. although the motion is stochastic/chaotic. it is in fact deterministic," Note that, although the motion is stochastic/chaotic, it is in fact deterministic"345The method to mitigate the effects of realization noise uses Eq.,The method to mitigate the effects of realization noise uses Eq.346" ] in a dimensionless form: In a departure from the previous practice, we have assumed that & obeys ascaling law &=A+BlogAv, as derived from the observation of thousands of CoRoT targets (?) and as observed by ?.."," \ref{tassoul} in a dimensionless form: In a departure from the previous practice, we have assumed that $\varepsilon$ obeys ascaling law $\varepsilon = A + B \log347\dnumoy$, as derived from the observation of thousands of CoRoT targets \citep{2010A&A...517A..22M} and as observed by \cite{huber2010}."348 This is justified by the observation that scaling laws apparently govern global asteroseismic parameters (222?) and is equivalent to assume that the underlying physics of & varies with the global stellar parameters.," This is justified by the observation that scaling laws apparently govern global asteroseismic parameters \citep{2009A&A...506..465H,2009MNRAS.400L..80S,2010ApJ...713L.176B,2010A&A...517A..22M}349 and is equivalent to assume that the underlying physics of $\varepsilon$ varies with the global stellar parameters."350" As the mixed nature of dipole modes (€= 1) is more pronounced, we did not include them in the template, but only doublets corresponding to the eigenmodes with even degrees (v4.15 and νο). withequal amplitudes."," As the mixed nature of dipole modes $\ell=1$ ) is more pronounced, we did not include them in the template, but only doublets corresponding to the eigenmodes with even degrees $\nu_{n-1,2}$ and $\nu_{n,0}$ ), withequal amplitudes."351" As a first guess, we set the small separation do» at —0.14 and then allowed it to vary with the value of Ay according to the same relationship as given for e."," As a first guess, we set the small separation $d_{02}$ at $- 0.14$ and then allowed it to vary with the value of $\dnumoy$ according to the same relationship as given for $\varepsilon$."352" For constructing the peaks of the template, we have also used the scaling laws of the Gaussian excess power derived by ?.."," For constructing the peaks of the template, we have also used the scaling laws of the Gaussian excess power derived by \cite{2010A&A...517A..22M}."353 We have assumed that the mode lifetime varies as v! and have used mode widths equal to about a few percent of Av., We have assumed that the mode lifetime varies as $\dnumoy^{-1}$ and have used mode widths equal to about a few percent of $\dnumoy$.354" Finally, we stress that no background model is needed."," Finally, we stress that no background model is needed."355 The measurement of the large separation is performed in two steps., The measurement of the large separation is performed in two steps.356" First, an initial-guess value Avguess of the large separation is computed by an automated pipeline (?).."," First, an initial-guess value $\dnug$ of the large separation is computed by an automated pipeline \citep{2009A&A...508..877M}."357 This is used to form the initial synthetic template to correlate with the real spectrum., This is used to form the initial synthetic template to correlate with the real spectrum.358 The best correlation between the observed and synthetic spectra provides then the corrected value of the large separation., The best correlation between the observed and synthetic spectra provides then the corrected value of the large separation.359 The template was iteratively adjusted by varying its parameters to maximize the correlation., The template was iteratively adjusted by varying its parameters to maximize the correlation.360" In Fig. 1,,"," In Fig. \ref{deter},"361 we show the results obtained with all high signal- CoRoT data (?).., we show the results obtained with all high signal-to-noise CoRoT data \citep{2010A&A...517A..22M}.362" In both cases the graphs show the spectra arranged in strips with the colour representing the strength of the signal, as was done by ?.."," In both cases the graphs show the spectra arranged in strips with the colour representing the strength of the signal, as was done by \citet{2010PASP..122..131G}."363 The spectra are sorted by increasing large separation with the smallest large separation at the top of the plots: in the upper plot we use the output from a conventional pipeline and in the lower one we use the corrected value., The spectra are sorted by increasing large separation with the smallest large separation at the top of the plots: in the upper plot we use the output from a conventional pipeline and in the lower one we use the corrected value.364 The remarkably regular structure within the oscillation spectra in the lower plot reveals the signature of comb-like structure of the asymptotic relationship in Eq. (2)), The remarkably regular structure within the oscillation spectra in the lower plot reveals the signature of comb-like structure of the asymptotic relationship in Eq. \ref{tassoul_m}) )365 already reported (????)..," already reported \citep{2009Natur.459..398D,2010A&A...509A..73C,2010ApJ...713L.176B,huber2010}."366" Further, it validates the scaling law in € included in the reference template."," Further, it validates the scaling law in $\varepsilon$ included in the reference template."367 The global agreement of all high signal-to-noise spectra of bright targets with the synthetic pattern (Fig. 2)), The global agreement of all high signal-to-noise spectra of bright targets with the synthetic pattern (Fig. \ref{universal}) )368 shows that these oscillation patterns are homologous and that the red-giant oscillation pattern is universal., shows that these oscillation patterns are homologous and that the red-giant oscillation pattern is universal.369" We further found that the template is significantly improved if it takes account of the linear dependence of the large separation in frequency, expressed by the degree-dependent gradient o;=(dlogAv/dn)¢: with Vmax the frequency of maximum oscillation amplitude."," We further found that the template is significantly improved if it takes account of the linear dependence of the large separation in frequency, expressed by the degree-dependent gradient $\alpha_\ell370= (\diff\log \dnumoy / \diff n)_\ell$: with $\numax$ the frequency of maximum oscillation amplitude."371 The corrected values of Av are derived from this template., The corrected values of $\dnumoy$ are derived from this template.372" The values of the 12free parameters that account for the variations in frequency of the parameter e, of the small separations do; and of the gradients o; as derived from the fits to more than 60000 eigenmodes (Fig. 3))"," The values of the 12free parameters that account for the variations in frequency of the parameter $\varepsilon$, of the small separations $d_{0\ell}$ and of the gradients $\alpha_\ell$ as derived from the fits to more than 000 eigenmodes (Fig. \ref{identi}) )"373 are given in Table 1.., are given in Table \ref{fits}. .374" The value of £, defined modulo 1, is fixed thanks to the extrapolation to the Solar case."," The value of $\varepsilon$ , defined modulo 1, is fixed thanks to the extrapolation to the Solar case."375" As noted by ? and ?,, the small separation do; is negative."," As noted by \cite{2010A&A...509A..73C} and \cite{huber2010}, , the small separation $d_{01}$ is negative."376 All these fits are consistent with Kepler results., All these fits are consistent with Kepler results.377£eo(0R) profiles are shown iu sieuificautl-niproved fit most p,profiles and corresponding $L_\mathrm{CO}(R)$ profiles are shown in Figure \ref{fig:fluxfit_plot1}. .378 = 0 caseplacesno coustraiuts on the Wa Oph 6 the CO emission aud has a sudden steep be a 1101iber occiiugat Z4., The $p=0$ case places no constraints on the inner edge of the CO emission and has a sudden steep drop-offin $L_\mathrm{CO}(R)$ occurring at $R_\mathrm{mid}$.379" The p= 1.5 case profiles(Bast et region free of CO between P, and Ry.", The $p=-1.5$ case has a distinct region free of CO between $R_\star$ and $R_\mathrm{in}$.380 We be eulianced by secoud class of models is wore plivsically al. 20113.. Thus. can be cleared out near the star due to appropriate in this tzuucation.," We believe that the second class of models is more physically motivated, as CO can be cleared out near the star due to photodissociation or disk truncation."381 However. we cannot model with p the other class of models.," However, we cannot empirically rule out the other class of models."382 There are than the model a few sources in which the p=0 solution results iu a notably AS 205 N aud Figure 2.. The (see Figure , There are a few sources in which the $p=0$ solution results in a significantly-improved fit — most notably AS 205 N and Wa Oph 6 (see Figure \ref{fig:fluxfit_plot1}) ).383"However. AS 205 N is known to inner οσοof of a πια]2)). subset of disks with ""peakv line drop-off in Loo?) al. 2011).inwhichlow-velocity fiux may was a distinct a low-velocity disk wind (Poutoppidau et "," However, AS 205 N is known to be a member of a small subset of disks with “peaky” line profiles \citep{Bast11}, in which low-velocity flux may be enhanced by a low-velocity disk wind \citep{Pontoppidan11}."384lieve thatthea I&epleriau disk model is probably not uotivated. as CO case. and we do not believe that the photodissociation or disk = 0 isnecessarilyiore plivsicallv realistic clupirically rule out with p — 1.5.," Thus, a Keplerian disk model is probably not appropriate in this case, and we do not believe that the model with $p=0$ is necessarily more physically realistic than the model with$p=-1.5$ ."385 Iu most cases. one class of fits is uot preferred over," In most cases, one class of fits is not preferred over"386 (CGladdersetal.2003).. (Bar,\citealt{Gladders:2005oi}) \citep{2003ApJ...593...48G}.387ricutosetal.2008). (Hicksetal.2008).. (Iicks, \citep{felipe07} \citep{hicks07}. \citep{hicks07}.388"etal.2008). Q,,= 0.3.0,=0.7. Hgτο |l Wide-field MOS. spauuius a field of iuueter using IMACS on the 6.532 Baade telescope was obtained on the night of 2006 October 28-29.", $\Omega_m=0.3$ $\Omega_\Lambda=0.7$ $H_0=70$ $^{-1}$ Wide-field MOS spanning a field of diameter using IMACS on the 6.5-m Baade telescope was obtained on the night of 2006 October 28-29.389 The observations consisted of |... IsO0s exposures of a single mass coluprising 725 slits utilizing a custom baund-nuaitiug filter. which restricted the waveleneth coverage toSDSOA.. allowing coverage of the kev spectral features from [Or1|A3727. to C-baud (~1301A)) aud somewhat bevond. at the redshift of the cluster.," The observations consisted of 4 $\times$ 1800s exposures of a single mask comprising 725 slits utilizing a custom band-limiting filter, which restricted the wavelength coverage to, allowing coverage of the key spectral features from $\lambda$ 3727 to G-band $\sim4304$ ) and somewhat beyond, at the redshift of the cluster."390 The spectra were reduced following a techuique similar to that described in Calbanketal.(2007).., The spectra were reduced following a technique similar to that described in \citet{gilbank:07a}.391 Drieflv. we used the COSMOS software to process the 2D spectra.," Briefly, we used the COSMOS software to process the 2D spectra."392 Our oxocedure required the additional step of masking secoud. and third order bright skvline contamination. which overlapped many of our first order science spectra due to 1e highly imulti-tiered. nature of our data.," Our procedure required the additional step of masking second and third order bright skyline contamination, which overlapped many of our first order science spectra due to the highly multi-tiered nature of our data."393 The spectra were extracted to ID usine the apall task in IRAF., The spectra were extracted to 1D using the apall task in IRAF.394 Redshifts were measured using the IRAF taskkvsao., Redshifts were measured using the IRAF task.395 All 16 spectra were visually inspected aud assigned redshitt confidences based. on the system described ii Cülbaukal. (2007).., All the spectra were visually inspected and assigned redshift confidences based on the system described in \citet{gilbank:07a}.396 Tleveatter we group redshifts with quality Haes 1-3 iuto a higher confidence category (302 objects) xl denote class 1 redshifts as lower confidence (113 jects)., Hereafter we group redshifts with quality flags 1-3 into a higher confidence category (302 objects) and denote class 4 redshifts as lower confidence (113 objects).397 The redshift histograms for all galaxies in this field are shown in Fie. L.., The redshift histograms for all galaxies in this field are shown in Fig. \ref{fig:fullhist}.398 Also included are 16 redshitts centered ou RCOS231953|0038.0 frou VLT spectroscopy (Barricutosctal.2008)., Also included are 16 redshifts centered on RCS231953+0038.0 from VLT spectroscopy \citep{felipe07}.399. A clear peak is seen at z~0.9., A clear peak is seen at $\sim$ 0.9.400 The insets show histograms within 3.2 αποας (1.5 Mpcc) of cach cluster ceuter., The insets show histograms within 3.2 arcmins (1.5 Mpc) of each cluster center.401 The properties of the three clusters are stuarized in Table 1 and we refer to the three clusters as A. D. C. as denoted iu the table.," The properties of the three clusters are summarized in Table \ref{table:props} and we refer to the three clusters as A, B, C, as denoted in the table."402 Fig., Fig.403 2. shows the skv distribution of all spectroscopically observed galaxies within the IMACS field., \ref{fig:sigmap} shows the sky distribution of all spectroscopically observed galaxies within the IMACS field.404 Although the field is sparsely, Although the field is sparsely405"mionentun is eiveu by where rds the Bover-Lindquist radial coordinate. £1 is the conserved specific augular momentum of a circular orbit at radius r. fois a function of radius defined. such that the flux at the disk surface in the fluid frame PF—/( liv). aud AL, is the rest-uass accretion rate.","momentum is given by where $r$ is the Boyer-Lindquist radial coordinate, $L^\dagger$ is the conserved specific angular momentum of a circular orbit at radius $r$, $f$ is a function of radius defined such that the flux at the disk surface in the fluid frame $F = \dot M_o f/(4\pi r)$ , and $\dot M_o$ is the rest-mass accretion rate."406 As usual. O is the angular frequency of a circular orbit at radius ss," As usual, $\Omega$ is the angular frequency of a circular orbit at radius $r$."407 We also follow Novikov Thorne (1973) bw defining four auxiliary functions: with w the radius in units of ry=GALe) and a the dimensionless black hole spin parameter., We also follow Novikov Thorne (1973) by defining four auxiliary functions: with $x$ the radius in units of $r_g=GM/c^2$ and $a_*$ the dimensionless black hole spin parameter.408 In the usual approach. the boundary condition ou f at the radius 1). of the mareinally stable orbit is fi.= 0.," In the usual approach, the boundary condition on $f$ at the radius $r_{ms}$ of the marginally stable orbit is $f_{ms} = 0$ ."409" The appropriate boundary condition when there is nou-zero stress at fas is where €,,4=Crs). aud Ae is the additional radiative eficiency relative to the oue computed in terms of the binding energy at ras. €y. so that εξAe|ey."," The appropriate boundary condition when there is non-zero stress at $r_{ms}$ is where $C_{ms}=C(r_{ms})$, and $\Delta \epsilon$ is the additional radiative efficiency relative to the one computed in terms of the binding energy at $r_{ms}$, $\epsilon_0$, so that $\epsilon = \Delta \epsilon + \epsilon_0$."410" This choice of fins ensures that the integrated. additional dissipation matches Ae. and corresponds to a stress We refer to a disk with Ae=0 as a ""Novikov-Thornue lish.”"," This choice of $f_{ms}$ ensures that the integrated additional dissipation matches $\Delta\epsilon$, and corresponds to a stress We refer to a disk with $\Delta \epsilon =0$ as a “Novikov-Thorne disk.”"411 Using this boundary condition. the locally generated surface fiux beconies where RMtr) is the expression found by Novikov Thorne (1973).," Using this boundary condition, the locally generated surface flux becomes where $R^{NT}_R(x)$ is the expression found by Novikov Thorne (1973)."412 The standard relativistic correction factor RAT eocs to zero as a approaches wy). frou above. so that F (when the inner-edge stress is zero) peaks well outside the mareinmally stable orbit.," The standard relativistic correction factor $R^{NT}_R$ goes to zero as $x$ approaches $x_{ms}$ from above, so that $F$ (when the inner-edge stress is zero) peaks well outside the marginally stable orbit."413 By contrast. the additional dissipation due to a torque on the iuuer edee is concentrated very close to fps. and is nou-zero at the inner edge.," By contrast, the additional dissipation due to a torque on the inner edge is concentrated very close to $r_{ms}$, and is non-zero at the inner edge."414 The degree of concentration can be quantified by iieasurmeg r£». the radius within which fifty percent of the radiation is cuuitted: the halflight radius is a factor of a fow sinaller for torque-driven flux than for Novikov-Thornue flux.," The degree of concentration can be quantified by measuring $r_{1/2}$, the radius within which fifty percent of the radiation is emitted: the half-light radius is a factor of a few smaller for torque-driven flux than for Novikov-Thorne flux."415" Figure 1 shows the halflieht radius for a Novikov-Thorne disk. ""n> and an infinite-cfiicieney disk. (53. as a function of «"," Figure 1 shows the half-light radius for a Novikov-Thorne disk, $r^0_{1/2}$, and an infinite-efficiency disk, $r^\infty_{1/2}$ , as a function of $a_*$."416 Iu the limit of iufiuite efiicieney or zero accretion rate. Ae vemaius finite. so the first term im equation [8| dominates: in this case. the fux scales as rος at large s yather than as s7o as in the standard thin disk.," In the limit of infinite efficiency or zero accretion rate, $\dot M_o\epsilon$ remains finite, so the first term in equation [8] dominates; in this case, the flux scales as $r^{-7/2}$ at large $r$ rather than as $r^{-3}$ as in the standard thin disk."417 The expression for the surface flux becomes: where Lea is the Eddiugton Iuninositv aud ΕΤ is the Thomson opacity per unit mass., The expression for the surface flux becomes: where $L_{Edd}$ is the Eddington luminosity and $\kappa_{T}$ is the Thomson opacity per unit mass.418 2nuu The angular moment conservation equation corresponding to equatiou [8| is where n is the torque correction factor (Novikov Thorne 1973. Page Thorue 1971) iu the notation of τοῖς (1999).," 2mm The angular momentum conservation equation corresponding to equation [8] is where $R^{NT}_T$ is the torque correction factor (Novikov Thorne 1973, Page Thorne 1974) in the notation of Krolik (1999)."419 To clarity the meaning of the extra dissipation. we will write down equation [S| pretending that gravity is purely Nowtouianu: where s; is the disk tuner edge.," To clarify the meaning of the extra dissipation, we will write down equation [8] pretending that gravity is purely Newtonian: where $r_{in}$ is the disk inner edge."420" The first term iu the xacket is the usual Shakura-Suuvaev (1973) correction actor. while the second terii is derived from the extra orque at the iuuer οσο,"," The first term in the bracket is the usual Shakura-Sunyaev (1973) correction factor, while the second term is derived from the extra torque at the inner edge."421 This equation (actually first derived by Popham Naravau 1993) never applies in he relativistic case. but can apply. for example. to a disk. around a star where a torque is exerted by the spiuuiug uaenetosphere or through aboundary laver. or to a thin disk surrounding a differeut disk solution. such as au ADAF. where a torqueis exerted by the flow inside the rausition point.," This equation (actually first derived by Popham Narayan 1993) never applies in the relativistic case, but can apply, for example, to a disk around a star where a torque is exerted by the spinning magnetosphere or through aboundary layer, or to a thin disk surrounding a different disk solution, such as an ADAF, where a torqueis exerted by the flow inside the transition point."422"llere is the number of wave quanta anc is (he wave Irequeney και,",Here is the number of wave quanta and is the wave frequency -ku.423 The left haad side has a usual Wamiltonian form that states the conservation of alone the lines of constant [requencey on the fer plane.," The left hand side has a usual Hamiltonian form that states the conservation of along the lines of constant frequency on the k,x plane."424 The first termi on the rls., The first term on the r.h.s.425 describes the wave generation on the cevcelotron instability of a sliebhtly anisotropic particle distribution., describes the wave generation on the cyclotron instability of a slightly anisotropic particle distribution.426 Lt can be expressed (hrough ils spatial gradient., It can be expressed through its spatial gradient.427 The resonance condition for (he wave-particle interaction contains also the particle pitch angle by means of the following expression =¢B/e which. eenerally speaking. requires the treatment of particle distribution in two dimensional momentum space 7).," The resonance condition for the wave-particle interaction contains also the particle pitch angle by means of the following expression =eB/c which, generally speaking, requires the treatment of particle distribution in two dimensional momentum space )."428" A significant simplification can be achieved by the so called ""resonance sharpening” procedure (Skilling1975:Drury.etal. 1996)) whereby a certain “optimal” value of is ascribed (o all particles and (he resonance condition puts & and p into a one-to-one relation.."," A significant simplification can be achieved by the so called “resonance ” procedure \citealt{skil75c, dru96}) ) whereby a certain ” value of is ascribed to all particles and the resonance condition puts k and p into a one-to-one relation,."429. The second term on the r.hi.s., The second term on the r.h.s.430 stuxds for nonlinear wave-particle and interactions such as the induced scattering of waves on thermal protons ancl mode coupling (Sagdeev&Galeev1969)., stands for nonlinear wave-particle and wave-wave interactions such as the induced scattering of waves on thermal protons and mode coupling \citep{gs69}.431. We will suggest a simple model for this nonlinear term 1n seclion 3.2.., We will suggest a simple model for this nonlinear term in section \ref{sec:modif}.432 To conclude this subsection we emphasize (hat while eqs.(4--6)) already treat (he acceleration process and flow structure on equal footing. the fluctuation part given bw eq.(9)) mist be included in this treatment and. as we shall see in the sequel. it by no means plays a subdominant role in this triad.," To conclude this subsection we emphasize that while \ref{dc1}- \ref{mom:c}) ) already treat the acceleration process and flow structure on equal footing, the fluctuation part given by \ref{wke}) ) must be included in this treatment and, as we shall see in the sequel, it by no means plays a subdominant role in this triad."433 There are (wo aspects of the acceleration where nonlinearity is crucial for ils outcome., There are two aspects of the acceleration where nonlinearity is crucial for its outcome.434 The first aspect is the excitation of scattering waves by accelerated particles and the second one is the backreaction of these particles on the shock structure., The first aspect is the excitation of scattering waves by accelerated particles and the second one is the backreaction of these particles on the shock structure.435 The latter is critical both for the particle injection and wave excitation that is. to particle confinement.," The latter is critical both for the particle injection and wave excitation that is, to particle confinement."436 Indeed. the svstem 4-7 sell-consistentlv describes particle acceleration ancl (he shock structure (nonlinearly modified by the particle pressure) only if the particle scattering law is known (which is contained in the diffusion coefficient #)) and the injection rate from the thermal plasma is also known (the normalization of the particle distribution f(p) in eq.(4))).," Indeed, the system \ref{dc1}- \ref{P_c} self-consistently describes particle acceleration and the shock structure (nonlinearly modified by the particle pressure) only if the particle scattering law is known (which is contained in the diffusion coefficient ) and the injection rate from the thermal plasma is also known (the normalization of the particle distribution f(p) in \ref{dc1}) ))."437 Physically. the scattering rate determines (he particle maximum momentpygy- as eq.(2)) indicates.," Physically, the scattering rate determines the particle maximum momentum, as \ref{t:acc}) ) indicates."438" The difficulty, however. is that both the cut-off momentum ancl the wavenumber cutoff of the scattering. turbulence change in (me (one controlling the other) due to the exclotron resonance condition."," The difficulty, however, is that both the cut-off momentum and the wavenumber cutoff of the scattering turbulence change in time (one controlling the other) due to the cyclotron resonance condition."439 However (he speed at which they change has not been caleulated sel-consistentlv., However the speed at which they change has not been calculated self-consistently.440 The solution given by eqs.(1)), The solution given by \ref{p:max}) )441To understand (he processes that govern galaxy formation and evolution. detailed information must be collected about the behavior of the different galaxy populations under different conditions.,"To understand the processes that govern galaxy formation and evolution, detailed information must be collected about the behavior of the different galaxy populations under different conditions."442 A common and useful way to achieve this. is the study of galaxy Iuminosities and (heir variation with the environment.," A common and useful way to achieve this, is the study of galaxy luminosities and their variation with the environment."443 The most suitable statistical tool to perform this kind of analvsis is the luminosity [unetion (LE) of galaxies., The most suitable statistical tool to perform this kind of analysis is the luminosity function (LF) of galaxies.444" This function describes the distribution of luminosities of a given. population of galaxies and. in most cases. il can be parametrized) bv a function with (wo parameters excluding the normalization 1976)). the characteristic absolute magnitude M"" and the faint end slope a."," This function describes the distribution of luminosities of a given population of galaxies and, in most cases, it can be parametrized by a function with two parameters excluding the normalization \citealt{schechter76}) ), the characteristic absolute magnitude $M^{\ast}$ and the faint end slope $\alpha$."445 The results obtained from the analvsis of these parameters are among (he most interesting issues in extragalactic astronomy., The results obtained from the analysis of these parameters are among the most interesting issues in extragalactic astronomy.446 Prior to 2000 the LF has been computed [or galaxies in the field. groups ancl in clusters of galaxies (see [or instance Marzke.IIuchra&Geller1994:Linetal.1996:Zucca1997:1998:Ranzy.Adami&MazureTrentham 19983).," Prior to 2000 the LF has been computed for galaxies in the field, groups and in clusters of galaxies (see for instance \citealt{mhg94,lin96,zucca97,lopcruz97,valotto97,ratclif98,mvl98,rauzy98,tren98}) )."447 Two lines of thought have arisen from these works: one of them states that the LF depends on (he environment while the other supports the idea of an universal LE., Two lines of thought have arisen from these works: one of them states that the LF depends on the environment while the other supports the idea of an universal LF.448 The dependence of (he LF with the environment was proposed by some authors due to the very steep faint end slope found for the LF in Clusters of galaxies which was interpreted as an excess of dwarf galaxies relative to the field., The dependence of the LF with the environment was proposed by some authors due to the very steep faint end slope found for the LF in clusters of galaxies which was interpreted as an excess of dwarf galaxies relative to the field.449 Nevertheless. in order {ο have more reliable results on this matter. large samples of galaxies with high «quality photometric and spectroscopic information were needed.," Nevertheless, in order to have more reliable results on this matter, large samples of galaxies with high quality photometric and spectroscopic information were needed."450 mince the advent. of the large survevs of galaxies. such as the Sloan Digital Sky Survey (Yorketal.2000) and the Two degree Field Galaxy Redshift Strvey (2dFGRS. al. 2001)). much better determinations of the LF have been obtained (Blantonetal.2001.2002b:Christlein&Zabludoff2003:Ekeetal. 2004h).," Since the advent of the large surveys of galaxies, such as the Sloan Digital Sky Survey \citep{sdss} and the Two degree Field Galaxy Redshift Survey (2dFGRS, \citealt{2df}) ), much better determinations of the LF have been obtained \citep{blanton01,blantonlf,blanton05,norb02,madgwick,trentu02,m02b,cz03,eke04b}."451. Most of these works agree with a flat LF of galaxies in the field (a~ —1) meanwhile a brighter characteristic magnitude A/* and asteeper faint end slope a have been found in galaxy systems., Most of these works agree with a flat LF of galaxies in the field $\alpha \sim -1$ ) meanwhile a brighter characteristic magnitude $M^{\ast}$ and a steeper faint end slope $\alpha$ have been found in galaxy systems.452" Analyzing a sample of rich clusters of galaxies obtained from a cross-correlation between the Sloan Digital Skv Survey id the Rosat All Sky Survey. Popessoetal.(2005). have found that the very [aint end slope (M,—5log(h)= —17) is remarkably steep (a~ —2) on these environments."," Analyzing a sample of rich clusters of galaxies obtained from a cross-correlation between the Sloan Digital Sky Survey and the Rosat All Sky Survey, \citet{pop05} have found that the very faint end slope $M_r-5\log(h)>-17$ ) is remarkably steep $\alpha \sim -2$ ) on these environments."453 Similar results have been found bv Gonzálezetal.(20055) when lower density environments. as Galaxy groups are analvzed., Similar results have been found by \citet{gonz05} when lower density environments as galaxy groups are analyzed.454 It should be noted that both works have been carried oul using statistical background subtraction methods owing to the lack of spectroscopic information for Taint galaxies., It should be noted that both works have been carried out using statistical background subtraction methods owing to the lack of spectroscopic information for faint galaxies.455 These methods are sensitive to the background computation and to the presence of structures along the line of sight, These methods are sensitive to the background computation \citep[see their Table 2]{pop05} and to the presence of structures along the line of sight456the velocities of the cussion horus cetermuued from the ceutral profile (Fig. 1)),the velocities of the emission horns determined from the central profile (Fig. \ref{fig1}) )457 aud the velocity rauge (VW.+ V.) of the SiO emission (Fig. 1))., and the velocity range $\rm V_c \pm V_o$ ) of the SiO emission (Fig. \ref{fig1}) ).458 Fic., Fig.459 1 reveals no resolvable kiueniatie structure im the EW direction. but shows velocity gradieuts in the NS direction. iu agreement with S92.," \ref{fig4} reveals no resolvable kinematic structure in the EW direction, but shows velocity gradients in the NS direction, in agreement with S92."460 Fie., Fig.461" Lb shows that the two horus on the CO(21) line profile arise frou differcut locations iu the slaw. separated by about 1y,"," \ref{fig4} shows that the two horns on the CO(2–1) line profile arise from different locations in the sky, separated by about $\rm 10''$."462 At higher velocities with respect to the line center. -(6to12)kins|. the declination - velocity curve turus over.," At higher velocities with respect to the line center, $\rm \pm (6 ~ to ~46312) ~ km~s^{-1}$, the declination - velocity curve turns over."464 At higher velocities vet. the position offsets are sunaller still and decrease esseutiallv to zero.," At higher velocities yet, the position offsets are smaller still and decrease essentially to zero."465 There is a second. lower amplitude inflection point iu the velocity - right ascension curve near he ceutral velocity. with a velocity eradicut of ~5kins1 over a region a few areseconds m diameter.," There is a second, lower amplitude inflection point in the velocity - right ascension curve near the central velocity, with a velocity gradient of $\rm \sim 5 ~ km~s^{-1}$ over a region a few arcseconds in diameter."466 First we use a smiple model for the molecular euvelope to estimate au approximate mass loss rate., First we use a simple model for the molecular envelope to estimate an approximate mass loss rate.467" The SiO(65) line profile sugeests simple spherical outflow. and we calculated a inodel CO cinissiou profile assuiiiug spherical outflow at coustant velocity and mass loss rate, with a relative abundance f= ΟΠ=65«! (Lambert et al 1986)) V,=10kms5|."," The SiO(6--5) line profile suggests simple spherical outflow, and we calculated a model CO emission profile assuming spherical outflow at constant velocity and mass loss rate, with a relative abundance f = $\rm CO/H_2 ~ = ~ 6.5 \times 10^{-4}$ (Lambert et al. \cite{lambert}) ), $\rm V_o ~ = ~ 10 ~ km~s^{-1}$,"468 and ME10=L5.10*M.vro ," and $\rm \mathaccent46995 M ~ = ~ 4.5 \times 10^{-7} ~ M_{\odot} ~ yr^{-1}$."470The model CO(21) line profile is parabolic and does uot reproduce the observed line shape., The model CO(2–1) line profile is parabolic and does not reproduce the observed line shape.471 We then investigated a model consisting of an expanding flattened system. or disk. tilted to the line of sight.," We then investigated a model consisting of an expanding flattened system, or disk, tilted to the line of sight."472 The line profiles xoduced by this configuration were calculate from a model of the euvelope ecometry. with the line formation caleulated by a Monte Carlo radiative transter code based on that of Bernes (1979)) modified for axisviunietrie geometries.," The line profiles produced by this configuration were calculated from a model of the envelope geometry, with the line formation calculated by a Monte Carlo radiative transfer code based on that of Bernes \cite{bernes}) ) modified for axisymmetric geometries."473 The euvelope is modeled by a set of conceutric tines. with sufficiently. fine. radial spacing to approxinate a smooth distribution iu optical depth (see Crosas Moeuten 1997)).," The envelope is modeled by a set of concentric rings, with sufficiently fine radial spacing to approximate a smooth distribution in optical depth (see Crosas Menten \cite{crosas}) )."474 The vines have 30 racdia and 30 height spacings., The rings have 30 radial and 30 height spacings.475 Within each of the 30 x 30 vines. the density and temperature are constaut.," Within each of the 30 x 30 rings, the density and temperature are constant."476 The 3D coniponuents of the velocity vector are calculated at cach photon step (cf., The 3D components of the velocity vector are calculated at each photon step (cf.477 Bernes 1979)., Bernes 1979).478 The level populations are solved for 30 rotational levels aud for infrared pumping to the first vibrational state (v = >1 at ο p) using the observed LG jan flux density of a! Gr (Cezari ct al. 19933).," The level populations are solved for 30 rotational levels and for infrared pumping to the first vibrational state (v = $\rightarrow$ 1 at 4.6 $\rm479\mu m$ ) using the observed 4.6 $\rm \mu m$ flux density of $\rm \pi^1$ Gru (Gezari et al. \cite{gezari}) )."480 The uass loss rate. racial expansion velocity.y turbulent velocity. kinetic temperature distribution and disk radius are put parameters.," The mass loss rate, radial expansion velocity, turbulent velocity, kinetic temperature distribution and disk radius are input parameters."481 The line profile alone a eiven liue of sight is calculated by rotating the structure. calculating the line emission across the structure and convolving the cussion with a two-dimensional circular eaussian beam.," The line profile along a given line of sight is calculated by rotating the structure, calculating the line emission across the structure and convolving the emission with a two-dimensional circular gaussian beam."482 The fast molecular wiud was not included in this model., The fast molecular wind was not included in this model.483addition to the photo-z estimate.,addition to the photo-z estimate.484 This error depends on the noise on the neural network inputs and not on the difference between the spectroscopic and photometric redshifts., This error depends on the noise on the neural network inputs and not on the difference between the spectroscopic and photometric redshifts.485" The variance that this noise on the input would introduce into the output of the network is given by a simple chain rule expression as follows: where the sum i is a sum over all the network inputs and 6m, is the photometric error on the magnitude in band i.", The variance that this noise on the input would introduce into the output of the network is given by a simple chain rule expression as follows: where the sum $i$ is a sum over all the network inputs and $\delta_{m_i}$ is the photometric error on the magnitude in band $i$ .486 The derivative LM is obtained using the formalism described in ?.., The derivative $\frac{\partial z}{\partial m_i}$ is obtained using the formalism described in \citet{Bishop}.487 This algorithmi is fully implemented within ANNz (?).., This algorithm is fully implemented within ANNz \citep{Collister:ANNZ}.488 In this section we look at the impact of different filter combinations and survey depths on the photometric redshift estimate., In this section we look at the impact of different filter combinations and survey depths on the photometric redshift estimate.489 We do this by running the neural network code described in §5 on the DES5yr sample described in §4.., We do this by running the neural network code described in $\S$ \ref{sec:ANNz} on the DES5yr sample described in $\S$ \ref{sec:catalogues}.490 ANNz was run on the mock data for five different filter configurations., ANNz was run on the mock data for five different filter configurations.491 These are summarised in Table 2.., These are summarised in Table \ref{tab:filters}.492" We computed photometric redshifts for each of these cases and from the available true redshifts, computed the scatter on thephoto-z estimate."," We computed photometric redshifts for each of these cases and from the available true redshifts, computed the scatter on thephoto-z estimate."493 The scatter is the rms, The scatter is the rms4940.0655. tkpe.,$h^{-1}$ kpc.495 The rotation velocity of the disk is 200knis , The rotation velocity of the disk is $s^{-1}$ .496ligure 2. presents the source and image plane for this model. with the elliptical and diamond caustic. and corresponding critical lines apparent.," Figure \ref{fig2}497 presents the source and image plane for this model, with the elliptical and diamond caustic, and corresponding critical lines apparent."498 In this model. the quasar images are not substantial magnified. with a total magnification of ~7. with the intrinsic source of being corresponcingly luminous. Lip~7107L..," In this model, the quasar images are not substantial magnified, with a total magnification of $\sim7$, with the intrinsic source of being correspondingly luminous, $L_{bol}\sim7\times10^{14}L_\odot$."499 While extreme. this value is not necessarily outrageous as the unlensed. quasar 1D1946|7658 possess an intrinsic luminosity of ~4LHL. (Lagan et al.," While extreme, this value is not necessarily outrageous as the unlensed quasar HD1946+7658 possess an intrinsic luminosity of $\sim4\times10^{14}L_\odot$ (Hagan et al."500 1992). anc nunay be a member of this very. Iuminous class of quasars.," 1992), and may be a member of this very luminous class of quasars."501 Lt must. be conceded. however. that the non-uniqueness of the lens model translates into uncertainty in the moce magnification and a true determination of the intrinsic properties of υπονο models. derived from better observationa constraints.," It must be conceded, however, that the non-uniqueness of the lens model translates into uncertainty in the model magnification and a true determination of the intrinsic properties of require models derived from better observational constraints."502 The CO source is taken to be have an circular surface rightness distribution centred upon the quasar position., The CO source is taken to be have an circular surface brightness distribution centred upon the quasar position.503 One important aspect of the results presented herein is that comes the second system for which the gravitational ens can be used to study structure on sub-kpe scales in he molecular gas associated with the AGN host. galaxy. he first svstem being the Clover Leaf quasar. 11413|117 (Yun et al.," One important aspect of the results presented herein is that becomes the second system for which the gravitational lens can be used to study structure on sub-kpc scales in the molecular gas associated with the AGN host galaxy, the first system being the Clover Leaf quasar, H1413+117 (Yun et al."504 1998: Ixneib. Alloin. DPello. I... 1998).," 1998; Kneib, Alloin, Pello, R. 1998)."505 For5255.. the observations and lens model require the CO to be distributed on a scale covering a substantial fraction of the caustics in the image plane. but not too large to lose the ring structure.," For, the observations and lens model require the CO to be distributed on a scale covering a substantial fraction of the caustics in the image plane, but not too large to lose the ring structure."506 The lower limit to the CO source size based on the modeling is ~4005.+ pe. while a rough upper limit is 1 kpc.," The lower limit to the CO source size based on the modeling is $\sim400h^{-1}$ pc, while a rough upper limit is $\sim$ 1 kpc."507 With this model. the CO(1-0) has been magnified by a factor of ~δρ3.," With this model, the CO(1-0) has been magnified by a factor of $\sim2.5-3$."508 Like the Clover Leaf. we find that the spatial extent. ancl mass of the molecular eas in aare comparable to those seen in nearby nuclear starburst ealaxies (Sanders and. A\lirabel 1996: Downes ancl Solomon 1998).," Like the Clover Leaf, we find that the spatial extent and mass of the molecular gas in are comparable to those seen in nearby nuclear starburst galaxies (Sanders and Mirabel 1996; Downes and Solomon 1998)."509 Downes et al. (, Downes et al. (5101999) determined. a CO source. size of ~(SO135)h tpe for the estimated. magnification factors of ~207.,1999) determined a CO source size of $\sim(80-135)h^{-1}$ pc for the estimated magnification factors of $\sim20-7$.511 This size is much smaller than the one caleulated above. while their magnification factors are larger.," This size is much smaller than the one calculated above, while their magnification factors are larger."512 Their analysis is based. upon modeling of CO emission in the eravitationally lensecl ultraluminous galaxy IRAS F1021414724 (Downes. Solomon Racllord 1995). whose image is clearly an extended: are-like feature which possesses an essentially linear magnification.," Their analysis is based upon modeling of CO emission in the gravitationally lensed ultraluminous galaxy IRAS F10214+4724 (Downes, Solomon Radford 1995), whose image is clearly an extended arc-like feature which possesses an essentially linear magnification."513 Such a simple model is probably a poor representation of the lensing in5255., Such a simple model is probably a poor representation of the lensing in.514.. Additionally. Downes ct al. (," Additionally, Downes et al. ("5151999) assumed that the velocity filling factor is unity. substantially larger than the value derived in Section ??:: as the intrinsic source radius in their model scales inversely with this value and the magnification factor is proportional to it.,"1999) assumed that the velocity filling factor is unity, substantially larger than the value derived in Section \ref{observations}; as the intrinsic source radius in their model scales inversely with this value and the magnification factor is proportional to it."516 For [40.35. a value well within our estimated range. the Downes ct al. (," For $\sim$ 0.35, a value well within our estimated range, the Downes et al. ("5171999) model vields an upper limit for the intrinsicsource,1999) model yields an upper limit for the intrinsicsource518"It should be made clear that by taking Ty estimates from literature we ignore potential errors due to non-uniform radius for extracting Tx, systematic differences between XMM-Newton and Chandra measurements, etc.","It should be made clear that by taking $T_X$ estimates from literature we ignore potential errors due to non-uniform radius for extracting $T_X$, systematic differences between XMM-Newton and Chandra measurements, etc."519" However, the mean slope for the P,4—Meas scaling relation, 3.2+0.7 with the full sample, is consistent with the global mass scaling derived from the Y—M relation (see refMsection)), indicating that no additional biases are incurred while using this non-uniform selection of X-ray temperatures."," However, the mean slope for the $P_{1.4}-M_{\mathrm{gas}}$ scaling relation, $3.2\pm 0.7$ with the full sample, is consistent with the global mass scaling derived from the $Y-M$ relation (see \\ref{Msection}) ), indicating that no additional biases are incurred while using this non-uniform selection of X-ray temperatures."520 A tentative argument for a selection bias in X-ray complete samples and the ensuing bi-modality can be given by comparing the relative frequency with which radio haloes and non-detections occur in the catalog., A tentative argument for a selection bias in X-ray complete samples and the ensuing bi-modality can be given by comparing the relative frequency with which radio haloes and non-detections occur in the catalog.521 In Venturi et al. (, In Venturi et al. (522"2008), GMRT data were obtained for a complete X-ray selected sample, with 6 detection of radio haloes plus 20 non-detections.","2008), GMRT data were obtained for a complete X-ray selected sample, with 6 detection of radio haloes plus 20 non-detections."523" The catalog contains 5 out of these 6 halo clusters, but only 4 out of 20 non-detection clusters."," The catalog contains 5 out of these 6 halo clusters, but only 4 out of 20 non-detection clusters."524 For the BO9 sample this ratio is 16 out of 21 radio halo clusters and 4 out of 20 non-detections (the same non-detections as in the Venturi et al., For the B09 sample this ratio is 16 out of 21 radio halo clusters and 4 out of 20 non-detections (the same non-detections as in the Venturi et al.525 sample)., sample).526" Since the catalog should not have a significant bias towards mergers, this provides an indirect evidence for our hypothesis that being SZ-bright (hence massive) is a better indicator for clusters hosting radio haloes, as opposed to being X-ray luminous."," Since the catalog should not have a significant bias towards mergers, this provides an indirect evidence for our hypothesis that being SZ-bright (hence massive) is a better indicator for clusters hosting radio haloes, as opposed to being X-ray luminous."527" Even though the RO9 sample is too shallow to directly test bi-modality, it interestingly follows this same trend: reports measurement of 12 out of 14 counterparts for haloes and other diffuse emissions, as opposed to only 15 out of 58 counterparts for non-detections."," Even though the R09 sample is too shallow to directly test bi-modality, it interestingly follows this same trend: reports measurement of 12 out of 14 counterparts for haloes and other diffuse emissions, as opposed to only 15 out of 58 counterparts for non-detections."528" The independent variable, Ysz, is defined as the integral of the total pressure in a spherical volume, and hence is proportional to the total gas mass: Here T, is the mean gas temperature within the integration radius, and fj, is the gas-to-mass ratio."," The independent variable, $\ysz$, is defined as the integral of the total pressure in a spherical volume, and hence is proportional to the total gas mass: Here $T_e$ is the mean gas temperature within the integration radius, and $f_{\mathrm{gas}}$ is the gas-to-mass ratio."529" Assuming hydrostatic equilibrium and isothermality, the temperature scales to the total mass as T,«M2?E(zy? (e.g. Bryan Norman 1998), where E(z) is the ratio of the Hubble parameter at redshift z to its present value."," Assuming hydrostatic equilibrium and isothermality, the temperature scales to the total mass as $T_e \propto M_{\mathrm{tot}}^{2/3} E(z)^{2/3}$ (e.g. Bryan Norman 1998), where $E(z)$ is the ratio of the Hubble parameter at redshift $z$ to its present value."530" Therefore, the scaling between the SZ observable and total mass is YszE(z)??0fasMp."," Therefore, the scaling between the SZ observable and total mass is $\ysz E(z)^{-2/3} \propto f_{\mathrm{gas}} M_{\mathrm{tot}}^{5/3}$."531" Numerical simulations, analytical models and SZ observations indicate that this mass scaling is extremely robust, with little scatter over a large range of cluster mass, dynamical state or other details of cluster physics (e.g. Motl et al."," Numerical simulations, analytical models and SZ observations indicate that this mass scaling is extremely robust, with little scatter over a large range of cluster mass, dynamical state or other details of cluster physics (e.g. Motl et al."532" 2005, Reid Spergel 2006, Andersson et al."," 2005, Reid Spergel 2006, Andersson et al."533 2011)., 2011).534" We thus assume this scaling to be valid also a cluster at different radii, provided that the radius is sufficiently large to exclude complex physics at clusters cores."," We thus assume this scaling to be valid also a cluster at different radii, provided that the radius is sufficiently large to exclude complex physics at clusters cores."535" The large halo sizes measured by C07 (Ry~600 kpc, typically of the same order as R»soo), ensures that they encompass a representative cluster volume."," The large halo sizes measured by C07 $\bar{R}_H \sim 600$ kpc, typically of the same order as $R_{2500}$ ), ensures that they encompass a representative cluster volume."536" The E(z)?? factor for self-similar evolution changes the scaling results only marginally, well within the statistical errors."," The $E(z)^{-2/3}$ factor for self-similar evolution changes the scaling results only marginally, well within the statistical errors."537" The gas mass fraction, fgas, has a weak dependence on cluster mass: ωςccΛάος (Bonamente et al."," The gas mass fraction, $f_{\mathrm{gas}}$, has a weak dependence on cluster mass: $f_{\mathrm{gas}} \propto M_{\mathrm{500}}^{~0.14}$ (Bonamente et al."538" 2008, Sun et al."," 2008, Sun et al."539 2009)., 2009).540" Assuming the same mass dependence of f, for all radii, we therefore obtain In the above, Mg is the total mass inside radio haloes, and My is the cluster virial mass which scales linearly with Mio(<5Rsoo)."," Assuming the same mass dependence of $f_{\mathrm{gas}}$ for all radii, we therefore obtain In the above, $M_H$ is the total mass inside radio haloes, and $M\vir$ is the cluster virial mass which scales linearly with $M_{\mathrm{tot}}(<5R_{500})$."541 The scaling index inside haloes is in good agreement with previous X-ray hydrostatic mass estimates (e.g. Cassano et al., The scaling index inside haloes is in good agreement with previous X-ray hydrostatic mass estimates (e.g. Cassano et al.542 2007)., 2007).543" The global scaling with total cluster mass can be a useful parameter for estimating radio halo statistics, particularly in simulations."," The global scaling with total cluster mass can be a useful parameter for estimating radio halo statistics, particularly in simulations."544" The radio halo sizesare known to scale non-linearly with cluster radius, in a break from self-similarity (Kempner Sarazin 2001, Cassano et al."," The radio halo sizesare known to scale non-linearly with cluster radius, in a break from self-similarity (Kempner Sarazin 2001, Cassano et al."545 2007)., 2007).546" Indeed, using the X-ray derived Rsoo measurements from the catalog, we obtain the empirical relation RycR39? with the C07 sample, consistent with the estimate by C07 using Ly—My scaling relation (Ryος R26:05),"," Indeed, using the X-ray derived $R_{500}$ measurements from the catalog, we obtain the empirical relation $R_H \propto R_{500}^{\ 3.1 \pm 0.2}$ with the C07 sample, consistent with the estimate by C07 using $L_X-M\vir$ scaling relation $R_H \propto R\vir^{2.6\pm 0.5}$ )."547 A consequence of this rapid increase in radius is a drop of the mean gas density inside haloes with increasing halo mass., A consequence of this rapid increase in radius is a drop of the mean gas density inside haloes with increasing halo mass.548" Our observed scaling between the halo radius and scaled SZ signal, Ryος Y$?5995. implies that the mean gas density (7j) scales"," Our observed scaling between the halo radius and scaled SZ signal, $R_H \propto Y_H^{\ 0.31\pm 0.03}$ , implies that the mean gas density $\bar{n}_H$ ) scales"549from Cen (1992) with some minor modifications (Lheuns 1998).,from Cen (1992) with some minor modifications (Theuns 1998).550 We take the photoheating rate in the optically. thin limit from IHaardt Alacdau (1996)., We take the photoheating rate in the optically thin limit from Haardt Madau (1996).551 This heating rate. denoted as in the ey. column of the Table. is imposed on models Li. Lleo.65 and Lleo.4.," This heating rate, denoted as in the $\epsilon_{\rm552He}$ column of the Table, is imposed on models L1, $\sigma .65$ and $\sigma .4$."553 Models L2 and L3 are identical to L1. except that we have multiplied the helium photoheating rate by factors two ancl three respectively (keeping the ionization rate constant)," Models L2 and L3 are identical to L1, except that we have multiplied the helium photoheating rate by factors two and three respectively (keeping the ionization rate constant)."554 Alodel L3b has the same heating rate as model L3., Model L3b has the same heating rate as model L3.555 In. model LO.3 we have reduced the helium photoheating by a factor 3., In model L0.3 we have reduced the helium photoheating by a factor 3.556 Model LX is identical to model L1. except that we have included Compton heating by the A-ray background. as a function of vreclshift z at a rate (Macau Efstathiou 1999) where Ha is the heating rate in erg env? Land nds number density of free electrons in 7.," Model LX is identical to model L1, except that we have included Compton heating by the X-ray background as a function of redshift $z$ at a rate (Madau Efstathiou 1999) where ${\cal H}_X$ is the heating rate in erg $^3$ $^{-1}$ and $n_e$ is number density of free electrons in $^{-3}$."557 Finally. model $3 is à standard CDM model. with the appropriate LHaardt Macau (1996) helium heating rate increased by a [actor 3.," Finally, model S3 is a standard CDM model, with the appropriate Haardt Madau (1996) helium heating rate increased by a factor 3."558 For each model we compute spectra along 1200 random. lines of sight through the simulation box at a given recshift (usually z= 3) and then scale the ionizing background Lux bv the factor cf in the analvsis stageIn such as to ὃνgive a chosen ellective optical depth τω.," For each model we compute spectra along 1200 random lines of sight through the simulation box at a given redshift (usually $z=3$ ) and then scale the ionizing background flux by the factor $A$ in the analysis stage such as to give a chosen effective optical depth $\tau_{\rm559eff}$."560 Phe factor 23 required. to give τω=0.33 at 23 is given in Table 1.., The factor $A$ required to give $\tau_{\rm eff}=0.33$ at $z=3$ is given in Table \ref{table:runs}.561 We process these simulated spectra using the following procedure. designed to introduce the same biases as present in observational data from the LILRIES spectrograph on the Ixeck telescope.," We process these simulated spectra using the following procedure, designed to introduce the same biases as present in observational data from the HIRES spectrograph on the Keck telescope."562 Each spectrum is first convolved with a Gaussian with full width at half maximum of EWIIM = 8 land. re-sampled onto pixels of width 3ο, Each spectrum is first convolved with a Gaussian with full width at half maximum of FWHM = 8 and re-sampled onto pixels of width 3.563"ι, Photon and. pixel noise is acded such that the total signal-to-noise is 50.", Photon and pixel noise is added such that the total signal-to-noise is 50.564 The ofthe spectra is then fitted with the method described in Theuns (1998)., The of the spectra is then fitted with the method described in Theuns (1998).565 We also compare Iux statistics for our simulated spectra to an observed. LILIIZS spectrum of QSO 1422|231. kindly provided to us by W. Sargent and M. Rauch.," We also compare flux statistics for our simulated spectra to an observed HIRES spectrum of QSO 1422+231, kindly provided to us by W. Sargent and M. Rauch."566 Phe forest of this QSO extends over à significant redshift range. over which the effective optical depth evolves significantly.," The forest of this QSO extends over a significant redshift range, over which the effective optical depth evolves significantly."567 1n addition. the signal-to-noise ratio varies às a function of wavelength. anc flux.," In addition, the signal-to-noise ratio varies as a function of wavelength and flux."568 We model these elfects. for this xwticular spectrum using the following detailed: procedure (κου also Rauch 1997)., We model these effects for this particular spectrum using the following detailed procedure (see also Rauch 1997).569 We begin bv dividing the spectrum in two halves., We begin by dividing the spectrum in two halves.570 For each half. we take the simulation output at the appropriate redshift and scale the background lux such as to match the observed mean elfective optical depth.," For each half, we take the simulation output at the appropriate redshift and scale the background flux such as to match the observed mean effective optical depth."571 We convolve the spectrum with a Gaussian. with ‘all width at half maximum of EWIIM = 6.6 tanel re-samiple it to pixels of the same size as the observed spectrum., We convolve the spectrum with a Gaussian with full width at half maximum of FWHM = 6.6 and re-sample it to pixels of the same size as the observed spectrum.572 We calculate the noise properties of the QSO spectrum as a function of [lux and add: Ciaussian noise to the simulated spectra appropriate for the flux in cach pixel., We calculate the noise properties of the QSO spectrum as a function of flux and add Gaussian noise to the simulated spectra appropriate for the flux in each pixel.573 In the observed spectrum we exclude regions with identified metal absorption lines and the region close to the emission redshift which might be influenced by the proximity effect., In the observed spectrum we exclude regions with identified metal absorption lines and the region close to the emission redshift which might be influenced by the proximity effect.574 Aelow we will show that this more cllaborate procedure produces [lux statistics in better agreement with the data than the simpler onc described: earlier., Below we will show that this more ellaborate procedure produces flux statistics in better agreement with the data than the simpler one described earlier.575 We use the same automated version of (Carswell LOST) to fit Voigt profiles to both simulated and observed: spectra (see Vheuns 1998 for more details)., We use the same automated version of (Carswell 1987) to fit Voigt profiles to both simulated and observed spectra (see Theuns 1998 for more details).576 In this section we illustrate the elfect of different broadening mechanisms on the widths of density peaks along a eiven line-of-sight., In this section we illustrate the effect of different broadening mechanisms on the widths of density peaks along a given line-of-sight.577 In particular. we discuss the relative importance of the three cillerent thermal cllects. naniely Jeans smoothing. pressure-induced peculiar velocities. ancl thermal broadening and compare these to the clleet of the amplitude of dark matter [Ductuations.," In particular, we discuss the relative importance of the three different thermal effects, namely Jeans smoothing, pressure-induced peculiar velocities and thermal broadening and compare these to the effect of the amplitude of dark matter fluctuations."578 In the following sections we will investigate how the different broadening mechanisms affect a number of cüllerent Dux statistics., In the following sections we will investigate how the different broadening mechanisms affect a number of different flux statistics.579 Figure 1. shows the temperature-cdensity relations for the LODAL models where the Hell. photo-heating is (0.3.1.3) times that in the optically thin limit. respectively.," Figure \ref{fig:eos} shows the temperature-density relations for the LCDM models where the HeII photo-heating is (0.3,1,3) times that in the optically thin limit, respectively."580 Over the interval shown. this relation is well approximated by a power law.," Over the interval shown, this relation is well approximated by a power law."581 The slope of this power law is determined by the reionization history (lui Cnedin 1997). which is the same for all models plotted here.," The slope of this power law is determined by the reionization history (Hui Gnedin 1997), which is the same for all models plotted here."582 Phe temperature Z5 at, The temperature $T_0$ at583 (2LO ," \citep[$\gtrsim 10\ M_\odot$ and possibly even up to 1000$\ M_\odot$; e.g.][]{Bromm et al. a,Nakamura & Umemura,Tan & McKee,Greif & Bromm,Ohkubo et al.}."5841A +>6 (e.g.Treuti&Stiavelli2007) z26 (e.g.Willottetal.2007).. al.2011:Cereifet201Tab).. ," \citep{Heger et al.} $1\ M_\odot$ $z>6$ \citep[e.g.][]{Sokasian et al.,Trenti & Stiavelli b}, \citep[e.g.][]{Trenti & Stiavelli a} $z\approx 6$ \citep[e.g.][]{Willott et al.}. \citep[e.g.][]{Stacy et al.,Clark et al.,Greif et al. d,Greif et al. e},"585carly supernovae with progenitor masses closer to ~10AZ. than ~100AL. (forreviews.seeBeers&Christlich2005:IWarlssouetal. 2011).," early supernovae with progenitor masses closer to $\sim 10\ M_\odot$ than $\sim 100\ M_\odot$ \citep[for reviews, see][]{Beers & Christlieb,Karlsson et al. b}."586. At the same iue. it is not clear that the chemical signatures of he most massive population III supernuovae would be detectable iun current halo samples.," At the same time, it is not clear that the chemical signatures of the most massive population III supernovae would be detectable in current halo samples."587 The stars bearing he mark of such superuovae may be too scarce (c.g.Salvadorietal.2007:Trenti&Shull 2010).. hidiug at oo high inetallicitics (Narlssonetal.2008) or in the inner regions of the Galaxy (e.g.Tuuliusou2010).," The stars bearing the mark of such supernovae may be too scarce \citep[e.g.][]{Salvadori et al.,Trenti & Shull}, hiding at too high metallicities \citep{Karlsson et al. a} or in the inner regions of the Galaxy \citep[e.g.][]{Tumlinson}."588. Direct observations of massive population IIT stars in the ligh-redshift Universe would help settle the issue. but this is »ovond the capabilities of current telescopes.," Direct observations of massive population III stars in the high-redshift Universe would help settle the issue, but this is beyond the capabilities of current telescopes."589 The very first population III stars are expected to form iu isolation or im stuall nuubers within ~10° 10947. dark matter halos at redshifts τ220 50 (c.e.Teemaretal.1997:Yoshida 2003).. but the prospects of detecting such stars on au individual basis appear bleak (e.g.Cardneretal.2006:Greif2009:Ryd-berg.Zackrisson&Scott 2010).. at least before they &o superuovae (Weimuuaun&Lilly2005:WhalenFrver 2010).," The very first population III stars are expected to form in isolation or in small numbers within $\sim$ $^5$ $10^6 M_\odot$ dark matter halos at redshifts $z\approx 20$ –50 \citep[e.g.][]{Tegmark et al.,Yoshida et al.}, but the prospects of detecting such stars on an individual basis appear bleak \citep[e.g.][]{Gardner et al.,Greif et al. b,Rydberg et al.}, at least before they go supernovae \citep{Weinmann & Lilly,Whalen & Fryer}."590. However.populationIT stars may coutiuue to form: within the more massive halos (210*7 M.) hosting thefirst at +X15 (Seaunapiecoet 2010).. anc this could iunprinciple allow their integrated signatures to be detected with the upcoming," However,populationIII stars may continue to form within the more massive halos $\gtrsim 10^{7-8} \ M_\odot$ ) hosting thefirst at $z\lesssim 15$ \citep{Scannapieco et al.,Schneider et al. a,Tornatore et al.,Johnson et al. a,Johnson et al. b,Stiavelli & Trenti,Johnson}, , and this could inprinciple allow their integrated signatures to be detected with the upcoming"591the erain’s surface. an electric field will build up which can be strong enough to cause an avalanche process that produces an exponentially increasing number of [ree electrons.,"the grain's surface, an electric field will build up which can be strong enough to cause an avalanche process that produces an exponentially increasing number of free electrons."592 As the recombination time back onto the grain surface is rather large. these electrons can exist for a lime in the gas phase. aud hence locally increase the degree of ionisation for a certain lime (Figs. 13.. 14)).," As the recombination time back onto the grain surface is rather large, these electrons can exist for a time in the gas phase, and hence locally increase the degree of ionisation for a certain time (Figs. \ref{fig:p_e}, , \ref{fig:taus}) )."593 But with which efficiency does this occur in the cloud and could it lead to the occurrence of lightning?, But with which efficiency does this occur in the cloud and could it lead to the occurrence of lightning?594 A superposition of avalanche-streamer processes will lead to more and more [ree electrons for a short lime period which then may be defined as lightning., A superposition of avalanche-streamer processes will lead to more and more free electrons for a short time period which then may be defined as lightning.595". An estimate of the time scale. /=1,LB""Due. on which dust. particles pass through such a previously formed electron cloud. and hence. potentially initiate another electron avalanche. shows that a certain fraction of the cloud is prone to lightnine-like discharge events in brown dwarls and in gas planets. namely where ty,«|«τα in Figs IH.."," An estimate of the time scale, $t=n_{\rm d}^{-1/3} / v^{\rm sed}$, on which dust particles pass through such a previously formed electron cloud, and hence, potentially initiate another electron avalanche, shows that a certain fraction of the cloud is prone to lightning-like discharge events in brown dwarfs and in gas planets, namely where $\tau_{\rm596str}<t<\tau_{\rm recom}^{\rm dust}$ in Figs \ref{fig:taus}."597 The borders of this lightning region are not verv clearly defined as turbulence will decrease (he effective sedimentation velocity (blue solid. vs. dashed lines)., The borders of this lightning region are not very clearly defined as turbulence will decrease the effective sedimentation velocity (blue solid vs. dashed lines).598 If dust particles pass an electron cloud slowly and the electrons can recombine. lightning is less likely aud a less powerful coronal discharge-like behaviour on smaller scales should be expected as long as DTTieuu-dust!recoin ," If dust particles pass an electron cloud slowly and the electrons can recombine, lightning is less likely and a less powerful coronal discharge-like behaviour on smaller scales should be expected as long as $\tau_{\rm str}<\tau_{\rm599recom}^{\rm dust}$."600The lightning and the coronal discharge regimes will exist in both brown dwarls and in eas planet atmospheres., The lightning and the coronal discharge regimes will exist in both brown dwarfs and in gas planet atmospheres.601 Our results suggest a hierarchy of lightning and coronal discharges with the lightning occurring at lower pressures in (le upper part of the cloud., Our results suggest a hierarchy of lightning and coronal discharges with the lightning occurring at lower pressures in the upper part of the cloud.602 However. the maximum of the collisional dust-dust energies (Fig. 12))," However, the maximum of the collisional dust-dust energies (Fig. \ref{fig:col_energy}) )"603 is more likely to be located in the coronal discharge regime in our planetary atmosphere example. while clust-clust collisions acl across both regimes in the brown dwarl example.," is more likely to be located in the coronal discharge regime in our planetary atmosphere example, while dust-dust collisions act across both regimes in the brown dwarf example."604 Low would then the cloud particles be charged if dust-dust collisions are unfavourable inside a potential lightning regime?, How would then the cloud particles be charged if dust-dust collisions are unfavourable inside a potential lightning regime?605 Cosmic rav ionisation mavbea possibility., Cosmic ray ionisation maybea possibility.606"For transiting planets. the Rossiter-MeLaughlin effect (2222?)., allows the measure of f (also called tin the literature). which is the projection on the sky of the obliquity v. between the stellar spin axis and the orbital spin axis.","For transiting planets, the Rossiter-McLaughlin effect \citep{Holt:1893, Rossiter:1924p869, McLaughlin:1924p872, Queloz:2000p247, Gaudi:2007p1507}, allows the measure of $\beta$ (also called $\lambda$ in the literature), which is the projection on the sky of the obliquity $\psi$, between the stellar spin axis and the orbital spin axis."607 Up until recently planets were thought to be mostly οἱ orbits coplanar with their star's equator (?).. something i1 line with predictions of dise migration (??)..," Up until recently planets were thought to be mostly on orbits coplanar with their star's equator \citep{Fabrycky:2009p1845}, something in line with predictions of disc migration \citep{Lin:1996p5847, Ward:1997p11274}."608 More recently a number of papers have shown that hot Jupiters on nori coplanar orbits are common. including some planets οἱ retrograde orbits (222222?)..," More recently a number of papers have shown that hot Jupiters on non coplanar orbits are common, including some planets on retrograde orbits \citep{Hebrard:2008p226, Moutou:2009p2007, Narita:2009p5188, Winn:2009p3712, Anderson:2010p5177, Queloz:2010p7376, Triaud:2010p8039}."609 Those measurements have beer interpreted as showing that dynamical events are probably not uncommon and that not all systems can be understooc by dise migration alone., Those measurements have been interpreted as showing that dynamical events are probably not uncommon and that not all systems can be understood by disc migration alone.610 Strong dynamical events such as planet-planet scattering (222).. or more secular processes such as Kozai-Lidov oscillations (????).. or chaotic interactions (?) would place a planet on a highly eccentric orbit. whose passage at periastron is sufficiently close that tidal dissipation causes the planet to lose angular momentum and circularise around its Understanding the origin of hot Jupiters is one of the keys to shedding light onto the processes that act during planet formation as well as those acting after planets have formed.," Strong dynamical events such as planet-planet scattering \citep{Rasio:1996p3680, Juric:2008p2882, Chatterjee:2008p2971}, or more secular processes such as Kozai-Lidov oscillations \citep{Wu:2007p4179, Fabrycky:2007p3141, Nagasawa:2008p2997, Naoz:2011p8938}, or chaotic interactions \citep{Wu:2011p14507} would place a planet on a highly eccentric orbit, whose passage at periastron is sufficiently close that tidal dissipation causes the planet to lose angular momentum and circularise around its Understanding the origin of hot Jupiters is one of the keys to shedding light onto the processes that act during planet formation as well as those acting after planets have formed."611 Those processes allow us to place constraints on what happened and did not happen m our own Solar System., Those processes allow us to place constraints on what happened and did not happen in our own Solar System.612 They will also help us match more accurately theoretical predictions of planet formation done in population synthesis simulations to the parameter space that planets currently occupy. as given by the observations (eg.," They will also help us match more accurately theoretical predictions of planet formation done in population synthesis simulations to the parameter space that planets currently occupy, as given by the observations (eg."613 ? and 2))., \citet{Ida:2004p11614} and \citet{Mordasini:2009p8294}) ).614 ? remark that if misaligned hot Jupiters do not require dise migration. aligned planets are not in contradiction with a scenario involving dynamical interactions and tidal migration. as planets will tend to realign with the star (see also ? and 2).," \citet{Matsumura:2010p8927} remark that if misaligned hot Jupiters do not require disc migration, aligned planets are not in contradiction with a scenario involving dynamical interactions and tidal migration, as planets will tend to realign with the star (see also \citet{Hut:1981p2945} and \citet{Barker:2009p11693}) )."615 ? point out a correlation between the stellar effective temperature and the spin/orbit angle., \citet{Winn:2010p7311} point out a correlation between the stellar effective temperature and the spin/orbit angle.616 For stars with Toy>6250 KK. fewer aligned systems are found compared to stars with lower effective temperatures.," For stars with $T_\mathrm{eff} > 6250$ K, fewer aligned systems are found compared to stars with lower effective temperatures."617 This would show that tidal realignment timescales are different for different. stars. as proposed by ? in the context of binaries.," This would show that tidal realignment timescales are different for different stars, as proposed by \citet{Zahn:1977p14439} in the context of binaries."618 ? presents an independent confirmation of that correlation. using a different methodology.," \citet{Schlaufman:2010p7946} presents an independent confirmation of that correlation, using a different methodology."619 The aim of this letter is to combine the observational facts and offer an explanation., The aim of this letter is to combine the observational facts and offer an explanation.620 The results will then be discuss in light of the currently available theoretical framework., The results will then be discuss in light of the currently available theoretical framework.621 The lack of aligned systems for stars with Typ>6250KK that is noticed in ? coulc also be explained by stellar physics combined with an observational bias: as predicted by stellar evolution. stars with masses greater than about 1.2M. start on the Zero Age Main Sequence with temperatures higher than 6250 KK. When H-core burning stops. they have cooled by several hundred Kelvin (fig.σι 1)).," The lack of aligned systems for stars with $T_\mathrm{eff} > 6250$ K that is noticed in \citet{Winn:2010p7311} could also be explained by stellar physics combined with an observational bias: as predicted by stellar evolution, stars with masses greater than about $\,1.2\,M_\odot$ start on the Zero Age Main Sequence with temperatures higher than $6250$ K. When H-core burning stops, they have cooled by several hundred Kelvin (fig. \ref{fig:tracks}) )."622 They do so in 3 to 4 Gyrs., They do so in 3 to 4 Gyrs.623 This means that. while the planet and the star progressively realign. the star itself cools down.," This means that, while the planet and the star progressively realign, the star itself cools down."624 We are thus left with an aligned planet around an older. cooler star.," We are thus left with an aligned planet around an older, cooler star."625 Some. more massive. stars will cool to temperatures above KK. but the timescale for realignment might be longer than the Main Sequence lifetime.," Some, more massive, stars will cool to temperatures above K, but the timescale for realignment might be longer than the Main Sequence lifetime."626 Once they leave the Main Sequence. stars becomes too large for planets to be discovered by ground-based transit surveys as the contrast becomes too small.," Once they leave the Main Sequence, stars becomes too large for planets to be discovered by ground-based transit surveys as the contrast becomes too small."627 We thus have a bias to see misaligned planets around hot stars. notably because we may not detect their aligned population.," We thus have a bias to see misaligned planets around hot stars, notably because we may not detect their aligned population."628 This explanation could be combined to the different realignment timescales described in ? and ? since. as the star ages and cools. its convective zone would become large too.," This explanation could be combined to the different realignment timescales described in \citet{Winn:2010p7311} and \citet{Zahn:1977p14439} since, as the star ages and cools, its convective zone would become larger too."629 If that explanation ts right. we should expect a correlation between stellar age and alignment.," If that explanation is right, we should expect a correlation between stellar age and alignment."630" The average stellar density. p,. 1s obtained directly from the planetary transit signal (?).. the effective temperature. Typ. and metallicity. Z. can be obtained via spectral analysis."," The average stellar density, $\rho_\star$, is obtained directly from the planetary transit signal \citep{Sozzetti:2007p2647}, the effective temperature, $T_\mathrm{eff}$, and metallicity, $Z$, can be obtained via spectral analysis."631 Stellar mass and stellar age can be estimated from interpolating the stellar evolution tracks in (pi.Za.Z) space.," Stellar mass and stellar age can be estimated from interpolating the stellar evolution tracks in $(\rho_\star, T_\mathrm{eff}, Z)$ space."632 Interestingly. stars >1.2M.. spend less time on the Main Sequence. but increase their radit more than solar mass stars do.," Interestingly, stars $>1.2\,M_\odot$ spend less time on the Main Sequence, but increase their radii more than solar mass stars do."633 We thus have a higher resolution on the tracks to estimate ages on more massive stars than on solar mass stars., We thus have a higher resolution on the tracks to estimate ages on more massive stars than on solar mass stars.634 Such a subsample should give the most, Such a subsample should give the most635A comparison of the projected number density of luminous stars above 0.8Me for the Monte Carlo and N-body simulations and from observations is presented in Fig. 13..,A comparison of the projected number density of luminous stars above $0.8M_\odot$ for the Monte Carlo and $N$ -body simulations and from observations is presented in Fig. \ref{fig:m67_sd}.636 This confirms the conclusions reached so far: the overall density of the Monte Carlo model is slightly larger than that of the N-body model and the half-mass radius of the Monte Carlo model is too small., This confirms the conclusions reached so far: the overall density of the Monte Carlo model is slightly larger than that of the $N$ -body model and the half-mass radius of the Monte Carlo model is too small.637 Both models exceed the observed surface density in the central part of the system but underpredict it in the outer halo., Both models exceed the observed surface density in the central part of the system but underpredict it in the outer halo.638" These regions require separate discussion: 'This discussion of the centre of M67 suggests that probably only some changes in the initial model of M67 can bring both observations and simulations into agreement, and we consider this in Sec.??.. ("," These regions require separate discussion: This discussion of the centre of M67 suggests that probably only some changes in the initial model of M67 can bring both observations and simulations into agreement, and we consider this in \ref{sec:refinement}. ("639"That was not our intention in the present section, where our aim is to check that the Monte Carlo code can produce results consistent with the N-body model for a realistic cluster model.)","That was not our intention in the present section, where our aim is to check that the Monte Carlo code can produce results consistent with the $N$ -body model for a realistic cluster model.)"640 In Fig., In Fig.641 14 the surface brightness profiles for the Monte Carlo and N-body models are presented., \ref{fig:m67_sb} the surface brightness profiles for the Monte Carlo and $N$ -body models are presented.642 To construct these surface brightness profiles all stars and binaries were used., To construct these surface brightness profiles all stars and binaries were used.643" The data are very noisy, particularly for the N-body simulation."," The data are very noisy, particularly for the $N$ -body simulation."644 The agreement between the two models is reasonably good., The agreement between the two models is reasonably good.645 Again the conclusion reached before are confirmed., Again the conclusion reached before are confirmed.646 The surface brightness in the central parts of the system is slightly larger for the Monte Carlo model than that of N-body model and outside in the cluster halo the surface brightness is larger for the N-body model., The surface brightness in the central parts of the system is slightly larger for the Monte Carlo model than that of $N$ -body model and outside in the cluster halo the surface brightness is larger for the $N$ -body model.647 The latter is again connected with the effective tidal radius for the Monte Carlo code which is smaller than the nominal tidal radius for the two models., The latter is again connected with the effective tidal radius for the Monte Carlo code which is smaller than the nominal tidal radius for the two models.648 Its effects are particularly clear in Fig.13.., Its effects are particularly clear in \ref{fig:m67_sd}.649" A form of colour-magnitude diagram is shown in Fig. 15,"," A form of colour-magnitude diagram is shown in Fig. \ref{fig:m67_cmd},"650 which can be compared with Fig.10 of Hurleyetal. (2005)., which can be compared with Fig.10 of \citet{hurleyetal2005}.651". The resemblance is qualitatively satisfactory, except for the relative paucity, already referred to, of blue stragglers in the Monte Carlo model, and the shortness of the sequence of blue stragglers, compared to the N-body model."," The resemblance is qualitatively satisfactory, except for the relative paucity, already referred to, of blue stragglers in the Monte Carlo model, and the shortness of the sequence of blue stragglers, compared to the $N$ -body model."652 Hurleyetal.(2005) discuss the different exotic populations of their model at some length., \citet{hurleyetal2005} discuss the different exotic populations of their model at some length.653" As already stated in connection with the blue straggler population, however, our model lacks important processes for the formation of"," As already stated in connection with the blue straggler population, however, our model lacks important processes for the formation of"654The existence of a relation between luminosity (or mass) and metallicity in irregular and. blue compact galaxies was first proposed by 2. and later confirmed by 2..,The existence of a relation between luminosity (or mass) and metallicity in irregular and blue compact galaxies was first proposed by \citet{leq79} and later confirmed by \citet{skillman89}.655 7. extended the relation to spiral galaxies., \citet{garnett87} extended the relation to spiral galaxies.656 Recently 2? examined. the relation at 20 using 753000 local star-forming galaxies in the SDSS and found that 12|log(O/11) increases steeply, Recently \citet{trem04} examined the relation at $z\!\approx\!0$ using $\sim$ 53000 local star-forming galaxies in the SDSS and found that $12+\log(O/H)$ increases steeply657In the fall of niv senior vear (1969) as a Berkeley physics undergraduate. Charles Ixittel eave me some staring advice.,"In the fall of my senior year (1969) as a Berkeley physics undergraduate, Charles Kittel gave me some startling advice."658" He. a pioneer of solid state physics. told me that I should not enter (hat [ied because il was mature ...""«lone."""," He, a pioneer of solid state physics, told me that I should not enter that field because it was mature ...“done.”"659" Ile told me that I should choose a field that would still be ""new when I was ten vears past mv PhD. and a “mature” scientist.", He told me that I should choose a field that would still be “new” when I was ten years past my PhD. and a “mature” scientist.660 lle suggested that I think about. astrophysics ancl biophyvsies and pressed me (to apply. to Princeton to do astrophyvsics., He suggested that I think about astrophysics and biophysics and pressed me to apply to Princeton to do astrophysics.661 I did apply to Princeton and was admitted to the physics department., I did apply to Princeton and was admitted to the physics department.662 Within my first vear of graduate school. I asked. Jim Peebles to supervise my research ... and he agreed.," Within my first year of graduate school, I asked Jim Peebles to supervise my research ... and he agreed."663 It was a very special and wonderful time to be starting out in astrophysics. particularly in (he Princeton physics departinent.," It was a very special and wonderful time to be starting out in astrophysics, particularly in the Princeton physics department."664 Dave Wilkinson and his group were leading the study ol the relatively recently discovered cosmic microwave background., Dave Wilkinson and his group were leading the study of the relatively recently discovered cosmic microwave background.665 Jim Peebles was thinking about the distribution of galaxies in the universe and he started me on the track of finding wavs lo extract physical constraints from catalogs of galaxies wilh redshifts., Jim Peebles was thinking about the distribution of galaxies in the universe and he started me on the track of finding ways to extract physical constraints from catalogs of galaxies with redshifts.666 The total store X redshifts was shockinely small by today's standards., The total store of redshifts was shockingly small by today's standards.667 In the second paper Peebles ancl I Evrote together. we used a catalog of527 redshifts along with an n-bocly simulation to make me of the first statistical estimates of the masses of galaxies (Geller Peebles 1973).," In the second paper Peebles and I wrote together, we used a catalog of redshifts along with an n-body simulation to make one of the first statistical estimates of the masses of galaxies (Geller Peebles 1973)."668 As a student I could not imagine how rapidly our ability to map the universe would ‘change., As a student I could not imagine how rapidly our ability to map the universe would change.669 I never would have predicted that in 1935 Valerie de Lapparent. John IHuchra. and I would measure redshifts [or ~1100 galaxies in a slice of the universe and that the stunning pattern (μον revealed would change the general perception of (he way galaxies are arranged on large scales (de Lapparent. Geller IHuchra 1986).," I never would have predicted that in 1985 Valerie de Lapparent, John Huchra, and I would measure redshifts for $\sim$ 1100 galaxies in a slice of the universe and that the stunning pattern they revealed would change the general perception of the way galaxies are arranged on large scales (de Lapparent, Geller Huchra 1986)."670 Figure 1. shows the now iconic stick ligure pattern in our slice., Figure \ref {fig:firstslice} shows the now iconic stick figure pattern in our slice.671 The torso of the sück figure is the “linger” of the Coma cluster., The torso of the stick figure is the “finger” of the Coma cluster.672 The band of galaxies running all the way across the survey is a eut through the Great Wall (Geller IIuchra 1989)., The band of galaxies running all the way across the survey is a cut through the Great Wall (Geller Huchra 1989).673" The sharply outlined voids surrounded or nearly surrounded by thin filaments and sheets containing aSgalaxies are the hallmarks of what we now call the “cosmic web.""", The sharply outlined voids surrounded or nearly surrounded by thin filaments and sheets containing galaxies are the hallmarks of what we now call the “cosmic web.”674 During the last twenty vears wide-fiekl nulti-object spectrographs have revolutionized our ability to map the universe., During the last twenty years wide-field multi-object spectrographs have revolutionized our ability to map the universe.675 The number of redshift measurements has increased exponentially: the NASA/IPAC Extragalactic Database includes ~2 million redshifts., The number of redshift measurements has increased exponentially; the NASA/IPAC Extragalactic Database includes $\sim 2$ million redshifts.676 Ambitious surveys including the Sloan Digital Skv Survey (Abazajian et al., Ambitious surveys including the Sloan Digital Sky Survey (Abazajian et al.677 2009). GDF (Jones et al.," 2009), 6DF (Jones et al."678 2009). and 2DF (Colless et al.," 2009), and 2DF (Colless et al."679 2001) are major contributors to this wealth of data., 2001) are major contributors to this wealth of data.680 In 2000. I calculated that if technology continued to improve as it had up to that point. we would have a redshift for everv galaxy in the visible universe by (hie vear 2100.," In 2000, I calculated that if technology continued to improve as it had up to that point, we would have a redshift for every galaxy in the visible universe by the year 2100."681 Perhaps (hat will really happen., Perhaps that will really happen.682 Rather (han review (he many remarkably successful projects (hat have changed (he field, Rather than review the many remarkably successful projects that have changed the field683schunke 1993: Schunke Mielke 2003).,Schunke 1998; Schunke Mielke 2003).684 There is no concept of an equation of state for these svslelus. as {μον are pure quanti svstenis that are held up against gravitational collapse by the ILeisenberg uncertaintv principle.," There is no concept of an equation of state for these systems, as they are pure quantum systems that are held up against gravitational collapse by the Heisenberg uncertainty principle."685 The pioneering studies in this field were done by Ixaup (1963) and Raving Bonazzola (1969)., The pioneering studies in this field were done by Kaup (1968) and Ruffini Bonazzola (1969).686" The main findings in (hese two seminal works are that (3) the mass of a boson star is of the order of Mg/myj. and Gi) its characteristic size Is of the order of (he de Broglie wavelength of bosons 1/104. where my is the mass of the boson parücle and Mp, is the Planck mass."," The main findings in these two seminal works are that (i) the mass of a boson star is of the order of $M^2_{\rmscr{Pl}}/m_b$, and (ii) its characteristic size is of the order of the de Broglie wavelength of bosons $1/m_b$ where $m_b$ is the mass of the boson particle and $M_{\rmscr{Pl}}$ is the Planck mass."687 Colpi. Shapiro Wasserman (1986) introduced the idea of sell-interaction of the scalar particles aud found that selfinteracting boson stars have masses of the order of AUTMgΤΗΝ. where A is a dimensionless quantity which characterizes the strength ofB the self οinteractions.," Colpi, Shapiro Wasserman (1986) introduced the idea of self-interaction of the scalar particles and found that self-interacting boson stars have masses of the order of $\Lambda^{1/2}M^2_{\rmscr{Pl}}/m_b$, where $\Lambda$ is a dimensionless quantity which characterizes the strength of the self interactions."688n For A?L7>>1. this. scaling. breaks down. and the mass is. instead. ~Mj/m?. which is similar to the result for fermion stars.," For $\Lambda^{1/2}\gg1$, this scaling breaks down, and the mass is instead $\sim M^3_{\rmscr{Pl}}/m^2$, which is similar to the result for fermion stars."689 Boson stars have several interesting/unique characteristics. including their transparency to photons and barvonie matter. their ability to be non-singular even for masses larger (han (he maxinuni mass of neutron stars (hence the interest in these objects as a mocel of BIICs). ancl the presence of a different metric than the Schwarzschild metric.," Boson stars have several interesting/unique characteristics, including their transparency to photons and baryonic matter, their ability to be non-singular even for masses larger than the maximum mass of neutron stars (hence the interest in these objects as a model of BHCs), and the presence of a different metric than the Schwarzschild metric."690 Various authors have discussed observational consequences of boson star. such as the Ceerenkov effect. gravitational lensing. the rotation curves of accreted matter. and the gravitational redshift of the radiation emitted within the effective radius of boson stars (Schunk Mielke 2003).," Various authors have discussed observational consequences of boson star, such as the Čeerenkov effect, gravitational lensing, the rotation curves of accreted matter, and the gravitational redshift of the radiation emitted within the effective radius of boson stars (Schunk Mielke 2003)."691 Also. the possibility of supermassive nonbarvonic stus (boson stars or neutrino balls) insteacding of supermassive black holes existing in the nuclei of galaxies has attracted attention (Schunk Liddle 1997. 1998: Torres. Capozziello Lambiase 2000: Tsiklauri Viollier 1993).," Also, the possibility of supermassive nonbaryonic stars (boson stars or neutrino balls) insteading of supermassive black holes existing in the nuclei of galaxies has attracted attention (Schunk Liddle 1997, 1998; Torres, Capozziello Lambiase 2000; Tsiklauri Viollier 1998)."692 1 has been argued that the line profile of an emission line from an accretion disk around a supermassive boson star may have signatures (hat might help to identily the existence of boson stars (Lu Torres 2003)., It has been argued that the line profile of an emission line from an accretion disk around a supermassive boson star may have signatures that might help to identify the existence of boson stars (Lu Torres 2003).693 The observational signatures of boson stars in X-ray binaries with DIICs has not been discussed. very much in the literature., The observational signatures of boson stars in X-ray binaries with BHCs has not been discussed very much in the literature.694 We show in (his paper that such stars will produce Type I X-ray bursts with clear signatures., We show in this paper that such stars will produce Type I X-ray bursts with clear signatures.695 Tlenriques (1989. 1990a.b) considered the possibility of compact stars that contain both bosons and fermions and wrote down the structural equations lor such objects.," Henriques (1989, 1990a,b) considered the possibility of compact stars that contain both bosons and fermions and wrote down the structural equations for such objects."696 We borrow from their analvsis in what follows., We borrow from their analysis in what follows.697 We analvse a boson-fermion star that consists of dark bosons plus ordinary fermionic gas., We analyse a boson-fermion star that consists of dark bosons plus ordinary fermionic gas.698" As in the case of the fermion-fermion star. we write the number of bosons as [N+ and the barvonic mass of the bosons as M""[=N°’+πι"," As in the case of the fermion-fermion star, we write the number of bosons as $N^b$ and the baryonic mass of the bosons as $M^b=N^bm_b$."699 The energv-momentunm tensor for bosons is completely different from (hat of fermions., The energy-momentum tensor for bosons is completely different from that of fermions.700 For a massive sell-interacting scalar field.(he Lagrangian reads (Colpi et al.," For a massive self-interacting scalar field,the Lagrangian reads (Colpi et al."701 1986), 1986)702The first goal of this work is the study of the hydrodynamical evolution of a jet when the wind interacting with it is clumpy.,The first goal of this work is the study of the hydrodynamical evolution of a jet when the wind interacting with it is clumpy.703" The second goal is to quantify for which values of the clump and jet parameters, clumpiness becomes a relevant factor."," The second goal is to quantify for which values of the clump and jet parameters, clumpiness becomes a relevant factor."704 It is also interesting to study the evolution of a clump under the impact of a microquasar jet., It is also interesting to study the evolution of a clump under the impact of a microquasar jet.705" The results can also be used to refine radiation models or interpret radio observations, although this will be treated qualitatively."," The results can also be used to refine radiation models or interpret radio observations, although this will be treated qualitatively."706" The paper is organized as follows: in Section ??,, the scenario studied here is briefly introduced; in Sect. ??,,"," The paper is organized as follows: in Section \ref{phys}, the scenario studied here is briefly introduced; in Sect. \ref{sim},"707 the simulations are described (Sect. ??));, the simulations are described (Sect. \ref{sim1}) );708 results are shown in Sect. ??;;, results are shown in Sect. \ref{sim2}; ;709" finally, in Sect. ??,,"," finally, in Sect. \ref{disc},"710" the results are discussed in the context of jet propagation in HMMQ (Sect. ??)),"," the results are discussed in the context of jet propagation in HMMQ (Sect. \ref{disc1}) ),"711" individual clump-jet interactions (Sect. ??)),"," individual clump-jet interactions (Sect. \ref{disc2}) ),"712 and their implications for the non-thermal emission (Sect. ??))., and their implications for the non-thermal emission (Sect. \ref{disc3}) ).713" Throughout the paper, we will use cgs units."," Throughout the paper, we will use cgs units."714 'The scenario studied here consists of a jet crossing the binary system in a HMMQ., The scenario studied here consists of a jet crossing the binary system in a HMMQ.715" The jet starts close to the compact object, which is located at a distance of d—2x1013 cm (following PBK10) from the massive star, and is perpendicular to the orbital plane."," The jet starts close to the compact object, which is located at a distance of $d=2\times 10^{12}$ cm (following PBK10) from the massive star, and is perpendicular to the orbital plane."716" The jet is initially conical, with a radius to height ratio of η=Rj/z0.1."," The jet is initially conical, with a radius to height ratio of $\eta=R_{\rm j}/z=0.1$."717 The scenario is similar to that studied in PBK10., The scenario is similar to that studied in PBK10.718" However, unlike in that work, the stellar wind is assumed here to be inhomogeneous, with a filling factor f~0.1."," However, unlike in that work, the stellar wind is assumed here to be inhomogeneous, with a filling factor $f\sim 0.1$."719 A sketch of the considered scenario is presented in Fig. 1.., A sketch of the considered scenario is presented in Fig. \ref{fig1}.720 The inhomogeneities or clumps are modelled as gaussians with o=Πο3x101? cm!., The inhomogeneities or clumps are modelled as gaussians with $\sigma=R_{\rm c}=3\times 10^{10}$ cm.721". In reality, the size, mass, and velocity of clumps in stellar winds may follow complex distributions (e.g.,Moffat2008)."," In reality, the size, mass, and velocity of clumps in stellar winds may follow complex distributions \citep[e.g.,][]{mof08}."722". However, we have adopted average and representative values for these quantities for simplicity."," However, we have adopted average and representative values for these quantities for simplicity."723" Bigger and thus less numerous clumps than assumed here would probably have a stronger impact on the jet dynamics, unless they were so few that interactions were rare."," Bigger and thus less numerous clumps than assumed here would probably have a stronger impact on the jet dynamics, unless they were so few that interactions were rare."724" The latter may be the case, provided that wind mass seems to concentrate in the small clumps."," The latter may be the case, provided that wind mass seems to concentrate in the small clumps."725 These small clumps may also be denser than big ones (Moffat2008)., These small clumps may also be denser than big ones \citep{mof08}.726". On the other hand, if Rp<3x101?cm, then the wind could be effectively considered as homogeneous (as in PBK10)."," On the other hand, if $R_{\rm c}\ll 3\times 10^{10}\,{\rm cm}$, then the wind could be effectively considered as homogeneous (as in PBK10)."727" The reason is that clumps cover inside the jet a fraction of its radius: x=R,/Rj~vwRe(1v;pc/2L)!? (for a Newtonian jet), where po.=M/4rfd?vy, is the clump density."," The reason is that clumps cover inside the jet a fraction of its radius: $\chi=R_{\rm c}/R_{\rm j}\sim v_{\rm w}\,R_{\rm c}\,(\pi\,v_{\rm j}\rho_{\rm c}/2L_{\rm j})^{1/2}$ (for a Newtonian jet), where $\rho_{\rm c}=\dot{M}/4\pi f d^2 v_{\rm w}$ is the clump density."728" This estimate is based on the clump disruption time, expected to be slightly longer than the clump shock crossing time: ta~Re/Cc, where e~(2Li/nvjpR2)? is the shocked clump sound speed."," This estimate is based on the clump disruption time, expected to be slightly longer than the clump shock crossing time: $t_{\rm d}\sim729R_{\rm c}/c_{\rm c}$, where $c_{\rm c}\sim(2\,L_{\rm j}/\pi v_{\rm j}\rho_{\rm c}R_{\rm j}^2)^{1/2}$ is the shocked clump sound speed."730" Another relevant timescale is the clump acceleration time along the jet, i.e., the time needed to accelerate the clump material up to a speed ~cc, which is tg, and because of quick expansion, it takes only several times this value for the clump material to reach ~vj (see, e.g., Blandford&Koenig]1979;; Kleinetal. 1994;; ABRO9; Pittardetal.2010;; Barkovetal. 2010;; for shocked clump evolution in different contexts)."," Another relevant timescale is the clump acceleration time along the jet, i.e., the time needed to accelerate the clump material up to a speed $\sim c_{\rm c}$ , which is $\sim t_{\rm d}$ , and because of quick expansion, it takes only several times this value for the clump material to reach $\sim v_{\rm j}$ (see, e.g., \citealt{bla79}; \citealt{kle94}; ABR09; \citealt{pit10}; \citealt{bar10}; for shocked clump evolution in different contexts)."731" For stellar mass-loss rates M~1079Ma /yr, L;~10°” erg/s, d~~2x1013 cm, and vj~1019 cm/s, x is ~0.1(Re/3x1019cm)(f/0.1)-1/2, ie., clumps with Πο<3x101?(f/0.1)cm are destroyed in the external jet layers."," For stellar mass-loss rates $\dot{M}\sim 10^{-6}\,M_\odot$ /yr, $L_{\rm j}\sim 10^{37}$ erg/s, $d\sim 2\times 10^{12}$ cm, and $v_{\rm j}\sim 10^{10}$ cm/s, $\chi$ is $\sim 0.1\,(R_{\rm c}/3\times 10^{10}\,{\rm cm})\,(f/0.1)^{-1/2}$, i.e., clumps with $R_{\rm c}\ll 3\times 10^{10}\,(f/0.1)\,{\rm cm}$ are destroyed in the external jet layers."732 In this small clump case the wind-jet contact discontinuity should probably develop a turbulent shear-layer faster than in the homogeneous case., In this small clump case the wind-jet contact discontinuity should probably develop a turbulent shear-layer faster than in the homogeneous case.733" Due to destruction, therefore, clumps will not be able to enter the jet if c;<vy within the binary, which occurs at f>0.1 for the parameters given above."," Due to destruction, therefore, clumps will not be able to enter the jet if $c_{\rm c}<v_{\rm w}$ within the binary, which occurs at $f>0.1$ for the parameters given above."734" For relatively weak jets, say L;<10°° erg/s, these clumps can otherwise cross the whole jet."," For relatively weak jets, say $L_{\rm j}\lesssim 10^{36}$ erg/s, these clumps can otherwise cross the whole jet."735" For L;~10?"" erg/s, the clumps considered may enter the jet, but it would be difficult for them to escape (see Sect. ??))."," For $L_{\rm736j}\sim 10^{37}$ erg/s, the clumps considered may enter the jet, but it would be difficult for them to escape (see Sect. \ref{disc3}) )."737" From the above discussion, we conclude that, under the jet-to-wind momentum flux ratios considered, if the wind is moderately inhomogeneous, say f<0.1, clumps can effectively penetrate and mass-load the jet, with a penetration effectiveness depending on Πε."," From the above discussion, we conclude that, under the jet-to-wind momentum flux ratios considered, if the wind is moderately inhomogeneous, say $f\lesssim 0.1$, clumps can effectively penetrate and mass-load the jet, with a penetration effectiveness depending on $R_{\rm c}$."738" As we show in what follows, clump penetration will have serious consequences on the jet stability and long-term collimation."," As we show in what follows, clump penetration will have serious consequences on the jet stability and long-term collimation."739" We note that we have assumed that the properties of the clumps, and the mean separation between them, areconstant all over the grid region in whichthey are locatedfor simplicity."," We note that we have assumed that the properties of the clumps, and the mean separation between them, areconstant all over the grid region in whichthey are locatedfor simplicity."740 This approximation, This approximation741respectvelv.,respectvely.742 A IX-S test shows that the distribution of Q values in M31 does not differ. at a statistically significant level. from that of the globular clusters in the Galaxy.," A K-S test shows that the distribution of Q values in M31 does not differ, at a statistically significant level, from that of the globular clusters in the Galaxy."743 For the M31 clusters listed in Table 1 the median value of Q = -0.37. compared to a median value of Q = -0.35 [or for the Galactic globulars in Table 2.," For the M31 clusters listed in Table 1 the median value of Q = -0.37, compared to a median value of Q = -0.35 for for the Galactic globulars in Table 2."744 From Equation 2 one then obtains median values of [Fe/H] = -1.64 and |Fe/II] = - 1.82 for the Galaxy and M31. respectively.," From Equation 2 one then obtains median values of [Fe/H] = -1.64 and [Fe/H] = - 1.82 for the Galaxy and M31, respectively."745 A Ίο test shows that the distribution of Q values in M31 does not differ at a statistically significant level. from that of the globular clusters in the Galaxy.," A K-S test shows that the distribution of Q values in M31 does not differ at a statistically significant level, from that of the globular clusters in the Galaxy."746 However. one should not read too much into this result because both the Galactic ancl M31. samples are strongly. biased by the requirement that UBV photometry be available.," However, one should not read too much into this result because both the Galactic and M31 samples are strongly biased by the requirement that UBV photometry be available."747 This selection criterion introduces a strong bias against metal-rich clusters which are faint (and therefore difficult to observe) in the U band of the UDV svstem., This selection criterion introduces a strong bias against metal-rich clusters which are faint (and therefore difficult to observe) in the U band of the UBV system.748 It is of some interest to compare the present compilation of reddening data in M31 with a similar listing given recently by Fan et al. (, It is of some interest to compare the present compilation of reddening data in M31 with a similar listing given recently by Fan et al. (7492008).,2008).750 Such a comparison shows that the reddening values adopted in Table 1l are systematically larger by 0.10 + 1 0.01 mas than are those obtained by Fan et al., Such a comparison shows that the reddening values adopted in Table 1 are systematically larger by 0.10 $\pm$ 1 0.01 mag than are those obtained by Fan et al.751 The reason for this difference is not vet clear., The reason for this difference is not yet clear.752 Alter correcting for (this svstematic difference the rms difference between (he present individual reddening values. ancl those adopted by Fan et al.," After correcting for this systematic difference the rms difference between the present individual reddening values, and those adopted by Fan et al."753 is 0.08 mag., is 0.08 mag.754 In a recent paper Peacock οἱ al. (, In a recent paper Peacock et al. (7552010) have identified 45 X-ray sources that appear to be associated wilh M31 globular clusters.,2010) have identified 45 X-ray sources that appear to be associated with M31 globular clusters.756 These authors speculate that high stellar collision rates are (he dominant. [actor that determines whether a globular cluster will contain an N-rav binary., These authors speculate that high stellar collision rates are the dominant factor that determines whether a globular cluster will contain an X-ray binary.757 This hypothesis is strongly supported by Che present data which show that, This hypothesis is strongly supported by the present data which show that758to occur following major racio Ilaring episodes (Ixoljonenal.2011).,to occur following major radio flaring episodes \citep{koljonen2}.759. In this paper we study the PDS of Cygnus X-3 using the extensive archive of timing data including pointings during and after major radio Haring events., In this paper we study the PDS of Cygnus X-3 using the extensive archive of timing data including pointings during and after major radio flaring events.760 We introduce the data and the analysis method in Section 2 and present our results in Section 3., We introduce the data and the analysis method in Section 2 and present our results in Section 3.761 In section 4 we brielly review possible causes for the QPOs in Cygnus N-3 and sumnmarise the paper in Section 5., In Section 4 we briefly review possible causes for the QPOs in Cygnus X-3 and summarise the paper in Section 5.762 We analvzed. following standard: procedures using. the archived observations [rom 1997 to 2011 totaling 172 pointings and more than 0.7 Msec of data. covering all spectral states as defined in Ixoljonen et al. (," We analyzed, following standard procedures using, the archived observations from 1997 to 2011 totaling 172 pointings and more than 0.7 Msec of data, covering all spectral states as defined in Koljonen et al. ("7632010: hereafter IX10). and orbital phases.,"2010; hereafter K10), and orbital phases."764 The lighteurves were extracted. using the generic binned data with a time resolution of 4 ms from channels 035 corresponding approximately to the energy range 215 keV (epoch dependent)., The lightcurves were extracted using the generic binned data with a time resolution of 4 ms from channels 0--35 corresponding approximately to the energy range 2–15 keV (epoch dependent).765 Subsequentlv. the lighteurves were binned to a LOO ms resolution.," Subsequently, the lightcurves were binned to a 100 ms resolution."766 We verified our results hy comparing the outcome to Standard. | data that have a time resolution of 125 ms., We verified our results by comparing the outcome to Standard 1 data that have a time resolution of 125 ms.767 In order to gauge the X-ray spectral of the source during the selected pointings (if not already done so in Ix10). we extracted lighteurves fron channels 3.11 and 24.37 corresponding to energy ranges 36 keV and 10.15 keV. using the Standard 2 data products and compared the resulting hardnesses and intensities of these bands to the hardnesscintensity diagram presented in Ix10.," In order to gauge the X-ray spectral of the source during the selected pointings (if not already done so in K10), we extracted lightcurves from channels 3–11 and 24–37 corresponding to energy ranges 3–6 keV and 10–15 keV using the Standard 2 data products and compared the resulting hardnesses and intensities of these bands to the hardness-intensity diagram presented in K10."768 Furthermore. in order to identify the correct radio/X- state simultaneous radio observations were inspected using archival data from the Green. Bank Interferometer (GBI). Reylef/AAL-LA. and RATAN-GOO.," Furthermore, in order to identify the correct radio/X-ray state simultaneous radio observations were inspected using archival data from the Green Bank Interferometer (GBI), Ryle/AMI-LA, and RATAN-600."769 Vo follow the overall evolution of the radio/N-rav spectral states within the context of the selected. pointings containing the QPOs. the monitoring cata from and were used in phase-selected format as in KIO in addition to the radio lishteurves from. the above-mentioned racio Observatories.," To follow the overall evolution of the radio/X-ray spectral states within the context of the selected pointings containing the QPOs, the monitoring data from, and were used in phase-selected format as in K10 in addition to the radio lightcurves from the above-mentioned radio observatories."770 ‘The timing analysis in this study was undertaken using (Interactive Spectral Interpretation. System. Denicola 2002)) with the timing analysis moclule.," The timing analysis in this study was undertaken using (Interactive Spectral Interpretation System, \citealt{houck}) ) with the timing analysis module."771 Phe usual procedure for searching for quasi-periodic phenomena in lighteurves is to Construct a power density spectrum (PDS) and search for sharp peaks in this spectrum., The usual procedure for searching for quasi-periodic phenomena in lightcurves is to construct a power density spectrum (PDS) and search for sharp peaks in this spectrum.772 To construct a PDS we prepared the 100 ms time resolution Lehtcurves (done separately for. each pointing) and caleulated the PDS for segments of length 8192 bins over the whole lighteurve rejecting the segments with data gaps and finally averaging the PDS over the whole lighteurve., To construct a PDS we prepared the 100 ms time resolution lightcurves (done separately for each pointing) and calculated the PDS for segments of length 8192 bins over the whole lightcurve rejecting the segments with data gaps and finally averaging the PDS over the whole lightcurve.773 “To determine the significance level of the possible QPO detections we followed the Alonte-Carlo analysis of Benllochetal.(2001) which relies on simulating random red-noise dominated lightcurves with the algorithn deseribec in Timmer&Ixónig(1995)., To determine the significance level of the possible QPO detections we followed the Monte-Carlo analysis of \citet{benlloch} which relies on simulating random red-noise dominated lightcurves with the algorithm described in \citet{timmer}.774. First. we performed simple fits to the PDS with (with high degree of binning). where we include a simple powerlaw for modelling the low-frequency noise ancl a constant for modelling. the Poisson noise.," First, we performed simple fits to the PDS with (with high degree of binning), where we include a simple powerlaw for modelling the low-frequency noise and a constant for modelling the Poisson noise."775 Then 5000 ighteurves were simulated. using the model of the PDS ensuring that the generated lishteurves had the same length and mean counts as the original observations.," Then 5000 lightcurves were simulated, using the model of the PDS ensuring that the generated lightcurves had the same length and mean counts as the original observations."776 Based on he clistribution of the resulting PDSs [rom simulated ighteurves for each frequency bin.954... ane confidence intervals were obtained.," Based on the distribution of the resulting PDSs from simulated lightcurves for each frequency bin, and confidence intervals were obtained."777 Also. root-niean square values were obtained from the dynamically caleulatec PDSs rom a frequency range 0.0040.1 Lz using the same segment eneth over the lighteurves as above.," Also, root-mean square values were obtained from the dynamically calculated PDSs from a frequency range 0.004–0.1 Hz using the same segment length over the lightcurves as above."778 The orbital phase of individual segments of lighteurves were determined using a cubic ephemeris (Singhetal.2002)., The orbital phase of individual segments of lightcurves were determined using a cubic ephemeris \citep{singh}.779. QPOs have been detected at least six times according to the literature in the first studies dedicated to this topic (Lable 1)., QPOs have been detected at least six times according to the literature in the first studies dedicated to this topic (Table 1).780 observations exhibited. QPOs with amplitudes between 5 and of the 110 keV flux and periods in the range 0.715 mllz (501500 s) which persisted. for 540. eveles and occurred in the phase interval 0.00.75 (vanderας&Jansen 1985)., observations exhibited QPOs with amplitudes between 5 and of the 1–10 keV flux and periods in the range 0.7–15 mHz (50–1500 s) which persisted for 5–40 cycles and occurred in the phase interval 0.0–0.75 \citep{vanderklis}.781.. A balloon study (Raoetal.1991). showed a QPO in the 20100 keV. lighteurve with a frequency of SN milz (121 s). pulse fraction and duty evele during maximum brightness.," A balloon study \citep{rao} showed a QPO in the 20–100 keV lightcurve with a frequency of 8 mHz (121 s), pulse fraction and duty cycle during maximum brightness."782 A later study based on pointing data from 1996 through 2000 was conducted. by Axelssonetal.(2009) and. as mentioned above. they found no evidence of QPOs on any timescale.," A later study based on pointing data from 1996 through 2000 was conducted by \cite{axelsson} and, as mentioned above, they found no evidence of QPOs on any timescale."783 Specifically. on the shorter timescales (210.7? Lz) they do not detect QPOs at all and the power density spectrum is well-ceseribec hy a powerlaw of index — 2. while on longer timescales («105 11). they find that the variability is dominated by the state transitions.," Specifically, on the shorter timescales $>10^{-3}$ Hz) they do not detect QPOs at all and the power density spectrum is well-described by a powerlaw of index $-$ 2, while on longer timescales $<10^{-3}$ Hz), they find that the variability is dominated by the state transitions."784 Llowever. as Scottetal.(2003) point out in their study of timing noise in the Crab. random. walk processes will vield a powerlaw index of 2.," However, as \cite{scott} point out in their study of timing noise in the Crab, random walk processes will yield a powerlaw index of $-$ 2."785 This suggests that the Uaring in Cvenus X-3 produces the red noise that essentially mimics a random walk process and thus hides any potential intrinsic. variabilitv., This suggests that the flaring in Cygnus X-3 produces the red noise that essentially mimics a random walk process and thus hides any potential intrinsic variability.786 Our studs νοοσα two PDSs that show clear peaks above the confidence Limit. as described. below.," Our study yielded two PDSs that show clear peaks above the confidence limit, as described below."787 llowever. we would like to note that while the PDSs are consistent with power law noise with 3~ 1.52.5 with a," However, we would like to note that while the PDSs are consistent with power law noise with $\beta\sim$ $-$ 1.5–2.5 with a"788We then compared our results to those we obtained when ignoring the relativistic corrections for the same random munbers.,We then compared our results to those we obtained when ignoring the relativistic corrections for the same random numbers.789 We compared the dimensions obtained in both cases using a icthod developed by Denuzi et al. (, We compared the dimensions obtained in both cases using a method developed by Benzi et al. (7901995).,1995).791 The advantage of this method is that part of systematic errors. like border problems. are less pronounced.," The advantage of this method is that part of systematic errors, like border problems, are less pronounced."792" We checked the case Dinu,=200 Alpe.", We checked the case ${\cal D}_{max} = 200$ Mpc.793 Comparing it to the nou relativistic case. no significant differeuce could be detected.," Comparing it to the non- relativistic case, no significant difference could be detected."794 Checkiug the differences for the closest and farthest imer point. we obtained that. for the non-relativistic case. 33.162 points were inside the sphere. when takine the closest point ιν=550 AIpc).," Checking the differences for the closest and farthest inner point, we obtained that, for the non-relativistic case, 33,162 points were inside the sphere, when taking the closest point $R_{min} = 550$ Mpc)."795 For the arthest point (Ria1100 Ape). we obtained. in the same sphere. 33.152 poiuts.," For the farthest point $R_{max} = 1100$ Mpc), we obtained, in the same sphere, 33,152 points."796 This was expected as we chose a homogeneous sample., This was expected as we chose a homogeneous sample.797 The results are presented in Table 1., The results are presented in Table 1.798" We denote by MI aud M2 the uniuber of points iu the two spheres of radius D, Whose centers are Ray, and ων respectively. and by Peer. the percentage of points retained in each saluple. i.e. for three values of L,,;,."," We denote by M1 and M2 the number of points in the two spheres of radius ${\cal D}_{max}$ whose centers are $R_{min}$ and $R_{max}$ respectively, and by $P_{RET}$, the percentage of points retained in each sample, i.e. for three values of $L_{min}$."799 We obtain definitely an infinence on the average density. depending ou the specific model," We obtain definitely an influence on the average density, depending on the specific model."800 For the three models. even though this value. (M1/M2). is quite appreciable. still this does not affect the dimension within a ιν200 Mpc radius.," For the three models, even though this value, $M1/M2$ ), is quite appreciable, still this does not affect the dimension within a ${\cal D}_{max} =200 $ Mpc radius."801 For all the cases. we obtain: D=3.00d0.05.," For all the cases, we obtain: $D = 3.00 \pm 0.03$."802 Our next purpose was to check to what extend the dimension diminishes when we eo to larger distances., Our next purpose was to check to what extend the dimension diminishes when we go to larger distances.803" We calculated. the case where we consider the whole sphere around our galaxy and take for the iuner region a nuidrauge of the radius so that the centers in that region are farther than D,,,, from the borders.", We calculated the case where we consider the whole sphere around our galaxy and take for the inner region a midrange of the radius so that the centers in that region are farther than ${\cal D}_{max}$ from the borders.804" The caleulatiou was performed just for one case. the Eimsteiu-de Sitter model. aud £,,;, was chosen so that 12 4 of the galaxies where retained. on average."," The calculation was performed just for one case, the Einstein-de Sitter model, and $L_{min}$ was chosen so that 42 $\%$ of the galaxies where retained, on average."805 We averaged over six sets of 120.000. points. chosen randomly. aud over all the abovementioned poiuts of the central region (about 12.000). aud checked the decrease i the dimension when averaging over the ranges 150 -300 AIpe versus 150-600 Alpe.," We averaged over six sets of 120,000 points, chosen randomly, and over all the abovementioned points of the central region (about 12,000), and checked the decrease in the dimension when averaging over the ranges 150 -300 Mpc versus 450-600 Mpc."806 We obtain that the dimension slightly decreases by 1.62:0.2*4which is consistent with our other caleulations.," We obtain that the dimension slightly decreases by $1.6 \pm 0.2 \%$, which is consistent with our other calculations."807" To compare these weak discrepancies with the light cone effect. ou the Iuuinositv-distauce relation. we note that - for the Eimstein-de Sitter case. at D,,,,,.=200 Mpc. the contribution of the second order teria m the power series expansion of d; is a little more than of the total in Eq.(36)). but at D,,,,=GOO ATpe. it is more than -"," To compare these weak discrepancies with the light cone effect on the luminosity-distance relation, we note that - for the Einstein-de Sitter case, at ${\cal D}_{max} = 200$ Mpc, the contribution of the second order term in the power series expansion of $d_l$ is a little more than of the total in \ref{dlexeds}) ), but at ${\cal D}_{max} = 600$ Mpc, it is more than. -"808" for the caseος O3;=0.3 and O4=0.7. at D,,,,=200 Alpe. this contribution is about of the total in E«q.(12)). -"," for the case $\Omega_M =0.3$ and $\Omega_{\Lambda} = 0.7$, at ${\cal D}_{max} = 200$ Mpc, this contribution is about of the total in \ref{dlexpar}) ). -"809" for Qay=0.01 and O4=0.99. at D,=200 Mpc. it is more thanL%."," for $\Omega_M =0.01$ and $\Omega_{\Lambda} = 0.99$ , at ${\cal D}_{max} = 200$ Mpc, it is more than."810". We thus see that. except for the BEiusteiu-«de Sitter case at Diya,=200 Alpe. this effect is stronger ou d; than ou D."," We thus see that, except for the Einstein-de Sitter case at ${\cal D}_{max} = 200$ Mpc, this effect is stronger on $d_l$ than on $D$."811 Furthermore. as; at μι=200 Alpe. this effect ou the fractal dimension D seenis to be model independoeut. the error made by ignoring the relativistic corrections iu classical analyses must be inaller. at this scahan the statistical noise of the method.," Furthermore, as, at ${\cal D}_{max} = 200$ Mpc, this effect on the fractal dimension $D$ seems to be model independent, the error made by ignoring the relativistic corrections in classical analyses must be smaller, at this scale, than the statistical noise of the method."812 Therefore. we can sately couclude that. within the studied class of models. the redshift-distance relation can actually be used to provide an upper limit to the relativistic corrections needed to οςuplete this kind of analysis.," Therefore, we can safely conclude that, within the studied class of models, the redshift-distance relation can actually be used to provide an upper limit to the relativistic corrections needed to complete this kind of analysis."813 Furthermore. as Eq.(17)) provides a general relation between d; aud the area distance d4. the smoothiug (L15)! terii appears im the calculation of E whatever cosmolocical model is retained to represeut the observed nuiverse.," Furthermore, as \ref{dlad}) ) provides a general relation between $d_l$ and the area distance $d_a$, the smoothing $(1+z)^4$ term appears in the calculation of $\Gamma^*$ whatever cosmological model is retained to represent the observed universe."814 We are thus inclined to sugeest that the above property could apply to anv model aud that the averaging procedure has actually some eeueral smoothing result., We are thus inclined to suggest that the above property could apply to any model and that the averaging procedure has actually some general smoothing result.815 Iu the present article. we have studied the effect of curvature on the results of fractal analyses of ealaxy distribution.," In the present article, we have studied the effect of curvature on the results of fractal analyses of galaxy distribution."816 First. we explored analytically the Eiusteiu-«de Sitter model aud found that.coutrary to the claim in R95. the sensitivity of the inteerated conditional density I to the redshift is far ess thanthe sensitivity of the luuinosity distance.," First, we explored analytically the Einstein-de Sitter model and found that,contrary to the claim in R95, the sensitivity of the integrated conditional density $\Gamma^*$ to the redshift is far less thanthe sensitivity of the luminosity distance."817 Therefore. in this model. the," Therefore, in this model, the"818higher SFR normalization.,higher SFR normalization.819" On the other hand, a shallower relationship (a= 0.29) with a much larger SFR normalization (SFR/BHAR ~3000 at Μην=0.1 Μο yr-!) was found by for a sample of 31 AGN-ULIRGs at z«0.5, where excess emission at 60 um was attributed to star formation."," On the other hand, a shallower relationship $\alpha=0.29$ ) with a much larger SFR normalization (SFR/BHAR $\sim3000$ at $\dot{M}_{BH}=0.1$ $_{\odot}$ $^{-1}$ ) was found by for a sample of 31 AGN-ULIRGs at $z<0.5$, where excess emission at 60 $\mu$ m was attributed to star formation."820" More recently, such a shallow slope (a< 0.5) has also been found by several studies of optically selected quasars in fields that have Spitzer or Herschel coverage."," More recently, such a shallow slope $\alpha\leq0.5$ ) has also been found by several studies of optically selected quasars in fields that have Spitzer or Herschel coverage."821 Several studies of (PilbrattX-ray selected 2010)AGNs have also found a shallow SFR-BHAR relationship., Several studies of X-ray selected AGNs have also found a shallow SFR–BHAR relationship.822 used the [O11]\3727 line to estimate SFRs for a (2009)sample of COSMOS X-ray AGNs and found SFRxM$25*97? with a SFR/BHAR ratio ~50 at Mgy=0.1 Mo yr-!., used the $\oii\lambda3727$ line to estimate SFRs for a sample of COSMOS X-ray AGNs and found $SFR\propto\dot{M}_{BH}^{0.28\pm0.22}$ with a SFR/BHAR ratio $\sim50$ at $\dot{M}_{BH}=0.1$ $_{\odot}$ $^{-1}$.823" considered a sample of X-ray and IR-selected AGNs in galaxy clusters, with SFRs estimated from spectral decompositions of mid-IR data2010),, and found SFRος"," considered a sample of X-ray and IR-selected AGNs in galaxy clusters, with SFRs estimated from spectral decompositions of mid-IR data, and found $SFR\propto\dot{M}_{BH}^{0.46\pm0.06}$."824" While these sources reside in denser environments, ΛΙΡΑtheirο, AGN luminosities and total SFRs fall in the range of RSA Seyferts."," While these sources reside in denser environments, their AGN luminosities and total SFRs fall in the range of RSA Seyferts."825" and measured 870 µπι and (2010)100-160 um emission, respectively, for samples of Chandra X-ray-selected AGNs2006), and compiled 60 jm measurements for local AGNs detected by Swift-BAT2010)."," and measured 870 $\mu$ m and 100--160 $\mu$ m emission, respectively, for samples of Chandra X-ray-selected AGNs, and compiled 60 $\mu$ m measurements for local AGNs detected by Swift-BAT."826". They also find a shallow SFR- slope (o~0.4), but argue that star formation and black hole growth are more closely linked at higher AGN luminosities."," They also find a shallow SFR--BHAR slope $\alpha\sim0.4$ ), but argue that star formation and black hole growth are more closely linked at higher AGN luminosities."827" Recently, found no correlation between X-ray luminosity and(2011) far-IR luminosity for moderate luminosity X-ray sources =1033 1044 erg s7!) up to z3, consistent with the(Lx weak relationship we find for total SFRs."," Recently, found no correlation between X-ray luminosity and far-IR luminosity for moderate luminosity X-ray sources $L_{X}=10^{42}$ $10^{44}$ erg $^{-1}$ ) up to $z\approx3$, consistent with the weak relationship we find for total SFRs."828 A number of authors have made theoretical predictions for the behavior of the SFR and the BHAR during the AGN phase., A number of authors have made theoretical predictions for the behavior of the SFR and the BHAR during the AGN phase.829" These models differ primarily in their predictions for the nuclear SFR/BHAR ratio, ranging from ~1 to ~10° for AGNs with 0.1(e.g., Mo yr-t."," These models differ primarily in their predictions for the nuclear SFR/BHAR ratio, ranging from $\sim1$ to $\sim10^3$ for AGNs with $\dot{M}_{BH}\sim0.1$ $_{\odot}$ $^{-1}$."830" For example, in the galaxy merger models of that produce a final black hole mass ~4x10: Mo, which is appropriate for our sample (see Figure 1)), the SFR/BHAR ratio reaches ~200 at the peak of star-formation activity as the galaxies coalesce and drops to ~5 at the end of the bright AGN phase (Mau>0.4 Mo yrl)"," For example, in the galaxy merger models of that produce a final black hole mass $\sim4\times10^{7}$ $_{\odot}$, which is appropriate for our sample (see Figure \ref{fig:ml}) ), the SFR/BHAR ratio reaches $\sim200$ at the peak of star-formation activity as the galaxies coalesce and drops to $\sim5$ at the end of the bright AGN phase $\dot{M}_{BH}>0.1$ $_{\odot}$ $^{-1}$ )."831" Although the RSA Seyferts show little evidence for merger activity, our results for nuclear SFRs are broadly consistent with these values."," Although the RSA Seyferts show little evidence for merger activity, our results for nuclear SFRs are broadly consistent with these values."832" For lower accretion rates =10-?-107? Μο yr7) characteristic of earlier merger(Mpg phases in the model, the SFR/BHAR ratio falls in the 500-1000 range, consistent with our results for total SFRs (see Figure 11))."," For lower accretion rates $\dot{M}_{BH}=10^{-3}$ $10^{-2}$ $_{\odot}$ $^{-1}$ ) characteristic of earlier merger phases in the model, the SFR/BHAR ratio falls in the 500–1000 range, consistent with our results for total SFRs (see Figure \ref{fig:total}) )."833" The starburst disk models of that produce Mgy~0.1 Mo yr7! suggest that most of the gas being supplied at an outer radius R54;=200 pc will be consumed by a starburst near that outer radius, resulting in SFR/BHAR~10°."," The starburst disk models of that produce $\dot{M}_{BH}\sim0.1$ $_{\odot}$ $^{-1}$ suggest that most of the gas being supplied at an outer radius $R_{out}=200$ pc will be consumed by a starburst near that outer radius, resulting in $\sim10^3$."834" While inconsistent with our measurements for local Seyfert galaxies, this model is perhaps consistent with the findings of for AGN-ULIRGs."," While inconsistent with our measurements for local Seyfert galaxies, this model is perhaps consistent with the findings of for AGN-ULIRGs."835 used a scaled-(2005)down version of the model to study less powerful starbursts around AGNs., used a scaled-down version of the model to study less powerful starbursts around AGNs.836" They found SFR/BHAR~200 inside r=100 pc for a fiducial model with Mgy0.3 Mo νι, which is more star formation than we observe in r=1 kpc apertures (see Figure "," They found $\sim200$ inside $r=100$ pc for a fiducial model with $\dot{M}_{BH}\sim0.3$ $_{\odot}$ $^{-1}$, which is more star formation than we observe in $r=1$ kpc apertures (see Figure \ref{fig:nuc}) )."837They also predict that the SFR/BHAR ratio should 9)).increase toward lower AGN luminosities due to competition for gas between between star formation and black hole accretion., They also predict that the SFR/BHAR ratio should increase toward lower AGN luminosities due to competition for gas between between star formation and black hole accretion.838" This model assumes a constant gas supply, and could perhaps be reconciled with our observations if the gas supply were depleted in such a way that the SFR decreased more quickly than the BHAR."," This model assumes a constant gas supply, and could perhaps be reconciled with our observations if the gas supply were depleted in such a way that the SFR decreased more quickly than the BHAR."839 studied the evolution of the central kpc of a (2007)massive nuclear disk with a central black hole and find that the SFR and BHAR each other during the primary growth phase (SFRtrace« Mgr) with SFR/BHAR ratios in the 3-50 range., studied the evolution of the central kpc of a massive nuclear disk with a central black hole and find that the SFR and BHAR trace each other during the primary growth phase $SFR\propto\dot{M}_{BH}$ ) with SFR/BHAR ratios in the 3–50 range.840 This is consistent with our results regarding nuclear SFRs for sources with Mgy>0.01 Mo yr-! (see Figure 9))., This is consistent with our results regarding nuclear SFRs for sources with $\dot{M}_{BH}>0.01$ $_{\odot}$ $^{-1}$ (see Figure \ref{fig:nuc}) ).841" Focusing on smaller scales, studied a 100 pc circumnuclear disk with accretion being"," Focusing on smaller scales, studied a 100 pc circumnuclear disk with accretion being"842"convective flux is probably not large enough to influence the thermodynamics of the ICM, but it could be important in other environments where the MTI can operate, such as the interiors of white dwarfs and neutron stars (?)..","convective flux is probably not large enough to influence the thermodynamics of the ICM, but it could be important in other environments where the MTI can operate, such as the interiors of white dwarfs and neutron stars \citep{Chang2010}."843" 'Thus far, we have described the development and saturation of buoyancy instabilities only in the idealized case of an otherwise quiescent plasma."," Thus far, we have described the development and saturation of buoyancy instabilities only in the idealized case of an otherwise quiescent plasma."844" In a more astrophysically realistic scenario, however, other processes and sources of turbulence may also act on the plasma and the resulting dynamics can be more complicated."," In a more astrophysically realistic scenario, however, other processes and sources of turbulence may also act on the plasma and the resulting dynamics can be more complicated."845" For example, the evolution of the HBI won't simply proceed until the growth rate is everywhere zero."," For example, the evolution of the HBI won't simply proceed until the growth rate is everywhere zero."846" Instead, we expect the saturated state to involve a statistical balance among the various forces; this balance depends on the buoyant properties of the plasma and provides a test of our understanding of the nonlinear behavior of the HBI and MTI."," Instead, we expect the saturated state to involve a statistical balance among the various forces; this balance depends on the buoyant properties of the plasma and provides a test of our understanding of the nonlinear behavior of the HBI and MTI."847" Furthermore, any change in the saturated state of the plasma due to the interaction between the HBI/MTI and other sources of turbulence could change the astrophysical implications of these instabilities."," Furthermore, any change in the saturated state of the plasma due to the interaction between the HBI/MTI and other sources of turbulence could change the astrophysical implications of these instabilities."848" We choose to explore the interaction between buoyancy instabilities and other sources of turbulence using the idealized, isotropic turbulence model described in section 3.4.."," We choose to explore the interaction between buoyancy instabilities and other sources of turbulence using the idealized, isotropic turbulence model described in section \ref{subsec:turbulence}."849" While this model glosses over the details of what generates the turbulence, we hope that it captures the essential physics of the problem, allowing us to study the effect of turbulence without unnecessarily restricting our analysis to specific applications."," While this model glosses over the details of what generates the turbulence, we hope that it captures the essential physics of the problem, allowing us to study the effect of turbulence without unnecessarily restricting our analysis to specific applications."850" We intend to specialize to specific sources of turbulence in future work, but our present analysis should apply in the ICM, accretion disks, and anywhere else the assumptions summarized in section 2.2 apply."," We intend to specialize to specific sources of turbulence in future work, but our present analysis should apply in the ICM, accretion disks, and anywhere else the assumptions summarized in section \ref{subsec:physics} apply."851" In order to characterize the turbulence, we define a timescale for it to influence the plasma."," In order to characterize the turbulence, we define a timescale for it to influence the plasma."852" We define this “distortion time” in terms of the spatial velocity spectrum: taist(€)=6/δυ(ϐ), where and óv(k) is the Fourier transform of the velocity field."," We define this “distortion time” in terms of the spatial velocity spectrum: $t_{\mr{dist}}(\ell) = \ell / \delta v (\ell)$, where and $\delta v(\vec{k})$ is the Fourier transform of the velocity field."853 We expect the relevant parameter describing the importance, We expect the relevant parameter describing the importance854CCLUSSIOM 1i bulee regions.,emission in bulge regions.855" Outside these regious. iu the disk-domunated parts of the profiles. the aand πια, light distributions are identical within the errors."," Outside these regions, in the disk-dominated parts of the profiles, the and $R$ -band light distributions are identical within the errors."856 Thus there is no evidence of. for example. the radial truncation of eenissiou found bv 7/ for a sample of 55 Virgo cluster spirals.," Thus there is no evidence of, for example, the radial truncation of emission found by \citet{koop04} for a sample of 55 Virgo cluster spirals."857 This is consistent with thei iuterxetatiou that the truucation is a consequence of the clust¢Y environment (they found uo truncation for a comparison sample of 29 isolated spiral galaxies). s3nce our sample is xedominautlv composed of feld galaxies.," This is consistent with their interpretation that the truncation is a consequence of the cluster environment (they found no truncation for a comparison sample of 29 isolated spiral galaxies), since our sample is predominantly composed of field galaxies."858 There is also uo evidence from these profiles to support mside-out ficories of disk formation: the old stellar population could have Deen produced by historical SE. distributed like that occuriug at the present epoch., There is also no evidence from these profiles to support inside-out theories of disk formation; the old stellar population could have been produced by historical SF distributed like that occurring at the present epoch.859 The possibility of large-scale radial uueration of disk material drivenby. for example. bar torques obviously complicates this conclusion.," The possibility of large-scale radial migration of disk material driven by, for example, bar torques obviously complicates this conclusion."860 Oue of the most important. aud problematic. stages in the reduction of narrow-band iuaeing is the removal of the contimmun lieht which passes through the narrow-band filter in addition to the desired line emissiou.," One of the most important, and problematic, stages in the reduction of narrow-band imaging is the removal of the continuum light which passes through the narrow-band filter in addition to the desired line emission."861 For WaGs lis was done using additional imagine through either a ποσο AR or an intermecdiate-width continuum filter., For GS this was done using additional imaging through either a broad $R$ or an intermediate-width continuum filter.862 The xocedures and associated (siguificaut) errors on derived otal fluxes are explained in Paper L The possib=.ity of errors leading to under- or over-stbtraction of the conun lieht is particularly important for the prese oper as. for example. systematic madersubtraction c“ould casily lead to a spurious apparent agreement between the shapes of R-baud aud Πα profiles due to possible red-ight contamination in the latter.," The procedures and associated (significant) errors on derived total fluxes are explained in Paper I. The possibility of errors leading to under- or over-subtraction of the continuum light is particularly important for the present paper as, for example, systematic under-subtraction could easily lead to a spurious apparent agreement between the shapes of $R$ -band and ' profiles due to possible red-light contamination in the latter."863 A test was performed to determine the mipact of coutimmun subtraction errors on rorlmatlised yprofile shapes. for 10 galaxies frou Tacs covering the," A test was performed to determine the impact of continuum subtraction errors on normalised profile shapes, for 10 galaxies from GS covering the"864We also have for the AGN-boosted star formation rate This is of course the optimal rate.,We also have for the AGN-boosted star formation rate This is of course the optimal rate.865" We also see that MAGN&g, This is not inconsistent with the observed dependence of outflow velocity on star formation rate −−", We also see that $\dot M_{\ast}^{AGN} \simpropto \sigma^4.$ This is not inconsistent with the observed dependence of outflow velocity on star formation rate \citep{mar05}.866" We may consider the case of a recently detected kiloparsec scale starburst at z=6.24, hosted by a luminous quasar which has spatially resolved [CI] emission as well ∙∙as a large reservoir of CO-detected molecular gas "," We may consider the case of a recently detected kiloparsec scale starburst at $z=6.24,$ hosted by a luminous quasar which has spatially resolved [CII] emission as well as a large reservoir of CO-detected molecular gas \citep{fab09}. ."867"Other similar high z objects, detected in CO, are believed to be super-Magorrian (Maiolin"," Other similar high $z$ objects, detected in CO, are believed to be super-Magorrian \citep{mai07}."868"o This quasar host galaxy also has a staretal. formation⋅⋅ rate of ~1000Moyear~!kpc~?, an order of magnitude larger than is typical of starbursts without luminous AGN."," This quasar host galaxy also has a star formation rate of $\sim 1000\rm M_\odot year^{-1}kpc^{-2}, $ an order of magnitude larger than is typical of starbursts without luminous AGN."869" For comparison, Arp 220, a low redshift starburst hosting an AGN of luminosity comparable to its starburst, has a similar surface brightness in star formation but only over a 100 pc scale."," For comparison, Arp 220, a low redshift starburst hosting an AGN of luminosity comparable to its starburst, has a similar surface brightness in star formation but only over a 100 pc scale."870" It is tempting to infer, admittedly with only two well-mapped examples, that we may be viewing AGN boosting of star formation, with the phenomenon being greatly magnified at high redshift for the most massive objects."," It is tempting to infer, admittedly with only two well-mapped examples, that we may be viewing AGN boosting of star formation, with the phenomenon being greatly magnified at high redshift for the most massive objects."871" We infer that if the SMBH mass is super-Magorrian, then t.«ts and f.<tg, and star formation is very efficient."," We infer that if the SMBH mass is super-Magorrian, then $t_\ast<t_S$ and $t_\ast<t_d$, and star formation is very efficient."872 This seems to be the case at high redshift., This seems to be the case at high redshift.873 The preponderance of data indeed suggests that the local relation becomes super-Magorrian prior to z~2 (McLureetal|[2006;2008) and indeed persists to z25 (Maiolinoet al.|2007])..," The preponderance of data indeed suggests that the local relation becomes super-Magorrian prior to $z\sim 2$ \citep{mcl06, woo08} and indeed persists to $z\simgt 5$ \citep{mai07}. ."874" Coevolution of AGN accretion and the co-moving star formation rate densities occurs to z~2, but the accretion rate falls off relatively towards higher redshift (Silvermanetal."," Coevolution of AGN accretion and the co-moving star formation rate densities occurs to $z\sim 2$, but the accretion rate falls off relatively towards higher redshift \citep{silv08}."875" Comparison of the cosmic star formation history and 2008)...AGN accretion rates in comoving number density as a function of luminosity suggests that the peak in massive black hole growth rate occurs several Gyr prior to the star formation peak and that downsizing at a1]9007]z<1 is due to diminishing accretion rates (Babieet """, Comparison of the cosmic star formation history and AGN accretion rates in comoving number density as a function of luminosity suggests that the peak in massive black hole growth rate occurs several Gyr prior to the star formation peak and that downsizing at $z<1$ is due to diminishing accretion rates \citep{bab07}. .876 Sub-millimeter galaxies (SMGs) are an exception., Sub-millimeter galaxies (SMGs) are an exception.877 SMGs at z~2 contain SMBH that are under-massive relative to the Magorrian relation et, SMGs at $z\sim 2$ contain SMBH that are under-massive relative to the Magorrian relation \citep{ale08}.878" This is suggestive of triggered star formation, which (Alexanderal.|2008)..reduces t,, and may be appropriate in major mergers that generate dense central gas environments where porosity feedback is suppressed."," This is suggestive of triggered star formation, which reduces $t_\ast$, and may be appropriate in major mergers that generate dense central gas environments where porosity feedback is suppressed."879" Note also that the peak in the major merger rate also precedes the peak in cosmic star formation rate (Ryanet and is approximately consistent with the peak in al.|008).,comoving AGN accretion rate density."," Note also that the peak in the major merger rate also precedes the peak in cosmic star formation rate \citep{rya08}, and is approximately consistent with the peak in comoving AGN accretion rate density."880" In summary, a general and robust treatment of disk star formation is developed from cloud collision model."," In summary, a general and robust treatment of disk star formation is developed from a cloud collision model."881 'The Schmidt-Kennicutt law emergesa naturally for star-forming disks., The Schmidt-Kennicutt law emerges naturally for star-forming disks.882 We predict that there is an inverse relation between Tully-Fisher law and Schmidt-Kennicutt law residuals., We predict that there is an inverse relation between Tully-Fisher law and Schmidt-Kennicutt law residuals.883 A multi-phase treatment of supernova feedback leads to a turbulent pressure-regulated generalization of the star formation law that is applicable to gas-rich starbursts., A multi-phase treatment of supernova feedback leads to a turbulent pressure-regulated generalization of the star formation law that is applicable to gas-rich starbursts.884 Negative feedback from star formation occurs in disks under turbulent pressure regulation., Negative feedback from star formation occurs in disks under turbulent pressure regulation.885" In combination with a cloud collision model, the Schmidt-Kennicutt law can be understood in diverse environments, spanning quiescent disks and starbursts."," In combination with a cloud collision model, the Schmidt-Kennicutt law can be understood in diverse environments, spanning quiescent disks and starbursts."886" Enhanced pressure, as expected in merger-induced star formation, enhances star formation efficiency."," Enhanced pressure, as expected in merger-induced star formation, enhances star formation efficiency."887 An upper limit is derived for the disk star formation rate in starbursts that depends only on the IMF and on the ratio of global to cloud pressures., An upper limit is derived for the disk star formation rate in starbursts that depends only on the IMF and on the ratio of global to cloud pressures.888" For clouds in approximate pressure with interstellar medium and a local IMF, we infer a limiting gas surface density of ~Ρε”. We extend these considerations to the1000M case where the interstellar gas pressure in the inner galaxy is dominated by outflows from a central AGN."," For clouds in approximate pressure with interstellar medium and a local IMF, we infer a limiting gas surface density of $\sim 1000\rm M_\odot \, pc^{-2}.$ We extend these considerations to the case where the interstellar gas pressure in the inner galaxy is dominated by outflows from a central AGN."889 The star formation rate is pressure-driven and depends on the excess pressure applied by the AGN outflows., The star formation rate is pressure-driven and depends on the excess pressure applied by the AGN outflows.890" During massive spheroid formation, AGN-driven winds trigger star formation, resulting in enhanced supernova feedback and outflows."," During massive spheroid formation, AGN-driven winds trigger star formation, resulting in enhanced supernova feedback and outflows."891 Downsizing is predicted to be a consequence of AGN-driven positive feedback., Downsizing is predicted to be a consequence of AGN-driven positive feedback.892" Our most important results refer to downsizing, for which we provide a new interpretation in terms of Bondi accretion feeding of the central black hole."," Our most important results refer to downsizing, for which we provide a new interpretation in terms of Bondi accretion feeding of the central black hole."893 'The specific accretion rate is proportional to the black hole mass., The specific accretion rate is proportional to the black hole mass.894" We found that Bondi accretion results in Mgg«x This means that if porosity self-regulates 0°°/7Q4(tgH/ts).to be constant, black hole growth proceeds rapidly until it saturates at the Magorrian relation Mpyxo* due to blow-out."," We found that Bondi accretion results in $M_{BH}\propto \sigma^{59/7}Q^4 (t_{BH}/t_S).$ This means that if porosity self-regulates to be constant, black hole growth proceeds rapidly until it saturates at the Magorrian relation $M_{BH}\propto \sigma^4$ due to blow-out."895 Black hole downsizing occurs if α is approximately constant., Black hole downsizing occurs if $\alpha$ is approximately constant.896 We clarify this as follows., We clarify this as follows.897 There are three specific rates that define our model., There are three specific rates that define our model.898" The Salpeter rate tg! is constant, the black hole growth rate is l/tgg=(l/ts)(LAaN/Lraa), and the star formation rate is 1/t,=€sN(GLAawT)!?(cof;)V2. Hence and we infer that This shows that the black hole growth rate and star formation rate are coupled."," The Salpeter rate $t_S^{-1}$ is constant, the black hole growth rate is $1/t_{BH}= (1/t_S)(L_{AGN}/L_{Edd}), $ and the star formation rate is $ 1/t_\ast=\bar\epsilon_899{SN}(GL_{AGN}\tau)^{1/2}(c\sigma^4f_g)^{-1/2}.$ Hence and we infer that This shows that the black hole growth rate and star formation rate are coupled."900" At given o, there is a critical AGN luminosity, above which AGN-triggered star formation rates dominates over the black hole growth rate."," At given $\sigma$, there is a critical AGN luminosity, above which AGN-triggered star formation rates dominates over the black hole growth rate."901" This critical luminosity is found to be At super-Eddington luminosities, AGN-triggered star formation dominates."," This critical luminosity is found to be At super-Eddington luminosities, AGN-triggered star formation dominates."902" The model contains two characteristic luminosities which are functions of σ. The Eddington luminosity, if combined with the quenching assumption, scales as c. The AGN-triggered star formation luminosity is eichésuo?(LAGNT)?(Gef,)2. This is proportional to a!""Mggo?. AdoptingMpggο:o* anda«oA/3 if Qis constant, we find that LAC’οςo?°/3. Hence we again infer a critical Eddington luminosity above which triggered star formation dominates the luminosity of the system."," The model contains two characteristic luminosities which are functions of $\sigma.$ The Eddington luminosity, if combined with the quenching assumption, scales as $\sigma^4.$ The AGN-triggered star formation luminosity is ${\epsilon_l}c^2{\bar\epsilon_{SN}} \sigma^2(L_{AGN}\tau)^{1/2}(Gcf_g)^{-1/2}.$ This is proportional to $\alpha^{1/2}M_{BH}\sigma^2 .$ Adopting$M_{BH}\propto \sigma^4$ and $\alpha \propto \sigma^{4/3} $ if $Q$is constant, we find that $L_\ast ^{AGN}\propto \sigma^{20/3}.$ Hence we again infer a critical Eddington luminosity above which triggered star formation dominates the luminosity of the system."903 This guaranteesefficient star formation for luminous AGN., This guaranteesefficient star formation for luminous AGN.904 Moreover if Mpr/o* increases with, Moreover if $M_{BH}/\sigma^4$ increases with905with our results taking into account the error bars.,with our results taking into account the error bars.906 In this scenario à positive metallicity gradient for the gas along the outer bar is required., In this scenario a positive metallicity gradient for the gas along the outer bar is required.907 Although this fact might be somewhat striking. from a stellar (not. gaseous) point of view there is evidence for such gradients.," Although this fact might be somewhat striking, from a stellar (not gaseous) point of view there is evidence for such gradients."908 Indeed. Pérezοἱal. study a sample of 2X barred. galaxies and find that some of them tend to become more metal-rich at the ends of the main bars.," Indeed, \citet{2009A&A...495..775P} study a sample of 20 barred galaxies and find that some of them tend to become more metal-rich at the ends of the main bars."909 Moreover. those objects have older mean ages and higher central velocity dispersions than the rest of the sample. which is in agreement with the properties found for 357.," Moreover, those objects have older mean ages and higher central velocity dispersions than the rest of the sample, which is in agreement with the properties found for 357."910 Unfortunately. the S/N ratio of our data is not enough to measure gradients along the main bar to check this possibility.," Unfortunately, the S/N ratio of our data is not enough to measure gradients along the main bar to check this possibility."911 We have performed for the first time a detailed analysis of the morphological. kinematical. ancl stellar population properties of a prototype couble-barred earlv-tvpe: disc ealaxv.," We have performed for the first time a detailed analysis of the morphological, kinematical, and stellar population properties of a prototype double-barred early-type disc galaxy."912 We put special emphasis on the inner bar in order to constrain its role in the evolution of this galaxy., We put special emphasis on the inner bar in order to constrain its role in the evolution of this galaxy.913 The observational strategy consisted in taking very deep long-slit spectra along the directions of the inner and outer bars and the major axis of the disc., The observational strategy consisted in taking very deep long-slit spectra along the directions of the inner and outer bars and the major axis of the disc.914 The presence of the two bars is clearly revealed: by 1f ellipticity. and. PA profiles. which show the usual gawip changes due to this kind of structure.," The presence of the two bars is clearly revealed by the ellipticity and PA profiles, which show the usual sharp changes due to this kind of structure."915 Moreover. the μαinematical analysis also presents clear signatures due to the inner bar: the double-hump profile in the velocity (IEmsellemal.2001) and the e-hollows in the velocity. dispersion deLorenzo-C'áceresctal.2008)...," Moreover, the kinematical analysis also presents clear signatures due to the inner bar: the double-hump profile in the velocity \citep{2001A&A...368...52E}916 and the $\sigma$ -hollows in the velocity dispersion \citep{2008ApJ...684L..83D}."917 These hollows are due o the contrast between the velocity dispersion values of the inner bar and the central structure. that might be a classical )ulee with a velocity dispersion higher than the inner bar. or à pseudobulge with a lower velocity dispersion than the xw.," These hollows are due to the contrast between the velocity dispersion values of the inner bar and the central structure, that might be a classical bulge with a velocity dispersion higher than the inner bar, or a pseudobulge with a lower velocity dispersion than the bar."918 The relative contribution of the inner bar to the total lux also influences the size ancl depth of the e-hollows., The relative contribution of the inner bar to the total flux also influences the size and depth of the $\sigma$ -hollows.919 Lt remains unclear if the e-hollows or other related. features niv appear for the case of the outer bar., It remains unclear if the $\sigma$ -hollows or other related features may appear for the case of the outer bar.920 Unfortunately. the S/N of the main bar spectrum is not sullicient to explore the kinematics at its ends.," Unfortunately, the S/N of the main bar spectrum is not sufficient to explore the kinematics at its ends."921 The analvsis of the kinematics of 3357 also reveals a kinematically-clecouplecl structure rotating faster than its surroundings at the centre of the galaxy., The analysis of the kinematics of 357 also reveals a kinematically-decoupled structure rotating faster than its surroundings at the centre of the galaxy.922 This signature matches in size with a central e-drop., This signature matches in size with a central $\sigma$ -drop.923 3357 is the first observed galaxy in which a e-drop and the e-hollows coexist., 357 is the first observed galaxy in which a $\sigma$ -drop and the $\sigma$ -hollows coexist.924 This fact illustrates the dilferences between both signatures: whereas the former are just due to the presence of the inner xw. the latter is caused by an inner. colder structure.," This fact illustrates the differences between both signatures: whereas the former are just due to the presence of the inner bar, the latter is caused by an inner, colder structure."925 Due o the dillerent nature of both signatures. we want to stress hat a double-barred galaxy might present a e-drop. the σ- rollows. or both. as in this case.," Due to the different nature of both signatures, we want to stress that a double-barred galaxy might present a $\sigma$ -drop, the $\sigma$ -hollows, or both, as in this case."926 The structural composition of 3357 has to account or all the observational evidences found in the analysis of he photometry and kinematies., The structural composition of 357 has to account for all the observational evidences found in the analysis of the photometry and kinematics.927 Phe presence of the disc and he two bars is clear. but the central region turns out to be more cüllicult to disentangle.," The presence of the disc and the two bars is clear, but the central region turns out to be more difficult to disentangle."928 In fact. two possible scenarios are compatible with the results obtained in this work.," In fact, two possible scenarios are compatible with the results obtained in this work."929 The irst possibility is that 3357| whichhosts a classical. hot bulge ogether with an inner disc. would. be responsible of the decoupling in the velocity. profile and. the a-drop.," The first possibility is that 357 hosts a classical, hot bulge together with an inner disc, which would be responsible of the decoupling in the velocity profile and the $\sigma$ -drop."930 The second scenario is that the bulee of 3357 is. in [act. a cold. pseudobulge. which is directly related to the kinematical central signatures.," The second scenario is that the bulge of 357 is, in fact, a cold pseudobulge, which is directly related to the kinematical central signatures."931 The main conclusion. of this work is that the bulge and inner bar show similar stellar population properties (age. metallicity anc o-enhancement). whereas the outer bar has no significant. dillerence in age but it is less metal- and more a-enhanced. indicating that it was assembled in shorter timescales than the inner structures.," The main conclusion of this work is that the bulge and inner bar show similar stellar population properties (age, metallicity and $\alpha$ -enhancement), whereas the outer bar has no significant difference in age but it is less metal-rich and more $\alpha$ -enhanced, indicating that it was assembled in shorter timescales than the inner structures."932 This result seems to discard for this ealaxy the traditional secular evolution scenario. in which the star formation triggered » the gas Lown along the outer structures is causing the ormation of the central parts.," This result seems to discard for this galaxy the traditional secular evolution scenario, in which the star formation triggered by the gas flown along the outer structures is causing the formation of the central parts."933 Therefore. 3357 has oen shaped by the redistribution. of the existing stars. mavbe in ai wav in which stars from the. clise orm the inner components. or mavbe in an initial Dramework so the inner bar is lately. formed rom the pseudobulge stars.," Therefore, 357 has been shaped by the redistribution of the existing stars, maybe in a way in which stars from the disc form the inner components, or maybe in an initial framework so the inner bar is lately formed from the pseudobulge stars."934 This last scenario is backed » the numerical work of Debattista&Shen(2007).. who create cdouble-barred svstems from a pure stellar cise and oeudobulge.," This last scenario is backed by the numerical work of \citet{2007ApJ...654L.127D}, who create double-barred systems from a pure stellar disc and pseudobulge."935 In this scenario. the fast rotation of the oeudobulge is the key clement to generate bars without he eas contribution.," In this scenario, the fast rotation of the pseudobulge is the key element to generate bars without the gas contribution."936 An analysis such as the one presented. in this work or a larger sample of cdouble-barred galaxies. is required o derive general and robust conclusions on the formation of these complex objects., An analysis such as the one presented in this work for a larger sample of double-barred galaxies is required to derive general and robust conclusions on the formation of these complex objects.937 Fortunately. the striking results obtained for 3357. are motivating and shed light on he importance of carefully studsing double-barred galaxies. rom the outer disc to the very central regions.," Fortunately, the striking results obtained for 357 are motivating and shed light on the importance of carefully studying double-barred galaxies, from the outer disc to the very central regions."938 We are indebted to Patricia Sánnchez-Dlázzquez and Isabel Pérrez for providing the linc-strength measurements for the reference barred. galaxies., We are indebted to Patricia Sánnchez-Blázzquez and Isabel Pérrez for providing the line-strength measurements for the reference barred galaxies.939" We are also very grateful to Jairo Alénndez-Xbreu. Jestiss Falcónn-Darroso. Lama Martínnez-Valpuesta. Nacho ""Frujillo. Revnier Peletier and Alina Ixoleva. whose help and useful comments have been very important."," We are also very grateful to Jairo Ménndez-Abreu, Jesúss Falcónn-Barroso, Inma Mart\'innez-Valpuesta, Nacho Trujillo, Reynier Peletier and Mina Koleva, whose help and useful comments have been very important."940 Comments and sugecstions from the anonymous referee have greatly. improved. this paper., Comments and suggestions from the anonymous referee have greatly improved this paper.941 Fhis work has been supported by the Programa Nacional de Xstronomífaa y Astrofissica of the Spanish Ministry. of Science and Innovation under grant AYAROLO-21322-C08-02., This work has been supported by the Programa Nacional de Astronomíaa y Astrofíssica of the Spanish Ministry of Science and Innovation under grant AYA2010-21322-C03-02.942 EAIC is supported by the University of Padua. through grants CPDAOS9220. GOA02-1283/10. and 60.302-5052/11 ancl by he Italian Space Ageney (ASL) through grant ASI-LNAL 1/009/10/0.," EMC is supported by the University of Padua through grants CPDA089220, 60A02-1283/10, and 60A02-5052/11 and by the Italian Space Agency (ASI) through grant ASI-INAF I/009/10/0."943" ""his work benefits from observations made with he NASA/ESA Llubble Space Telescope. obtained from the Hlubble Legaxy Archive. which is a collaboration between he Space Telescope Science. Institute (STScl/NASA). he Space Telescope European Coordinating Facility (ST- and the Canadian Astronomy Data Centre (CADC/NDIC/CSA)."," This work benefits from observations made with the NASA/ESA Hubble Space Telescope, obtained from the Hubble Legaxy Archive, which is a collaboration between the Space Telescope Science Institute (STScI/NASA), the Space Telescope European Coordinating Facility (ST-ECF/ESA) and the Canadian Astronomy Data Centre (CADC/NRC/CSA)."944Ligh resolution Optical imaging instruments based on aperture svnthesis have been developed over the last decades with the aim of reaching angular resolution in the nano radian range.,High resolution Optical imaging instruments based on aperture synthesis have been developed over the last decades with the aim of reaching angular resolution in the nano radian range.945 These dillerent instruments (Lawson19097) use the property of the Zernike van Cittert theorem to recover the intensity distribution of the object by means of spatial coherence analysis., These different instruments \citep{Law} use the property of the Zernike van Cittert theorem to recover the intensity distribution of the object by means of spatial coherence analysis.946 With this method. the instrument can never select. the light. coming. only from one of the pixels composing the full object because the measuremnts are being carried out on the Fourier spectral domain.," With this method, the instrument can never select the light coming only from one of the pixels composing the full object because the measuremnts are being carried out on the Fourier spectral domain."947 For high-dyvnamies objects. such as a star | exoplanet system. this technique is limited: since. the information on the [aint object is always mixed with the light emitted by the main source.," For high-dynamics objects, such as a star + exoplanet system, this technique is limited since the information on the faint object is always mixed with the light emitted by the main source."948 Consequently. direct imaging is o be preferred and the analysis of the object is made easier in the image domain than in the Fourier spectrum one.," Consequently, direct imaging is to be preferred and the analysis of the object is made easier in the image domain than in the Fourier spectrum one."949" Since he beginning of high resolution imaging. measurements iive never been achieved both with a very high resolution in the range of nanoracian and a very high dvnamies in the range of 10""."," Since the beginning of high resolution imaging, measurements have never been achieved both with a very high resolution in the range of nanoradian and a very high dynamics in the range of $10^6$."950 In order to meet this challenge A. Labevrie has oxoposed a solution which is known as the hypertelescope (Labevric1996)., In order to meet this challenge A. Labeyrie has proposed a solution which is known as the hypertelescope \citep{L}.951. This new type of instrument solves the xoblem. of the highly structured Point Spread: Function (PSE) of a diluted array thanks to a pupil densification process., This new type of instrument solves the problem of the highly structured Point Spread Function (PSF) of a diluted array thanks to a pupil densification process.952 “The PSE of a hyperteclescope being sharp and smooth. it is possible to use the instrument for clirect imaging.," The PSF of a hypertelescope being sharp and smooth, it is possible to use the instrument for direct imaging."953 Phe image { which equals the convolution of the object O by the PSE. looks like the object but with a limited resolution.," The image $I$ which equals the convolution of the object $O$ by the PSF, looks like the object but with a limited resolution."954 Different versions of hypertelescopes have been proposed. using field combination in the pupil plane (Vakilietal2004). or pupil densification thanks to the use of monomoce optical fibres (Patructal2008)., Different versions of hypertelescopes have been proposed using field combination in the pupil plane \citep{V} or pupil densification thanks to the use of monomode optical fibres \citep{P}.955. Parallel to the hypertelescope studies. promoted. by A. Labevrie. we have proposed a temporal alternative to the initial design that used. spatial classical optics (el Fig.l).," Parallel to the hypertelescope studies promoted by A. Labeyrie, we have proposed a temporal alternative to the initial design that used spatial classical optics (cf \ref{Fig:SpatHyp}) )."956 The main purpose of this new concept is to answer some technical dillieulties met with classical hypertelecopes ancl to propose new functionalities., The main purpose of this new concept is to answer some technical difficulties met with classical hypertelecopes and to propose new functionalities.957 In Revnaucd&Delage(2007) we theoretically demonstrated: the possibility to design a hvpertelescope bv using temporal optical path modulation., In \citet{RD} we theoretically demonstrated the possibility to design a hypertelescope by using temporal optical path modulation.958 In. the next paragraphs.we brielly recall the principle of a classical and a temporal hypertelescope.," In the next paragraphs,we briefly recall the principle of a classical and a temporal hypertelescope."959 Figure 1 recalls the structure of a hvpertelescope as proposed by A. Labevrie., Figure \ref{Fig:SpatHyp} recalls the structure of a hypertelescope as proposed by A. Labeyrie.960 This simplified drawing does not detail the reconfiguration ancl densification process., This simplified drawing does not detail the reconfiguration and densification process.961 Εις technique makes it necessary to remap the input pupil taking care to apply an homothetic contraction of beams center distribution in the output pupil according to the golden rule of imaging interlerometry”.," This technique makes it necessary to remap the input pupil taking care to apply an homothetic contraction of beams center distribution in the output pupil according to the ""golden rule of imaging interferometry""."962 Denoting 1/6 the pupil, Denoting $1/G$ the pupil963"In this well-known formula, B is the baseline length of each visibility point u, A the effective wavelength, and A the Airy function (Fourier transform of a uniform disk).","In this well-known formula, $\base$ is the baseline length of each visibility point $\vis{}$, $\lambda{}$ the effective wavelength, and $\airy{}$ the Airy function (Fourier transform of a uniform disk)."964" In the following, we assume an effective wavelength of 1.625um, as measured by Bauvir et al. ("," In the following, we assume an effective wavelength of $1.625\mu{}$ m, as measured by Bauvir et al. ("965private communication).,private communication).966 Results are plotted in Fig. 5.., Results are plotted in Fig. \ref{fig:tf}.967" Given the overall stability of the transfer function, we decided to average all points of a given setup, defined as the same night and the same detector integration time (DIT)."," Given the overall stability of the transfer function, we decided to average all points of a given setup, defined as the same night and the same detector integration time (DIT)."968 We used this average transfer function to calibrate all observed visibilities of the corresponding setup: The resulting calibrated visibilities are plotted against the baseline length in Fig. 6.., We used this average transfer function to calibrate all observed visibilities of the corresponding setup: The resulting calibrated visibilities are plotted against the baseline length in Fig. \ref{fig:diam}.969" To extract uniform disk diameters for each target, we fit the full µ(Β) data set with the expression A(@ B/A)."," To extract uniform disk diameters for each target, we fit the full $\vis(\base{})$ data set with the expression $\airy(\dUD{}\,\base/\lambda)$ ."970" Measured uniform disk diameters are summarized in Table 2,, as well as comparisonof previously published values."," Measured uniform disk diameters are summarized in Table \ref{tab:diam}, as well as comparisonof previously published values."971 All four measured diameters are within 596 of the previously published diameters., All four measured diameters are within $5\%$ of the previously published diameters.972 This was the goal of the study: the good agreement proves the capability of the FINITO/OPDC/RMNrec facility to provide meaningful interferometric visibility measurements., This was the goal of the study: the good agreement proves the capability of the FINITO/OPDC/RMNrec facility to provide meaningful interferometric visibility measurements.973" Interestingly, the transfer function is stable over several hours."," Interestingly, the transfer function is stable over several hours."974 It is one of the most important parameters in obtaining robust visibility measurements., It is one of the most important parameters in obtaining robust visibility measurements.975 Total uncertainty on our visibility points is difficult to estimate., Total uncertainty on our visibility points is difficult to estimate.976 We used the bootstrapping method to compute the contribution of the statistical dispersion inside each file., We used the bootstrapping method to compute the contribution of the statistical dispersion inside each file.977 This technique has the important advantage of not assuming a Gaussian distribution of the measurements., This technique has the important advantage of not assuming a Gaussian distribution of the measurements.978" Resulting statistical errors are very small, on the order of +0.1%, twhich is inside the symbol size of Fig. 5.."," Resulting statistical errors are very small, on the order of $\pm0.1\%$, twhich is inside the symbol size of Fig. \ref{fig:tf}. ."979 This does not explainthe, This does not explainthe980"EUNIS comprises two independent, spatially co-aligned telescope/spectrographs of identical optical design, one covering EUV lines between 300 and 370 seen in first order (LW channel), and a second covering lines between 170 and 205 seen in second order channel)","EUNIS comprises two independent, spatially co-aligned telescope/spectrographs of identical optical design, one covering EUV lines between 300 and 370 seen in first order (LW channel), and a second covering lines between 170 and 205 seen in second order (SW channel)."981 Each telescope is a 110-mm diameter off-axis(SW parabola that forms a real image on a precision slit formed from single-crystal silicon wafer using a technique developeda at GSFC., Each telescope is a 110-mm diameter off-axis parabola that forms a real image on a precision slit formed from a single-crystal silicon wafer using a technique developed at GSFC.982" The slit image is dispersed, magnified and reimaged by a toroidal grating onto the entrance face of a microchannel plate (MCP) intensifier."," The slit image is dispersed, magnified and reimaged by a toroidal grating onto the entrance face of a microchannel plate (MCP) intensifier."983" Each slit has a *dumbbell"" configuration."," Each slit has a “dumbbell"" configuration."984" The center 660"" is a conventional narrow slit (2).", The center $^{''}$ is a conventional narrow slit $^{''}$ ).985" Above and below the narrow slit is a 150"" x200' “lobe” that acts as a slitless spectrograph to produce monochromatic context images in strong emission lines."," Above and below the narrow slit is a $^{''}\times$ $^{''}$ “lobe"" that acts as a slitless spectrograph to produce monochromatic context images in strong emission lines."986 These images have proven to be extremely useful for coaligning EUNIS spectra with other instruments., These images have proven to be extremely useful for coaligning EUNIS spectra with other instruments.987 EUNIS has a designed first-order spectral dispersion of 25 ppixel! and a designed spatial scale of 0” .927 pixel-! (Thomas&Davila, EUNIS has a designed first-order spectral dispersion of 25 $^{-1}$ and a designed spatial scale of $^{''}$ .927 $^{-1}$ \citep{tho01}.988" For the flight of EUNIS-06, its optics limited the 2001)..actual spatial resolution to about 5” and the measured spectral resolution was ~200 and ~100 FFWHM in the LW and SW channels."," For the flight of EUNIS-06, its optics limited the actual spatial resolution to about $^{''}$ and the measured spectral resolution was $\sim$ 200 and $\sim$ 100 FWHM in the LW and SW channels."989" For the flight of EUNIS-07, the lobe-slit fields of view (FOVs) were oriented North-South near the center of the solar disk."," For the flight of EUNIS-07, the lobe-slit fields of view (FOVs) were oriented North-South near the center of the solar disk."990 In this flight all observations were made in scanning mode., In this flight all observations were made in scanning mode.991 The solar image was scanned perpendicular to the slit at a continuous rate of about 2.4 s-! with full spectral images on all detectors recorded every 1.3 s (maximum frame rate)., The solar image was scanned perpendicular to the slit at a continuous rate of about $^{''}$ $^{-1}$ with full spectral images on all detectors recorded every 1.3 s (maximum frame rate).992" Pointing began at nominal field center, scanned eastward to —50"", reversed, scanned westward to 450, and returned to center."," Pointing began at nominal field center, scanned eastward to $-$ $^{''}$, reversed, scanned westward to $+$ $^{''}$, and returned to center."993" This operation was repeated until the door was closed, giving almost 7 complete 660"" x100"" spectroheliograms in addition to 253 lobe images in LW channel and 256 in SW channel."," This operation was repeated until the door was closed, giving almost 7 complete $^{''}\times$ $^{''}$ spectroheliograms in addition to 253 lobe images in LW channel and 256 in SW channel."994" All of the raw data were processed with several routine adjustments, including dark image subtraction, flat-fielding and non-linearity correction before being converted from the recorded Data Numbers (DN) into Relative Exposure Units (REU), which are then used in all subsequent analyses."," All of the raw data were processed with several routine adjustments, including dark image subtraction, flat-fielding and non-linearity correction before being converted from the recorded Data Numbers (DN) into Relative Exposure Units (REU), which are then used in all subsequent analyses."995" EIS has both imaging (40 and 266” slots) and spectroscopic (1"" and 2"" slits) capabilities, in the short wavelength (SW) range of 170—210 aand the long wavelength (LW) range of 250—290 A."," EIS has both imaging $^{''}$ and $^{''}$ slots) and spectroscopic $^{''}$ and $^{''}$ slits) capabilities, in the short wavelength (SW) range of $-$ 210 and the long wavelength (LW) range of $-$ 290."996. EIS has a spectral resolution of about 55 aand a spatial resolution of about 3-4” per pixel., EIS has a spectral resolution of about 55 and a spatial resolution of about $^{''}$ per pixel.997 Its spectroscopic mode can operate in a rastering mode (repeated exposures while scanning over the observation target) or a sit-and-stare mode (repeated exposures at the same spatial location)., Its spectroscopic mode can operate in a rastering mode (repeated exposures while scanning over the observation target) or a sit-and-stare mode (repeated exposures at the same spatial location).998 TheHinode spacecraft tracks the solar rotation., The spacecraft tracks the solar rotation.999 The EIS observations were conducted on 2007 November 6 using EIS Study 209Cross., The EIS observations were conducted on 2007 November 6 using EIS Study 209.1000"Calibration. Two rastered images were obtained using 2""x512 slit at 60 or 61 positions with 50 s exposures.", Two rastered images were obtained using $^{''}$$\times$ $^{''}$ slit at 60 or 61 positions with 50 s exposures.1001" One began at 17:09:41 and ended at 18:00:43 UT prior to the EUNIS flight, and the other from 18:02:41 to 18:54:34 UT started during the EUNIS flight."," One began at 17:09:41 and ended at 18:00:43 UT prior to the EUNIS flight, and the other from 18:02:41 to 18:54:34 UT started during the EUNIS flight."1002 The EIS sequence includes 5 spectral windows in SW covering nearly the full spectrum and 17 windows in LW covering selected spectral lines., The EIS sequence includes 5 spectral windows in SW covering nearly the full spectrum and 17 windows in LW covering selected spectral lines.1003" The raw data were processed by the standard routineprep provided by SolarSoftWare (SSW) to remove detector bias and dark current, hot pixels, and cosmic rays, and to make absolute radiometric calibration."," The raw data were processed by the standard routine provided by SolarSoftWare (SSW) to remove detector bias and dark current, hot pixels, and cosmic rays, and to make absolute radiometric calibration."1004 The EIS slit tilt and orbital variation in the line centroids were also removed from the data., The EIS slit tilt and orbital variation in the line centroids were also removed from the data.1005" The pointing between EIS SW and LW detectors has offsets of 2"" in the x-direction and about in the y-direction (Youngetal.2007).", The pointing between EIS SW and LW detectors has offsets of $^{''}$ in the x-direction and about $^{''}$ in the y-direction \citep{you07}.1006. The CDS includes a Normal Incidence Spectrometer (NIS) that can be used to obtain stigmatic EUV spectra within its 308—381 ((NIS 1) and 513—633 ((NIS 2) wavebands along its 240” long slit., The CDS includes a Normal Incidence Spectrometer (NIS) that can be used to obtain stigmatic EUV spectra within its $-$ 381 (NIS 1) and $-$ 633 (NIS 2) wavebands along its $^{''}$ long slit.1007" Several slit widths are available, the most commonly used being 4""."," Several slit widths are available, the most commonly used being $^{''}$."1008 'The instrument can be operated in sit-and-stare mode or a rastering mode., The instrument can be operated in a sit-and-stare mode or a rastering mode.1009" In the latter acase, the CDS scans a region of the Sun from the West to East without compensation for solar rotation, thus the actual FOV"," In the latter case, the CDS scans a region of the Sun from the West to East without compensation for solar rotation, thus the actual FOV"1010no beaming (b~ 0.5) except for the very. brightest. ULXs (Lx—107 +).,no beaming $b \sim 0.8$ ) except for the very brightest ULXs $L_X = 10^{41}$ $^{-1}$ ).1011 Here beaming approaches10. since InGQU/Ae) cannot realistically exceed 10. and Le is similarly limited to a few times 107 ss (," Here beaming approaches, since $\ln(\dot M/\dot M_E)$ cannot realistically exceed 10, and $L_E$ is similarly limited to a few times $10^{39}$ $^{-1}$. ("1012"b) tvpical ULXs with Ly=107Lay sLand em can be explained in either of two wavs: neutron star binaries accreting at ~100 times their Eddington rates. Le at M73105M. vet, or black hole binaries accreting at ~40 times their Eddington rates. Lc. at M=L010M.νε|.","b) typical ULXs with $L_X = 10^{40}L_{40}$ $^{-1}$ and $R\simeq 10^9$ cm can be explained in either of two ways: neutron star binaries accreting at $\sim 100$ times their Eddington rates, i.e at $\dot M \sim 3\times 10^{-6}\msun\, {\rm yr}^{-1}$ , or black hole binaries accreting at $\sim 40$ times their Eddington rates, i.e. at $\dot M = 1.0\times 10^{-5}\msun\, {\rm yr}^{-1}$."1013 ] note that both required accretion rates are explicable in terms of thermaltimescale mass transfer., I note that both required accretion rates are explicable in terms of thermal–timescale mass transfer.1014 “Phis occurs when a hieh or intermediatemass radiative star transfers mass to a less massive companion. and gives rates AE~Bo10“SmsPALove Ll where me is the companion mass in AL. (Ixing DBegelman. 1999).," This occurs when a high– or intermediate–mass radiative star transfers mass to a less massive companion, and gives rates $\dot M \sim 3\times101510^{-8}m_2^{2.6}\msun\, {\rm yr}^{-1}$ , where $m_2$ is the companion mass in $\msun$ (King Begelman, 1999)."1016 We thus require companion masses Alsz6M..10M. in the neutron.star and blackhole cases respectively. with blackhole masses slightly greater than 10M..," We thus require companion masses $M_2 \ga 6\msun, 10\msun$ in the neutron–star and black–hole cases respectively, with black–hole masses slightly greater than $10\msun$."1017 As emphasized by Ixing et al. (, As emphasized by King et al. (10182001). this tvpe of binary evolution predicts source lifetimes ancl numbers in good agreement with observation.,"2001), this type of binary evolution predicts source lifetimes and numbers in good agreement with observation."1019 Some very bright transicnts may be able to achieve these accretion rates during outbursts (cf Ixing. 2002).," Some very bright transients may be able to achieve these accretion rates during outbursts (cf King, 2002)."1020 This is likely to be the only wav of making ULXs in old stellar populations (ling et al.," This is likely to be the only way of making ULXs in old stellar populations (King et al.,"1021 1997). (, 1997). (1022"c) accretion of hydrogenpoor matter generally reduces the requirements for beaming still further. and is the most likely explanation for the very brightest. ULNS (Ly=104by ty, ","c) accretion of hydrogen–poor matter generally reduces the requirements for beaming still further, and is the most likely explanation for the very brightest ULXs $L_X = 10^{41}L_{41}$ $^{-1}$ )."1023Accretion from massive WolfRavet ἵνρο companions is the most likely origin. of these very. high luminosities. althoughother explanations are possible in rare cases (cf Wine Dehnen. 2005).," Accretion from massive Wolf–Rayet type companions is the most likely origin of these very high luminosities, althoughother explanations are possible in rare cases (cf King Dehnen, 2005)."1024the delay. too short.,"the delay, too short."1025 Truncating the disc further out forces the reprocessing region to appear at a larger distance from the X-ray source and determines the delay., Truncating the disc further out forces the reprocessing region to appear at a larger distance from the X-ray source and determines the delay.1026 Intrinsic cise lux expected for a standard accretion disc (Shakura&Svunvaev1973) was added to the reprocessed Hux. for each radius and time delay. to calculate the B band. response.," Intrinsic disc flux expected for a standard accretion disc \citep{shakura} was added to the reprocessed flux, for each radius and time delay, to calculate the B band response."1027 The curves shown in the middle plot of Fig., The curves shown in the middle plot of Fig.1028" 9. correspond to a face-on view (least smoothing at long time-scales). an intermediate viewing angle of 45"" and an edge-on view (most smoothing on long time-scales)."," \ref{transfer} correspond to a face-on view (least smoothing at long time-scales), an intermediate viewing angle of $45^o$ and an edge-on view (most smoothing on long time-scales)."1029 The inner truncation radius needed to produce a 6 day lag in cach case was 1950. 1550 and. 1300 I. respectively.," The inner truncation radius needed to produce a 6 day lag in each case was 1950, 1550 and 1300 $R_g$, respectively."1030 The third geometry corresponds to a Faved disc. illuminated bv a central X-ray source.," The third geometry corresponds to a flared disc, illuminated by a central X-ray source."1031 The region of the cise where the scale height increases presents a large area facing the illuminating source and dominates the reprocessed emission., The region of the disc where the scale height increases presents a large area facing the illuminating source and dominates the reprocessed emission.1032 This scenario can therefore produce a large lag without requiring a large inner truncation radius of the clise., This scenario can therefore produce a large lag without requiring a large inner truncation radius of the disc.1033 For the transfer function calculation. we assumed that the dise surface bends upwards sharply at a radius Z2; and the normal to the Dared surface makes an inclination angle α with respect to the plane of the flat section of the disc and has length 5.," For the transfer function calculation, we assumed that the disc surface bends upwards sharply at a radius $R_f$ and the normal to the flared surface makes an inclination angle $a$ with respect to the plane of the flat section of the disc and has length $S$."1034 We neglect. cilferences in emissivity and time delavs from clifferent vertical positions on the [are surface., We neglect differences in emissivity and time delays from different vertical positions on the flare surface.1035 The elective area of this regiono that receives emissionfrom a central primary source is di=(fySÜ|Dusina)H)cosade., The effective area of this region that receives emissionfrom a central primary source is $dA=(R_f\times S+S^2\sin{a}) \cos{a} d{\theta}$.1036 If 8 is the azimuthal angle on the dise from the projection of the line of sight. the celay from cach position is τ(θ}=C(1cos@sin?7) and the area seen by the observer is dA(r)/dr=(cosisinasin/cosecos)dA/d6défdr. where / ds the viewing angle with respect to the axis of symmetry of the disc.," If $\theta$ is the azimuthal angle on the disc from the projection of the line of sight, the delay from each position is $\tau(\theta)=R_f/c \quad (1-\cos{\theta}\sin{i})$ and the area seen by the observer is $dA'(\tau)/d\tau=(\cos{i}\sin{a}-\sin{i}\cos{a}\cos{\theta})dA/d\theta \quad d\theta/d\tau$, where $i$ is the viewing angle with respect to the axis of symmetry of the disc."1037 When 7ze the near side of the disc is seen [rom behind. which makes eL. negative. as the disc is assumed to be optically thick. this area does not contribute to the transfer function.," When $i>a$ the near side of the disc is seen from behind, which makes $dA'$ negative, as the disc is assumed to be optically thick, this area does not contribute to the transfer function."1038 The curves shown in the bottom panel of Lig, The curves shown in the bottom panel of Fig.1039 correspond to dillerent. viewing angles 7 and opening angles a., \ref{transfer} correspond to different viewing angles $i$ and opening angles $a$.1040" The strongest. smoothing shown is produced for @=70"" and i£=45"". requiring a value of Rp=315041."," The strongest smoothing shown is produced for $a=70^o$ and $i=45^o$, requiring a value of $R_f=3150R_g$."1041 The intermediate curves show cases where the opening anc inclination angles are similar so the near side of the [are disc is viewed almost edge-on., The intermediate curves show cases where the opening and inclination angles are similar so the near side of the flared disc is viewed almost edge-on.1042 In these cases the reprocessec flux concentrates only at the far side of the disc. which is viewed more face-on.," In these cases the reprocessed flux concentrates only at the far side of the disc, which is viewed more face-on."1043 For this reason the response is retarclec so the lag can increase while producing less long-term smoothing., For this reason the response is retarded so the lag can increase while producing less long-term smoothing.1044" The curves shown correspond to @=ij15"" and @=i45° with Hare radii of Ry=235044, ane Ry=27O00R,. respectively."," The curves shown correspond to $a=i=75^o$ and $a=i=45^o$ with flare radii of $R_f=2350R_g$ and $R_f=2700 R_g$, respectively."1045" The least amount of long-term smoothing is produced for face-on viewing angles. 7=0 in this case shown with an opening angle of e=45"" and a radius Ry=340072,."," The least amount of long-term smoothing is produced for face-on viewing angles, $i=0$ in this case shown with an opening angle of $a=45^o$ and a radius $R_f=3400R_g$."1046 We note that in all the transfer functions cleseribecl above. the required. lag of 6 days strongly limits the smoothing power below ~2.10τ Lz so the observed. ratio of N-rav versus D band PDS cannot' be reconstructed by a single transfer function.," We note that in all the transfer functions described above, the required lag of 6 days strongly limits the smoothing power below $\sim 2\times 10^{-7}$ Hz so the observed ratio of X-ray versus B band PDS cannot be reconstructed by a single transfer function."1047 This adds to the [ασ that the Bo band has slightly larger long-term variations in normalised. [lux than the N-ravs. which is hard to reconcile with a picture where these laree amplitude optical trenes are produced by reprocessing.," This adds to the fact that the B band has slightly larger long-term variations in normalised flux than the X-rays, which is hard to reconcile with a picture where these large amplitude optical trends are produced by reprocessing."1048 We therefore conclude that another source of long term optical variability must. exist ancl it is probably produced by the intrinsic optical emitting region., We therefore conclude that another source of long term optical variability must exist and it is probably produced by the intrinsic optical emitting region.1049 As shown in Arévaloectal.(2008) rapid optical variability. imprinted. by reprocessing on a long-term intrinsic Ductuation. can shift the CCE peak to the delay produced. by reprocessing. regardless of the delay between the long term fluctuations.," As shown in \cite{MR2251} rapid optical variability, imprinted by reprocessing on a long-term intrinsic fluctuation, can shift the CCF peak to the delay produced by reprocessing, regardless of the delay between the long term fluctuations."1050 This is true even if the long term. intrinsic Ductuations in the optical bands have much larger amplitude than those produced by reprocessing.," This is true even if the long term, intrinsic fluctuations in the optical bands have much larger amplitude than those produced by reprocessing."1051 Lt is therefore. possible that a small amount of the optical Lux is produced by reprocessing of X-rays at a [arge distance from the corona. while the rest of the optical emission anc variability are produced. intrinsically by the accretion disc ata cifferent radius.," It is therefore possible that a small amount of the optical flux is produced by reprocessing of X-rays at a large distance from the corona, while the rest of the optical emission and variability are produced intrinsically by the accretion disc at a different radius."1052 In this case. the measured lag is the inprint of X-ray reprocessing on optically thick material a some distance from the X-ray source. which produces the rapid optical variability ancl G-day delay.," In this case, the measured lag is the inprint of X-ray reprocessing on optically thick material at some distance from the X-ray source, which produces the rapid optical variability and 6-day delay."1053 We now estimate the possible location of the optical intrinsic and reprocesse emitting regions., We now estimate the possible location of the optical intrinsic and reprocessed emitting regions.1054" A qadiatively οποίοι, optically thick cise racliates approximately as a black body with a racially-depencen characteristic temperature and a total energv output define by the gravitational energy loss."," A radiatively efficient, optically thick disc radiates approximately as a black body with a radially-dependent characteristic temperature and a total energy output defined by the gravitational energy loss."1055 Assuming such a cise enits the optical Dux observed in wwe can calculate the location of the optical emitting regions., Assuming such a disc emits the optical flux observed in we can calculate the location of the optical emitting regions.1056 We used the prescription of Lux as a function of radius given in ‘Trevesetal.(1988). to caleulate the local temperature and optical band Lux for à mass of 3.10A1.., We used the prescription of flux as a function of radius given in \citet{trevesetal88} to calculate the local temperature and optical band flux for a mass of $3\times 10^{7} M_\odot$.1057 We fitted the cise aceretion rate in this formula to reproduce the observed optical [ux obtaining a value of mi=0.01 of the I5ddington value., We fitted the disc accretion rate in this formula to reproduce the observed optical flux obtaining a value of $\dot m=0.01$ of the Eddington value.1058 We note that this accretion rate is lower than that estimated [rom the bolometric Luminosity because it will only produce the thermal optical/Ii. emission from the accretion disc., We note that this accretion rate is lower than that estimated from the bolometric luminosity because it will only produce the thermal optical/IR emission from the accretion disc.1059 It does not include the fraction of power directed. into the corona (which results in X-ray emission) nor the additional LR llux directed into the line of sight hy reprocessing structures such as the torus., It does not include the fraction of power directed into the corona (which results in X-ray emission) nor the additional IR flux directed into the line of sight by reprocessing structures such as the torus.1060" The resulting (90:43) of the D band intrinsic disc emission is contained within τὸ (208) A,.", The resulting ) of the B band intrinsic disc emission is contained within 73 (208) $R_g$.1061 Given that the long termi variability is probably intrinsic to this optical emitting region. we estimate the relevant characteristic time-scales.," Given that the long term variability is probably intrinsic to this optical emitting region, we estimate the relevant characteristic time-scales."1062" At a radius of 10072,. which contains of the B and of the V tux. the dynamical time-scale (time it takes orbiting material to travel 1 rad. of a Weplerian orbit) is 6.7 hours."," At a radius of $R_g$ , which contains of the B and of the V flux, the dynamical time-scale (time it takes orbiting material to travel 1 rad of a Keplerian orbit) is 6.7 hours."1063 Optical variability is observed on time-scales of 300 clays. 1000 times longer thanthe dynamical timescale at this racius. so accretion rate Lluctuations on the local viscous time-scale are not an unreasonable source of this variability.," Optical variability is observed on time-scales of 300 days, $\sim 1000$ times longer thanthe dynamical timescale at this radius, so accretion rate fluctuations on the local viscous time-scale are not an unreasonable source of this variability."1064 “Phe viscous time-scale of a standard a-cise (Shakura&Svunvaeyv1973) is Tice=Lienα11R)7). sointhiscasea(4/R)=107.," The viscous time-scale of a standard $\alpha$ -disc \citep{shakura} is $T_{\rm visc}=T_{\rm dyn}/(\alpha(H/R)^2)$, so in this case $\alpha(H/R)^2=10^{-3}$."1065 Assuming a typical a=0.1 this implies a scale height-to- ratio f/f= 0.1. a relatively thick accretion clisc.," Assuming a typical $\alpha=0.1$ this implies a scale height-to-radius ratio $H/R=0.1$ , a relatively thick accretion disc."1066 Alternatively. this variability time-seale could correspond to the thermal time-scale of the thin disc. as discussedin kellyear. ," Alternatively, this variability time-scale could correspond to the thermal time-scale of the thin disc, as discussedin \\citet{liuht,kelly_optvar}. ."1067The location of the optical emission depends on the location of the X-ray source and the geometry. of, The location of the optical emission depends on the location of the X-ray source and the geometry of1068N. O. Weiss. and. J.-P. Zahn. as well as an anonymous referee. for reading this work and for their very constructive criticisms which greatly helped improve on the clarity of this paper.,"N. O. Weiss, and J.-P. Zahn, as well as an anonymous referee, for reading this work and for their very constructive criticisms which greatly helped improve on the clarity of this paper."1069 Following the work of Proudman (1956). the equations are first solved. in the main body. of the [uid then successively near the bottom. and. top boundaries.," Following the work of Proudman (1956), the equations are first solved in the main body of the fluid, then successively near the bottom and top boundaries."1070" In. the main body of the Duid. the viscous stresses are negligible. so that τι is independent of z. and the solutions are where x is defined such that In order to solve the problem near the lower boundary. lroudman introduces the stretebhed variable & such tha This recognizes the presence of a boundary layer with thickness. 8,-=E27cos.24g78."," In the main body of the fluid, the viscous stresses are negligible, so that $\bu$ is independent of $z$, and the solutions are where $\chi$ is defined such that In order to solve the problem near the lower boundary, Proudman introduces the stretched variable $\zeta$ such that This recognizes the presence of a boundary layer with thickness $\delta_{\nu} = \Enu^{1/2} \cos^{-1/2}\theta$."1071 opThe equations. (31)). become. to zeroth order in20 £7;χαἐν Note that these approximations are not. valid near the poles. where Iatitudinal derivatives may become important. and near the equator. where the thickness of the boundary laver 9 diverges.," The equations \ref{eq:31})) become, to zeroth order in $\Enu^{1/2}$ Note that these approximations are not valid near the poles, where latitudinal derivatives may become important, and near the equator, where the thickness of the boundary layer $\delta$ diverges."1072" Assuming that the whole svstem is rotating with angular velocity Qi, so that cllectively ΟιQn (this only calls for a slight re-definition of the Ekman number). matching with the boundary conditions at the bottom boundary requires that y= Qasr =lore +0."," Assuming that the whole system is rotating with angular velocity $\Omega_{\rm in}$ so that effectively $\Oc = \Omega_{\rm in}$ (this only calls for a slight re-definition of the Ekman number), matching with the boundary conditions at the bottom boundary requires that $\chi \rightarrow 0$ as $r\rightarrow 1$, or $\zeta1073\rightarrow 0$."1074 Moreover. the impermeable boundary condition requires that io=0 on the boundary. as well as διὗ=0.," Moreover, the impermeable boundary condition requires that $\psi = 0$ on the boundary, as well as $\ptl \psi/\ptl1075\zeta=0$."1076" The solution to equations (35)) which fulfills all these boundary concitions. and which is bounded as à.7x is where ey(9) remains to be determined. and As Cκπο, these functions must match onto the solution obtained. previously for the main body of the uid region so that is then easy to see that one must have This result can be combined with equation (37)) and vields the matching condition In order to study the boundary. laver. near the top boundary. another stretched variable is introcuced: The scaled. equations. are the same as before (cf equations 2r (35))): the boundary. conditions for the stream function are also the same as for the lower boundary when vU. but the differential rotation must now match onto that of the convection zone. so that where"," The solution to equations \ref{eq:tea3}) ) which fulfills all these boundary conditions, and which is bounded as $\zeta \rightarrow \infty$ is where $\psi_1(\theta)$ remains to be determined, and As $\zeta \rightarrow \infty$, these functions must match onto the solution obtained previously for the main body of the fluid region so that is then easy to see that one must have This result can be combined with equation \ref{eq:teabc1}) ) and yields the matching condition In order to study the boundary layer near the top boundary, another stretched variable is introduced: The scaled equations are the same as before (cf equations \ref{eq:tea4}) )); the boundary conditions for the stream function are also the same as for the lower boundary when $\chi1077\rightarrow 0$ , but the differential rotation must now match onto that of the convection zone, so that where"1078a particular. Ixepler. radius. (V(r).=VGadCAL/r) as has been observed in tomographic studies of other binaries.,a particular Kepler radius $V(r)=\sqrt{GM/r}$ ) as has been observed in tomographic studies of other binaries.1079 Note that the (wo arms are not perfectIv svmmetric. the arm in the upper right of the tomogram is slightly stronger.," Note that the two arms are not perfectly symmetric, the arm in the upper right of the tomogram is slightly stronger."1080 The presence of the companion star will perturb the disc material from thei circular Weplerian orbits in the outer disc. ultimately resulting in intersecting orbits outside the radius referred to as the tidal raclius (Paezvuski 1977).," The presence of the companion star will perturb the disc material from their circular Keplerian orbits in the outer disc, ultimately resulting in intersecting orbits outside the radius referred to as the tidal radius (Paczynski 1977)."1081" Lor IP Peg this occurs at ~0.7 £2, and is thought to represent the maximum radius of a quiescent disc.", For IP Peg this occurs at $\sim$ 0.7 $R_{L_1}$ and is thought to represent the maximum radius of a quiescent disc.1082 This tidal interaction is essential in extracting the angular momentum. transported outwards through the dise by viscous processes. from the dise via a tidal torque.," This tidal interaction is essential in extracting the angular momentum, transported outwards through the disc by viscous processes, from the disc via a tidal torque."1083 Hyvdrodynamic simulations (Sawada ct al., Hydrodynamic simulations (Sawada et al.1084 1986. Savonije et al.," 1986, Savonije et al."1085 1994. Heemskerk. 1904) and analytical work (Spruit et al.," 1994, Heemskerk 1994) and analytical work (Spruit et al."1086 LOST. Deani ct al.," 1987, Dgani et al."1087 1992) on this tidal interaction show that spiral waves. ancl even shocks. are expected to be generated in the accretion disc down to quite small racdii. depending on the Mach number of the disc How.," 1992) on this tidal interaction show that spiral waves, and even shocks, are expected to be generated in the accretion disc down to quite small radii, depending on the Mach number of the disc flow."1088 For hot accretion disces (low Mach numbers). these trailing waves can provide a steady mass transfer rate bv transporting angular momentum outwards without the need of intrinsic disc viscosity.," For hot accretion discs (low Mach numbers), these trailing waves can provide a steady mass transfer rate by transporting angular momentum outwards without the need of intrinsic disc viscosity."1089 For the high Mach numbers expected in CV dises. the elfective à is low. however (< 0.01). and is therefore. likely not. the ominant transpor mechanism in the inner disc. but will still dominate. the dynamics of the outer disc.," For the high Mach numbers expected in CV discs, the effective $\alpha$ is low, however $\leq$ 0.01), and is therefore likely not the dominant transport mechanism in the inner disc, but will still dominate the dynamics of the outer disc."1090 Alany Doppler maps have previously been constructe from observations of discs. but. those have never. shown obvious evidence for he spiral waves predicted. by theory.," Many Doppler maps have previously been constructed from observations of discs, but those have never shown obvious evidence for the spiral waves predicted by theory."1091 Our observations now or the first time provide observationa evidence for a two arncd trailing spiral in a cbwarf novae disc., Our observations now for the first time provide observational evidence for a two armed trailing spiral in a dwarf novae disc.1092 ‘To confirm whether a two armed spiral can indeed. produce the observed. line proiles. we constructed a Doppler map of a model cise cont:üning two symmetric trailing spiral arms. as shown in Lieure 2.," To confirm whether a two armed spiral can indeed produce the observed line profiles, we constructed a Doppler map of a model disc containing two symmetric trailing spiral arms, as shown in Figure 2."1093 This model assumes a two-armed. trailing spiral xdtern in the spatial line emissivity of the disce. covering t10 outer part of the dise between 0.4 and 0.9 ες (Figure 2. bottom).," This model assumes a two-armed trailing spiral pattern in the spatial line emissivity of the disc, covering the outer part of the disc between 0.4 and 0.9 $R_{L_1}$ (Figure 2, bottom)."1094 The velocity coordinates conserve its azimuthal shape. resulting in a model Doppler Lage with two spirals as well (Figure 2. micelle panel).," The velocity coordinates conserve its azimuthal shape, resulting in a model Doppler image with two spirals as well (Figure 2, middle panel)."1095 Note hat the model was oplimiusecl to reproduce the velocities of the observed. spirals., Note that the model was optimised to reproduce the velocities of the observed spirals.1096 The arms span ~110 in azimuth. and appear to be very open.," The arms span $\sim 110^{\circ}$ in azimuth, and appear to be very open."1097 The quoted radii corresponding o this are the Ixepler orbits that. limit the spirals., The quoted radii corresponding to this are the Kepler orbits that limit the spirals.1098 The wedieted. Line profiles of this model are shown in the top xunel and demonstratS a close resemblance to the observed data of Figure 1., The predicted line profiles of this model are shown in the top panel and demonstrates a close resemblance to the observed data of Figure 1.1099 The| kev signature is he mocdulation of he double peak separation., The key signature is the modulation of the double peak separation.1100 The two peaks measure the radial velocity of material on either side of the disc moving almost clirectly towards aid away from the observer., The two peaks measure the radial velocity of material on either side of the disc moving almost directly towards and away from the observer.1101 Their separation would be constant as a function of binary phase for an axisvmnmetric Ixeplerian) disc for example., Their separation would be constant as a function of binary phase for an axisymmetric (Keplerian) disc for example.1102 Note also the jump in velocity around: phase 0.7 where one crosses from one arm to the other., Note also the jump in velocity around phase 0.7 where one crosses from one arm to the other.1103 While general asvmmetries in the local emissivity can be produced by non circular orbits. the fact that it has the shape of a spiral strongly favors the interpretation that we are indeed seeing a spiral density wave in the outer disc.," While general asymmetries in the local emissivity can be produced by non circular orbits, the fact that it has the shape of a spiral strongly favors the interpretation that we are indeed seeing a spiral density wave in the outer disc."1104 As the orbits start to intersect pressure and viscous forces will setup density. waves ancl possibly even shocks., As the orbits start to intersect pressure and viscous forces will setup density waves and possibly even shocks.1105 ‘Tomography of the final stages of the outburst. about a week after our data (Steeghs et al.," Tomography of the final stages of the outburst, about a week after our data (Steeghs et al."1106 1996). reveals a similar asvmmetry pattern in the disc. most obviously in Hel. The much stronger companion star emission dominates over the disc emission and the fainter disc structure suggests the disc is shrinking and the tidal distortions are damping out.," 1996), reveals a similar asymmetry pattern in the disc, most obviously in HeI. The much stronger companion star emission dominates over the disc emission and the fainter disc structure suggests the disc is shrinking and the tidal distortions are damping out."1107 Simulations suggest large. hot discs are needed to generate strong waves (Savonije et al.," Simulations suggest large, hot discs are needed to generate strong waves (Savonije et al."1108 1994)., 1994).1109 Dwarf novae discs are considerably larger ancl hotter during outburst than in quiescence (e.g. Ichikawa Osaki 1992. Wood et al.," Dwarf novae discs are considerably larger and hotter during outburst than in quiescence (e.g. Ichikawa Osaki 1992, Wood et al."1110 1989) due to their high mass accretion rate state., 1989) due to their high mass accretion rate state.1111 Tical forces will therefore be similarly enhanced., Tidal forces will therefore be similarly enhanced.1112 A combination of those two factors (tempoerature and size) would explain why quiescent dises do no μα... o show such structure while (early) outburst clises do., A combination of those two factors (temperature and size) would explain why quiescent discs do not seem to show such structure while (early) outburst discs do.1113 Doppler mapping studies of dwarf novae in the early phase of outburst on several consecutive days. may be able to record he dynamical behaviour of the spiral waves.," Doppler mapping studies of dwarf novae in the early phase of outburst on several consecutive days, may be able to record the dynamical behaviour of the spiral waves."1114 The very start of the outburst is were the two competing models for the outburst. a disc instability (DI) on one hand (Osaki 1974) or a mass transfer burst CAELI) (Bath 1985) on the other. predict different disc behaviour.," The very start of the outburst is were the two competing models for the outburst, a disc instability (DI) on one hand (Osaki 1974) or a mass transfer burst (MTI) (Bath 1985) on the other, predict different disc behaviour."1115 In the MTI model. the sudden addition of low angular momentum gas causes the disc to shrink initially before. it grows. again through viscous forces.," In the MTI model, the sudden addition of low angular momentum gas causes the disc to shrink initially before it grows again through viscous forces."1116 In the DI model. the disc expands as soon as it switches to the high viscosity state at the onset of the outburst (e.g. Lehikawa Osaki 1992).," In the DI model, the disc expands as soon as it switches to the high viscosity state at the onset of the outburst (e.g. Ichikawa Osaki 1992)."1117 Our data suggests a large (almost filling the full Roche lobe). non Ixeplerian accretion disc. possiby exceeding its tidal radius. is present very early on in the «xitburst. and therefore favors a DI as the trigger of the outULES.," Our data suggests a large (almost filling the full Roche lobe), non Keplerian accretion disc, possibly exceeding its tidal radius, is present very early on in the outburst, and therefore favors a DI as the trigger of the outburst."1118 The tidal interaction manilestatec in the spiral pattern turns out to be an important factor for outburst disces., The tidal interaction manifestated in the spiral pattern turns out to be an important factor for outburst discs.1119 Work is now in progress to use different observations of this phenomenon in different emission lines and at different epochs to sample 16 physical conditions of the disc material, Work is now in progress to use different observations of this phenomenon in different emission lines and at different epochs to sample the physical conditions of the disc material.1120 Observing high ionization lines like Hell can show the presence of shocks and will indicate the implication for the angular momentum budget., Observing high ionization lines like HeII can show the presence of shocks and will indicate the implication for the angular momentum budget.1121 Furthermore future observations of disc structure in cillerent objects (with dilferent mass ratios and disc sizes) will provide us with a new insight in tidal theory ancl perhaps the outburst mechanism., Furthermore future observations of disc structure in different objects (with different mass ratios and disc sizes) will provide us with a new insight in tidal theory and perhaps the outburst mechanism.1122 In this wav warf novae cise provide an excellent. laboratory for tides in astrophysical discs. since the time scales of the outbursts lasting à week and recurring every couple of months. allows one to study the dvnamical behaviour of the disc ancl its," In this way dwarf novae disc provide an excellent laboratory for tides in astrophysical discs, since the time scales of the outbursts lasting a week and recurring every couple of months, allows one to study the dynamical behaviour of the disc and its"1123Clearly. our results will be different for dillerent assumptions about cosmological parameters.,"Clearly, our results will be different for different assumptions about cosmological parameters."1124 The code described in Spaans (1996) and applied as in Silk Spaans (1997). has been used to rerun the models oesented in (Silk&Spaans1997). with the latest atomic and molecular collision ancl chemistry data.," The code described in Spaans \shortcite{s96} and applied as in Silk Spaans \shortcite{ss}1125 has been used to rerun the models presented in \cite{ss} with the latest atomic and molecular collision and chemistry data."1126 These moclels use the Orion molecular eloud and its so-called bar region as cing representative of a region of active star formation., These models use the Orion molecular cloud and its so-called bar region as being representative of a region of active star formation.1127 The star formation rate in A. vr.+ of a fiducial model galaxy is hen related to the total number of Orion-like star formation sites through division by the average star formation rate of he Orion region. 3.LO1 AZ. + (Llillenbrand.1997).," The star formation rate in $M_\odot$ $^{-1}$ of a fiducial model galaxy is then related to the total number of Orion-like star formation sites through division by the average star formation rate of the Orion region, $\sim 3\times 10^{-4}$ $M_\odot$ $^{-1}$ \cite{h97}."1128. In Silk Spaans (L997) it has been shown that the CMD »ecomes an important source of excitation at high redshif »ecause Of the fortuitous coincidence between the €O [eve spacing and the 1|z increase in the CAIB temperature., In Silk Spaans \shortcite{ss} it has been shown that the CMB becomes an important source of excitation at high redshift because of the fortuitous coincidence between the CO level spacing and the $1+z$ increase in the CMB temperature.1129 ‘This causes galaxies at 2=5 and z=10 to be observable a similar (lux density levels. provided they in fact are present.," This causes galaxies at $z=5$ and $z=10$ to be observable at similar flux density levels, provided they in fact are present."1130 Lt has been assumed that the Orion-like regions responsible for the star formation activity occur throughout the moce galaxy. ancl are not all confined to the inner few LOO pe as in Combes. Maoli. Omont (1999) ‘This assumption decreases the mean optical depth of the CO lines and is most likely to hold at high (2> 3) redshifts. when galaxies are still being built up through mergers and accretion.," It has been assumed that the Orion-like regions responsible for the star formation activity occur throughout the model galaxy, and are not all confined to the inner few 100 pc as in Combes, Maoli, Omont \shortcite{cmo}1131 This assumption decreases the mean optical depth of the CO lines and is most likely to hold at high $z>3$ ) redshifts, when galaxies are still being built up through mergers and accretion."1132" In order to compute the spectrum of CO emission. as a [function of wavelength. for a given bandwidth A,<A<Ay and a given transition /*J—l. we identify a range of cosmological scale factors a,«aas that correspond to our bandwidth."," In order to compute the spectrum of CO emission as a function of wavelength, for a given bandwidth $\lambda_1<\lambda<\lambda_2$ and a given transition $J\rightarrow J-1$, we identify a range of cosmological scale factors $a_1<a<a_2$ that correspond to our bandwidth."1133 This range of scale factors in turn corresponds to the range of comoving distances wyorore., This range of scale factors in turn corresponds to the range of comoving distances $x_1<x<x_2$.1134 However. due to periodic boundary conditions adopted in the simulations. we cannot always model this range of comoving distances directly - if it is large enough. it will correspond to more than one box size.," However, due to periodic boundary conditions adopted in the simulations, we cannot always model this range of comoving distances directly - if it is large enough, it will correspond to more than one box size."1135 IE we simply stack a sullicient number of simulation boxes together. we will eet an unphysical result. duc to periodicitv.," If we simply stack a sufficient number of simulation boxes together, we will get an unphysical result due to periodicity."1136 In. order to break this periodicitv. we use the approach deseribed in CGnedin Jalfe (2001): we randomize the neighboring boxes by randomly Hipping. transposing. and shifting cach of the periodic images of the computational box.," In order to break this periodicity, we use the approach described in Gnedin Jaffe \shortcite{gj}: we randomize the neighboring boxes by randomly flipping, transposing, and shifting each of the periodic images of the computational box."1137 Figure 1 serves to illustrate the uncertainty of our calculations due to the finite size of the computational box and finite numerical resolution. as measured by the cilference between the two simulations A and D. In addition. since both simulations were stopped at z=4. a contribution from later redshifts cannot be included.," Figure \ref{figAE} serves to illustrate the uncertainty of our calculations due to the finite size of the computational box and finite numerical resolution, as measured by the difference between the two simulations A and B. In addition, since both simulations were stopped at $z=4$, a contribution from later redshifts cannot be included."1138 In order to estimate the ellect of this contribution. we caleulated the CO emission for two cases: no star formation after z=4. ancl constant star formation after z=4.," In order to estimate the effect of this contribution, we calculated the CO emission for two cases: no star formation after $z=4$, and constant star formation after $z=4$."1139 The dillerence between those two cases quantifies the uncertainty due to the finite value for the final redshift of our simulation., The difference between those two cases quantifies the uncertainty due to the finite value for the final redshift of our simulation.1140 For À«0.3em our calculation is not reliable even in à qualitative sense (to within a factor of 2)., For $\lambda<0.3\dim{cm}$ our calculation is not reliable even in a qualitative sense (to within a factor of 2).1141 At higher wavelengths finite numerical resolution still prevents us [rom achieving better than about accuracy., At higher wavelengths finite numerical resolution still prevents us from achieving better than about accuracy.1142 More than that. since the star formation rate in our simulations is normalized to the observed value at 2=4. which is in turn uncertain to at least a factor of two (Nagamine.Cen.&Ostriker2000:Steideletal. 1909).. our results in general are uncertain to a [actor of two to three.," More than that, since the star formation rate in our simulations is normalized to the observed value at $z=4$, which is in turn uncertain to at least a factor of two \cite{nce,sea}, our results in general are uncertain to a factor of two to three."1143 Llowever this is quite sullicient. for our purpose. which is to emphasize the possibilities rather than to make some definite predictions.," However this is quite sufficient for our purpose, which is to emphasize the possibilities rather than to make some definite predictions."1144 Because ALALA will not be commissioned until about 2010. theorists have plenty of time to improve upon our calculations and come up with more definitive predictions.," Because ALMA will not be commissioned until about 2010, theorists have plenty of time to improve upon our calculations and come up with more definitive predictions."1145 Figure 2. shows the evolution of the mean mass-weighted metallicity. of the eas and stars in our large simulation (run A)., Figure \ref{figZA} shows the evolution of the mean mass-weighted metallicity of the gas and stars in our large simulation (run A).1146 One can see that stars quickly eain a metallicity of solar by 2~15. and then gain another order of magnitude on average by the end of the simulation at z=4.," One can see that stars quickly gain a metallicity of solar by $z\sim15$, and then gain another order of magnitude on average by the end of the simulation at $z=4$."1147 The metallicity of the gas is abvays lower than stellar. but. increases more rapidly.," The metallicity of the gas is always lower than stellar, but increases more rapidly."1148 The decrease in stellar. metallicities at higher redshifts slightly mitigates the increase in the CO emission due to higher CMD temperature. however it is not sullicient to completely remove the negative Ix-correction. and. thus high redshift," The decrease in stellar metallicities at higher redshifts slightly mitigates the increase in the CO emission due to higher CMB temperature, however it is not sufficient to completely remove the negative K-correction, and thus high redshift"1149iudex results is plotted as a liue aud also presented in Table 1..,index results is plotted as a line and also presented in Table \ref{tab1}.1150 The er‘ors [listed »elow the iuclex entries in Table 1 are indicative errors for the sum of data points near each tzvbulated radius., The errors listed below the index entries in Table \ref{tab1} are indicative errors for the sum of data points near each tabulated radius.1151 That is to say. they are larger than the formal error from the curve fi.," That is to say, they are larger than the formal error from the curve fit."1152I t was iought that the data-basecl error was more appropriate since many curves could be fit. eiviug a spread of results despite fo‘wally small errors.," It was thought that the data-based error was more appropriate since many curves could be fit, giving a spread of results despite formally small errors."1153 Table 2. weights the Table 1 results by suTac'e brieliness alid radius ο situtlate the iudex. value measured inside a circular aperture., Table \ref{tab2} weights the Table \ref{tab1} results by surface brightness and radius to simulate the index value measured inside a circular aperture.1154 The |:isl entry i1 Table 2 Is an extrapolajon to two effective racii. or about of light enclosed assnine aur tél exponential »rofile.," The last entry in Table \ref{tab2} is an extrapolation to two effective radii, or about of light enclosed assuming an $r^{1/4}$ exponential profile."1155 Coupariug iudices 1 COMO1 with C03. we note that. as C93 predicted because of a chronatic ocus p‘oblem aud. nigh-sky lines at Lick Observatory. Fe5015. Mey. auc Mes drift quite a lot.," Comparing indices in common with G93, we note that, as G93 predicted because of a chromatic focus problem and night-sky lines at Lick Observatory, Fe5015, $_1$, and $_2$ drift quite a lot."1156 Other indices match well. except ‘or À& b. discussed imunediately below.," Other indices match well, except for Mg $b$, discussed immediately below."1157 C'adieut streuetlis 1ratch yetweel the data ses except lor Hj axl Fe5270. for which we obtain shalower slopes.," Gradient strengths match between the data sets except for $\beta$ and Fe5270, for which we obtain shallower slopes."1158 Fits to all of the daa with liles |dicae. via the F-test. that Ca1227. Call55. H94. ane Hey are statistically cousistei twithavalue hat is constant rather than sloped with radius.," Fits to all of the data with lines indicate, via the $F$ -test, that Ca4227, Ca4455, $\delta_A$, and $\gamma_F$ are statistically consistent with a value that is constant rather than sloped with radius."1159 Fits tol igher order polyuomiials itdicate. even or tese {οu. statistically better fits at 1igher order.," Fits to higher order polynomials indicate, even for these four, statistically better fits at higher order."1160 However. I decided agaiust polynomials more CollXicatede t1an a quadratic to model tie racial trends (except Co L668. for whieh a cubic was ir'es]sible).," However, I decided against polynomials more complicated than a quadratic to model the radial trends (except $_2$ 4668, for which a cubic was irresistible)."1161" vote that the fact that I lind few coustaut indices is not inconsistent with delBurgoetal.(2001).. Ww10 detected no radial gradieuts in αν index. since their ¢ala go to a rac of5"".. equlvaent to the irst SIX points in Figure 3.. auc with larger errors."," Note that the fact that I find few constant indices is not inconsistent with \citet{delburgo01}, who detected no radial gradients in any index, since their data go to a radius of, equivalent to the first six points in Figure \ref{fig3ab}, and with larger errors."1162 Over tis spatial rauge. only the CN indices 5LOW a strong deviation [rom coustant behavior.," Over this spatial range, only the CN indices show a strong deviation from constant behavior."1163 There is no hiut that any stelar population feature inalifests itself at the clcliscotintuty in tlie suface brightness profile., There is no hint that any stellar population feature manifests itself at the discontinuity in the surface brightness profile.1164 Te near-nuclear drop of the CN iudices is surprisiug. given tie lack of auy such feature iu aby other iudex. aud it may or may not be real.," The near-nuclear drop of the CN indices is surprising, given the lack of any such feature in any other index, and it may or may not be real."1165 If it is due mostv toa drop in N abuudance. hen te violet NH feature eradieut data of Davidgeetal.(1990) provide5 sup»ort for its reality since this gradieut is aso negative.," If it is due mostly to a drop in N abundance, then the violet NH feature gradient data of \citet{dav90} provides support for its reality since this gradient is also negative."1166" However. whereas the present cla aset turns over at 1-5 arcsec. he Davidgeetal.(1990) data keep clitubing to the limit of their data at cAvL1""..."," However, whereas the present data set turns over at 4-5 arcsec, the \citet{dav90} data keep climbing to the limit of their data at $\approx$."1167 Flattening is ;»ossible. eiven the error bars. so the two data sets may agree.," Flattening is possible, given the error bars, so the two data sets may agree."1168 Alteriativel:v. future modeling may indicate that age ellects dominate over abuudauce ellects I “the NH iudex. atd iu that case we should expect it to weaken toward the nucleus [rom straig1lforwarc Sese agesoraclieit effects.," Alternatively, future modeling may indicate that age effects dominate over abundance effects for the NH index, and in that case we should expect it to weaken toward the nucleus from straightforward age gradient effects."1169 Clearly. his issue is oue that should be resolved with further observalon.," Clearly, this issue is one that should be resolved with further observation."1170 Greater than 16 zero-point discrepancies occur betweet his data set and the original Lick/IDS 132 nuclear data for iudices Mg 6 and. Fe5709., Greater than 1 $\sigma$ zero-point discrepancies occur between this data set and the original Lick/IDS M32 nuclear data for indices Mg $b$ and Fe5709.1171 Indices . Mg». aud Na D also were initially somewhat cdiscrepaut. but a second aualysis pass mocliliec he systematic Corrections (based ou stars and represented by arrows in Figure 3)) that were appied.," Indices $_1$, $_2$, and Na D also were initially somewhat discrepant, but a second analysis pass modified the systematic corrections (based on stars and represented by arrows in Figure \ref{fig3ab}) ) that were applied."1172 The relatively large corrections lor Mey and Mes are expected because they are very broad aud subject to the effects of instrumeutal response more tlian other indices., The relatively large corrections for $_1$ and $_2$ are expected because they are very broad and subject to the effects of instrumental response more than other indices.1173 Of tle persistently discrepant iudices Fe52709 has uo measurements from other sources besides Lick/IDS. so it is hard to assess which data source might be in error.," Of the persistently discrepant indices Fe5709 has no measurements from other sources besides Lick/IDS, so it is hard to assess which data source might be in error."1174be subtle svstematic errors that could. distort. the results or in any case render the results very poorly. constrained.,be subtle systematic errors that could distort the results or in any case render the results very poorly constrained.1175 This has triggered. olf the recent debate concerning the reliability. of the cata and how well the mass models. are really constrained., This has triggered off the recent debate concerning the reliability of the data and how well the mass models are really constrained.1176 There are claims that the observations could actually be consistent with the dark matter density profiles. predicted. by the CDAL simulations. not only hy considering the data alone (vandenBoschetal.2000 and vandenBosch&Swaters 2001)). but also by combining La and data (Primack2002 and Swatersetal.2003a)).," There are claims that the observations could actually be consistent with the dark matter density profiles predicted by the CDM simulations, not only by considering the data alone \citealt{vdB:00} and \citealt{vdBS:01}) ), but also by combining $\alpha$ and data \citealt{P:02} and \citealt{S:03}) )."1177 This is the reason why particular care should be taken in choosing a suited sample and in performing the data analysis., This is the reason why particular care should be taken in choosing a suited sample and in performing the data analysis.1178 Note iu recent simulations (e.g. Navarroctal. 2003)) do not 'onverge to a well-defined: value of the inner slope down to 16 resolution limit (about 1 kpe). even though the slope of 1edark matter density profile (defined as dlap/dlor) at of the virial radius is still about 1.2 fora typical galaxy.," Note that recent simulations (e.g. \citealt{N:03}) ) do not converge to a well-defined value of the inner slope down to the resolution limit (about 1 kpc), even though the slope of thedark matter density profile (defined as $ -d{\rm ln}\rho/d{\rm ln}r$ ) at of the virial radius is still about 1.2 for a typical galaxy."1179 otice also that the observational results on spiral galaxies garow a discrepancy with the standard ACDAL predictions =vell bevond | προ ie. well bevond the resolution limit of 1e simulations.," Notice also that the observational results on spiral galaxies show a discrepancy with the standard $\Lambda$ CDM predictions well beyond 1 kpc, i.e. well beyond the resolution limit of the simulations."1180 In this paper we study a of galaxy. rotation curves ideal for deriving the properties of the dark matter aloes around galaxies: it Consists of five late-tvpe bulge-less normal (high surface brightness) spiral galaxies: compared o the sample of Dorriello&Salucci(2001) we have the same resolution in the central regions. but a larger spatial extension allowing us to determine the size of the core raclii.," In this paper we study a of galaxy rotation curves ideal for deriving the properties of the dark matter haloes around galaxies; it consists of five late-type bulge-less normal (high surface brightness) spiral galaxies; compared to the sample of \citet{BS:01} we have the same resolution in the central regions, but a larger spatial extension allowing us to determine the size of the core radii."1181 One of the main concerns is that the rotation curve has both a high spatial resolution and a large extension. i.c. bevond the optical radius: this is tvpically achieved: by combining optical (La) and radio (111) data (see e.g. deBlok&Bosma2002. and Swatersctal. 2003a)).," One of the main concerns is that the rotation curve has both a high spatial resolution and a large extension, i.e. beyond the optical radius; this is typically achieved by combining optical $\alpha$ ) and radio ) data (see e.g. \citealt{dBB:02} and \citealt{S:03}) )."1182 The former provide the necessary high resolution (1... 27) while the latter allow us to trace the potential out to large radii. twpically 23 times the optical radius.," The former provide the necessary high resolution $\arcsec \dots 2 \arcsec$ ) while the latter allow us to trace the potential out to large radii, typically 2–3 times the optical radius."1183 It has been known for a long time that data usually suller from the lack of resolution. which can allect the results. especially in the innermost parts: this problem is nicely reviewed by vandenBoschetal.(2000).," It has been known for a long time that data usually suffer from the lack of resolution, which can affect the results, especially in the innermost parts; this problem is nicely reviewed by \citet{vdB:00}."1184 The cilliculty in deriving reliable rotation curves [rom data cubes resides in the fact that a data cube is 4-dimensional (lA. dec. tux density and. racial velocity). while the rotation curve is 2-cimensional (rotation velocity vs. radius).," The difficulty in deriving reliable rotation curves from data cubes resides in the fact that a data cube is 4-dimensional (RA, dec, flux density and radial velocity), while the rotation curve is 2-dimensional (rotation velocity vs. radius)."1185 This means that starting from the data cube we have to take into account two tvpes of considerations: one concerning the in which the rotation curve should be traced. i.e. how to reduce the spatial dimensions [ron (RA. Dec) to galactocentric radius.," This means that starting from the data cube we have to take into account two types of considerations: one concerning the in which the rotation curve should be traced, i.e. how to reduce the spatial dimensions from (RA, Dec) to galactocentric radius."1186 Fhis is usually achieved by taking the position-velocity diagram along the major axis or by fitting concentric ellipses around the centre. (tilted-ring modelling of the velocity field)., This is usually achieved by taking the position-velocity diagram along the major axis or by fitting concentric ellipses around the centre (tilted-ring modelling of the velocity field).1187 Phe other consideration concerns the that should be attributed to these galactocentrie radii: at the positions delined above we want to associate only one of the possible velocities that could in principle be derived from the spectra at single points (Ilux censity vs. radial velocity). i.e. the radial component of the rotation velocity at that racius.," The other consideration concerns the that should be attributed to these galactocentric radii: at the positions defined above we want to associate only one of the possible velocities that could in principle be derived from the spectra at single points (flux density vs. radial velocity), i.e. the radial component of the rotation velocity at that radius."1188 Εις is usually done via clifferent methods. most of them assuming symmetry of the profiles. like the first-momoent analysis (the intensity weighted mean). or the single Gaussian fitting: therefore. when the profiles are not symmetric. Le. in galaxies with a high inclination and/or a poor to intermediate resolution. these methods cannot be applied.," This is usually done via different methods, most of them assuming symmetry of the profiles, like the first-moment analysis (the intensity weighted mean), or the single Gaussian fitting; therefore, when the profiles are not symmetric, i.e. in galaxies with a high inclination and/or a poor to intermediate resolution, these methods cannot be applied."1189 We have developed. a new method. for both of these considerations: a) concerning the positions. we traced. the rotation curve along the ridge of the warp (this step is discussed in Verganietal.2004)). when the velocity Lele was not sullicienthy sampled. (.e.. for the galaxies ESO 116-CG12. ESO 2s7-G13. ESO 79-GI4 and NGC 7339) and the tilted-ring modelling of the velocity field was therefore no possible: b) for the velocities we only. considered the velocity SLe of the profiles opposite to the systemic velocity. anc then corrected. for the effects that artificially broaden the profile. i.e: the turbulence of the ISM. the instrumenta velocity resolution ancl the beam-broadening.," We have developed a new method for both of these considerations: a) concerning the positions, we traced the rotation curve along the ridge of the warp (this step is discussed in \citealt{V:04}) ), when the velocity field was not sufficiently sampled (i.e., for the galaxies ESO 116-G12, ESO 287-G13, ESO 79-G14 and NGC 7339) and the tilted-ring modelling of the velocity field was therefore not possible; b) for the velocities we only considered the velocity side of the profiles opposite to the systemic velocity, and then corrected for the effects that artificially broaden the profile, i.e.: the turbulence of the ISM, the instrumental velocity resolution and the beam-broadening."1190 “Phe presen paper concentrates on step hb)., The present paper concentrates on step b).1191 When both steps a) and b) were applied. we callec our method WAMISZTE (WaArped Modified Envelope Tracing method): when only step b) was applied and a velocity fiel was constructed (io. when the velocity Bele was sullicientlv sampled. the case of NGC 1090) we called our method MATE (Modified. Envelope “Tracing method).," When both steps a) and b) were applied we called our method WAMET (WArped Modified Envelope Tracing method); when only step b) was applied and a velocity field was constructed (i.e., when the velocity field was sufficiently sampled, the case of NGC 1090) we called our method MET (Modified Envelope Tracing method)."1192 οσο approaches were tested. by constructing artificial cata cubes based on geometrical models. of the dise that were iteratively compared to the observed data cubes., These approaches were tested by constructing artificial data cubes based on geometrical models of the disc that were iteratively compared to the observed data cubes.1193 The MITP/WAMIET method: proves to provide a better initial estimate of the rotation curve then more traditional methods. such as the first-moment analvsis and the sinele-Caussian fitting.," The MET/WAMET method proves to provide a better initial estimate of the rotation curve then more traditional methods, such as the first-moment analysis and the single-Gaussian fitting."1194 Alodelling the data cubes results in a powerful way to test and improve the derived. rotation curves. as shown c.g. by Gentileetal.(2003).," Modelling the data cubes results in a powerful way to test and improve the derived rotation curves, as shown e.g. by \cite{Gea:03}."1195. This work is structured as follows: in Section 2 we present the sample ancl optical data that were used in this study. in Section 3 we describe the observations and the data reduction and Section 4 shows the data analysis: in Section 5 we present the results of cata analysis. the new method for extracting the rotation curves is shown in Section 6 and the comparison between the observed anc the modelled clata cubes is presented in Section 7.," This work is structured as follows: in Section 2 we present the sample and optical data that were used in this study, in Section 3 we describe the observations and the data reduction and Section 4 shows the data analysis; in Section 5 we present the results of data analysis, the new method for extracting the rotation curves is shown in Section 6 and the comparison between the observed and the modelled data cubes is presented in Section 7."1196 In Section SN we introduce the dillerent mass models that were considered: the results of the mass decompositions are shown in Section ϱ and in Section LO we draw the conclusions concerning the derivation of the rotation curves and the dark matter haloes around the galaxies of our sample., In Section 8 we introduce the different mass models that were considered; the results of the mass decompositions are shown in Section 9 and in Section 10 we draw the conclusions concerning the derivation of the rotation curves and the dark matter haloes around the galaxies of our sample.1197" Throughout this paper we adopted. a value for. the Hubble parameter 44,275 km | |.", Throughout this paper we adopted a value for the Hubble parameter $H_0$ =75 km $^{-1}$ $^{-1}$.1198 The present sample is. ideal for the study of dark matter within galaxies. not only for the characteristics of the galaxies. but also for the quality of the data.," The present sample is ideal for the study of dark matter within galaxies, not only for the characteristics of the galaxies, but also for the quality of the data."1199 ‘Table 1 presents the galaxy sample and its. physical characteristics.," Table \ref1200{physical} presents the galaxy sample and its physical characteristics."

Showing the first 1,200 of 10365 lines. Download the file for the rest.