source,target They are not obviously offset from cach other iu οίIE)., They are not obviously offset from each other in $S_{2}(CH)$. This may be simply an effect of the extremely nuited range in CN aud CTL baud streneths periiitte> x the low overall metallicity of NGC 5166., This may be simply an effect of the extremely limited range in CN and CH band strengths permitted by the low overall metallicity of NGC 5466. Another wav to visualize the distribution of CN baa strength iu our data set is the generalized histogram. which ds constructed bv represcuting cach star as a Caussian in ó5(3839) with a width equal to the ueasurenieut error os. aud then sununiue the individual Gaussians.," Another way to visualize the distribution of CN band strength in our data set is the generalized histogram, which is constructed by representing each star as a Gaussian in $\delta S(3839)$ with a width equal to the measurement error $\sigma_{S}$, and then summing the individual Gaussians." The result is shown iu Figure 7.. in which he solid curve is the eeneralized histogram for the ull data set and the dashed curves are the generalized Ustoeraus caleulated just for the relatively CN-weak. and CN-stroug eroups.," The result is shown in Figure \ref{fig7}, in which the solid curve is the generalized histogram for the full data set and the dashed curves are the generalized histograms calculated just for the relatively CN-weak and CN-strong groups." The upper paucl of Figure 5 shows the single Gaussian that best fits the eeneralized Ustoeraim frou Fieure 7.. aud the lower panel showine," The upper panel of Figure \ref{fig8} shows the single Gaussian that best fits the generalized histogram from Figure \ref{fig7}, , and the lower panel, showing" enerev and kinetic energy due to the formation of current sheets ancl other sharp gradients is being implicitly put back into the thermal energy of (he plasma. resulting in an increase of the entropy.,"energy and kinetic energy due to the formation of current sheets and other sharp gradients is being implicitly put back into the thermal energy of the plasma, resulting in an increase of the entropy." " We have identified regions where there is significant entropy increase wilh AS/C,>115 and also high electric current density concentration with J/D>1/7 where |—10 mes the grid size.", We have identified regions where there is significant entropy increase with $\Delta S / C_v > 1.15$ and also high electric current density concentration with $J/B > 1/l$ where $l = 10$ times the grid size. Such regions are outlined by the orange iso-surlaces in panels (a) and (ο) of Figure 8.. and thev appear as an inverse-5 shaped laver (as viewed from the top). which likely corresponds to the formation of an electric current sheet underlving (he anchored fhix rope (e.gTitovandDemoulin1999:LowBerger2003:Gibsonetal.2006).," Such regions are outlined by the orange iso-surfaces in panels (a) and (c) of Figure \ref{fig8}, and they appear as an inverse-S shaped layer (as viewed from the top), which likely corresponds to the formation of an electric current sheet underlying the anchored flux rope \citep[e.g][]{td1999, low_berger2003,gibsonetal2006}." ". We have also plotted field lines (purple field lines shown in panels b ancl d) going trough the region of the current laver. which are preferentially heated ancl are expected to brighten throughout (heir lengths (due to the high heat conduction along the field lines) in soft-N. ταν, producing (he central dominant X-ray sigmoid seen in the Hinode NST image (panel e)."," We have also plotted field lines (purple field lines shown in panels b and d) going through the region of the current layer, which are preferentially heated and are expected to brighten throughout their lengths (due to the high heat conduction along the field lines) in soft-X ray, producing the central dominant X-ray sigmoid seen in the Hinode XST image (panel e)." Thus our coronal magnetic field resulüng from (he emergence of a nearly east-west oriented magnetic flix rope could reproduce the observed overall morphology and connectivity of the coronal magnetic field. including the presence of the observed pre-eruption X-ray. signmoid.," Thus our quasi-equilibrium coronal magnetic field resulting from the emergence of a nearly east-west oriented magnetic flux rope could reproduce the observed overall morphology and connectivity of the coronal magnetic field, including the presence of the observed pre-eruption X-ray sigmoid." " We lind that both J/2B as well as AS peak along the ""left elbow portion of the current laver. where the positive polarity [lux of the emerged fIux rope comes in contact wilh the [lux of the dominant pre-existing negative polarity sunspot. consistent with the briehtness distribution along the observed. X-ray sigmoid (panel e of Figure 3))."," We find that both $J/B$ as well as $\Delta S$ peak along the “left elbow” portion of the current layer, where the positive polarity flux of the emerged flux rope comes in contact with the flux of the dominant pre-existing negative polarity sunspot, consistent with the brightness distribution along the observed X-ray sigmoid (panel e of Figure \ref{fig8}) )." Reconnections in (his part of the current laver cause some of the [lux in the emerged [hax rope to become connected wilh the major negative sunspot (see the green field lines connecting between the dominant negalive spot and the emerging positive spot in panel (d) of Figure 8))., Reconnections in this part of the current layer cause some of the flux in the emerged flux rope to become connected with the major negative sunspot (see the green field lines connecting between the dominant negative spot and the emerging positive spot in panel (d) of Figure \ref{fig8}) ). We have also done a few simulations where we varied the tilt of the emerging flux rope. ancl found that to reproduce the observed orientation of the sigmoid. (he emergime flux rope needs to be nearly east-west oriented.," We have also done a few simulations where we varied the tilt of the emerging flux rope, and found that to reproduce the observed orientation of the sigmoid, the emerging flux rope needs to be nearly east-west oriented." With the onset of the eruptive Hare. the soft-N rax observation [ist shows a (transient brghtening of the sigmoid. and subsequenilv (he enmuüssion is completely dominated. by the brightness of the post-IIare loops (see panels (a)(c)(e) of Figure 9)).," With the onset of the eruptive flare, the soft-X ray observation first shows a transient brightening of the sigmoid, and subsequently the emission is completely dominated by the brightness of the post-flare loops (see panels (a)(c)(e) of Figure \ref{fig9}) )." In the simulated coronal magnetic field. we find that (he current density in the inverse-S shaped current laver intensilies as (he flux rope begins to erupt.," In the simulated coronal magnetic field, we find that the current density in the inverse-S shaped current layer intensifies as the flux rope begins to erupt." We can deduce qualitatively (he evolution of the post-reconnection (or post-flare) loops [rom our modeled magnetic field evolution., We can deduce qualitatively the evolution of the post-reconnection (or post-flare) loops from our modeled magnetic field evolution. We traced field lines (see the red field lines in panels (b)(e)(h) of Figure 10. and panels (b)(d)(E) ol Figure 11)) whose apexes are located in the laver of the most intense current. density and heating.," We traced field lines (see the red field lines in panels (b)(e)(h) of Figure \ref{fig10} and panels (b)(d)(f) of Figure \ref{fig11}) ) whose apexes are located in the layer of the most intense current density and heating." These field lines are the ones who have just reconnected al their apexes ancl would slingshot dowuwards. corresponding to the downwarel collapsing: post-llare loops.," These field lines are the ones who have just reconnected at their apexes and would slingshot downwards, corresponding to the downward collapsing post-flare loops." The laver of the most intense current clensity ancl heating. as outlined by the orange iso-surlaces in panels (a)(d)(g) of Figure 19 and panels (a)(c)(e). is identified as where J/D>1/7 ," The layer of the most intense current density and heating, as outlined by the orange iso-surfaces in panels (a)(d)(g) of Figure \ref{fig10} and panels (a)(c)(e), is identified as where $J/B > 1/l$ " As described in refseciderive.. we represent distortions in the structure of halo in a biorthogonal basis.,"As described in \\ref{sec:derive}, we represent distortions in the structure of halo in a biorthogonal basis." Any distortion can then be summarized ow ἃ set of cocllicients., Any distortion can then be summarized by a set of coefficients. Because large spatial scales are most important in understanding global evolution. we can truncate his expansion and still recover most of the power.," Because large spatial scales are most important in understanding global evolution, we can truncate this expansion and still recover most of the power." Internal and therefore quasi-periodic distortions contribute at a discrete spectrum. of frequencies., Internal and therefore quasi-periodic distortions contribute at a discrete spectrum of frequencies. Paper 1. 822 (see eqns.," Paper 1, 2 (see eqns." 21-22 in Paper 1: for the final result) derives the response of a halo to a »oint perturbation at a single frequency., 21-22 in Paper 1 for the final result) derives the response of a halo to a point perturbation at a single frequency. Similar arguments lead to an expression for a continuous spectrum of perturbation requencies., Similar arguments lead to an expression for a continuous spectrum of perturbation frequencies. In the latter case. one computes the response of the stellar system to each frequeney in the spectrum and then sunis over all frequencies.," In the latter case, one computes the response of the stellar system to each frequency in the spectrum and then sums over all frequencies." We will begin with the development common to both cases., We will begin with the development common to both cases. The goal is calculation of the coellicients defined by equations (4)) and (5))., The goal is calculation of the coefficients defined by equations \ref{eq:kramers}) ) and \ref{eq:diff}) ). We begin by determining these coelficients or action variables and transform to (C£.s.cos3) in the end.," We begin by determining these coefficients for action variables and transform to $(E, \kappa, \cos\beta)$ in the end." Because orbits in the equilibrium phase space are euasi-periocdic and. representable as fixed actions and. constantly. advancing angles. any perturbed quantity can be represented. as a Fourier series in angles with coefficients depending on actions.," Because orbits in the equilibrium phase space are quasi-periodic and representable as fixed actions and constantly advancing angles, any perturbed quantity can be represented as a Fourier series in angles with coefficients depending on actions." Following Paper 1. the perturbed Llamiltonian is where 1=ἐνος is a triple of integers. rie7) and Wid(T) are the rotation matrices and gravitational potential transforms defined in Paper 1.," Following Paper 1, the perturbed Hamiltonian is where ${\bf l}={l_1, l_2, l_3}$ is a triple of integers, $r^l_{ij}(\beta)$ and $W^{l_1\,j}_{ll_2l_3}(\bI)$ are the rotation matrices and gravitational potential transforms defined in Paper 1." The time dependence of the coellicients describing the response. «7(0). is represented. as its Fourier transform.," The time dependence of the coefficients describing the response, $a^{lm}_j(t)$, is represented as its Fourier transform." This allows cach frequeney to be treated: separately., This allows each frequency to be treated separately. The response matrix Vf describes the reaction of the galaxy to the perturbation: so the entire response is the sum of both the response and. direct. forcing. M|9j.," The response matrix ${\cal M}$ describes the reaction of the galaxy to the perturbation; so the entire response is the sum of both the response and direct forcing, ${\cal M}^{lm}_{jk} + \delta_{jk}$ ." We may integrate the equations of motion directly to evaluate στ0., We may integrate the equations of motion directly to evaluate $\bI(\tau+t)$. " Hamiltons equations vield and therefore we have The evolution of perturbed distribution function in time follows from the linearized collisionless Boltzmann equation and the total time derivative for a Hamiltonian svsteni: Analogous to the development above for ££,(1). we have and therefore ↾↓∖∪⋖⋅∖⇁⋜↧↓⋯⋯⊾∢⊾⊏↥⊔⋜∐⊲↓∪⊔↿∖⋅↱≻∣∩∖∖⊽⋖⋅⊔∢⊾∢⊾∠⇂↿↓↕∢⊾∐↓⋅⊳∖↿⋜⋯∠⇂≱∖⋖⋅≼∙∪⊔∠⇂∪↓⋅∠⇂∢⋅↓⋅⋜↧≼∙↿↕∢≱↓↕⊔↓∪⊔↓∢⊾⊔⇂⊳∖∠⇂⋖⋅∐⊔⋯⇂∣⋡∙∖⇁⋖⋅⊏↥⇂⇂⋜↧↿↕⋖⋟↓"," Hamilton's equations yield and therefore we have The evolution of perturbed distribution function in time follows from the linearized collisionless Boltzmann equation and the total time derivative for a Hamiltonian system: Analogous to the development above for $H_1(t)$, we have and therefore To evaluate equation \ref{eq:diff}) ) we need the first and second order action moments defined by equation \ref{eq:moms}) )." ↕⋯∩⊳∖∖⊽∢⊾⋜↧⊳∖⊳∖⊔⊔↓∢⋅⊳ ∣⋡∙∖⇁⋯⇂∩↓≻↿⊀↓⊔⋏∙≟⇂↓↕∢⊾∣↕↓↥↓∢⊾−⋜↧≻∙∖⇁↓↕↓↓≻⇂∪↿⊲⊔⇍↓⋅⋖⋅⊳∖↓≻∪⊔⊳∖⋖⋅⊔↓⋜∐↓⋰∟∖⋅⋈∣⋯⊲↓⊔∠⇂∢⊾↓⋰↓∖⋰↓⊔⋏∙≟⇂↓⋯↿⇠∕⊲⊥⋜⋯∠⇂∐⊥⋜↧∣⋯∖⇁∢⊾⊳↿⇂⋯↿⊤↕≻↓⋜⊔⋅⋏∙≟∢⊾↓⋅↿↓↥⋜↧↓↕↕↓↕⇂↓⋅↕↓↕≻↕≼∼ ∠⇂∙∖⇁⊔⋜⋯↓⊲⊔⇍⋜↧↓↿⊲↓⊔↓∢⊾⊳∖⊳≼⇍∪⊔⊳∖⊲↓⊳∖∩⋅↓∐∖∖⋰↓∣↓↕∣↓↕⋖⊾∪↓⋅∠⇂∢⊾↓⋰↓⊔⋏∙≟∪⇂⋅⋯," We assume, by adopting the time-asymptotic response matrix ${\cal M}^{lm}$ in deriving that $f_1$ and $H_1$ above, that $\tau$ is larger than intrinsic dynamical times, consistent with the ordering of our slow and fast time scales." ⊔⋅⊳∖↓∪∖∖⊽⋜⋯∠⊔⋅⋜↧⊳∖⇂↿⊲↓⊔↓∢⊾⊳∖≼⇍⋜↧↓∢⊾⊳∖⋡↓↴↓⋅⋖⋅∖⋰↓∪⊔≱∖∖∖⊽∪↓⋅↳⊳⊀↓⊔≼⇍↓⋯⇂⊲↓⊔⋏∙≟≼∼∪⊔↓↓≻⋜⊔⋰↓≱∖∪⊔↥∪⊔−∣⋡⇜⇂∙∖⇁ ⊳∖⊲↓⊔↓⊔↓⋜∐⊲↓∪⊔⊳∖⊳⊳∖⊔⋏∙≟⋏∙≟∢⊾⊳∖⇂⊳∖⇂↓⋯↿↿↓↥↕≻↕≻⋜↧∖⇁⋖⋅↓⋅∙∖⇁⋏∙≟∪⇜⇂⋜↧↓≻," Previous work, including comparison to n-body simulations, suggests that this is a very good approximation for time scales longer than several crossing times." ↓≻↓⋅∪⇀∖⊲↓⊔↓⋜∐⊀↓∪⊔⇂⋅∪↓⋅↿⊀↓⊔↓∢⊾⊳∖≼⇍⋜↧↓∢⊾⊳∖↓∪⊔⋏∙≟∢⊾↓⋅↿↓⋯⊔⊳∖∢⊾∖⇁⋖⋅↓⋅⋜↧⇂≼⇍↓⋅∪⊳∖⊳∖⊲↓⊔⋏∙≟↿⊀↓⊔↓∢⊾⊳∖⊳↾↓∖↓↥⋖⊾↓⋅∢⋅⊳∖↓≻∪⊔⊳∖⋖⊾ to the distortion induces a shift in the actions I and the overall response causes a change in the distribution function., The response to the distortion induces a shift in the actions $\bI$ and the overall response causes a change in the distribution function. " This is represented in the matrix equation defined by equation (20)) for an external perturbation described by the coellicients whee),", This is represented in the matrix equation defined by equation \ref{eq:h1}) ) for an external perturbation described by the coefficients $b^{lm}_j(t)$. " The fiducial stochastic variables are the coellicients 7"" themselves.", The fiducial stochastic variables are the coefficients $b^{lm}_j(t)$ themselves. Theoverall conditional probability required. in equation (2)) and the following development for the moments therefore, Theoverall conditional probability required in equation \ref{eq:cprob}) ) and the following development for the moments therefore whereda(o)/do.,where. . The upper limits on [5| are of the order of (Hagiwara et al., The upper limits on | are of the order of (Hagiwara et al. 2002). so that is constrained to be smaller than roughly.," 2002), so that is constrained to be smaller than roughly." For as concerns the cosmological evolution at small z.. (his is equivalent to assuming =0.. so (hat our starting assumption that the dark energy couples only (or preferentially) to dark matter. is justified.," For as concerns the cosmological evolution at small z, this is equivalent to assuming =0, so that our starting assumption that the dark energy couples only (or preferentially) to dark matter, is justified." Similar species-dependent couplings have been discussed in other contexts since the first proposal bv Damour. Gibbons. Gundlach (1990). see e.g. the astrophysical bounds discussed by Gradwohl Frieman (1992).," Similar species-dependent couplings have been discussed in other contexts since the first proposal by Damour, Gibbons, Gundlach (1990), see e.g. the astrophysical bounds discussed by Gradwohl Frieman (1992)." Ilowever. if the barvons are uncoupled they dilute with the usual behavior Le. faster (han the coupled dark energv/dark matter fluid.," However, if the baryons are uncoupled they dilute with the usual behavior i.e. faster than the coupled dark energy/dark matter fluid." This mocilies the Friecdimanni equation (2)) as follows There appears therefore an epoch in the past before which the barvons were dominating and. as a consequence. the expansion decelerated.," This modifies the Friedmann equation \ref{dl}) ) as follows There appears therefore an epoch in the past before which the baryons were dominating and, as a consequence, the expansion decelerated." Denoting with a eeneric uncoupled component (in this case the baryons) this epoch in flat space ls which therefore replaces (1))., Denoting with a generic uncoupled component (in this case the baryons) this epoch in flat space is which therefore replaces \ref{zacc}) ). It appears then that the factor that limits the acceleradion epoch is the present abundance of barvons., It appears then that the factor that limits the acceleration epoch is the present abundance of baryons. Asstuning 00.02 the maximum turns out to be around 5 as shown in Fig., Assuming 0 .02 the maximum turns out to be around 5 as shown in Fig. 4., 4. " It is to be noticed that if and are constant at all epochs. the present accelerated epoch is preceded by a clecelerated barvon-dominated epoch beforez;,4,."," It is to be noticed that if and are constant at all epochs, the present accelerated epoch is preceded by a decelerated baryon-dominated epoch before." . Such an epoch would however be in conflict with the CAIB. as shown in Tocchini-Valentini Amendola (2001). because of an extvemely large integrated Sachs-Wolle effect on the CAIB.," Such an epoch would however be in conflict with the CMB, as shown in Tocchini-Valentini Amendola (2001), because of an extremely large integrated Sachs-Wolfe effect on the CMB." It is therefore necessary (o modilv Che simplest case with. for instance. a modulation of the coupling parameter or the potential C in order to prevent the barvon domination. as in Amendola Tocchini-Valentini (2001) and in Amenclola et al. (," It is therefore necessary to modify the simplest case with, for instance, a modulation of the coupling parameter or the potential U in order to prevent the baryon domination, as in Amendola Tocchini-Valentini (2001) and in Amendola et al. (" 2002).,2002). These models also account for the observed level of present Hactuations., These models also account for the observed level of present fluctuations. This paper shows that high-z acceleration is a viable possibility if dark energy couples to dark matter., This paper shows that z acceleration is a viable possibility if dark energy couples to dark matter. Although the present abundance of barvons limit the epoch of acceleration {ο <5. (is is still much earlier than the standard models of uncoupled dark energv. which hardly reaches -—L.," Although the present abundance of baryons limit the epoch of acceleration to <5, this is still much earlier than the standard models of uncoupled dark energy, which hardly reaches =1." . The future observations of SNla at high redshift will be well suited to detect or reject an early acceleration., The future observations of SNIa at high redshift will be well suited to detect or reject an early acceleration. A strong coupling between dark energy. ancl dark matter can also be detected through the biasing and the rate of growth of perturbations. as discussed in Amendola," A strong coupling between dark energy and dark matter can also be detected through the biasing and the rate of growth of perturbations, as discussed in Amendola" A strong coupling between dark energy. ancl dark matter can also be detected through the biasing and the rate of growth of perturbations. as discussed in Amendola.," A strong coupling between dark energy and dark matter can also be detected through the biasing and the rate of growth of perturbations, as discussed in Amendola" (Miles1961:Llowarel1961;Chimonas1970).,"\citep{jwm61,how61,chi70}." ".."" Lere NZ23 is the square of the local Brunt-Vaisala frequency in the radial direction. where and Ly=5590/5, we the equilibrium pressure and entropy length scales in the radial direction."," Here N_x^2 is the square of the local $\ddot{\rm{a}}$ $\ddot{\rm{a}}$ $\ddot{\rm{a}}$ frequency in the radial direction, where $L_P \equiv \gamma P_0/P_0^\prime$ and $L_S \equiv \gamma S_0/S_0^\prime$ are the equilibrium pressure and entropy length scales in the radial direction." " The solutions for the other perturbation variables are related to 06, by = and Hox aei(oe-) ag n2 ]."," The solutions for the other perturbation variables are related to $\delta v_{xs}$ by =, = dt and = ) + - 1) ]." (25) since (he solutions to equation (??)) are hvpergeometric functions. which have a time dependence. it cannot in general be accurately treated with a WIXD analvsis: there is no asymptotic region in time where equation (?2)) can be reduced (o a dispersion relation.," Since the solutions to equation \ref{BOUSSVX2D}) ) are hypergeometric functions, which have a power-law time dependence, it cannot in general be accurately treated with a WKB analysis; there is no asymptotic region in time where equation \ref{BOUSSVX2D}) ) can be reduced to a dispersion relation." " If, however. there is a region of the disk where the effective shear is zero. 7—constant ancl equation (??)) can be expressed as a WIND dispersion relation: nno with 0(/)xexp(—Acl)."," If, however, there is a region of the disk where the effective shear is zero, $\tilde{\tau} \rightarrow constant$ and equation \ref{BOUSSVX2D}) ) can be expressed as a WKB dispersion relation: ^2 = with $\delta(t) \propto \exp(-i\omega t)$." For 4~0 and V2<0. then. there is convective instability.," For $\qe \simeq 0$ and $N_x^2 < 0$, then, there is convective instability." For disks with nearly-heplerian rotation profiles aud modest radial gradients. 471.5 and one would expect that the instability is suppressed by (he strong shear.," For disks with nearly-Keplerian rotation profiles and modest radial gradients, $\qe \simeq 1.5$ and one would expect that the instability is suppressed by the strong shear." Due to the lack of, Due to the lack of 1994).. and the logarithmic dependence of the asvimpltotic structure on οἵ has been pointed out.,", and the logarithmic dependence of the asymptotic structure on $x$ has been pointed out." However. the (transition from maenetic-enerev dominated state into kinelic-enerev dominated one is an important unsolved problem which is bevond (he usual scheme of the asymptotic analvsis based on (he naive approximation .r1 in the poloidal wind and Grad-Shalranov equations.," However, the transition from magnetic-energy dominated state into kinetic-energy dominated one is an important unsolved problem which is beyond the usual scheme of the asymptotic analysis based on the naive approximation $x\gg 1$ in the poloidal wind and Grad-Shafranov equations." In our approach presented in the previous section. such an approximation corresponds to for which we have from equation (30)). (," In our approach presented in the previous section, such an approximation corresponds to for which we have from equation \ref{largex}) ). (" This should be the case of £<£.),"This should be the case of $\xi\leq \xi_{\rm c}$ .)" The kev point missed in this calculation is that the fine-tuning of 1—£?=O(1/E?) to realize the οποίον equipartition (M?~ L) may occur at a radius à in the range |> 1)., The existence of the intermediate range of $x$ is a main feature of highly relativistic outflows with a very large specific energy $E\gg 1$ ). Recalling that we obtain APx€/ αἱ the light evlincler surface c7=l1. we expect M? (o increase [rom a sub-[ast-magnetosonie value in (the range l/E-««APnee.," Inserting $\bar{\rho}$ for the inner 20-km cores of the cold stars, we have $\tau_r \approx 10~\rmn{s}\gg \tau_{\rm bar}$." Phe evolution of the bar-mode secular instability has. only been studied. in. detail for the Maclaurin spheroids., The evolution of the bar-mode secular instability has only been studied in detail for the Maclaurin spheroids. These objects evolve through a sequence of deformed: non-axisvnunetric configurations eventually to settle down as a more slowly rotating stable axisvmnmetric star. (Lindblom&Detweiler1977:LaiShapiro 1995).," These objects evolve through a sequence of deformed non-axisymmetric configurations eventually to settle down as a more slowly rotating stable axisymmetric star \cite{lindblom77,lai95}." . Lt is generally expected. that stars having more realistic LOS will behave similarly., It is generally expected that stars having more realistic EOS will behave similarly. We have constructed: equilibrium. models. of dillerentially rotating neutron stars which model the end products of the accretion induced collapse of rapidly rotating white cdwarls., We have constructed equilibrium models of differentially rotating neutron stars which model the end products of the accretion induced collapse of rapidly rotating white dwarfs. We considered. three models. for. the pre-collapse white chvarts., We considered three models for the pre-collapse white dwarfs. All of them are rigiclv rotating at the maximum possible angular velocities., All of them are rigidly rotating at the maximum possible angular velocities. TIre white dwarfs are described by the EOS of degenerate electrons at zero temperature with Coulomb corrections derived w Salpeter (LOG1)., The white dwarfs are described by the EOS of degenerate electrons at zero temperature with Coulomb corrections derived by Salpeter \shortcite{salpeter61}. . We assumed. that (1) the collapsed objects are axisvmmetric and are in roational equilibrium. with no meridional circulation. (2) the EOS is barotropic. (3) Viscosity can be neglected. and (4) any ejectecl material carries negligible amounts of mass and angular momentum.," We assumed that (1) the collapsed objects are axisymmetric and are in rotational equilibrium with no meridional circulation, (2) the EOS is barotropic, (3) viscosity can be neglected, and (4) any ejected material carries negligible amounts of mass and angular momentum." We then built. the equilibrium. models of the collapsed stars based on the fact that their final configurations must have the same masses. total angular momenta anc specific angular momentum distributions. j(mzz). as the pre-collapse white cwarls.," We then built the equilibrium models of the collapsed stars based on the fact that their final configurations must have the same masses, total angular momenta and specific angular momentum distributions, $j(m_{\varpi})$, as the pre-collapse white dwarfs." Two EOS have been used for the collapsed objects., Two EOS have been used for the collapsed objects. One of them is one of the standard cold neutron-star LOS., One of them is one of the standard cold neutron-star EOS. The other is a hot EOS suitable for protoneutron stars. which are characterized by their high temperature and high lepton [raction.," The other is a hot EOS suitable for protoneutron stars, which are characterized by their high temperature and high lepton fraction." The equilibrium structure of the collapsed. objects in all of our models consist of a high density central core of size about 20 km. surrouncecl by a massive accretion torus extending over 1000 km from the rotation axis.," The equilibrium structure of the collapsed objects in all of our models consist of a high density central core of size about 20 km, surrounded by a massive accretion torus extending over 1000 km from the rotation axis." More than 90 per cent of the stellar mass is contained in the core and core-Lorus transition region. which is within about 100 km from the rotation axis (see Figure 11)).," More than 90 per cent of the stellar mass is contained in the core and core-torus transition region, which is within about 100 km from the rotation axis (see Figure \ref{fig:mpm}) )." " Phe central densities of the hot protoneutron stars are in the sub-nuclear density regime; (4.10LlσοιBe""zzpSPR2.10m5em "")."," The central densities of the hot protoneutron stars are in the sub-nuclear density regime $4\times 10^{11}~\rmn{g}~\rmn{cm}^{-3} \la \rho \la 2\times 10^{14}~\rmn{g}~\rmn{cm}^{-3}$ )." h The structures of these protoneutron stars are very different from. rose of the cold neutron stars. which the protoneutron stars will evolve to in roughly 20 s. “Phe protoneutron stars have lower central densities. rotate less rapidly. and have smaller values of 3.," The structures of these protoneutron stars are very different from those of the cold neutron stars, which the protoneutron stars will evolve to in roughly 20 s. The protoneutron stars have lower central densities, rotate less rapidly, and have smaller values of $\beta$." On the other hand. the structures of the three cold neutron stars are similar.," On the other hand, the structures of the three cold neutron stars are similar." Their central densities are around 3.5;107οem.* and their central cores are nearly rigidly rotating with periods of about 1.4 ms. slightlv less than the fastest observed millisecond. pulsar (1.56 ms)," Their central densities are around $3.5\times 10^{14}~\rmn{g}~\rmn{cm}^{-3}$ and their central cores are nearly rigidly rotating with periods of about 1.4 ms, slightly less than the fastest observed millisecond pulsar (1.56 ms)." Zwerger and. Mülller (1997). performed 2D simulations of the core collapse of massive stars., Zwerger and Mülller \shortcite{zwerger97} performed 2D simulations of the core collapse of massive stars. The major cdillerence between their models anc ours. is that they used: rather simplified LOS for both the pre-collapse ancl the collapsed models., The major difference between their models and ours is that they used rather simplified EOS for both the pre-collapse and the collapsed models. When compared with their fastest rigidly rotating model. ALBS. we found their. pre-collapse star has. less total angular momentum ancl smaller 3 than the pre-collapse white dwarf of our Model Lo although both have the same central density.," When compared with their fastest rigidly rotating model, AlB3, we found their pre-collapse star has less total angular momentum and smaller $\beta$ than the pre-collapse white dwarf of our Model I, although both have the same central density." Ehe dilferences between their final collapsed. models CXID3GI-X1D3CG5) and ours are even more significant., The differences between their final collapsed models (A1B3G1-A1B3G5) and ours are even more significant. Phe values of ο our collapsed objects are much larger than theirs. suggesting that the EOS plavs an important role in the equilibrium configurations of both the pre-collapse white dwarls and the resulting collapsed stars.," The values of $\beta$ of our collapsed objects are much larger than theirs, suggesting that the EOS plays an important role in the equilibrium configurations of both the pre-collapse white dwarfs and the resulting collapsed stars." The values of 3 o£ the colel neutron stars are. only slightly less than the traditionalcritical value of dynamical instability. 0.27. frequently quoted in the literature.," The values of $\beta$ of the cold neutron stars are only slightly less than the traditionalcritical value of dynamical instability, 0.27, frequently quoted in the literature." The cold neutron stars may. still be cdvnamically unstable and a detailed study is requirecl to settle the issue., The cold neutron stars may still be dynamically unstable and a detailed study is required to settle the issue. Ewen if they, Even if they We estimate 7 and Vz used in Section 4.4..,We estimate $\mathcal{R}$ and $\mathcal{Y}_{Z}$ used in Section \ref{subsec:enrichment}. " With an initial mass function IMF) ó(m), R and yz are written as where m is the turn-off stellar mass, my is the upper mass cutoff of stellar mass, m is the stellar mass, w,, is the remnant mass, pz(m) is the fraction of mass converted into metals in a star of mass m."," With an initial mass function (IMF) $\phi (m)$, $\mathcal{R}$ and $\mathcal{Y}_{Z}$ are written as where $m_t$ is the turn-off stellar mass, $m_\mathrm{u}$ is the upper mass cutoff of stellar mass, $m$ is the stellar mass, $w_m$ is the remnant mass, $p_\mathrm{Z}(m)$ is the fraction of mass converted into metals in a star of mass $m$." We assume the Salpeter IMF (¢(m)οςm ???) with stellar mass range 0.1Mc; 100$ mJy. These are shown in Fig., These are shown in Fig. 4 and listed in Table 3., 4 and listed in Table 3. Of these. Bj is NGC 6251 and B5:Bs probably correspond to emission from the jet of NGC 6251.," Of these, $B_1$ is NGC 6251 and $B_2\cdots B_5$ probably correspond to emission from the jet of NGC 6251." No significant X-ray emission 15 seen at the positions of the other sources and the NASA Extragalactic Database (NED) reveals that these are steep spectrum radio sources., No significant X-ray emission is seen at the positions of the other sources and the NASA Extragalactic Database (NED) reveals that these are steep spectrum radio sources. Mack. Kerp Klein note another X-ray/radio coincidence east of source 7 at RA: 16 26 24.8 and Dec: 82 35 07.," Mack, Kerp Klein note another X-ray/radio coincidence east of source 7 at RA: 16 26 24.8 and Dec: 82 35 07." This source is 5C 16314-8206. and has an X-ray flux density of (9.8+2.9)«102 ply.," This source is 8C 1631+826, and has an X-ray flux density of $(9.8\pm2.9)\times 10^{-3}$ $\mu$ Jy." It should be noted that that the most effective way to look for radio candidates for gamma-ray sources ts to start not with the NVSS. but with a high-frequency radio catalog that is most likely to isolate the flat-spectrum. blazar candidates.," It should be noted that that the most effective way to look for radio candidates for gamma-ray sources is to start not with the NVSS, but with a high-frequency radio catalog that is most likely to isolate the flat-spectrum, blazar candidates." The best such catalog in the northern hemisphere is the Becker. White. Edwards (1991) 4.85 GHz survey.," The best such catalog in the northern hemisphere is the Becker, White, Edwards (1991) 4.85 GHz survey." " However. it covers only declinations between 0° and +75."" which excludes this field."," However, it covers only declinations between $^\circ$ and $^\circ$ which excludes this field." Our analysis of the archival X-ray data of the field containing 3EG J16214-8203 reveals that the region contains several bright stars. weak radio sources. a radio galaxy. and a galaxy cluster.," Our analysis of the archival X-ray data of the field containing 3EG J1621+8203 reveals that the region contains several bright stars, weak radio sources, a radio galaxy, and a galaxy cluster." We note that unlike the majority of the identified EGRET sources. 3EG J162148203 lacks a radio-loud. spectrally flat. blazar-like source catalogued within its error circle that could," We note that unlike the majority of the identified EGRET sources, 3EG J1621+8203 lacks a radio-loud, spectrally flat, blazar-like source catalogued within its error circle that could" The excess al large pileh angle. those up to 150 degree as observed by large field of view detectors such as neutron monitors. are constituted bv low energy particles.,"The excess at large pitch angle, those up to 180 degree as observed by large field of view detectors such as neutron monitors, are constituted by low energy particles." They are in the tail of the distribution. where the intensity is minimum.," They are in the tail of the distribution, where the intensity is minimum." Even so. the FRED GLE could be an event connected via the file magnetic lines. with a flare on the other side of the Sun. and not seen by satellites.," Even so, the FRED GLE could be an event connected via the file magnetic lines, with a flare on the other side of the Sun, and not seen by satellites." The probability of detection using a clirectional telescope of small field of view (0.082 sr of angular window) pointed in a random direction. an event above the horizon is approximately p~0.082/2*=0.013.," The probability of detection using a directional telescope of small field of view (0.082 sr of angular window) pointed in a random direction, an event above the horizon is approximately $p \sim 0.082/2\pi =0.013$." " IHlowever. because the telescope can detect a fraction of muons. A,,(7). even when the core of the air shower is al a distance 7(-2Aim) from the telescope center. the probability is enhanced Lo ~3% (~5% for primary gammiacrays)."," However, because the telescope can detect a fraction of muons, $\Delta_{\mu}(r)$, even when the core of the air shower is at a distance $r(\cong 2\;km)$ from the telescope center, the probability is enhanced to $\sim 3\%$ $\sim 5\%$ for primary gamma-rays)." ar) is calculated using the lateral distribution function of muons (see sec.6)., $\Delta_{\mu}(r)$ is calculated using the lateral distribution function of muons (see sec.6). The detection of an event that happens on the other side of the Sun would correspond to a very laree pitch angle. and from the considerations mentioned above. we estimate the probability of detecting a solar flare connected to the back of the Sun al less than4.," The detection of an event that happens on the other side of the Sun would correspond to a very large pitch angle, and from the considerations mentioned above, we estimate the probability of detecting a solar flare connected to the back of the Sun at less than." .. Another possibility (although remote) to explain the origin of this GLE is to invoke ihe GRD hypothesis., Another possibility (although remote) to explain the origin of this GLE is to invoke the GRB hypothesis. The temporal and cirectional coincidences of a GLE with satellite observations of GRBs are strong indications of a common detection., The temporal and directional coincidences of a GLE with satellite observations of GRBs are strong indications of a common detection. " In [act this has been (he main objective of several ground experiments. not only the detection of the GRBs TeV counterpart but also their afterglows at ταν, optical and radio wavelengths."," In fact this has been the main objective of several ground experiments, not only the detection of the GRBs TeV counterpart but also their afterglows at X-ray, optical and radio wavelengths." Nowadavs il is expected that the rate of observation of GRBs by the GRB coordinate network (GCN) satellites (Darthelmy2001) with the field of view of a large ground. based detector such as MILAGRO is smaller (han one per month (Smith2001)., Nowadays it is expected that the rate of observation of GRBs by the GRB coordinate network (GCN) satellites \citep{barthelmy01} with the field of view of a large ground based detector such as MILAGRO is smaller than one per month \citep{smith01}. . llowever. we have found GRB satellite notification around (wo hours from the beginning ol the FRED GLE (see Table 2).," However, we have found GRB satellite notification around two hours from the beginning of the FRED GLE (see Table 2)." While we don't have other evidences which indicates a common detection wilh GRBs Irom GCN satellites., While we don't have other evidences which indicates a common detection with GRBs from GCN satellites. EFig.6 shows a comparison between the light curve shapes of the BATSE burst Trigger 7989 and the GLE 2003/12/16., Fig.6 shows a comparison between the light curve shapes of the BATSE burst Trigger 7989 and the GLE 2003/12/16. Both are eenuine FREDs., Both are genuine FREDs. We have also examined the light curve for (his GLE for other pulse-hieht amplitude discrimination levels. as shown in Fie.7.," We have also examined the light curve for this GLE for other pulse-hight amplitude discrimination levels, as shown in Fig.7." The signal persists even when a hieh pulse auplitude is used as discrimination level. while the background is basically eliminate.," The signal persists even when a high pulse amplitude is used as discrimination level, while the background is basically eliminated." It is possible to see that the signal observed in the GLE linked with the solar flare is more intense when compared with (he signal of the FRED GLE., It is possible to see that the signal observed in the GLE linked with the solar flare is more intense when compared with the signal of the FRED GLE. On the other hand. there is evidence for two classes of bursts when thev are classified according to their duration.," On the other hand, there is evidence for two classes of bursts when they are classified according to their duration." The result comes from BATSE catalog (Paciesasetal.1999) as, The result comes from BATSE catalog \citep{paciesas99} as particle acceleration.,particle acceleration. " Finally, in Sec."," Finally, in Sec." Lo we explore the vatio of GCR. assunied to be accelerated mside a superbubhble. and we show that it cannot match the oberved one (unless extreme assumptions are made).," 4 we explore the ratio of GCR, assumed to be accelerated inside a superbubble, and we show that it cannot match the oberved one (unless extreme assumptions are made)." The results are stummarized in Sec., The results are summarized in Sec. 5., 5. The method adopted here im order to calculate the coniposition of matter accelerated by a single SN explosion is schematically illustrated in Fig. , The method adopted here in order to calculate the composition of matter accelerated by a single SN explosion is schematically illustrated in Fig. \ref{Fig:SNStruct}. "At the end of its ife aud at the time of its SN explosion. a star of initial nass is left with a massAfp,,.. surrounded bv a cireunistellar shell of massALE) which has been lost through stellar wind diving its prior hwdrostatie evolution After the SN explosion. a mass of ejecta (owhere dis j=the mass of the compact renuuant. neutron star or black hole) expands first within he shell of mass iud hen in the ISM. with the orward shock having initial velocity ey=VE, Mz; where £y is the kinetic energy of the SN explosion."," At the end of its life and at the time of its SN explosion, a star of initial mass is left with a mass, surrounded by a circumstellar shell of mass, which has been lost through stellar wind during its prior hydrostatic evolution After the SN explosion, a mass of ejecta (where is the mass of the compact remmant, neutron star or black hole) expands first within the shell of mass and then in the ISM, with the forward shock having initial velocity $\upsilon_0=\sqrt{2 E_0/M_{Ej}}$ , where $E_0$ is the kinetic energy of the SN explosion." " Iu the case of stars eudiugtheir lives as WR stars. the wind coutains both the original (uuclearly uuprocessed) euvelope of nass{Εμ and uuclearly processed lavers of nassAMp,,.. enriched in products of W-buruing. aud iu sole cases of He-buruiug as well."," In the case of stars ending their lives as WR stars, the wind contains both the original (nuclearly unprocessed) envelope of mass, and nuclearly processed layers of mass, enriched in products of H-burning, and in some cases of He-burning as well." " For those stars. aand Hs calculated as the differeuce vetween the mass of the unclearly processed core aand the mass at the explosion:Mrg,,."," For those stars, and is calculated as the difference between the mass of the nuclearly processed core and the mass at the explosion:." For lower nass stars. exploding as red superelauts. the wind composition results esseutiallv from he Ist dredge-up. ie. if is a inixture of ILInrnusg xoducts from the stellar core with the original cuvelope composition (1.0. mass loss has not uncovered the Ie-core at the time of the explosion).," For lower mass stars, exploding as red supergiants, the wind composition results essentially from the 1st dredge-up, i.e. it is a mixture of H-burning products from the stellar core with the original envelope composition (i.e. mass loss has not uncovered the He-core at the time of the explosion)." " The limit 1tween the two classes of stars depends on thei initial mass. mass loss rate and rotational velocity aud it is rather poorly kuowu at present: in general. in models with no rotation stars with M.;532.35M, ybecome WR stars e.g. (eecr et al."," The limit between the two classes of stars depends on their initial mass, mass loss rate and rotational velocity and it is rather poorly known at present: in general, in models with no rotation stars with $>$ 32-35 become WR stars e.g. (Heger et al." 2002). while iu nodels with rotation that limi navy be as low as 22 ({Alevuet aud Maedoer 2000).," 2002), while in models with rotation that limit may be as low as 22 (Meynet and Maeder 2000)." The first phase of the supernova remnant (free expansion) takes place at shock velocity οconst. and ends when a nass Afs;~+Afe; las been swept up in frout of the shock wave. at which point the ST phase sets du.," The first phase of the supernova remnant (""free expansion"") takes place at shock velocity $\upsilon\sim const.$ and ends when a mass $\sim$ has been swept up in front of the shock wave, at which point the ST phase sets in." Following Ptuskin ct al. (, Following Ptuskin et al. ( 2010). we asstune that efhicient CCR acceleration starts at this time. where the situation is euergeticallv most favorable.,"2010), we assume that efficient GCR acceleration starts at this time, where the situation is energetically most favorable." In our baseline model we shall cousider constant acceleration efüciency: time-dependent efficiency. of particle acceleration is the subject of current researches (see Ellison and Bykov 2011. Diury 2011. and references therein) aud will be Irietiv discussed in Sec.," In our baseline model we shall consider constant acceleration efficiency; time-dependent efficiency of particle acceleration is the subject of current researches (see Ellison and Bykov 2011, Drury 2011, and references therein) and will be briefly discussed in Sec." 3.3., 3.3. "2c The ST phase proceeds adiabatically. i.e. at ~coust aut CLOITSON""and with decreasing velocity. until the temperature of the eas eugulfed by the shock front drops to levels allowing a significaut fraction (about πο) of the roiunainiug enerev to be radiated away."," The ST phase proceeds adiabatically, i.e. at $\sim$ constant energy and with decreasing velocity, until the temperature of the gas engulfed by the shock front drops to levels allowing a significant fraction (about ) of the remaining energy to be radiated away." At that time. an anionut of matter ΟΛΕΣ; thas been swept up aud the shock euters the suow-plow phase.," At that time, an amount of matter $>>$ has been swept up and the shock enters the ""snow-plow"" phase." At this point - aud. perhaps. even earlier. duriug he ST phase - the fors shock is too weak to accelerate particles to CCR euergies aly Wore.," At this point - and, perhaps, even earlier, during the ST phase - the forward shock is too weak to accelerate particles to GCR energies any more." Iu the aforementioned scenario. GCR are accelerate from a pool of particles with composition characteristic of the mass ecarlv ou.," In the aforementioned scenario, GCR are accelerated from a pool of particles with composition characteristic of the mass early on." " Depending ou the initial stellar mass, this composition may be rich in products of IT- (ane IIc-) burning."," Depending on the initial stellar mass, this composition may be rich in products of H- (and He-) burning." It is progressively diluted with ambient (firs wind - with normal ολο and then interstellar) Cas al at the eud of the ST phase it resscubles closely the oue of the ISAL, It is progressively diluted with ambient (first wind - with normal - and then interstellar) gas and at the end of the ST phase it ressembles closely the one of the ISM. The GCR source composition observed on Earth should correspond to the average composition between the carly ST phase anc some later evolutionary. stage of the remnant. and should result frou the whole mass spectrum of exploding stars. io. it should be averaged over a stellar initial mass function (IME).," The GCR source composition observed on Earth should correspond to the average composition between the early ST phase and some later evolutionary stage of the remnant, and should result from the whole mass spectrum of exploding stars, i.e. it should be averaged over a stellar initial mass function (IMF)." We adopt two sets of stellar models in this work., We adopt two sets of stellar models in this work. They are caleulated for stars of solu metallicity. and in both cases the solar mixture of Anders and Crevesse (1979) is adopted.," They are calculated for stars of solar metallicity, and in both cases the solar mixture of Anders and Grevesse (1979) is adopted." The corresponding imoetallicitv is 00.019. substantially larger than more recen values (Lodders 2003. Asplund ct al.," The corresponding metallicity is 0.019, substantially larger than more recent values (Lodders 2003, Asplund et al." 2010) and this difference results in particular from the reduction iu the pas decade of the solar abundances of C. N. O and Ne. which are kev eloiueuts for the purpose of this work.," 2010) and this difference results in particular from the reduction in the past decade of the solar abundances of C, N, O and Ne, which are key elements for the purpose of this work." For obvious consistency reasons. we keep here the Anders aud Crevesse (1979) values. when comparing our results for CCR to solar oues.," For obvious consistency reasons, we keep here the Anders and Grevesse (1979) values, when comparing our results for GCR to solar ones." The first se of stellar models is the one of he Frascati group (Linonei and Chief 2006 1hereafter LCUG6).," The first set of stellar models is the one of the Frascati group (Limongi and Chieffi 2006, hereafter LC06)." It concerns 15 model stars between and 120 with mass loss but no rotation., It concerns 15 model stars between 11 and 120 with mass loss but no rotation. " The model includes all stages of hwdrostatic nuclear burning and simulates the fina stellar explosion by imparting an initial velocity to a mass coordinate of 1 (νο, well inside the Fe core of the stars): the mass cut (the init separating the ejecta of mass ffroii the compact reumant of mass )) 15 chosen such as VIAL. oof"" Ni is ejected by the explosion.", The model includes all stages of hydrostatic nuclear burning and simulates the final stellar explosion by imparting an initial velocity to a mass coordinate of 1 (i.e. well inside the Fe core of the stars); the mass cut (the limit separating the ejecta of mass from the compact remnant of mass ) is chosen such as 0.1 of $^{56}$ Ni is ejected by the explosion. The various masses involved in the“tov model” of Sec.," The various masses involved in the ""toy model"" of Sec." 2.1 and Fi, \ref{sub:Toy} and Fig. e.d are providedin Table 2 of LCO6 aux are displaved in Fig.2. left)," \ref{Fig:SNStruct} are provided in Table 2 of LC06 and are displayed in Fig.\ref{Fig:SNmasses} )" of this work. whereas derived quantities are displaved in Fig.," of this work, whereas derived quantities are displayed in Fig." 2. left)., \ref{Fig:SNmasses} ). It can be seen that stars with 30204. hhave lost a neeslieible amount of mass prior to the explosion CMiisngiMgj)) andthe ST. phase starts within the ambient ISAL, It can be seen that stars with $<$ 20 have lost a negligible amount of mass prior to the explosion $<$ ) andthe ST phase starts within the ambient ISM. Stars with L30M hhave i Wir," Stars with $>$ 30 have $>$ ," Stars with L30M hhave i Wire," Stars with $>$ 30 have $>$ ," Stars with L30M hhave i WireM," Stars with $>$ 30 have $>$ ," Stars with L30M hhave i WireMg," Stars with $>$ 30 have $>$ ," Stars with L30M hhave i WireMg.," Stars with $>$ 30 have $>$ ," reanalyse the Baskin Laor (2005) data. and the CIV line in a larger sample of AGN. and conclude that CIV is a robust measure BLR rotational velocity.,"reanalyse the Baskin Laor (2005) data, and the CIV line in a larger sample of AGN, and conclude that CIV is a robust measure BLR rotational velocity." This result is confirmed in Peng et al. (, This result is confirmed in Peng et al. ( Q006b). who find no significant offset between H.? and CIV linewidths in a sample of six ο1 quasars.,"2006b), who find no significant offset between $\beta$ and CIV linewidths in a sample of six $z\sim1$ quasars." Although possibly inferior to H.? and Mel. as the only line available at 21.5 it would seem both necessary and acceptable to utilise the CIV line as a proxy for BLR rotational velocity.," Although possibly inferior to $\beta$ and MgII, as the only line available at $z>1.5$ it would seem both necessary and acceptable to utilise the CIV line as a proxy for BLR rotational velocity." In Fig., In Fig. 5 (adapted from Miley De Breuck 2008 following, 5 (adapted from Miley De Breuck 2008 following 10960 and two less-eruptive ARs NOAA 10961 ancl 10963 obtained from the Solar Optical Telescope/Spectrvo-polarimeter (SOT/SP: Tsunetaetal.(2008):SuematsuIchimotoetal.(2003):Shimizu (2008))) onboard. IHinode (xosugietal.2007).,"10960 and two less-eruptive ARs NOAA 10961 and 10963 obtained from the Solar Optical Telescope/Spectro-polarimeter (SOT/SP: \cite {tsun08,suem08,ichi08,shim08}) ) onboard Hinode \citep{kosu07}." ". The Ilinode (SOT/SP) data have been calibrated by (he standard ""SP.PPREP routine developed bv D. Lites and available in the Solar-Solt package.", The Hinode (SOT/SP) data have been calibrated by the standard PREP” routine developed by B. Lites and available in the Solar-Soft package. The prepared polarization spectra have been inverted to obtain vector magnetic field components using an Unno-Rachkowsky (Unno1956:Rachkowsky1967). inversion under (he assumption of Milne-Eldington (ME) atinosphere (Landolli&LandiDeelInnocenti1982:Lites 1937).," The prepared polarization spectra have been inverted to obtain vector magnetic field components using an Unno-Rachkowsky \citep{unno56,rach67} inversion under the assumption of Milne-Eddington (ME) atmosphere \citep{lando82,skum87}." . We use the “STOWKESFIT™ inversion code which is available in the Solar-Solt package and was developed bx T. R. Metcall.," We use the “STOKESFIT"" inversion code which is available in the Solar-Soft package and was developed by T. R. Metcalf." The latest version of the inversion code is used which returns the true field strengths along with the filling factor., The latest version of the inversion code is used which returns the true field strengths along with the filling factor. There is an inherent 180 ambiguity in the azimuth determination due to the insensilivily of the Zeeman ellect to the sense of orientation of the transverse magnetic fields., There is an inherent $^{\circ}$ ambiguity in the azimuth determination due to the insensitivity of the Zeeman effect to the sense of orientation of the transverse magnetic fields. Numerous techniques have been developed and applied to resolve this problem (forMetcealfοἱal.2006:Lekaet 2009).. but a complete resolution is not expected from the physics of the Zeeman effect.," Numerous techniques have been developed and applied to resolve this problem \citep[for details see][]{metc06,leka09}, but a complete resolution is not expected from the physics of the Zeeman effect." The chirality of chromospheric aud coronal structures can be used as guides to complement the other methods., The chirality of chromospheric and coronal structures can be used as guides to complement the other methods. The 1807 azimuthal ambiguity in our data sets have been removed by using the acute angle method (llarvey1969:Sakurai1985:Cupermanοἱal. 1992).," The $^{\circ}$ azimuthal ambiguity in our data sets have been removed by using the acute angle method \citep{harv69,saku85,cupe92}." .. This method of ambiguity. resolution works very well for magnetic shear angles that are less (han 90 degrees., This method of ambiguity resolution works very well for magnetic shear angles that are less than 90 degrees. Less (han one percent pixels of anv vector magnetogram studied has shear 90 degrees., Less than one percent pixels of any vector magnetogram studied has shear $\sim 90$ degrees. Therefore. we expect that the acute angle method works well in all our cases.," Therefore, we expect that the acute angle method works well in all our cases." Most of the data sets used have a spatial sampling of ~0.3 arcsec/pixel., Most of the data sets used have a spatial sampling of $\sim0.3$ arcsec/pixel. " A few data sets are observed in “Normal Mode"" of SOT wilh a spatial sampling of ~0.16 arcsec/pixel."," A few data sets are observed in “Normal Mode"" of SOT with a spatial sampling of $\sim0.16$ arcsec/pixel." The noise in the data has been minimized in the similar wav as was done in, The noise in the data has been minimized in the similar way as was done in "lere n ids the plasma density. and. £5;,;. £7, and CE) are the injection energy of positrons. the energy. of thermal plasma. and the positron velocity. respectively. a;; is the cross-section of in-flieht annihilation.","Here $n$ is the plasma density, and $E_{inj}$ , $E_{th}$ and $v(E)$ are the injection energy of positrons, the energy of thermal plasma, and the positron velocity, respectively, $\sigma_{if}$ is the cross-section of in-flight annihilation." Phe function (dieδι is the rate of energy losses defined as sum of Coulomb. svnchrotron. inverse Compton. bremsstrahlung etc.," The function $(dE/dt)_{cl}$ is the rate of energy losses defined as sum of Coulomb, synchrotron, inverse Compton, bremsstrahlung etc." " losses: Η cooling of the positrons is only due to the Coulomb losses. then ry, and τι are proportional to n and the relation (1)) is independent of the medium. density."," losses: If cooling of the positrons is only due to the Coulomb losses, then $\tau_{if}$ and $\tau_{cl}$ are proportional to $n^{-1}$, and the relation \ref{tt_by}) ) is independent of the medium density." So. this ratio of the continuum in-lieht and the annihilation emission is universal and can be applied even to a medium. with an unknown clensity.," So, this ratio of the continuum in-flight and the annihilation emission is universal and can be applied even to a medium with an unknown density." Beacomand.Ytksel(2006) assumed. that positrons in the Galactic. center (CC) loose their energv by Coulomb interactions only. and they suggested to use this ratio for the analysis of the annihilating positron origin in the GC.," \citet{by2006} assumed that positrons in the Galactic center (GC) loose their energy by Coulomb interactions only, and they suggested to use this ratio for the analysis of the annihilating positron origin in the GC." In the above-mentioned. models the injection energv of positrons is expected in the range [rom several to. hundreds. MeV. Therefore. the in-Hieht gamma-ray emission is also expected in this energy range.," In the above-mentioned models the injection energy of positrons is expected in the range from several to hundreds MeV. Therefore, the in-flight gamma-ray emission is also expected in this energy range." The MeV. flux from the central part of the Galaxy was observed by COAIPTIEL (see.Strongetal.1905].," The MeV flux from the central part of the Galaxy was observed by COMPTEL \citep[see,][]{compt}." The origin of this emission is still unclear since the known processes of ganuna-ray production (like inverse Compton. bremsstrahlung etc.)," The origin of this emission is still unclear since the known processes of gamma-ray production (like inverse Compton, bremsstrahlung etc.)" are unable to generate the observed lux (Strongetal.2005:Porterc," are unable to generate the observed flux \citep{strong, portt}." t2008).. Chengetal.(2007) assumed that this excess in the GC clirection might be due to the in-flieht annihilation of fast. positrons., \citet{cheng2} assumed that this excess in the GC direction might be due to the in-flight annihilation of fast positrons. Llowever. it is observed. not only in the direction of the GC.," However, it is observed not only in the direction of the GC." Phe excess is almost constant along the Galactic disk (Strongetal.1998). where the intensity of annihilation emission is lower than in the Galactic centre., The excess is almost constant along the Galactic disk \citep{compt} where the intensity of annihilation emission is lower than in the Galactic centre. This makes problematic the in-Hight. interpretation of this excess in the disk since the ratio 511 keV. Dlux/in-Ilisht continuum is constant., This makes problematic the in-flight interpretation of this excess in the disk since the ratio 511 keV flux/in-flight continuum is constant. LE the in-Uieht flux is. responsible for. the MeV excess in a relatively narrow central region (Ss 57). absolutely the same excess in other parts of the disk remains unexplained (seeSizunetal.2006:Chernyshov2008).," If the in-flight flux is responsible for the MeV excess in a relatively narrow central region $\la 5^\circ$ ), absolutely the same excess in other parts of the disk remains unexplained \citep[see][]{sizun,chern1}." ". ""Therefore. in DeacomandYüksel(2006). and latter in Sizunetal.(2006) a more firm constraint on the in-light eamma-ray flux from the Calactic center was suggested."," Therefore, in \citet{by2006} and latter in \citet{sizun} a more firm constraint on the in-flight gamma-ray flux from the Galactic center was suggested." According to their. criterion. the in-Hlight. [Lux should not exceed several statistical errors of the COAL?PEL measurements., According to their criterion the in-flight flux should not exceed several statistical errors of the COMPTEL measurements. That. gives an upper limit for the injection energv about several MeV. Vhen moclels assuming higher injection energy should undoubtedly be rejected., That gives an upper limit for the injection energy about several MeV. Then models assuming higher injection energy should undoubtedly be rejected. Below we show that under some conditions the injection energy may be higher than LO MeV in contrast toconclusions made in papers mentioned above. and. thus. there is à room for models assuming injection of high energy positrons.," Below we show that under some conditions the injection energy may be higher than 10 MeV in contrast toconclusions made in papers mentioned above, and, thus, there is a room for models assuming injection of high energy positrons." Thus. Chengetal.(2006.2007) assumed that these positrons are secondary and generated. by collisions of relativistic protons injected. from. black hole jets.," Thus, \citet{cheng1,cheng2} assumed that these positrons are secondary and generated by collisions of relativistic protons injected from black hole jets." " Phe theoretical analysis of Istomin&Sol(2000)— confirmed the hadronic origin of jets and showed that protons were accelerated there by the stochastic and the centrifugal acceleration up to energies £,c107"" eV that might olfer an explanation to the recent results of the Pierre. Auger collaboration (Abrahamctal.2007).", The theoretical analysis of \cite{ist} confirmed the hadronic origin of jets and showed that protons were accelerated there by the stochastic and the centrifugal acceleration up to energies $E_p\simeq 10^{20}$ eV that might offer an explanation to the recent results of the Pierre Auger collaboration \citep{auger}. . LE such or similar mechanism produces indeed enough relativistic protons with Lorentz factor +z2 in the vicinity of the central black hole then we do expect there an elective production of secondary positrons with energies above 30 MeV. just as assumed in Chengetal.(2006.2007).," If such or similar mechanism produces indeed enough relativistic protons with Lorentz factor $\gamma \ga 2$ in the vicinity of the central black hole then we do expect there an effective production of secondary positrons with energies above 30 MeV, just as assumed in \cite{cheng1,cheng2}." . Processes of pop collisions produce also a lux of eamma-ravs in the range above 100 MeV by decay of zx -meson. and below this energy by. so-called. internal xenmsstrahlung radiation of secondary electrons. (sec.[ordetailLlavakawa1964).," Processes of $p-p$ collisions produce also a flux of gamma-rays in the range above 100 MeV by decay of $\pi^\circ$ -meson, and below this energy by, so-called, internal bremsstrahlung radiation of secondary electrons \citep[see for detail][]{haya}." . A Εις of gamma-rays in the 1 o 30 MeV. range from internal bremsstrahlung may be uveher than the mentioned in-Dight flux., A flux of gamma-rays in the 1 to 30 MeV range from internal bremsstrahlung may be higher than the mentioned in-flight flux. Phus. Beacometal.(2005) showed that the internal bremsstrahlung [lux is very significant. if positrons in the GC are. generated. by. dark matter annihilation.," Thus, \citet{bbb} showed that the internal bremsstrahlung flux is very significant, if positrons in the GC are generated by dark matter annihilation." Hlowever. in the dark. matter mocel »ositron. production in the GC is stationary.," However, in the dark matter model positron production in the GC is stationary." On the other vane. from the restrictions derived. from EGRET data it ollows that the positron production in the GC should. be strongly non-stationary. if these positrons are generated by pp collisions (Chengetal.2006.2007).," On the other hand, from the restrictions derived from EGRET data it follows that the positron production in the GC should be strongly non-stationary, if these positrons are generated by $p-p$ collisions \citep{cheng1, cheng2}." . Ehe Dux of gamma-ravs [rom pp collisions is significant during a very. short period after a star accretion onto the black hole., The flux of gamma-rays from $p-p$ collisions is significant during a very short period after a star accretion onto the black hole. At present this [lux has decreased in several orders of magnitude from its initial value and. therefore. is unseen.," At present this flux has decreased in several orders of magnitude from its initial value and, therefore, is unseen." 3clow in section ?? we shall show that the condition of non-stationarity is also required to fit radio observations.," Below in section \ref{sc_mag} we shall show that the condition of non-stationarity is also required to fit radio observations." As follows from observations. the central 200 pe region of the Galaxy is strongly. nonuniform.," As follows from observations, the central 200 pc region of the Galaxy is strongly nonuniform." The inner bulge (200-300 pe) contains (7.9)«10AZ. of hydrogen gas., The inner bulge (200-300 pc) contains $(7-9)\times 10^7~M_\odot$ of hydrogen gas. In spite of relatively small radius this region. contains about of the Galaxy's molecular mass., In spite of relatively small radius this region contains about of the Galaxy's molecular mass. Most. of the molecular gas is contained in very compact elouds of mass 103—107AZ.. average censities -10tem.," Most of the molecular gas is contained in very compact clouds of mass $10^4-10^6M_\odot$, average densities $\geq 10^4$ $^{-3}$." Llowever. this molecular gas occupies a rather small part of the central region. most of which is filled. with a very hot gas.," However, this molecular gas occupies a rather small part of the central region, most of which is filled with a very hot gas." ASC'A Ixovamaetal.(1996). measured the X-rav spectrum in the inner 150 pe region which exhibited a number of emission lines from highly ionized. elements which are characteristics fora S10 keV plasma with the density 0.4 cm.?., ASCA \cite{koya1} measured the X-ray spectrum in the inner 150 pc region which exhibited a number of emission lines from highly ionized elements which are characteristics fora $8-10$ keV plasma with the density 0.4 $^{-3}$. " Later on Chandra observations of Munoetal.(2004). showed an intensive X-rav emission at the energy ££,~δ keV [rom the inner 20 pe of the Galaxy.", Later on Chandra observations of \cite{muno} showed an intensive X-ray emission at the energy $E_x\sim 8$ keV from the inner 20 pc of the Galaxy. Phe plasma density was estimated in limits 0.1.0.2 *., The plasma density was estimated in limits $0.1-0.2$ $^{-3}$. Recent SUZAKU measurements of the 6.9/6.7 keV iron line ratio (Ixovanmactal.2007) was naturally explained by a thermal emission of 6.5keV-tempoerature plasma., Recent SUZAKU measurements of the 6.9/6.7 keV iron line ratio \citep{koya2} was naturally explained by a thermal emission of 6.5keV-temperature plasma. One should. note that there is no consensus on the magnetic field strength in the GC., One should note that there is no consensus on the magnetic field strength in the GC. Estimations ranges from about or smaller than hundred. µ (seeSpergelandBlitz 2009)... up to several mG (Plante.LoandCrutcher1995:Yuseft-Zadoehetal. 1999.. see in this respect the review of Ferriere 2009)).," Estimations ranges from about or smaller than hundred $\mu$ G \citep[see][]{spergel, radio, higdon}, , up to several mG \citealt{plante, yuza1}, , see in this respect the review of \citealt{ferri}) )." Itaclio observations of the central regions show that the structure of, Radio observations of the central regions show that the structure of 2006).,. . This program is highly specialized and generally cannot be applied outside of pulsar timing observations. but many of the effects they consider are relevant to optical observers in the exoplanet community.," This program is highly specialized and generally cannot be applied outside of pulsar timing observations, but many of the effects they consider are relevant to optical observers in the exoplanet community." In this article. we summarize the effects one must consider in order to achieve timing accuracy of | js — well beyond the accuracy that will likely be required by the exoplanet community for the foreseeable future.," In this article, we summarize the effects one must consider in order to achieve timing accuracy of 1 $\mu$ s – well beyond the accuracy that will likely be required by the exoplanet community for the foreseeable future." Section 2 provides the background required to understand each of the effects that could change the arrival time of a photon., Section \ref{theory} provides the background required to understand each of the effects that could change the arrival time of a photon. They are listed in order of decreasing magnitude. so latter subsections can be ignored for low-precision measurements.," They are listed in order of decreasing magnitude, so latter subsections can be ignored for low-precision measurements." Section 3. discusses the practical limitations to achieving high-precision timing., Section \ref{practice} discusses the practical limitations to achieving high-precision timing. We begin with the effects which may cause errors that are comparable to or exceed the BJD correction., We begin with the effects which may cause errors that are comparable to or exceed the BJD correction. These should be read and understood by everyone., These should be read and understood by everyone. We continue with remaining effects. in order of decreasing magnitude. which can be ignored for low-precision (730 ms) measurements.," We continue with remaining effects, in order of decreasing magnitude, which can be ignored for low-precision $> 30$ ms) measurements." We conclude 33 by listing additional effects. the errors due to which are negligible (— {μ5).," We conclude 3 by listing additional effects, the errors due to which are negligible $< 1\mu$ s)." We begin refsec:calculating by detailing the procedure one must follow in order to calculate theBJD;pg.. which is designed to be a useful reference for those already familiar with the concepts of precision timing.," We begin \\ref{sec:calculating} by detailing the procedure one must follow in order to calculate the, which is designed to be a useful reference for those already familiar with the concepts of precision timing." In the latter part of this section. we describe our particular IDL and web-based implementation of this procedure.," In the latter part of this section, we describe our particular IDL and web-based implementation of this procedure." Lastly. in the Appendix. we discuss some of our specific findings about the time stamps currently in use and how these are calculated throughout the exoplanet community.," Lastly, in the Appendix, we discuss some of our specific findings about the time stamps currently in use and how these are calculated throughout the exoplanet community." While we focus on the effects of timing on the optical/infrared exoplanet community. timing precision of order | minute is necessary for many other areas. such as the study of rapidly rotating white dwarfs (Euchneretal.2006).," While we focus on the effects of timing on the optical/infrared exoplanet community, timing precision of order 1 minute is necessary for many other areas, such as the study of rapidly rotating white dwarfs \citep{euchner06}." . This article should be equally applicable in such cases., This article should be equally applicable in such cases. The biggest source of confusion comes from the fact that time standards and reference frames are independent from one another. even though there are many overlapping concepts between the two.," The biggest source of confusion comes from the fact that time standards and reference frames are independent from one another, even though there are many overlapping concepts between the two." " We will use the following terminology: ""reference frame"" will refer to the geometric location from which one could measure time — different reference frames differ by the light-travel time between them: ""time standard"" will refer to the way a particular clock ticks and its arbitrary zero point. as defined by international standards: and ""time stamp"" is the combination of the two. and determines the timing accuracy of the event."," We will use the following terminology: “reference frame” will refer to the geometric location from which one could measure time – different reference frames differ by the light-travel time between them; “time standard” will refer to the way a particular clock ticks and its arbitrary zero point, as defined by international standards; and “time stamp” is the combination of the two, and determines the timing accuracy of the event." TheBJD4pp.. the time stamp we advocate. can be calculated using the equation: where us the Julian Date in Coordinated Universal Time: Ay... is the Romer Delay. discussed in refsec:roemer: Ac is the clock correction discussed in refsee:clock:; Ag.. is the Shapiro delay discussed in refsee:shapiro:: and A.. is the Einstein delay. discussed in refsec:einstein..," The, the time stamp we advocate, can be calculated using the equation: where is the Julian Date in Coordinated Universal Time; $\Delta_{R\odot}$ is the mer Delay, discussed in \\ref{sec:roemer}; $\Delta_{C}$ is the clock correction discussed in \\ref{sec:clock}; $\Delta_{S\odot}$ is the Shapiro delay discussed in \\ref{sec:shapiro}; and $\Delta_{E\odot}$ is the Einstein delay, discussed in \\ref{sec:einstein}." The order of these terms is such that they are of decreasing magnitude. so one need only keep the terms up to the precision required.," The order of these terms is such that they are of decreasing magnitude, so one need only keep the terms up to the precision required." The timing precision required by current exoplanet studies (~ 1 s) requires only the terms up to and including Ac., The timing precision required by current exoplanet studies $\sim$ 1 s) requires only the terms up to and including $\Delta_{C}$. Because future Solar System ephemerides may enable more precise calculations of the arrival time at the Barycenter. or in order to allow others to check that the original conversion was done accurately enough for their purpose. the site arrival time (e.g.. the JDuyc)) should always be quoted in addition to thepp.," Because future Solar System ephemerides may enable more precise calculations of the arrival time at the Barycenter, or in order to allow others to check that the original conversion was done accurately enough for their purpose, the site arrival time (e.g., the ) should always be quoted in addition to the." Due to the finite speed of light. as the Earth travels in its orbit. light from an astrophysical object may arrive early or be delayed by as much as 8.3 minutes from the intrinsic time of the extraterrestrial event.," Due to the finite speed of light, as the Earth travels in its orbit, light from an astrophysical object may arrive early or be delayed by as much as 8.3 minutes from the intrinsic time of the extraterrestrial event." This is called the Romer delay. Ap. in honor of Ole Rémer's demonstration that the speed of light is finite.," This is called the mer delay, $\Delta_{R}$, in honor of Ole mer's demonstration that the speed of light is finite." Since most observers cannot observe during daylight. a bias is introduced and in practice the delay (as distinct from the early arrival time) is only as much as 7 minutes. for a peak- variation of 15 minutes.," Since most observers cannot observe during daylight, a bias is introduced and in practice the delay (as distinct from the early arrival time) is only as much as 7 minutes, for a peak-to-peak variation of 15 minutes." Figure 1. shows an example of this effect for a maximally affected object on the ecliptic., Figure \ref{fig:bjdvjd} shows an example of this effect for a maximally affected object on the ecliptic. In order to show the observational bias. our example assumes the object is at O right ascension and 07 declination.," In order to show the observational bias, our example assumes the object is at $^\textrm{h}$ right ascension and $^{\circ}$ declination." This curve shifts in phase with ecliptic longitude and in amplitude with ecliptic latitude., This curve shifts in phase with ecliptic longitude and in amplitude with ecliptic latitude. We also place our observer at the Earth's equator. but note that the asymmetry will be larger at different latitudes.," We also place our observer at the Earth's equator, but note that the asymmetry will be larger at different latitudes." The solution to this problem is to calculate the time when a photon would have arrived at an inertial reference frame., The solution to this problem is to calculate the time when a photon would have arrived at an inertial reference frame. This time delay 15 the dot product of the unit vector from the observer to the object. 7. and the vector from the origin of the new reference frame to the observer. 7 where c is the speed of light and 7 can be written in terms of its right ascension (0) and declination (à).," This time delay is the dot product of the unit vector from the observer to the object, $\hat{n}$, and the vector from the origin of the new reference frame to the observer, $\vec{r}$ where $c$ is the speed of light and $\hat{n}$ can be written in terms of its right ascension $\alpha$ ) and declination $\delta$ )," According to the stanclarcl Cosmological |mocel. CAB temperature anisotropies are caused by the inhomogeneities in the distribution of matter and radiation. present at the decoupling time.,"According to the standard cosmological model, CMB temperature anisotropies are caused by the inhomogeneities in the distribution of matter and radiation present at the decoupling time." These inhomogeneities are the product of quantum. [uctuations amplified in the inflationary cra and follow a Gaussian statistical distribution., These inhomogeneities are the product of quantum fluctuations amplified in the inflationary era and follow a Gaussian statistical distribution. " ""Therefore. the observed CMD anisotropies are a realization. of a homogeneousὃν ancl isotropic Caussian random field on the sphere."," Therefore, the observed CMB anisotropies are a realization of a homogeneous and isotropic Gaussian random field on the sphere." Nevertheless. some degree of non-Ciaussianity can be introduced. for instance. by non standard inllation etαἱ.2004). or by topological defects (TurokandSperecl990:Durrer 1999).," Nevertheless, some degree of non-Gaussianity can be introduced, for instance, by non standard inflation \citep{bar04} or by topological defects \citep{tur90,dur99}." . The analysis of the first and three-vear Wilkinson Microwave Anisotropy Probe (WALAP) data by the WALAP team shows that CMD temperature [uctuations are consistent with a Gaussian distribution (Ixomatsuetal.2003:Spergeletal.2006). in agreement with the standard inflation paradigm.," The analysis of the first and three-year Wilkinson Microwave Anisotropy Probe (WMAP) data by the WMAP team shows that CMB temperature fluctuations are consistent with a Gaussian distribution \citep{kom03,spe06} in agreement with the standard inflation paradigm." However. some studies have detected non-Gaussian features in the WALAD data. for instance in Vielvaοἱal.(2004) and Cruzetal.CX105.2006) à cold non-Gaussian spot of unknown origin was detected and studied by using the Spherical Mexican Hat Wavelet.," However, some studies have detected non-Gaussian features in the WMAP data, for instance in \cite{vie04} and \cite{cru05,cru06} a cold non-Gaussian spot of unknown origin was detected and studied by using the Spherical Mexican Hat Wavelet." Non-Caussian signatures have also been found by using dillerent methods:, Non-Gaussian signatures have also been found by using different methods: eravothermal contraction makes the iuner regions of clusters rouuder as they evolve.,gravothermal contraction makes the inner regions of clusters rounder as they evolve. Furticrinore. the outer regions of clusters are exected. to become roundoer wit1 age due to the striyping of stars by external tidal fields.," Furthermore, the outer regions of clusters are expected to become rounder with age due to the stripping of stars by external tidal fields." Ou the other haud. tidal fields wieht also be able to stretch custers and mase theu more elongated.," On the other hand, tidal fields might also be able to stretch clusters and make them more elongated." Finally Goodwin (1997) 1las poluted out that strong tidal fields might rapidlv destroy velocity anisotropics in initially tri-axial rotatirg elolnmlar clusters., Finally Goodwin (1997) has pointed out that strong tidal fields might rapidly destroy velocity anisotropies in initially tri-axial rotating globular clusters. Mergers night produc! highly flattenvcd clusters., Mergers might produce highly flattened clusters. However. the absence of binary Galactic ο]ο]mlar clusters. and the paucity of voine binary cluscrs ise and. \ Persei. suggests that this process may not have been an iuporaut factor in shaping Calactie stew clusters.," However, the absence of binary Galactic globular clusters, and the paucity of young binary clusters like and $\chi$ Persei, suggests that this process may not have been an important factor in shaping Galactic star clusters." In this connection it is of interes to note tha the clusters NGC 6388 aud NGC 61l. which might be regarded as possible merger suspects because they :we composed of sellar populaions with slielrlv different ages (Piotto 2008). ive observed to be almost circuar in outline with axial ratios of 0.99 aud 0.98. res)ectively.," In this connection it is of interest to note that the clusters NGC 6388 and NGC 6441, which might be regarded as possible merger suspects because they are composed of stellar populations with slightly different ages (Piotto 2008), are observed to be almost circular in outline with axial ratios of 0.99 and 0.98, respectively." Following Hubble (1936) the flattening of globular clusters will be defined as εξ fa-b}/u. where«aud b are the major and muner axes of the cluster.," Following Hubble (1936) the flattening of globular clusters will be defined as $\epsilon$ =, where and are the major and minor axes of the cluster." Miickey aud van deu Bergh list values of e for 91 globular clusters., Mackey and van den Bergh list values of $\epsilon$ for 94 globular clusters. " The flatteningC» values of Calactic Ooglobular clusters were derived by Wute Shawl (1987) frou images iu blue helt uxiug the Palomar aud SRC Sky Survevs,", The flattening values of Galactic globular clusters were derived by White Shawl (1987) from images in blue light using the Palomar and SRC Sky Surveys. A weakuess of this database is that the derived cluster flattening values do not all refer to asandard isophote such as tie cluser halflieht radius., A weakness of this database is that the derived cluster flattening values do not all refer to a standard isophote such as the cluster half-light radius. Mackey aud van den Berel (2005) list values of e for a total of 91 Galactic elobula rclusters., Mackey and van den Bergh (2005) list values of $\epsilon$ for a total of 94 Galactic globular clusters. " Two of these objects. w Centauri = NGC5]39 aud M51 = NGC 6715 :we widely regarded as beiis the stripped cores of now de""nct dwarf spheroidals aud wi] therefore be oiited from the present stilv."," Two of these objects, $\omega$ Centauri = NGC 5139 and M54 = NGC 6715 are widely regarded as being the stripped cores of now defunct dwarf spheroidals and will therefore be omitted from the present study." Daa on the ellipticity of al POMS Caactic globular custers for which this infornation is available are plotted i Figure 1., Data on the ellipticity of all remaining Galactic globular clusters for which this information is available are plotted in Figure 1. This fisoκure clearly shows tha the faiatest Galactic globular clusters are also the flattes ones., This figure clearly shows that the faintest Galactic globular clusters are also the flattest ones. Furthermore the data in the re strongly lin at the possibility that tl1C luos stronely reddened Galactic elobular clusers (which are plotted im red) lay appear more flattened than he less redeued Galactic elobular clusters (plotted iu blue)., Furthermore the data in the figure strongly hint at the possibility that the most strongly reddened Galactic globular clusters (which are plotted in red) may appear more flattened than the less reddened Galactic globular clusters (plotted in blue). " Iun tje the present analysis are all clusters wit LA, > 1.0 mag [A = 3.1 E(D-V) assmucd have been excluded because t1011 apparent fliatteniug nielt have been affected by patchy foreground absorption.", In the the present analysis are all clusters with $A_{v}$ $>$ 1.0 mag $A_{v}$ = 3.1 E(B-V) assumed] have been excluded because their apparent flattening might have been affected by patchy foreground absorption. " The most blatant examje of this effect is provide by AD9 (= NGC 6273). which has A, = 1.27 mag aud is the flattest (e = 0.27) shown Galactic elobular cluster."," The most blatant example of this effect is provided by M19 (= NGC 6273), which has $A_{v}$ = 1.27 mag and is the flattest $\epsilon$ = 0.27) known Galactic globular cluster." It suffers heavy absorption along its castern edee (van den Bergh 1982a)., It suffers heavy absorption along its eastern edge (van den Bergh 1982a). M19 is also observed to exubit srong cdiffercutial iuterual reddening (Iiis. Racine deRoux 1976). but according to unpublished «ybservations by Rosine. quoted by Coutts Clement Sawyer Ποσο (1978). it shows little fattening at infrared svaveleuethis.," M19 is also observed to exhibit strong differential internal reddening (Harris, Racine deRoux 1976), but according to unpublished observations by Rosino, quoted by Coutts Clement Sawyer Hogg (1978), it shows little flattening at infrared wavelengths." " A IKoliuosorov-Suuiruov test shows a probability that Calactic elobilar clusters wi hA, lO mag appear. oji average. more lighly fattened than those with A, « 1.0 mac."," A Kolmogorov-Smirnov test shows a probability that Galactic globular clusters with $A_{v}$ $>$ 1.0 mag appear, on average, more highly flattened than those with $A_{v}$ $<$ 1.0 mag." This result justies a strong suspicion that he appareut flateniues of lighly reddened clusters have Όσοι adfected by asvietric foreground absorption., This result justifies a strong suspicion that the apparent flattenings of highly reddened clusters have been affected by asymmetric foreground absorption. It therefore seemed prudent to ouut such highly absorbed clusers from our ¢iscussion of the iutrisic flatenine distribuion in all nearby ealaxies., It therefore seemed prudent to omit such highly absorbed clusters from our discussion of the intrinsic flattening distribution in all nearby galaxies. Data on the flattening disributious of the 51 Galactic globular clusers having bot dehy 1.0 mas. and published e values. are collected in Table 1.," Data on the flattening distributions of the 54 Galactic globular clusters having both $A_{v}$ $<$ 1.0 mag, and published $\epsilon$ values, are collected in Table 1." " The data iu this table. which are plotted im Figure 2. show that intriusicallv faint Galactic elobular clusters with M,> -7.0 are flatter than more luinous ones having AL, τιν"," The data in this table, which are plotted in Figure 2, show that intrinsically faint Galactic globular clusters with $M_{v} >$ -7.0 are flatter than more luminous ones having $M_{v} <$ -7.0." A KRoliogorov-Suirov test shows that there is only a probability that the uuimous aud the faiut cluster samples were drawn frou the same pareut population., A Kolmogorov-Smirnov test shows that there is only a probability that the luminous and the faint cluster samples were drawn from the same parent population. This conclusion strenetlens aud coufiruis, This conclusion strengthens and confirms The constraints we placed previously were on how high Neptune’s eccentricity and inclination can remain indefinitely.,The constraints we placed previously were on how high Neptune's eccentricity and inclination can remain indefinitely. " During secular evolution, planetesimals reach eccentricities up to 2€forceeq and inclinations up to 2erocea."," During secular evolution, planetesimals reach eccentricities up to $2 \eforced$ and inclinations up to $2\eforced$." " However the planetesimals evolve to final values less than these maximum values, when Neptune's eccentricity and inclination damp."," However the planetesimals evolve to final values less than these maximum values, when Neptune's eccentricity and inclination damp." " Here we refine the limits on Neptune's eccentricity and inclination in light of damping, considering a range of timescales for the dynamical-friction-driven damping rates of ew and iyw."," Here we refine the limits on Neptune's eccentricity and inclination in light of damping, considering a range of timescales for the dynamical-friction-driven damping rates of $e_N$ and $i_N$." The actual damping timescales depend on the surface density and size distribution of the planetesimals., The actual damping timescales depend on the surface density and size distribution of the planetesimals. " To first order the effects on the planetesimals of Neptune’s inclination and eccentricity, including damping, can be treated independently."," To first order, the effects on the planetesimals of Neptune's inclination and eccentricity, including damping, can be treated independently." " In first-order secular theory (Section 3.2)), the evolution of a planetesimal’s e is independent of Neptune’s inclination in and of a planetesimal’s { is independent of Neptune’s eccentricity ew."," In first-order secular theory (Section \ref{subsec:sec}) ), the evolution of a planetesimal's $e$ is independent of Neptune's inclination $i_N$ and of a planetesimal's $i$ is independent of Neptune's eccentricity $e_N$." Thus we can place constraints on the evolution of Neptune’s eccentricity without taking into account its inclination or vice versa., Thus we can place constraints on the evolution of Neptune's eccentricity without taking into account its inclination or vice versa. Fig., Fig. 8 illustrates the independence of the eccentricity and inclination parameters., \ref{fig:dampboth} illustrates the independence of the eccentricity and inclination parameters. doown decreasesthe fromx-axis.,own the x-axis. "top In this section, we take labelsec:halo,rojectionsthe opposite approach from the previous section and examine projections of individual objects."," In this section, we take the opposite approach from the previous section and examine projections of individual objects." " We begin with our list of halos and make radial profiles that start at the density peak and continue to the previously found rogo, defined here as the radius where ó=p/p200."," We begin with our list of halos and make radial profiles that start at the density peak and continue to the previously found $r_{200}$, defined here as the radius where $\delta \equiv \rho/\bar{\rho} = 200$." " We call the mass enclosed within this radius the virialmass, and also record several other quantities, such as X-ray luminosity and radio power within the virial radius."," We call the mass enclosed within this radius the $virial~mass$, and also record several other quantities, such as X-ray luminosity and radio power within the virial radius." We begin by demonstrating the power of having a large sample of clusters in a single simulation by projecting the 51 most massive clusters at z=0 along the in in Figure 7.., We begin by demonstrating the power of having a large sample of clusters in a single simulation by projecting the 51 most massive clusters at $z=0$ along the x-axis in in Figure \ref{fig:halos}. The width and depth of each individual projection here is 4 The most important result gleaned Mpc/h.from these images is the morphological properties of cluster structure., The width and depth of each individual projection here is 4 Mpc/h. The most important result gleaned from these images is the morphological properties of cluster structure. " If we first examine the gas density we see that while there is some amount of substructure,(top), the density is centrally concentrated."," If we first examine the gas density (top), we see that while there is some amount of substructure, the density is centrally concentrated." " Since X-ray emission closely follows the density distribution of the gas, this implies that the X-ray emission will be brightest in the centers of clusters."," Since X-ray emission closely follows the density distribution of the gas, this implies that the X-ray emission will be brightest in the centers of clusters." " However, the radio emission (bottom) is brightest on the edges of the clusters and has very little correlation with the density structure."," However, the radio emission (bottom) is brightest on the edges of the clusters and has very little correlation with the density structure." " Instead, it more closely follows the temperature structure "," Instead, it more closely follows the temperature structure (middle)." This is because the temperature is more strongly (middle).affected by shocks than the density (recall p2/p1<4 from shock jump conditions for y= , This is because the temperature is more strongly affected by shocks than the density (recall $\rho_2/\rho_1 \le 4$ from shock jump conditions for $\gamma=5/3$ ). "Note, however, that the emission is still confined 5/3).within high density regions inside the virial radius."," Note, however, that the emission is still confined within high density regions inside the virial radius." " Immediately from these images, we expect radio emission to be anti-coincident with the X-ray emission, as is seen in existing relic examples (????).."," Immediately from these images, we expect radio emission to be anti-coincident with the X-ray emission, as is seen in existing $relic$ examples \citep{Giacintucci:2008aa, van-Weeren:2009ab, Bonafede:2009aa, Clarke:2006aa}." This behavior implies that shocks are more likely to appear in radio imaging than in X-ray surface brightness maps., This behavior implies that shocks are more likely to appear in radio imaging than in X-ray surface brightness maps. Also visible in the radio emission are common features such as arcs and rings., Also visible in the radio emission are common features such as arcs and rings. These features are due to merging subclusters as their bow shocks propagate through the ICM., These features are due to merging subclusters as their bow shocks propagate through the ICM. These shapes are similar to what is seen in observed radio relics., These shapes are similar to what is seen in observed radio relics. " T'his similarity supports our claim that the morphology of these objects is related to the location of shocks, as was originally suggested in ?.."," This similarity supports our claim that the morphology of these objects is related to the location of shocks, as was originally suggested in \citet{Ensslin:1998aa}." " In a few rare situations (here in 2-3 clusters), these arcs appear in the very center of the cluster."," In a few rare situations (here in 2-3 clusters), these arcs appear in the very center of the cluster." " Because the surrounding medium is both hot and quite dense in these cases, the radio emission is very strong."," Because the surrounding medium is both hot and quite dense in these cases, the radio emission is very strong." " This agrees with our previous results from Section ??,, where we found the bulk of the emission at late times to be in the hot, dense phase of the gas."," This agrees with our previous results from Section \ref{sec:phase}, where we found the bulk of the emission at late times to be in the hot, dense phase of the gas." " From the projectionsass of individual halos in Figure 7,, we can see that there is a general trend for the more massive halos to have higher radio emission (note masses decrease from the top left to bottom right)."," From the projections of individual halos in Figure \ref{fig:halos}, we can see that there is a general trend for the more massive halos to have higher radio emission (note masses decrease from the top left to bottom right)." We now want to quantify this scaling relationship by studying the radio luminosity-mass relationship for the halos in our simulations., We now want to quantify this scaling relationship by studying the radio luminosity-mass relationship for the halos in our simulations. We begin with the earlier list of halos and use the virial quantities of each halo., We begin with the earlier list of halos and use the virial quantities of each halo. " For each halo, we use their total mass and 1.4 GHz radio power (integrated out to rogo) to populate Figure 8.."," For each halo, we use their total mass and 1.4 GHz radio power (integrated out to $r_{200}$ ) to populate Figure \ref{fig:lum_mass_64}." " Second, for the distribution of halos, we now determine the linear-least squares fit to log(PiacHz)=Alog(Moo) for all halos with Maog>10?Mc and 2x101?Mo for --Bthe relic64 and"," Second, for the distribution of halos, we now determine the linear-least squares fit to $\mathrm{log}(P_{1.4GHz}) = \mathrm{A} \mathrm{log}(M_{200}) + \mathrm{B}$ for all halos with $M_{200} > 10^{13}M_\odot$ and $2\times10^{13}M_\odot$ for the $relic64$ and" parameters from cosmic shear and galaxy survey data.,parameters from cosmic shear and galaxy survey data. " With this approach, the extra information about IAs provided by galaxy surveys is used to produce less biased cosmological constraints from cosmic shear."," With this approach, the extra information about IAs provided by galaxy surveys is used to produce less biased cosmological constraints from cosmic shear." We combine constraints from the two datasets by simply adding together their x? values., We combine constraints from the two datasets by simply adding together their $\chi^2$ values. This is acceptable given that the surveys do not overlap significantly., This is acceptable given that the surveys do not overlap significantly. We calculate x? values from both datasets as a function of both IA parameters and cosmological parameters., We calculate $\chi^2$ values from both datasets as a function of both IA parameters and cosmological parameters. For the shear-shear dataset the IA parameters enter via the IA power spectra (Eq., For the shear-shear dataset the IA parameters enter via the IA power spectra (Eq. and Eq. [16)), \ref{eq:P_II_halo_general} and Eq. \ref{eq:P_GI_halo_general}) ) which are projected onto the sky (Eq., which are projected onto the sky (Eq. [5] and Eq. [9 , \ref{eq:C_II_fn_of_PEE} and Eq. \ref{eq:C_GI_fn_of_PdgI}) ) and added to the cosmic shear contribution to produce the full shear-shear power spectrum (Eq. a, and added to the cosmic shear contribution to produce the full shear-shear power spectrum (Eq. \ref{eq:shear_shear_Cl}) ) nd the correlation function is calculated by Eq. Bl., and the correlation function is calculated by Eq. \ref{eq:Cl_to_corrfn}. The B)shear-position correlation functions are computed from the shear-density correlation function (Eq. w, The shear-position correlation functions are computed from the shear-density correlation function (Eq. \ref{eq:wgplus}) ) hich is a inverseHankel transform (Eq. of the [I8)), which is a inverseHankel transform (Eq. \ref{eq:wdeltaplus}) ) relevant IA power spectrum (Eq. , of the relevant IA power spectrum (Eq. \ref{eq:C_GI_fn_of_PdgI}) ). The bias [))values given in are [6)).calculated from measurements of galaxy clustering (position-position correlation functions) and therefore depend on the assumed value of og., The bias values given in \cite{hirataea07} are calculated from measurements of galaxy clustering (position-position correlation functions) and therefore depend on the assumed value of $\sigma_8$. We take this into account to obtain a bias values for each og value considered., We take this into account to obtain a bias values for each $\sigma_8$ value considered. " As discussed at the end of Section we fix og in the IA power spectra and allow (μι to vary in [2.2],the linear theory matter power spectrum contribution to the two-halo term."," As discussed at the end of Section \ref{sec:IA_basics}, we fix $\sigma_8$ in the IA power spectra and allow $\Omega_m$ to vary in the linear theory matter power spectrum contribution to the two-halo term." " First we allow only og and A, the amplitude of the IA signal, to vary, with the rest of the cosmological parameters set to their fiducial values and a fixed luminosity dependence power law slope B=1.44 (thebest-fitvaluegivenin"," First we allow only $\sigma_{\rm 8}$ and $A$, the amplitude of the IA signal, to vary, with the rest of the cosmological parameters set to their fiducial values and a fixed luminosity dependence power law slope $\beta = 1.44$ \citep[the best-fit value given in][]{hirataea07}." results are shown in Fig., The results are shown in Fig. [ῆ 68% confidence contours Thein og-A parameter space., \ref{fig:Cls_s8_A} as $\%$ confidence contours in $\sigma_8$ $A$ parameter space. Contours areas shown for the shear-position correlation functions (nearly vertical lines) shear-shear correlation functions (nearly horizontally elongated contour)and the combined constraint (roughly at the intersection)., Contours are shown for the shear-position correlation functions (nearly vertical lines) shear-shear correlation functions (nearly horizontally elongated and the combined constraint (roughly at the intersection). The shear-position correlation function constraints on the IA amplitude parameter A for the fiducial og value are as expected from Fig., The shear-position correlation function constraints on the IA amplitude parameter $A$ for the fiducial $\sigma_8$ value are as expected from Fig. " [8 for the fixed 8 value, with A significantly larger than zero."," \ref{fig:Cls_A_beta} for the fixed $\beta$ value, with $A$ significantly larger than zero." In the analysis of the shear-position correlation function data os is held fixed in in the calculation of all our ΤΑ models., In the analysis of the shear-position correlation function data $\sigma_{\rm 8}$ is held fixed in in the calculation of all our IA models. " However, the variation of galaxy bias as a function of cs produces the expected degeneracy with A."," However, the variation of galaxy bias as a function of $\sigma_{\rm 8}$ produces the expected degeneracy with $A$." " Increasing og above the fiducial value decreases galaxy bias, requiring a greater A to compensate and vice-versa."," Increasing $\sigma_{\rm 8}$ above the fiducial value decreases galaxy bias, requiring a greater $A$ to compensate and vice-versa." " The shear-shear correlation functions do themselves place some constraint on the IA parameter A, preferring a range of order unity."," The shear-shear correlation functions do themselves place some constraint on the IA parameter $A$, preferring a range of order unity." A negative value of A would correspond to galaxies pointing in the opposite direction to that used in the standard models., A negative value of $A$ would correspond to galaxies pointing in the opposite direction to that used in the standard models. The linear alignment model (two-halo term) would contain galaxies pointing perpendicular to the tidal stretching expected by the gravitational potential curvature., The linear alignment model (two-halo term) would contain galaxies pointing perpendicular to the tidal stretching expected by the gravitational potential curvature. The one-halo picture would contain galaxies which are aligned tangentially to the center of the halo., The one-halo picture would contain galaxies which are aligned tangentially to the center of the halo. We described earlier a rough picture of shear-shear correlation function constraints in which essentially the data measure the amplitude and slope of the correlation function., We described earlier a rough picture of shear-shear correlation function constraints in which essentially the data measure the amplitude and slope of the correlation function. " The amplitude essentially fixes a degenerate combination of og and A, and the constraint on A must therefore come from the shape of the correlation function."," The amplitude essentially fixes a degenerate combination of $\sigma_8$ and $A$, and the constraint on $A$ must therefore come from the shape of the correlation function." " For the fiducial Qm, Fig."," For the fiducial $\Omega_{\rm m}$, Fig." [7] tells us that a large IA contribution to the shear-shear power spectra distorts them too much., \ref{fig:Cls_s8_A} tells us that a large IA contribution to the shear-shear power spectra distorts them too much. " This can be understood by examining Fig. D],"," This can be understood by examining Fig. \ref{fig:corrfns_100sqdeg}," " in which the data points fit well with the shape of the lensing-only (“No IA"") predictions, whereas the halo model predictions tend to be more curved over the scales probed."," in which the data points fit well with the shape of the lensing-only (“No IA"") predictions, whereas the halo model predictions tend to be more curved over the scales probed." The direction of degeneracy between A and og from shear-shear information alone can also be understood in terms of the shear-shear correlation function datapoints in Fig. [D]., The direction of degeneracy between $A$ and $\sigma_8$ from shear-shear information alone can also be understood in terms of the shear-shear correlation function datapoints in Fig. \ref{fig:corrfns_100sqdeg}. In general there is a balance of effects between the II and GI contributions., In general there is a balance of effects between the II and GI contributions. " If we imagine a universe in which the GI term did not exist but the II term did, an increase in the IA amplitude parameter A would add power to the predicted shear-shear correlation function."," If we imagine a universe in which the GI term did not exist but the II term did, an increase in the IA amplitude parameter $A$ would add power to the predicted shear-shear correlation function." To keep the predictions consistent with the data points it would be necessary to decrease og to reduce the lensing contribution., To keep the predictions consistent with the data points it would be necessary to decrease $\sigma_8$ to reduce the lensing contribution. " This would give a negative correlation between A and og, seen for larger positive A values."," This would give a negative correlation between $A$ and $\sigma_8$, seen for larger positive $A$ values." " In this unphysical universe containing only II terms, the direction of degeneracy would appear reversed for negative A because A appears as a squared quantity in the II terms."," In this unphysical universe containing only II terms, the direction of degeneracy would appear reversed for negative $A$ because $A$ appears as a squared quantity in the II terms." Indeed we do see the direction reversed in this figure., Indeed we do see the direction reversed in this figure. " In the physical Universe the effect of the GI contribution is to break the symmetry slightly, and prefer slightly more positive A values since it causes a slight cancellation in the IA effect for positive A values which fits better to the shape of the correlation functions that an addition of power."," In the physical Universe the effect of the GI contribution is to break the symmetry slightly, and prefer slightly more positive $A$ values since it causes a slight cancellation in the IA effect for positive $A$ values which fits better to the shape of the correlation functions that an addition of power." The great complementarity of the two datasets is most clearly illustrated in this figure., The great complementarity of the two datasets is most clearly illustrated in this figure. The main constraints on cosmology come from the shear-shear correlation data and the main constraints on IAs from the shear-position data., The main constraints on cosmology come from the shear-shear correlation data and the main constraints on IAs from the shear-position data. " The joint constraints focus at the intersection between the two relatively degenerate constraints, as expected."," The joint constraints focus at the intersection between the two relatively degenerate constraints, as expected." " The analysis was repeated, allowing A, 6 and os to vary."," The analysis was repeated, allowing $A$ , $\beta$ and $\sigma_{\rm 8}$ to vary." We marginalised over og to produce the results shown, We marginalised over $\sigma_8$ to produce the results shown suggest away to improve our treatment of the interaction between galaxies and their environment.,suggest a way to improve our treatment of the interaction between galaxies and their environment. Opt We thank Simone Weinmann for providing us the SDSS blue fraction data in electronic format., 6pt We thank Simone Weinmann for providing us the SDSS blue fraction data in electronic format. We are grateful to Simon White for a careful reading of the manuscript and for useful suggestions., We are grateful to Simon White for a careful reading of the manuscript and for useful suggestions. We also acknowledge Michael Balogh. Michael Brown ancl David Wake for useful discussions.," We also acknowledge Michael Balogh, Michael Brown and David Wake for useful discussions." SE is supported by a SPEC Fellowship at the Institute for Computational Cosmology in Durham., ASF is supported by a STFC Fellowship at the Institute for Computational Cosmology in Durham. ROB acknowledges the support of a SPEC senior fellowship., RGB acknowledges the support of a STFC senior fellowship. LGAL acknowledges support from a postdoctoral fellowship from the Natural Sciences and Engineering. Research Council (NSERC) of Canada., IGM acknowledges support from a postdoctoral fellowship from the Natural Sciences and Engineering Research Council (NSERC) of Canada. AJB acknowledges the support of the Gordon and Betty Moore Foundation., AJB acknowledges the support of the Gordon and Betty Moore Foundation. Vhis work was supported in part by a STEC rolling grant to Durham University., This work was supported in part by a STFC rolling grant to Durham University. detailed structure of the interaction zone rather than from modeling the global dynamics of the whole PWN citeke$4a)).the latter of which is difficult to apply to the complicated morphology surrounding PSRB1I509-38.,"detailed structure of the interaction zone rather than from modeling the global dynamics of the whole PWN \\cite{kc84a}) ), the latter of which is difficult to apply to the complicated morphology surrounding PSR." . We note that if features E and 5 are indeed analogs of the wisps seen in the Crab. then we similarly expect them to move away from the pulsar at high velocity.," We note that if features E and 5 are indeed analogs of the wisps seen in the Crab, then we similarly expect them to move away from the pulsar at high velocity." For example. motion outwards at 0.5c would correspond to proper motions of a few aresee per year at the distance of PSRB1IS09-S8.. which could easily be detected by aat subsequent epochs.," For example, motion outwards at $0.5c$ would correspond to proper motions of a few arcsec per year at the distance of PSR, which could easily be detected by at subsequent epochs." The high resolution of hhas revealed emission from several small-scale features close to the pulsar. as seen in Figure 5," The high resolution of has revealed emission from several small-scale features close to the pulsar, as seen in Figure \ref{fig_g320_center}." Feature 6 1s likely to correspond to emission from the O star Muzzio 10 (Muzzio1979:; Orsatti&Muzzio1980))., Feature 6 is likely to correspond to emission from the O star Muzzio 10 \cite{muz79}; \cite{om80}) ). X-ray emission from an O6.SILE star can be typically approximated by a Raymond-Smith spectrum with KT.z:0.2—0.5 keV and an unabsorbed luminosity (0.3-10.0 keV) of ~1-3«I0? erg s! (Berghófer.Schmitt.&Cassinelli 1996)). corresponding to an unabsorbed flux density (0.3-10.0 keV) f.~(0.4—4)«107% erg em™ s! for a photometric distance in the range 2.5-4.6 kpe (Sewardetal.1983:: Arendt 1991)).," X-ray emission from an O6.5III star can be typically approximated by a Raymond-Smith spectrum with $kT\approx 0.2-0.5$ keV and an unabsorbed luminosity (0.3–10.0 keV) of $\sim 1-3\times10^{32}$ erg $^{-1}$ \cite{bsc96}) ), corresponding to an unabsorbed flux density (0.3–10.0 keV) $f_x \sim (0.4-4)\times10^{-13}$ erg $^{-2}$ $^{-1}$ for a photometric distance in the range 2.5–4.6 kpc \cite{shmc83}; \cite{are91}) )." The crude spectral parameters inferred for this source in Table 2 are consistent with these values., The crude spectral parameters inferred for this source in Table \ref{tab_spec} are consistent with these values. What features 1—4 represent is not immediately clear., What features 1–4 represent is not immediately clear. " If we accept the argument made in orusthatr,7rs. then features 1-3 (and possibly feature 4. depending on projection effects) originate in the zone in which the wind is still freely expanding."," If we accept the argument made in \\ref{sec_disc_torus} that $r_s \approx r_5$, then features 1–3 (and possibly feature 4, depending on projection effects) originate in the zone in which the wind is still freely expanding." " In the Crab Nebula. a variety of small-scale structures has similarly been identified within the unshocked wind zone. """," In the Crab Nebula, a variety of small-scale structures has similarly been identified within the unshocked wind zone. “" "Knot 1"" and ""knot 2 (the latter of which ts also termed “the sprite”) are resolved optical structures lying 1500 and 9000 AU. respectively. from the Crab pulsar along the jet axis (Hesteretal. 1995)).","Knot 1” and “knot 2” (the latter of which is also termed “the sprite”) are resolved optical structures lying 1500 and 9000 AU, respectively, from the Crab pulsar along the jet axis \cite{hss+95}) )." It has been proposed that these features correspond to quasi-stationary shocks in the polar outflow from the pulsar (Micheletal.1996:; Lou1998)). or. in the case of knot 1. to a sheath of emission surrounding this outflow (Grahametal. 1996)).," It has been proposed that these features correspond to quasi-stationary shocks in the polar outflow from the pulsar \cite{msh+96}; \cite{lou98}) ), or, in the case of knot 1, to a sheath of emission surrounding this outflow \cite{gsh+96}) )." The two knots both show significant variability in their brightness. position and morphology on time scales of days to months (Hesteretal.1996:: Hester 1998)).," The two knots both show significant variability in their brightness, position and morphology on time scales of days to months \cite{hss+96}; \cite{hes98}) )." Similarly time-variable knots of emission are also seen in X-rays close to the Vela pulsar (Pavlovetal. 2001)), Similarly time-variable knots of emission are also seen in X-rays close to the Vela pulsar \cite{pksg01}) ). In the following discussion. we focus on feature |. the knot of emission closest to PSRB1509—58.," In the following discussion, we focus on feature 1, the knot of emission closest to PSR." ". We estimate feature | to have approximate dimensions 3«5"". and its projected separation from the pulsar to be rye2:4""20.1 pe."," We estimate feature 1 to have approximate dimensions $3''\times5''$, and its projected separation from the pulsar to be $r_{\rm knot} \approx 4'' = 0.1$ pc." We assume that this emission is generated by particles accelerated in some localized turbulent region. such as might be produced by the collision of inhomogeneous wind streams proposed by Lou (1998)).," We assume that this emission is generated by particles accelerated in some localized turbulent region, such as might be produced by the collision of inhomogeneous wind streams proposed by Lou \nocite{lou98}) )." The spectrum observed for feature 1 (D—1.2) is somewhat harder than the uncooled spectrum for the overall PWN (I— 1.6). supporting the possibility that this 15 a region of separate particle acceleration.," The spectrum observed for feature 1 $\Gamma \sim 1.2$ ) is somewhat harder than the uncooled spectrum for the overall PWN $\Gamma \sim 1.6$ ), supporting the possibility that this is a region of separate particle acceleration." In this case. we can interpret the extent of this feature as corresponding to the relativistic Larmor radius of gyrating pairs.," In this case, we can interpret the extent of this feature as corresponding to the relativistic Larmor radius of gyrating pairs." Although the number of photons available is limited. there is the suggestion in the data that the extent of the knot increases slightly with increasing photon energy. en with this interpretation.," Although the number of photons available is limited, there is the suggestion in the data that the extent of the knot increases slightly with increasing photon energy, consistent with this interpretation." " Ata photon energy 5 keV and in a magnetic field Bj,4, j/G. the pair Larmor radius Is Rag=0.13(7B;; pe."," At a photon energy $\varepsilon$ keV and in a magnetic field $B_{\rm knot}$ $\mu$ G, the pair Larmor radius is $\mathcal{R}$$_{\rm knot} = 0.13(\varepsilon/B_{\rm knot}^3)^{1/2}$ pc." " Adopting Rin~0.05 pe and s25 keV. we can infer Bia~3 μα. We computedin iv! f refsecyisc.nergythattherateo pairproductioninthe pulsarwindisN,zzÀ«1076 s!."," Adopting $\mathcal{R}$$_{\rm knot} \sim 0.05$ pc and $\varepsilon=5$ keV, we can infer $B_{\rm knot} \sim 3$ $\mu$ G. We computed in \\ref{sec_disc_energy} that the rate of pair production in the pulsar wind is $\dot{N}_\pm \approx 4\times10^{36}$ $^{-1}$." " The pair density in feature | is therefore In Equation (5)) we computed an upstream flow Lorentz factor ,22.6«10°.", The pair density in feature 1 is therefore In Equation \ref{eq:gamma1}) ) we computed an upstream flow Lorentz factor $\gamma_1 = 2.6 \times10^6$. Combining these estimates for Big. 24454 and >). we can infer by analogy with Equation (16)) that o4.<3«107 in this region. (," Combining these estimates for $B_{\rm knot}$, $n_{\pm, \rm knot}$ and $\gamma_1$, we can infer by analogy with Equation \ref{eq:pair_sigma_theory}) ) that $\sigma_\pm < 3 \times 10^{-3}$ in this region. (" We adopt this value as an upper limit. since compression and turbulence likely enhance the magnetic field in this feature above the ambient value.),"We adopt this value as an upper limit, since compression and turbulence likely enhance the magnetic field in this feature above the ambient value.)" This low value of σ is consistent with the various models for energy transport in the unshocked wind. which generally require the transition from σ>>| (at the light cylinder) to 7 is a specified multiple of the ordered feld strength."," The strength of the random component is established by scaling so that $<{\bf B}^2_{\rm ran}>$ is a specified multiple of the ordered field strength." In the absence of a fully sclbconsistent maguetolivdrodyvuaiic model. it is not clear whether the random field strenet[um should be a multiple of theZocel ordered field strenetl (correspondius. for example. to a turbulent geucration of the former from the latter by a fixed umber of eddy turn-overs}: or spatially fixed for a given jet radius. a iuultiple of the axial ordered field strenetl (correspondius. for example. to a turbulent eeuceratiou of the former to fixed multiple of the kinetic energv density in flow turbulence).," In the absence of a fully self-consistent magnetohydrodynamic model, it is not clear whether the random field strength should be a multiple of the ordered field strength (corresponding, for example, to a turbulent generation of the former from the latter by a fixed number of eddy turn-overs); or spatially fixed for a given jet radius, a multiple of the axial ordered field strength (corresponding, for example, to a turbulent generation of the former to fixed multiple of the kinetic energy density in flow turbulence)." " Both approaches have Όσοι tried. revealing that the choice has no dmupact on the final results. merely chaneing the precise value of FP=~1 where a transition in the characteristicBef behavior of the polarized flux deusitv is evideut."," Both approaches have been tried, revealing that the choice has no impact on the final results, merely changing the precise value of $f^2={\bf B}^2_{\rm ord}/<{\bf B}^2_{\rm ran}>\sim 1$ where a transition in the characteristic behavior of the polarized flux density is evident." It is extraordinarily dificult to define a quiesceut state from data., It is extraordinarily difficult to define a quiescent state from data. The UMRAO monitoring data exhibit almost continuous activity. aud even apparently inactive phases nav be periods in which simallaimplitude outbursts are temporally uuresolved.," The UMRAO monitoring data exhibit almost continuous activity, and even apparently inactive phases may be periods in which small-amplitude outbursts are temporally unresolved." VLBI imonitonug similarly reveals few df any inactive epochs. aud appareuth-quiescent flows lay contain spatially unresolved components.," VLBI monitoring similarly reveals few if any inactive epochs, and apparently-quiescent flows may contain spatially unresolved components." The UMRAO database has been searched to ideutify periods of ‘quiescence’. during which there is incastrable linearly polarized cussion.," The UMRAO database has been searched to identify periods of `quiescence', during which there is measurable linearly polarized emission." Between 1998 and 2001 0735|175 exhibited a low level of coustaut flux deusitv at the UMRAO frequencies. with ~2% polarization and EVPA nmuplviug au ordered maguetic field ling within some tens of deerees of the jet direction determined from MOJAVE data (Listeretal.2009).," Between 1998 and 2001 0735+178 exhibited a low level of constant flux density at the UMRAO frequencies, with $\sim2$ polarization and EVPA implying an ordered magnetic field lying within some tens of degrees of the jet direction determined from MOJAVE data \citep{lis09}." . Sinilu nuubers apply to NRAO 530 from 2002 to 2010 as illustrated in Figure 1., Similar numbers apply to NRAO 530 from 2002 to 2010 as illustrated in Figure \ref{fig4}. Based ou (aciuittedly sparse) exainples such as these. it is plausible to assume that in the quiescent state a weals axial field is added to any random coniponent. and in all simulations that follow. an axial mean field with 2% the enerev density of the random component is added.," Based on (admittedly sparse) examples such as these, it is plausible to assume that in the quiescent state a weak axial field is added to any random component, and in all simulations that follow, an axial mean field with $2$ the energy density of the random component is added." " This establishes a defined EVPA in the quiesceut state,", This establishes a well-defined EVPA in the quiescent state. Modelug a transverse structure comprising forward and reverse shocks. separated by a coutact discoutinuitv. is straightforward. as no lateralflowis required: the shocked fiow domainexpands in the frame ofthe contact surface. aud either the expansion may be ignored during the brief iuterval that the structure traverses the 7=1 surface. or the expansion can be modeled," Modeling a transverse structure comprising forward and reverse shocks, separated by a contact discontinuity, is straightforward, as no lateralflowis required: the shocked flow domainexpands in the frame ofthe contact surface, and either the expansion may be ignored during the brief interval that the structure traverses the $\tau=1$ surface, or the expansion can be modeled" The residuals shown in Figure Ibb indicate the deviation of the data from a power-law. and the presence of an iron Ko emission line is clear.,"The residuals shown in Figure \ref{fig:spectrum}b b indicate the deviation of the data from a power-law, and the presence of an iron $\alpha$ emission line is clear." When we add a Gaussian to model the emission line. we measure a line energy of 6.455503 keV. consistent with neutral to moderately 10nized iron. a line width of o20.14750: keV. and anequivalent width (EW) of 71's eV. With the addition of the iron line. the quality of the fit improves dramatically to \7/17=792/594.," When we add a Gaussian to model the emission line, we measure a line energy of $6.45^{+0.03}_{-0.02}$ keV, consistent with neutral to moderately ionized iron, a line width of $\sigma = 0.14^{+0.04}_{-0.03}$ keV, and anequivalent width (EW) of $77^{+12}_{-10}$ eV. With the addition of the iron line, the quality of the fit improves dramatically to $\chi^{2}/\nu = 792/594$." The total I-100 keV unabsorbed flux is 2.4«107! eres em s7!. which is à factor ~9 lower than the lowest level at which an iron line was previously detected for GX 339-4 (Tomsicketal.2005). and this flux corresponds to a luminosity of Lega.," The total 1--100 keV unabsorbed flux is $2.4\times 10^{-10}$ ergs $^{-2}$ $^{-1}$, which is a factor $\sim$ 9 lower than the lowest level at which an iron line was previously detected for GX 339–4 \citep{tomsick08}, and this flux corresponds to a luminosity of $L_{\rm Edd}$." Before discussing the implications of the presence of this narrow iron line. it is critical to determine if the tron line could be related either to poor background subtraction or to emission from other sources in the Galactic plane.," Before discussing the implications of the presence of this narrow iron line, it is critical to determine if the iron line could be related either to poor background subtraction or to emission from other sources in the Galactic plane." For the XIS detectors. we examined the background spectrum from two 4.4«3.7 rectangular regions on the detectors and verified that only internal background lines of the detector appear (seebackground) without any evidence for other background lines with strong emission in the iron Ka region.," For the XIS detectors, we examined the background spectrum from two $4^{\prime}.4\times 3^{\prime}.7$ rectangular regions on the detectors and verified that only internal background lines of the detector appear \citep[see][for information about the XIS internal background]{koyama07} without any evidence for other background lines with strong emission in the iron $\alpha$ region." Emission from the Galactic. ridge includes iron. Κα emission with the most prominent line being due to He-like iron at 6.7 keV (Koyamaetal.1986;Kaneda1997;Revnivtsevetal. 2009).," Emission from the Galactic ridge includes iron $\alpha$ emission with the most prominent line being due to He-like iron at 6.7 keV \citep{koyama86,kaneda97,revnivtsev09}." . Although the emission Is very strong in the Galactic center region. it decreases for lines-of-sight away from the Galactic center and drops especiallyrapidly with Galactic latitude (5).," Although the emission is very strong in the Galactic center region, it decreases for lines-of-sight away from the Galactic center and drops especiallyrapidly with Galactic latitude $b$ )." In the Scutum region. at a Galactic longitude of /=28.57. a scale height of 0.57 is estimated (Kanedaetal.1997).," In the Scutum region, at a Galactic longitude of $l = 28.5^{\circ}$, a scale height of $0.5^{\circ}$ is estimated \citep{kaneda97}." ". Thus. at the position of GX 339-4 (2338.97, bZ —4.3). the Galactic ridge emission is expected to be weak. but possibly not negligible."," Thus, at the position of GX 339–4 $l = 338.9^{\circ}$, $b =$ $4.3^{\circ}$ ), the Galactic ridge emission is expected to be weak, but possibly not negligible." The fact that the XISO&-XIS3 background spectrum does not show an emission line at 6.7 keV suggests that we are not detecting Galactic ridge emission in our observation of GX 339-4., The fact that the XIS0+XIS3 background spectrum does not show an emission line at 6.7 keV suggests that we are not detecting Galactic ridge emission in our observation of GX 339–4. As an additional check. we produced a new GX 339-4 spectrum using a circular extraction region centered on the source with a radius of 0/.86. which is five times smaller than the 4’.3 radius region used previously.," As an additional check, we produced a new GX 339–4 spectrum using a circular extraction region centered on the source with a radius of $0^{\prime}.86$, which is five times smaller than the $4^{\prime}.3$ radius region used previously." This causes a reduction in the source count rate by a factor of 2.1 while reducing the background by a factor of 25., This causes a reduction in the source count rate by a factor of 2.1 while reducing the background by a factor of 25. Thus. the strength of any background features will decrease by an order of magnitude.," Thus, the strength of any background features will decrease by an order of magnitude." " Fitting the new GX 339-4 XIS spectrum with an absorbed power-law model and inspecting the residuals still clearly shows an iron line at 6.4 keV. Adding a Gaussian to fit the iron line. we measure an EW of 73"" eV. which is consistent with no change from the EW of 7171) eV that we measure with XIS with the larger extraction region."," Fitting the new GX 339–4 XIS spectrum with an absorbed power-law model and inspecting the residuals still clearly shows an iron line at 6.4 keV. Adding a Gaussian to fit the iron line, we measure an EW of $73^{+18}_{-14}$ eV, which is consistent with no change from the EW of $71^{+11}_{-10}$ eV that we measure with XIS with the larger extraction region." Based on this and the background spectrum discussed above. we conclude that the iron line is from GX 339-4.," Based on this and the background spectrum discussed above, we conclude that the iron line is from GX 339–4." To use the shape of the tron line to constrain Αι we return to fitting the full spectrum shown in Figure .. and we replaced the Gaussian component with the model (Laor1991).. which accounts for the relativistic effects near a rotating black hole.," To use the shape of the iron line to constrain $R_{\rm in}$, we return to fitting the full spectrum shown in Figure \ref{fig:spectrum}, and we replaced the Gaussian component with the model \citep{laor91}, which accounts for the relativistic effects near a rotating black hole." The line energy and EW are 6.475501 keV and 7213 eV. respectively.," The line energy and EW are $6.47^{+0.04}_{-0.03}$ keV and $72^{+9}_{-7}$ eV, respectively." " The other model parameters are Αι the inclination of the inner disk. # and the emissivity index. q. which is a power-law index that sets how the line-emissivity (J) of the disk changes with radius according to Jxr“, "," The other model parameters are $R_{\rm in}$, the inclination of the inner disk, $i$, and the emissivity index, $q$, which is a power-law index that sets how the line-emissivity $J$ ) of the disk changes with radius according to $J\propto r^{-q}$." Although a broad line allows for good constraints on all 3 parameters. this is not the case for a narrow line.," Although a broad line allows for good constraints on all 3 parameters, this is not the case for a narrow line." Thus. we restricted the range of q to be between 2. which corresponds to a value where the contribution to the iron line from large radii begins to diverge(Laor 1991).. and 3. which is consistent with the value obtained from previous measurements of the GX 339-4 tron line in the hard state (Milleretal.2006.2008:Tomsicketal.2008:Reis 2008).," Thus, we restricted the range of $q$ to be between 2, which corresponds to a value where the contribution to the iron line from large radii begins to diverge\citep{laor91}, , and 3, which is consistent with the value obtained from previous measurements of the GX 339–4 iron line in the hard state \citep{miller06a,miller08,tomsick08,reis08}." . The inclination has been previously measured to be ;=18+2 degrees (Milleretal. 2008)., The inclination has been previously measured to be $i = 18\pm 2$ degrees \citep{miller08}. . For Ri. the spectral fits indicate and confidence lower limits of 784 Αι and 765 ΑΟ. respectively. if (=187.," For $R_{\rm in}$, the spectral fits indicate and confidence lower limits of $>$ 84 $R_{g}$ and $>$ 65 $R_{g}$, respectively, if $i = 18^{\circ}$." " As à value of Ri,22.4 Αι was obtained when the source was bright (Milleretal.2008).. our results indicate that the inner radius changes by a factor of 921."," As a value of $R_{\rm in} = 2.4$ $R_{g}$ was obtained when the source was bright \citep{miller08}, our results indicate that the inner radius changes by a factor of $>$ 27." " Figure 2 illustrates the huge difference between the profile that we measure and a profile with Aj,=2.4 R..", Figure \ref{fig:profile} illustrates the huge difference between the profile that we measure and a profile with $R_{\rm in} = 2.4$ $R_{g}$. Fixing the disk inclination to /=187 is appropriate for constraining the ratio of inner radii at and Lega Since we do not expect the disk inclination to change significantly with luminosity. being set either by the binary inclination or the spin axis of the black hole.," Fixing the disk inclination to $i = 18^{\circ}$ is appropriate for constraining the ratio of inner radii at and $L_{\rm Edd}$ since we do not expect the disk inclination to change significantly with luminosity, being set either by the binary inclination or the spin axis of the black hole." However. for obtaining a physical value of Αμ. we needto consider the inclination.," However, for obtaining a physical value of $R_{\rm in}$, we needto consider the inclination." We refitted the full spectrum with the power-law plus model. allowing / to be a free parameter and q to be free in the range 2-3.," We refitted the full spectrum with the power-law plus model, allowing $i$ to be a free parameter and $q$ to be free in the range 2–3." " Then. we performed a grid search of inclinations covering 07 to 40° and values of Ri; covering 10 to 210 R,."," Then, we performed a grid search of inclinations covering $0^{\circ}$ to $40^{\circ}$ and values of $R_{\rm in}$ covering 10 to 210 $R_{g}$ ." Figure 3. shows the results in terms of the and confidence contours., Figure \ref{fig:contour} shows the results in terms of the and confidence contours. " The contours show that at lower inclinations. the constraint on. Aj, becomes somewhat weaker. but even at /2 0. theresults indicate a truncated disk with Ri,735R, confidence)."," The contours show that at lower inclinations, the constraint on $R_{\rm in}$ becomes somewhat weaker, but even at $i = 0^{\circ}$ , theresults indicate a truncated disk with $R_{\rm in} > 35 R_{g}$ confidence)." On the other hand. at disk inclinations above 187. the inferred values of Ri rise rapidly.," On the other hand, at disk inclinations above $18^{\circ}$ , the inferred values of $R_{\rm in}$ rise rapidly." " For example. at /= 30°. the limit is Rj,7 ΕΝ."," For example, at $i = 30^{\circ}$ , the limit is $R_{\rm in} > 175 R_{g}$ ." " There are at least two reasons why our limits on Aj, are", There are at least two reasons why our limits on $R_{\rm in}$ are We have observed the magnetar 197in. full »olarisation using three cillerent telescopes simultaneously at three dillerent frequencies.,We have observed the magnetar in full polarisation using three different telescopes simultaneously at three different frequencies. We find that some properties ΠΑΝΟ 1975s are similar to those of normal racio ulsars while many more features are observed that are strikingly cillerent., We find that some properties of s are similar to those of normal radio pulsars while many more features are observed that are strikingly different. We find strong evidence for propagation ellects in the magnetosphere while the observed. emission o»operties are Consistent with a multi-pole. configuration of the magnetic field., We find strong evidence for propagation effects in the magnetosphere while the observed emission properties are consistent with a multi-pole configuration of the magnetic field. Continued observations of this radio emitting magnetar. together with the future studies of LRATLS sources. will allow us to study a variety of neutron gaars in the radio regime and to contrast their emission ooperties with those of normal pulsars.," Continued observations of this radio emitting magnetar, together with the future studies of RRATS sources, will allow us to study a variety of neutron stars in the radio regime and to contrast their emission properties with those of normal pulsars." We thanks Comma. Janssen for help with the data acquisition and Patrick Weltevrede for software and. useful discussions., We thanks Gemma Janssen for help with the data acquisition and Patrick Weltevrede for software and useful discussions. We thank II. Spruit and. C. Smith for useful cdisceussions., We thank H. Spruit and G. Smith for useful discussions. SZ Her (BD+33°2930. GSC 2610-1209. HIP 56130. TYC 2610-1209-1) is an Algol-type system. with an orbital period of 0.515 d and was announced to be a variable by Ceraski (1908) ancl also Dunérr et al. (," SZ Her $\rm BD+33^{o} 2930$, GSC 2610-1209, HIP 86430, TYC 2610-1209-1) is an Algol-type system with an orbital period of 0.818 d and was announced to be a variable by Ceraski (1908) and also Dunérr et al. (" 1909).,1909). Although the first observations of the system date back to 1902 (Shapley 1913: Russell Shapley 1911: Dugan 1923). its properties are poorly kuown compared to those of other short-periocd Aleols.," Although the first observations of the system date back to 1902 (Shapley 1913; Russell Shapley 1914; Dugan 1923), its properties are poorly known compared to those of other short-period Algols." To date iu the published literature. only one light-curve analysis has been published aud it was presented by Ciuricin Mardirossiau (1981).," To date in the published literature, only one light-curve analysis has been published and it was presented by Giuricin Mardirossian (1981)." They analyzed the photoelectric light curves of Broglia et al. (, They analyzed the two-color photoelectric light curves of Broglia et al. ( 1955) using the WININ model (Wood 1972) and,1955) using the WINK model (Wood 1972) and "↴Ihe b,""(2) coellicients∙− are and In equation (80)). ο indicates that one nist sum over both --2 and A——2.","The $b^{\,(2)}_{n,k}$ coefficients are and In equation \ref{b(2)-3}) ), $\sum_{k=\pm 2}$ indicates that one must sum over both $k=2$ and $k=-2$." To calculate the eigenvectors and eigenvalues of LP. we use (he eigenvectors of the angular momentum operator as the basis of the Hilbert space.," To calculate the eigenvectors and eigenvalues of $H_0^{\,R}$, we use the eigenvectors of the angular momentum operator as the basis of the Hilbert space." We denote these eigenvectors by το).," We denote these eigenvectors by $|\chi_{\,j,\,k,\,m}\rangle $ ." From: quantum mechanics. one knows that [Xjo40m) satisfies the following eigenvalueequations [?] ," From quantum mechanics, one knows that $|\chi_{\,j,\,k,\,m}\rangle $ satisfies the following eigenvalueequations \cite{Landau} " We demonstrate the procedure in section 4 in the case where the input observations. after correcting for evolution. are in the RAV form.,"We demonstrate the procedure in section \ref{sec:theorems} in the case where the input observations, after correcting for evolution, are in the RW form." Wo turns out that the LED arbitrary functions assume their RW form., It turns out that the LTB arbitrary functions assume their RW form. This amounts to a proof that a racially inhomogeneous cust universe is RAW ilf the area distance anc number count relations as a function of redshift take the RAW form., This amounts to a proof that a radially inhomogeneous dust universe is RW iff the area distance and number count relations as a function of redshift take the RW form. Lt is a special case of Theorem (D) where we assume that there is no evolution., It is a special case of Theorem (B) where we assume that there is no evolution. These RW relations are and respectively., These RW relations are and respectively. Then we can integrate the null Ravchaucdburi equation (37)) once obtaining ‘This may be integrated once again (illustrating with the case qu«1 5) to obtain. We continue by solving the first order linear cillerential equation for AZ(z) (the elective gravitational mass) (14)).," Then we can integrate the null Raychaudhuri equation \ref{eq:nraych}) ) once obtaining This may be integrated once again (illustrating with the case $q_0 < {1 \over 2}$ ) to obtain We continue by solving the first order linear differential equation for $M(z)$ (the effective gravitational mass) \ref{eq:M}) )." This equation may be written as We substitute the RAW area distance and number count Functions into this and find that and from (13)) it follows that, This equation may be written as We substitute the RW area distance and number count functions into this and find that and from \ref{eq:E}) ) it follows that A linear least-squaresl fit to the times of mid-eclipsepse ggiven in ‘Table 1 (Ccaleulated using the techniques described in section 4 and taking5 the midpoint of the white dwarl eclipse as the point of mid-eclipse) and those of 7.private gives the following ephemeris: Errors of 4.107 days were used for the ULTRACAAL data. and errors of x7«10! davs for the ?.privatecom-munication data.,"A linear least-squares fit to the times of mid-eclipse given in Table \ref{eclipse_times} (calculated using the techniques described in section \ref{contact} and taking the midpoint of the white dwarf eclipse as the point of mid-eclipse) and those of \citet[][ private communication]{vanmunster00} gives the following ephemeris: Errors of $\pm 4\times 10^{-5}$ days were used for the ULTRACAM data, and errors of $\pm 7\times 10^{-4}$ days for the \citet[][ private communication]{vanmunster00} data." This ephemeris was used to phase all of our data., This ephemeris was used to phase all of our data. " The derivation of the svstem parameters relies upon the fact that there is a unique relationship between the mass ratio ancl orbital inclination for a given eclipse phase width Qu, Quit The shape of the svstem does not depend on the orbital separation e: this just determines the scale."," The derivation of the system parameters relies upon the fact that there is a unique relationship between the mass ratio and orbital inclination for a given eclipse phase width $\Delta\phi = \phi_{we} - \phi_{wi}$ : The shape of the system does not depend on the orbital separation $a$; this just determines the scale." “Phe orbital separation is determined by assuming a mass-racdius relation for the primary (see later)., The orbital separation is determined by assuming a mass-radius relation for the primary (see later). " The trajectory of the gas stream originating from the inner Lagrangian point £L, is calculated: by solving the equations of motion (7) using a second-order RungeIxutta technique and conserving the Jacobi ποιον to 1 part in 10.", The trajectory of the gas stream originating from the inner Lagrangian point $L_{1}$ is calculated by solving the equations of motion \citep{flannery75} using a second-order Runge–Kutta technique and conserving the Jacobi Energy to 1 part in $10^{4}$. " ""Phis assumes that the gas stream follows a ballistic path.", This assumes that the gas stream follows a ballistic path. Figure 3. shows a theoretical eas stream for q=0.175., Figure \ref{mass} shows a theoretical gas stream for $q=0.175$. Figures + and 5 show expanded: views of the bright spot region., Figures \ref{bs_horizontal} and \ref{bs_vertical} show expanded views of the bright spot region. As q decreases. the path of the stream moves away from the white dwarf.," As $q$ decreases, the path of the stream moves away from the white dwarf." For a given mass ratio q cach point on the stream has a unique phase of ingress and egress., For a given mass ratio $q$ each point on the stream has a unique phase of ingress and egress. For cach phase. the limb of the secondary. forms an are when projected along the line of sight onto a given plane (hereafter referred to as a phase are): cach point on an individual phase are is eclipsed at the same time.," For each phase, the limb of the secondary forms an arc when projected along the line of sight onto a given plane (hereafter referred to as a phase arc): each point on an individual phase arc is eclipsed at the same time." The intersection of the phase ares corresponding to the respective eclipse contact phases can be used to constrain the size of the white cdwarl and the structure of the bright spot., The intersection of the phase arcs corresponding to the respective eclipse contact phases can be used to constrain the size of the white dwarf and the structure of the bright spot. The light centres of the white dwarl and bright spot must lic at the intersection of the phase ares corresponding to the relevant phases of mid-ingress and mid-egress. ó; anc ó..," The light centres of the white dwarf and bright spot must lie at the intersection of the phase arcs corresponding to the relevant phases of mid-ingress and mid-egress, $\phi_{i}$ and $\phi_{e}$." Phe phase ares were calculated using full Roche lobe geometry rather than an approximate calculation., The phase arcs were calculated using full Roche lobe geometry rather than an approximate calculation. The mass ratio and hence the inclination may be determined. by comparing the bright spot light centres corresponding to the measured. eclipse contact phases ὧν; and Ow. with the theoretical stream trajectories for dilferent mass ratios d., The mass ratio and hence the inclination may be determined by comparing the bright spot light centres corresponding to the measured eclipse contact phases $\phi_{wi}$ and $\phi_{we}$ with the theoretical stream trajectories for different mass ratios $q$. This requires the assumption that the eas stream passes directly through the light centre of the bright spot., This requires the assumption that the gas stream passes directly through the light centre of the bright spot. As illustrated in Figures 4 and r5.. we constrain the light centre of the bright spot to be the point where the eas stream and outer edge of the disc intersect. so that the distance from the primary at which the gas stream. passes through the light centre of the bright spot gives the relative outer disc radius £2)α.," As illustrated in Figures \ref{bs_horizontal} and \ref{bs_vertical}, we constrain the light centre of the bright spot to be the point where the gas stream and outer edge of the disc intersect, so that the distance from the primary at which the gas stream passes through the light centre of the bright spot gives the relative outer disc radius $R_{d}/a$." The bright spot timings thus vield a mass ratio of q=0.175+0.025 and an inclination of ;=τοοτεον for an eclipse phase width Ao=0.041585., The bright spot timings thus yield a mass ratio of $q=0.175 \pm 0.025$ and an inclination of $i=79\fdg2 \pm0 \fdg7$ for an eclipse phase width $\Delta\phi = 0.041585$. The errors are determined. by the rms. variations in the measured. contact phases., The errors are determined by the rms variations in the measured contact phases. Figures 4. and ο show the eclipse constraints on the structure of the bright spot.," Figures \ref{bs_horizontal} and \ref{bs_vertical} show the eclipse constraints on the structure of the bright spot." We use these to determine upper limits on the angular size and the racial and vertical, We use these to determine upper limits on the angular size and the radial and vertical where 4A—»55»(jte⋅⋅-phy?⋉⋅↽≻o?>p=τοDjeeadiplo;C=551i l/o?. j⋅⋅∙ is the distance modulus obtained [rom observations and o; is (he total uncertainty of SNe Ia data.,"where $A=\sum_i^{557}{(\mu^{\rm data}-\mu^{\rm th})^2}/{\sigma^2_i}~, B=\sum_i^{557}{\mu^{\rm data}-\mu^{\rm th}}/{\sigma^2_i}~, C=\sum_i^{557}{1}/{\sigma^2_i}$ $\mu^{\rm data}$ is the distance modulus obtained from observations and $\sigma_i$ is the total uncertainty of SNe Ia data." The model parameters are determined by applving the maximum likelihood method of A? fit bv using the Markov. Chain Monte Carlo (MCMC) method., The model parameters are determined by applying the maximum likelihood method of $\chi^{2}$ fit by using the Markov Chain Monte Carlo (MCMC) method. We minimize \? to determine the best-fit parameters and our method is based on cosmodIC 2002)., We minimize $\chi^{2}$ to determine the best-fit parameters and our method is based on cosmoMC \citep{Lewis02}. ". Basically. The model parameters are determined by minimizing If the interaction term is Q=35,,//py. 3 spatially flat. FRW metric. for the the 5,, IDE model with a constant Eos of dark enerey (ey. the Friedinann equation is The joint confidence regions in εν ον, plane with different observational data sets (Jf(2). (2)4+BAO+CA3IB. SNe lat+BAO+CMB. aid Z(2)2-S9Ne lat+DAO--CMD) lor the 5,, IDE model model are showed in Fig."," Basically, The model parameters are determined by minimizing If the interaction term is $Q=3\gamma_m H\rho_m$, in spatially flat FRW metric, for the the $\gamma_m$ IDE model with a constant EoS of dark energy $w_X$ , the Friedmann equation is The joint confidence regions in $w_X$ $\gamma_m$ plane with different observational data sets $H(z)$, $H(z)$ +BAO+CMB, SNe Ia+BAO+CMB, and $H(z)$ +SNe Ia+BAO+CMB) for the $\gamma_m$ IDE model model are showed in Fig." 1., 1. We also present the best-fit values of parameters with 1-0 and 2-0 uncertaintiesin Table 1.., We also present the best-fit values of parameters with $\sigma$ and $\sigma$ uncertaintiesin Table \ref{tab2}. With the /(z) data only (Fig., With the $H(z)$ data only (Fig. " la). the best-fit values of the parameters (ey. ορ)Qn ate wy=—2.79 and 5,,=0.22."," 1a), the best-fit values of the parameters $w_X, \gamma_m$ ) are $w_X=-2.79$ and $\gamma_m=0.22$." With H(2)2-DAO--CMD (Fig., With $H(z)$ +BAO+CMB (Fig. " Lb). (he best-fit values at1-0 are wy=—1.10Pet. 54,=—0.013.(t."," 1b), the best-fit values at$\sigma$ are $w_X=-1.10_{-0.17}^{+0.16}$, $\gamma_m=-0.013_{-0.011}^{+0.013}$." For comparison. fitting results from the joint data with SNe Ia--DAO--CMD are given in Fig.," For comparison, fitting results from the joint data with SNe Ia+BAO+CMB are given in Fig." Le., 1c. " with the best-fit values wy=—1.0215 and 54,=—0.009.0005.", with the best-fit values $w_X=-1.02_{-0.13}^{+0.12}$ and $\gamma_m=-0.009_{-0.012}^{+0.013}$. In Fig., In Fig. " Id. we show the fitting results fron the joint data with //(2)4+5Ne Ia--DAO--CMD. with the best-fit values wy=—1.05ME and 5,,=—0.011(rui."," 1d, we show the fitting results from the joint data with $H(z)$ +SNe Ia+BAO+CMB, with the best-fit values $w_X=-1.05_{-0.12}^{+0.11}$ and $\gamma_m=-0.011_{-0.011}^{+0.012}$." lt is obvious that. //(2) only gives a relatively weak constraint on all of the relevant model parameters., It is obvious that $H(z)$ only gives a relatively weak constraint on all of the relevant model parameters. We lind that the £7(2) data.when combined to CAIB and BAO observations. caneive more siringent constraints on this phenomenological interacting scenario .," We find that the $H(z)$ data,when combined to CMB and BAO observations, cangive more stringent constraints on this phenomenological interacting scenario ." " Moreover. the special case (5,,=0.icy —1. corresponding to the ACDM with no interaction) is excluded"," Moreover, the special case $\gamma_m=0, w_X=-1$ , corresponding to the $\Lambda$ CDM with no interaction) is excluded" quite non-trivial to calculate analytically for arbitrary values of y and concentration.,quite non-trivial to calculate analytically for arbitrary values of $\gamma$ and concentration. We therefore calculate Fur) in a numerical fashion., We therefore calculate $F_{\mathrm{ss}}(r)$ in a numerical fashion. " We make a dense grid of y and concentration values, and at each grid point we create an artificial spherical halo by putting down 30k particles that satisfy the radial profile for that grid point."," We make a dense grid of $\gamma$ and concentration values, and at each grid point we create an artificial spherical halo by putting down 30k particles that satisfy the radial profile for that grid point." We then measure the pair distribution by counting all the particle pairs in our constructed halo., We then measure the pair distribution by counting all the particle pairs in our constructed halo. " Once we have a table of Fi(r) functions on our grid, we can estimate PF..(r) for any values of y and concentration by interpolating in the grid."," Once we have a table of $F_{\mathrm{ss}}(r)$ functions on our grid, we can estimate $F_{\mathrm{ss}}(r)$ for any values of $\gamma$ and concentration by interpolating in the grid." " As before, we wish to keep the same number of free parameters in order to more fairly compare different models."," As before, we wish to keep the same number of free parameters in order to more fairly compare different models." " We thus keep Mo fixed to Mj, and we keep fea) fixed to unity.", We thus keep $\Mzero$ fixed to $\Mmin$ and we keep $\fgal$ fixed to unity. " Therefore, we now vary the following 4 free parameters: Mmin, Mi, a, and »y, and we refer to this model as PNMG."," Therefore, we now vary the following 4 free parameters: $\Mmin$, $\Mone$, $\alpha$, and $\gamma$, and we refer to this model as PNMG." We find a best-fit model with a reduced X? of 0.82 (x? of 4.11 with 5 degrees of freedom)., We find a best-fit model with a reduced $\chi^2$ of 0.82 $\chi^2$ of 4.11 with 5 degrees of freedom). The dashed-dotted red curves in Figure 1. show this best fit., The dashed-dotted red curves in Figure \ref{fig:wpgg_Slope} show this best fit. 'The PNMG model is clearly successful in fitting the M06 small-scale data., The PNMG model is clearly successful in fitting the M06 small-scale data. Allowing the inner slope of the satellite LRG density profile to become steeper than r~! is exactly what was needed to match the data., Allowing the inner slope of the satellite LRG density profile to become steeper than $r^{-1}$ is exactly what was needed to match the data. The value of » is well constrained and our MCMC yields y=2.06+0.21., The value of $\gamma$ is well constrained and our MCMC yields $\gamma= 2.06 \pm 0.21$. " It is certainly not surprising that the inner slope of the satellite density profile is similar to the slope of €(r) at small scales because, as we argued in ??,, most LRG pairs should be central-satellite pairs whose pair distribution is essentially the density profile itself."," It is certainly not surprising that the inner slope of the satellite density profile is similar to the slope of $\xi(r)$ at small scales because, as we argued in \ref{2pt_xigg}, most LRG pairs should be central-satellite pairs whose pair distribution $F_{\mathrm{cs}}(r)$ is essentially the density profile itself." " We have establishedF;.(r) that neither P(N|M), nor the concentration of satellite LRGs, are sufficient to explain the M06 small-scale data, and that a profile other than NFW is needed."," We have established that neither $P(N|M)$, nor the concentration of satellite LRGs, are sufficient to explain the M06 small-scale data, and that a profile other than NFW is needed." We thus now allow our model to have more than 4 free parameters and we vary both y and faa., We thus now allow our model to have more than 4 free parameters and we vary both $\gamma$ and $\fgal$. " Since our density profile is no longer NFW, there is no reason to keep the concentration fixed to what was found for NFW dark matter halos."," Since our density profile is no longer NFW, there is no reason to keep the concentration fixed to what was found for NFW dark matter halos." " In our final model, we thus vary 5 parameters: Mis, M1, a, feai, and y, and we refer to this model as PNMCG."," In our final model, we thus vary 5 parameters: $\Mmin$, $\Mone$, $\alpha$, $\fgal$, and $\gamma$, and we refer to this model as PNMCG." Our goal for investigating this model is to determine exactly what constraints the M06 data place on the density profile of satellite LRGs., Our goal for investigating this model is to determine exactly what constraints the M06 data place on the density profile of satellite LRGs. We find a best-fit model with a reduced X? of 0.71 (x? of 2.82 with 4 degrees of freedom)., We find a best-fit model with a reduced $\chi^2$ of 0.71 $\chi^2$ of 2.82 with 4 degrees of freedom). " Figure 2 shows our 1-,2- and 3-c contours for y and fg41."," Figure \ref{fig:hist_Slope} shows our 1-,2- and $\sigma$ contours for $\gamma$ and $\fgal$." " As before, we find that the satellite LRG profile is much steeper than NFW (for NFW, y=1 and [ρω= 1), with y=—2.17+0.12."," As before, we find that the satellite LRG profile is much steeper than NFW (for NFW, $\gamma =1$ and $\fgal =1$ ), with $\gamma = -2.17\pm 0.12$." " As we argued in ??,, most of the LRG satellites reside in halos of mass close to M1."," As we argued in \ref{HOD}, most of the LRG satellites reside in halos of mass close to $\Mone$." " At our best-fit value for Mi (10149257! M5), the dark matter concentration fitting formula from ?? gives a halo concentration of 4.25."," At our best-fit value for $\Mone$ $10^{14.62}\hMsun$ ), the dark matter concentration fitting formula from \ref{HOD} gives a halo concentration of $c = 4.25$ ." Applying our 1-σ range for implies that cgaj~0.1 —4.1., Applying our $\sigma$ range for $\fgal$ implies that $\Cgal\sim 0.1 - 4.1$ . " Concentration values of f;4;unity or less mean that the scale radius r, is larger than the virial radius, which essentially means that the density profile retains its inner slope most of the way out."," Concentration values of unity or less mean that the scale radius $r_s$ is larger than the virial radius, which essentially means that the density profile retains its inner slope most of the way out." " In other words, our fit shows that the density profile for LRG satellites is consistent with a simple isothermal profile."," In other words, our fit shows that the density profile for LRG satellites is consistent with a simple isothermal profile." " Our results show that the distribution of satellite LRGs within dark matter halos requires a steeper inner density profile than NFW, which suggests that these galaxies are poor tracers of the dark matter distribution at these scales."," Our results show that the distribution of satellite LRGs within dark matter halos requires a steeper inner density profile than NFW, which suggests that these galaxies are poor tracers of the dark matter distribution at these scales." " The density profile of dark matter halos in the ACDM model has been measured extensively using high resolution N-body simulations, and recent inner profile measurements seem to confirm the NFW ~r-l predictions (Navarroetal.2008) — with some slight deviations found in separate work (Diemandetal.Popolo&Kroupa"," The density profile of dark matter halos in the $\Lambda$ CDM model has been measured extensively using high resolution N-body simulations, and recent inner profile measurements seem to confirm the NFW $\sim r^{-1}$ predictions \citep{navarro08} – with some slight deviations found in separate work \citep{diemand04,fukushige04,reed05,delpopolo09}." " However, NFW does not consider baryons, which2009). can affect the dark matter density profile at small scales."," However, NFW does not consider baryons, which can affect the dark matter density profile at small scales." The interaction between baryons and dark matter is addressed by the adiabatic contraction model that describes the gravitational effect of baryons on dark matter as the gas condenses and sinks to the center of the dark matter potential well., The interaction between baryons and dark matter is addressed by the adiabatic contraction model that describes the gravitational effect of baryons on dark matter as the gas condenses and sinks to the center of the dark matter potential well. " The gravitational influence of the baryons draws the dark matter in, and this can steepen the density profile (Gnedinetal.2004;Romano-Díaz2008;Weinbergetal.2008;Sommer-Larsen&Limousin 2009)."," The gravitational influence of the baryons draws the dark matter in, and this can steepen the density profile \citep{gnedin04, romanodiaz08, weinberg08, sommerlarsen09}." ". Although it has been shown that the inner profile can significantly steepen (Gustafssonetal.2006),, the majority of results show only a moderate steepening."," Although it has been shown that the inner profile can significantly steepen \citep{gustafsson06}, the majority of results show only a moderate steepening." This has also been observationally confirmed using galaxy-galaxy lensing by Mandelbaumetal.(2006) who find that the mass density profile of LRG clusters is consistent with NFW., This has also been observationally confirmed using galaxy-galaxy lensing by \citet{mandelbaum06a} who find that the mass density profile of LRG clusters is consistent with NFW. LRG satellites therefore have a steeper density profile than dark matter even with the effects of baryons taken into consideration., LRG satellites therefore have a steeper density profile than dark matter even with the effects of baryons taken into consideration. It is not necessarily surprising that LRGs are poor tracers of the dark matter density distribution within halos., It is not necessarily surprising that LRGs are poor tracers of the dark matter density distribution within halos. " LRGs presumably live in subhalos, which can certainly have a different distribution than their host halos."," LRGs presumably live in subhalos, which can certainly have a different distribution than their host halos." " Nagai&Kravtsov(2005) found that subhalos actually have a shallower profile than dark matter at larger scales, but this has not been studied for the massive halos and small scales we consider here."," \citet{nagai05} found that subhalos actually have a shallower profile than dark matter at larger scales, but this has not been studied for the massive halos and small scales we consider here." It is difficult to model this regime because simulations must, It is difficult to model this regime because simulations must model to represent the disk SFR.,model to represent the disk SFR. " The first is a constant SFR of 1M. /vr for 10"" ves with a Gaussian tail with &=0.6."," The first is a constant SFR of 1 $_{ \odot}$ /yr for $10^{10}$ yrs with a Gaussian tail with $\sigma=0.6$." " For tgx10. the second component is given by while lor tg>10 a Gaussian tail with σι,=0.6 was assiuned."," For $_{9} \leq10$, the second component is given by while for $_{9}>10$ a Gaussian tail with $\sigma_{t_{9}}=0.6$ was assumed." The sum of these two components is shown in Figure d., The sum of these two components is shown in Figure 4. " Integrating the rate over Gime and nmultiplving the result by the assumed value of (1—R) —0.7 gives a model equivalent M, of 10! ML, which is identical with Mrs; (Table 1) and hence consistent with our model."," Integrating the rate over time and multiplying the result by the assumed value of $1-$ R) $=0.7$ gives a model equivalent $_{s}$ of $^{10}$ $_{\odot}$, which is identical with $_{ml,red}$ (Table 1) and hence consistent with our model." We estimate that the ratio of present SER. to average SET. lor this disk component is 0.6. which is well within the range expected for an Sb-Sbe galaxy. according to Table 8.2 of Binney Merrilield (1998) which is based on data from Nennicutt et ((1994).," We estimate that the ratio of present SFR to average SFR for this disk component is $\sim0.6$, which is well within the range expected for an Sb-Sbc galaxy, according to Table 8.2 of Binney Merrifield (1998) which is based on data from Kennicutt et (1994)." We note from Figure 4 that there is a relatively large overlap in SFR. between the disk and the red spheroidal component., We note from Figure 4 that there is a relatively large overlap in SFR between the disk and the red spheroidal component. Star formation associated with the latter component goes on until tog~6—7 Gyr (54.1). implying that the last protogalactic clumps (o arrive must have originated5 al a 5great. distance [rom the 5galactic center.," Star formation associated with the latter component goes on until $_{9}\sim6-7$ Gyr $\S4.1$ ), implying that the last protogalactic clumps to arrive must have originated at a great distance from the galactic center." This late arrival would allow time for dynamical friction to cause the still quiescently evolving clumps to spiral in to the center of the lorming galaxy before colliding to make metal rich globular clusters and to provide gas for the observed ongoing star lormation towards the inner galaxy., This late arrival would allow time for dynamical friction to cause the still quiescently evolving clumps to spiral in to the center of the forming galaxy before colliding to make metal rich globular clusters and to provide gas for the observed ongoing star formation towards the inner galaxy. To observers looking5 towards the Galactic center. this relatively voung.5 relatively metal rich. relatively hieh angular momentum «disk component could easily appear to be associated with the bulge.," To observers looking towards the Galactic center, this relatively young, relatively metal rich, relatively high angular momentum `disk' component could easily appear to be associated with the bulge." S One could then understand why the inner metal rich clusters eg<4 kpe) appear to be associated with the bulge5 even though5 they possess significant5 rotation while the outer red clusters exhibit disk characteristics (Cote 1999. Forbes et 22001).," One could then understand why the inner metal rich clusters $_{g}<4$ kpc) appear to be associated with the bulge even though they possess significant rotation while the outer red clusters exhibit disk characteristics (Cote 1999, Forbes et 2001)." " Further. from equation (10). the ratio of mass in red clusters to blue clusters should be equal to the ratio ΑΕ M,uu whieh from Table 1 is ~2.4."," Further, from equation (10), the ratio of mass in red clusters to blue clusters should be equal to the ratio $_{t,red}$ $_{t,blue} $ which from Table 1 is $\sim2.4$." As the observed red to blue cluster ratio is closer to unity. we must assume that either many of the red clusters whieh do form are disrupted or that the efficiency of red cluster formation is lower due perhaps to tidal effects aud to the presence of a substantial existing disk component.," As the observed red to blue cluster ratio is closer to unity, we must assume that either many of the red clusters which do form are disrupted or that the efficiency of red cluster formation is lower due perhaps to tidal effects and to the presence of a substantial existing disk component." In a later discussion. we will attribute the surviving red clusters to a thick disk component.," In a later discussion, we will attribute the surviving red clusters to a thick disk component." Also part of the thick disk are the stars [from disrupted clusters and the earliest formed disk stars resulting from (he compression of in situ disk eas from late collisions with still intact protogalactie «πας (assumed to be responsible for the initial burst in the disk SFR at 10 Gyr)., Also part of the thick disk are the stars from disrupted clusters and the earliest formed disk stars resulting from the compression of in situ disk gas from late collisions with still intact protogalactic clumps (assumed to be responsible for the initial burst in the disk SFR at 10 Gyr). »en measured in the last few vears by. cdilferent groups using SCA (Llorner ct al.,been measured in the last few years by different groups using ASCA (Horner et al. 1999. Nevalainen et al.," 1999, Nevalainen et al." 2000. Finoguenoy et al.," 2000, Finoguenov et al." 2001. FOL hereafter) and BeppoSAX data (Ettori. De Grandi Alolendi 2002).," 2001, F01 hereafter) and Beppo–SAX data (Ettori, De Grandi Molendi 2002)." Such analyses consistently find that:(a) MxQV? for Pe4 keV. but with a normalization significantly lower than that found by E96 from simulations (cl.," Such analyses consistently find that: $M\propto T^{3/2}$ for $T\magcir 4$ keV, but with a normalization significantly lower than that found by E96 from simulations (cf." Ettori et al., Ettori et al. 2002): à steeper slope for colder systenis. possibly interpreted as an elect of pre.heating.," 2002); a steeper slope for colder systems, possibly interpreted as an effect of pre–heating." We compare in the right panel of Figure 160. data on the Alsou Lou relation by FOL. which include cata on systems down to Teesld keV. to results from our simulations and to the relation found by E96.," We compare in the right panel of Figure \ref{fi:mtvir} data on the $M_{500}$ $T_{ew}$ relation by F01, which include data on systems down to $T_{ew}\mincir 1$ keV, to results from our simulations and to the relation found by E96." The somewhat lower normalization with respect to the E96 results on the group scale is likely to be due to our improved. resolution., The somewhat lower normalization with respect to the E96 results on the group scale is likely to be due to our improved resolution. However the effect of extra heating is at most marginal and not sullicient to reconcile simulations to data. thus indicating that some other physical process should be at work in establishing the Al T scaling.," However the effect of extra heating is at most marginal and not sufficient to reconcile simulations to data, thus indicating that some other physical process should be at work in establishing the $M$ $T$ scaling." Finoguenoy et al. (, Finoguenov et al. ( 2001. FOL hereafter) suggest that the dillerence between observed and simulated AZ. E. relation is due to the combined. effect. of preheating ancl the effect of formation redshift. on the temperature of the system.,"2001, F01 hereafter) suggest that the difference between observed and simulated $M$ $T$ relation is due to the combined effect of pre–heating and the effect of formation redshift on the temperature of the system." Llowever. our simulations show that preheating has a minor impact on this relation.," However, our simulations show that pre–heating has a minor impact on this relation." As for the ellect. of formation redshift. it may introduce a bias in the definition of the observational data set: observations could. tend to. select fairly relaxed systems. which formed at higher recdshift and. therefore. are characterized by a somewhat higher temperature at a fixed mass (c.g. Ixitavama Suto 1996. Voit Donahue 1998).," As for the effect of formation redshift, it may introduce a bias in the definition of the observational data set: observations could tend to select fairly relaxed systems, which formed at higher redshift and, therefore, are characterized by a somewhat higher temperature at a fixed mass (e.g. Kitayama Suto 1996, Voit Donahue 1998)." Our simulations define an Al T relation with a small scatter. thus suggesting that differences in the formation epoch or dillerences in the current dvnamical status among systems should have a small elfect.," Our simulations define an $M$ $T$ relation with a small scatter, thus suggesting that differences in the formation epoch or differences in the current dynamical status among systems should have a small effect." A larger set of simulated. clusters would be required to properly address this point., A larger set of simulated clusters would be required to properly address this point. Ettort et al. (, Ettori et al. ( 2002) detect a seereeation in the AZ Y relation for cooling[low anc non coolingflow clusters. the latter being characterized by a larger scatter.,"2002) detect a segregation in the $M$ $T$ relation for cooling–flow and non cooling–flow clusters, the latter being characterized by a larger scatter." TNO showed that their ICM model. which incorporates the οσοι» of preheating and cooling. reprocuces the observed: AL T relation.," TN01 showed that their ICM model, which incorporates the effects of pre–heating and cooling, reproduces the observed $M$ $T$ relation." They. also find that the predicted relation is weakly sensitive to the. value of the precollapse entropy. Loor., They also find that the predicted relation is weakly sensitive to the value of the pre--collapse entropy floor. Phis suggests that cooling should be responsible for the lower normalization of the relation. through the steepening of the temperature profiles in cluster central regions.," This suggests that cooling should be responsible for the lower normalization of the relation, through the steepening of the temperature profiles in cluster central regions." “Phe clleet of cooling on the AL T. relation will be further discussed in Section 5 below., The effect of cooling on the $M$ $T$ relation will be further discussed in Section 5 below. The observed. relation between bolometric Luminosity anc temperature is considered a standard argument against the selfsimilar behavior of the ICM., The observed relation between bolometric luminosity and temperature is considered a standard argument against the self–similar behavior of the ICM. Dremsstrahlung emissivity predicts LxκAlpray17.," Bremsstrahlung emissivity predicts $L_X\propto M\rho_{\rm gas}T^{1/2}$." " 'Pherefore. as long as clusters of cillerent mass are scaled versions of each other. then the Al T scaling [rom hyverostatic equilibrium gives Lxκ13(1|ο)nτσ or. equivalently LyκAPUpuU? for ον,= (Ixaiser. 1986. sce Eke et al."," Therefore, as long as clusters of different mass are scaled versions of each other, then the $M$ $T$ scaling from hydrostatic equilibrium gives $L_X\propto T_X^2(1+z)^{3/2}$ or, equivalently $L_X\propto M^{4/3}(1+z)^{7/2}$ for $\Omega_m=1$ (Kaiser 1986, see Eke et al." " 1998. for an extension to £9,, cosmologies)."," 1998, for an extension to $\Omega_m$ cosmologies)." As we also discussed in the introduction. this prediction is at variance with respect to observational evidence of a steeper relation. Lyx127 for 2Z keV and. possibly. even steeper for colder systems.," As we also discussed in the introduction, this prediction is at variance with respect to observational evidence of a steeper relation, $L_X\propto T^{\sim 3}$ for $T\magcir 2$ keV and, possibly, even steeper for colder systems." This result is also in line with the observed. slope of the Ly ÀJ relation. LyxM withaLS+0.1 (Reiprich Boóhhringer 2002).," This result is also in line with the observed slope of the $L_X$ $M$ relation, $L_X\propto M^\alpha$ with $\alpha\simeq 1.8\pm 0.1$ (Reiprich Böhhringer 2002)." The first determinations of the relation. for clusters showed that it has a quite large scatter (e.g. David et al., The first determinations of the relation for clusters showed that it has a quite large scatter (e.g. David et al. 1993. White. Jones Forman 1997).," 1993, White, Jones Forman 1997)." A significant part of this has been recognized. to be the οσο of cooling: central spikes associated with cooling regions provide a Large fraction of total Yo rav [uminositv. so that dilflerences in the cooling structure among clusters of similar temperature induce a spread in the corresponding Ly values.," A significant part of this has been recognized to be the effect of cooling: central spikes associated with cooling regions provide a large fraction of total $X$ –ray luminosity, so that differences in the cooling structure among clusters of similar temperature induce a spread in the corresponding $L_X$ values." After correcting for this effect. different authors (Allen Fabian 1998. Markevitch 1998. Arnaud LEvrarc 1999) were able to," After correcting for this effect, different authors (Allen Fabian 1998, Markevitch 1998, Arnaud Evrard 1999) were able to" , "scattering which we have applied to a magnetic cataclysmic variable (mCV) accretion column (McNamara,Kuncic&Wu2008a).",scattering which we have applied to a magnetic cataclysmic variable (mCV) accretion column \citep*{McNamara08a}. . We demonstrated that the X-ray polarization levels are significantly higher in a shock heated accretion column which is stratified in density and temperature than in a uniform column (Matt2004)., We demonstrated that the X-ray polarization levels are significantly higher in a shock heated accretion column which is stratified in density and temperature than in a uniform column \citep{Matt04}. . We also demonstrated that the degree of polarization depends on the emission sites in the source region., We also demonstrated that the degree of polarization depends on the emission sites in the source region. We now extend our study to model X-ray polarization in relativistic jets., We now extend our study to model X-ray polarization in relativistic jets. " Although our focus is on jets in AGN, the results obtained here are also applicable to relativistic jets in galactic X-ray binaries (e.g.Fender2006) and ultra-luminous X-ray sources (e.g.Freelandetal.2006)."," Although our focus is on jets in AGN, the results obtained here are also applicable to relativistic jets in galactic X-ray binaries \citep[e.g.][]{Fender06} and ultra-luminous X-ray sources \citep[e.g.][]{Freeland06}." . Jets in radio-loud active galatic nuclei (AGN) have been studied for the last 25 years with radio and optical observations (e.g.Bregman1990;Tavecchio2007).," Jets in radio-loud active galatic nuclei (AGN) have been studied for the last 25 years with radio and optical observations \citep[e.g.][]{Bregman90, Tavecchio07}." ". It is only since the launch of the X-ray observatory, with sub-arcsecond angular resolution, that jets have become an important topic in X-ray astronomy."," It is only since the launch of the X-ray observatory, with sub-arcsecond angular resolution, that jets have become an important topic in X-ray astronomy." " has provided imaging spectroscopy studies of extended jets, revealing that jet X-ray emission is much more complex than previously thought (seeMarshalletal.2005;Sambruna2004,forX-rayjet surveys).."," has provided imaging spectroscopy studies of extended jets, revealing that jet X-ray emission is much more complex than previously thought \citep[see][for X-ray jet surveys]{Marshall05,Sambruna04}." " In particular, the origin of the X-ray emission is not clear from the available data and considerable effort has gone into explaining the featureless power-law spectrum seen in all these sources."," In particular, the origin of the X-ray emission is not clear from the available data and considerable effort has gone into explaining the featureless power-law spectrum seen in all these sources." X-ray emission in relativistic jets in AGN may arise from a number of different processes., X-ray emission in relativistic jets in AGN may arise from a number of different processes. " Polarization studies in the radio and optical bands, indicate that this emission mainly originates from synchrotron radiation (Jorstadetal.2007)."," Polarization studies in the radio and optical bands, indicate that this emission mainly originates from synchrotron radiation \citep{Jorstad07}." ". Thus, synchrotron and synchrotron self-Compton (SSC) emission are obvious candidates for the X-ray continuum emission (Maraschi,Ghisellini&Celotti1992)."," Thus, synchrotron and synchrotron self-Compton (SSC) emission are obvious candidates for the X-ray continuum emission \citep{Maraschi92}." ". However, jet X-rayemission may also originate from external Comptonization (EC) of disk blackbody radiation (Dermer&Schlickeiser1993;Wagner1995) or of the cosmic microwave background (CMB) (Tavecchioetal.2000;Celotti,Ghisellini&Chi-aberge 2001).."," However, jet X-rayemission may also originate from external Comptonization (EC) of disk blackbody radiation \citep{Dermer93, Wagner95} or of the cosmic microwave background (CMB) \citep{Tavecchio00, Celotti01}." X-ray polarization measurements may be able to provide an independent diagnostic for discriminating between these competing emission mechanisms., X-ray polarization measurements may be able to provide an independent diagnostic for discriminating between these competing emission mechanisms. " While the polarization properties of synchrotron emission are well known, only a few approximate analytical predictions have been made for SSC polarization (Bjornsson&Matt1994) or for external Comptonized emission (Poutanen1994)."," While the polarization properties of synchrotron emission are well known, only a few approximate analytical predictions have been made for SSC polarization \citep{Bjornsson82b, Begelman87, Celotti94} or for external Comptonized emission \citep{Poutanen94}." ". In this paper, we calculate the X-ray polarization arising from photons scattered by energetic electrons in jets at relativistic bulk speeds."," In this paper, we calculate the X-ray polarization arising from photons scattered by energetic electrons in jets at relativistic bulk speeds." We consider Compton scattering of thermal photons emitted from an underlying accretion disk as well as scattering of the intrinsically polarized synchrotron photons emitted within the jet., We consider Compton scattering of thermal photons emitted from an underlying accretion disk as well as scattering of the intrinsically polarized synchrotron photons emitted within the jet. We also examine the effects of Compton scattering of CMB photons within the jet., We also examine the effects of Compton scattering of CMB photons within the jet. " The paper is outlined as follows: in Section 2 we describe the jet model, outline the theory of polarization due to Compton scattering and describe our computational algorithm."," The paper is outlined as follows: in Section \ref{theory} we describe the jet model, outline the theory of polarization due to Compton scattering and describe our computational algorithm." In Section 3 we present our Monte Carlo modelling results for EC polarization and SSC polarization., In Section \ref{results} we present our Monte Carlo modelling results for EC polarization and SSC polarization. We summarise our results in Section 4.., We summarise our results in Section \ref{conclusion}. " We consider a relativistic jet with Lorentz factor 1«ΓΙ«10 for central object masses M=109—105 with a mass accretion rate M,.", We consider a relativistic jet with Lorentz factor $1 < \Gamma_{\rm j} < 10$ for central object masses $M = 10^6 -10^8 \Msun$ with a mass accretion rate $\dot M_{\rm a}$. The jet is modelled withMc a conical shape as shown in Fig., The jet is modelled with a conical shape as shown in Fig. 1 and is launched at a height zo above the disk midplane., \ref{altgeo} and is launched at a height $z_{\rm 0}$ above the disk midplane. " The jet electrons have a non-thermal powerlaw energy distribution, where Ne is the electron number density, y is the electron Lorentz factor, p is the particle spectral index and K is a normalization factor obtained from Λίο=nsN-(y) dy."," The jet electrons have a non-thermal powerlaw energy distribution, where $N_{\rm e}$ is the electron number density, $\gamma$ is the electron Lorentz factor, $p$ is the particle spectral index and $K$ is a normalization factor obtained from $N_{\rm e} = \int_{\gamma_{\rm min}}^{\gamma_{\rm max}} N_{\rm e} (\gamma) \, d\gamma$ ." " The electron number density at zo can be calculated from energy conservation assuming that the bulk kinetic energy dominates (e.g.Celottietal. 2006),, Here, Pj is the jet power and ry is the radius of the base of the jet."," The electron number density at $z_{\rm 0}$ can be calculated from energy conservation assuming that the bulk kinetic energy dominates \citep[e.g.][]{Celotti98, Freeland06}, Here, $P_{\rm j}$ is the jet power and $r_{\rm b}$ is the radius of the base of the jet." " We let the electron number density in the jet fall off according to mass continuity, We consider the accretion disk model of Shakura&Sunyaev (1973).."," We let the electron number density in the jet fall off according to mass continuity, We consider the accretion disk model of \cite{SS73}. ." " A blackbody temperature is determined for each disk annulus R+ óR, from oT(R)=F(R) where σ is the Stefan-Boltzmann constant and"," A blackbody temperature is determined for each disk annulus $R + \delta R$ , from $\sigma T^4(R) = F(R)$ where $\sigma$ is the Stefan-Boltzmann constant and" integration in ógj. we have used (he following relations among the mean anomaly M. the (rue anomaly / and the eccentric anomaly £m an orbital ellipse. From Eqs. (7)),"integration in $\phiml$, we have used the following relations among the mean anomaly $M$, the true anomaly $f$ and the eccentric anomaly $E$ in an orbital ellipse, From Eqs. \ref{ME}) )" aud (8)). we get where z(f/)=(L-e7)!/?sinf/(124-6cosf).," and \ref{Ef}) ), we get where $z(f)=(1-e^2)^{1/2}\sin f/(1+e\cos f )$." Inserting M(f) to equation (4)). the numerical integration can be done directly.," Inserting $M(f)$ to equation \ref{phiml}) ), the numerical integration can be done directly." In the calculation of the truncation eriterion (2)). /=n(m—1) for the inner Lindblad resonance. (he parameter of the summation is only 7 then.," In the calculation of the truncation criterion \ref{alpha}) ), $l=n(m-1)$ for the inner Lindblad resonance, the parameter of the summation is only $m$ then." Because the high order components contribute little. we sum the inner Lindblad resonance torque Irom m=2 to the value al which the component is three orders smaller (han that of nm=2.," Because the high order components contribute little, we sum the inner Lindblad resonance torque from $m=2$ to the value at which the component is three orders smaller than that of $m=2$." " The truncation radius deduced from the inner Lindblad radius is then The timescale to open the gap between r4, and the inner Lagrangian point dp, with Ar=dp—Fue is about foy8Peserec)Poe(2% as in Avivmowicz& (1994).. where Rea=olUr)? denotes the Revnolds number for which the gap is opened [rom ria."," The truncation radius deduced from the inner Lindblad radius is then The timescale to open the gap between $\rtrunc$ and the inner Lagrangian point $\dlo$ with $\Delta r=\dlo-\rtrunc$, is about $t_{\rm open}\approx Re_{\rm {crit}}({\Delta r}/{\rtrunc})^2\Porb/2\pi$ as in \citet{art94}, where $Re_{\rm crit}=\alpha_{\rm crit}^{-1} ({H}/{r})^{-2}$ denotes the Reynolds number for which the gap is opened from $\rtrunc$." " Since the outflow in the dise is subsonic (Okazaki&Negueruela2001).. the timescale Tijg~Ar/e, of a particle drifting [rom rq to the Roche lobe will be longer than the truncation timescale."," Since the outflow in the disc is subsonic \citep{oka01}, the timescale $\tau_{\rm drift}\sim \Delta r/\velr$ of a particle drifting from $\rtrunc$ to the Roche lobe will be longer than the truncation timescale." " Thus. the efficient (rumeation is defined as (Okazaki&2001) where (CusQ.lec, and di,=(0.500—0.227leq,)a(1€) - the distance of the imer Lagrangian point point lrom the center of the donor (Frank.Ning&Raine2002) al periastron have been used instead of the Roche radius. since it is (ie flat disk rather (han the star itself expanding to the Roche lobe."," Thus, the efficient truncation is defined as \citep{oka01} where $\velr_{\rm max}\sim 0.1 \cs$ and $\dlo=(0.500-0.227\lg \qx)a(1-e)$ - the distance of the inner Lagrangian point point from the center of the donor \citep{fra02} at periastron have been used instead of the Roche radius, since it is the flat disk rather than the star itself expanding to the Roche lobe." enission nav have two components: the first is produced bv relativistic electrons scatterine off locally produced svuchrotron photons (SSC). while the second corresponds to the scattering of photons produced iu other regions (EC). either elsewhere in the jet or bv the broad emission line clouds. or bw some scattering plasma within these clouds.,"emission may have two components: the first is produced by relativistic electrons scattering off locally produced synchrotron photons (SSC), while the second corresponds to the scattering of photons produced in other regions (EC), either elsewhere in the jet or by the broad emission line clouds, or by some scattering plasma within these clouds." (ακομα ct al. (, Ghisellini et al. ( 1998). analvzine all blazirs of kuowu redshift detected by EGRET with spectral information in the 5 ray band. found that the EC component decreases its contribution as the total,"1998), analyzing all blazars of known redshift detected by EGRET with spectral information in the $\gamma$ –ray band, found that the EC component decreases its contribution as the total" colors.,colors. " The nuclear color is the color of the inner10"".", The nuclear color is the color of the inner. . The luminosity weighted color is the color as measured through a large isophotal aperture covering almost the entire galaxy., The luminosity weighted color is the color as measured through a large isophotal aperture covering almost the entire galaxy. The area weighted color is determined from the average of the colors of many pixel-sized apertures over the entire disk., The area weighted color is determined from the average of the colors of many pixel-sized apertures over the entire disk. " When determining luminosity weighted colors most weight is given to bright regions (nucleus, regions) of the galaxy."," When determining luminosity weighted colors most weight is given to bright regions (nucleus, regions) of the galaxy." This is in contrast with area weighted colors where all parts have equal weight and only the area matters., This is in contrast with area weighted colors where all parts have equal weight and only the area matters. Table 3 gives total colors of our sample., Table \ref{colors} gives total colors of our sample. The estimated errors are ~0.1 mag., The estimated errors are $\sim 0.1$ mag. Here and in the next subsection we will discuss the structural parameters and colors of bulge dominated LSB galaxies and compare them to disk dominated LSB galaxies and HSB galaxies., Here and in the next subsection we will discuss the structural parameters and colors of bulge dominated LSB galaxies and compare them to disk dominated LSB galaxies and HSB galaxies. " We will focus on trends to explore the question whether bulge dominated LSB galaxies fit in with the general trends defined by HSB galaxies, and more importantly, whether they form the ""missing link"" between HSB and giant LSB galaxies."," We will focus on trends to explore the question whether bulge dominated LSB galaxies fit in with the general trends defined by HSB galaxies, and more importantly, whether they form the “missing link” between HSB and giant LSB galaxies." The majority of disk dominated LSB and HSB galaxies has disk scale lengths between 2 and 6 kpc (McGaugh Bothun 1994;; de Blok 1997;; dJ95)., The majority of disk dominated LSB and HSB galaxies has disk scale lengths between 2 and 6 kpc (McGaugh Bothun \cite{mc gaugh}; ; de Blok \cite{de blok}; dJ95). The galaxies in our sample have much larger disk scale lengths and the largest galaxies also have bulges., The galaxies in our sample have much larger disk scale lengths and the largest galaxies also have bulges. There appears a trend that the longest disk scale lengths appear in galaxies with the longest bulge scale lengths., There appears a trend that the longest disk scale lengths appear in galaxies with the longest bulge scale lengths. We use the Pearson correlation coefficient to determine the significance of the correlation and find r = 0.59., We use the Pearson correlation coefficient to determine the significance of the correlation and find r = 0.59. We thus, We thus instability developing there as the jet progresses through the medi. the thermal conduction beiug mefficieut iu damping the instability (see Bonitoetal.20102.) ).,"instability developing there as the jet progresses through the medium, the thermal conduction being inefficient in damping the instability (see \citealt{bom10,bop10}) )." The nozzle determines a diamond-shaped shock past the nozzle exit with peak temperature Tz8«10 Ix. (see right bottom panel in Fie. [))., The nozzle determines a diamond-shaped shock past the nozzle exit with peak temperature $T\approx 8\times 10^6$ K (see right bottom panel in Fig. \ref{mappa}) ). This diunuonud structure has its origin inside the nozzle and appears as a shock eicrgiug from the nozzle aud reflecting just past of the nozzle exit., This diamond structure has its origin inside the nozzle and appears as a shock emerging from the nozzle and reflecting just past of the nozzle exit. After its formation (f~50 yrs). the diamond shock is almost stationary until the end of the simulation for ~100 vrs.," After its formation $t\approx 50$ yrs), the diamond shock is almost stationary until the end of the simulation for $\approx 100$ yrs." The thermal conduction is rather efficicut iu the post-shock region eiven the lieh temperatures there (P.>10° IK) and is crucial in stabilizing the diamond structure. damping the wdrodvuamiuc instability developing past the nozzle exit.," The thermal conduction is rather efficient in the post-shock region given the high temperatures there $T> 10^6$ K) and is crucial in stabilizing the diamond structure, damping the hydrodynamic instability developing past the nozzle exit." Ausiliary simulations performed without the thermal conduction have shown that the diamond shock would )o unstable if the thermal conduction is neglected. the wdrodvuamuc instability. heavily perturbing the flow structure at the nozzle exit.," Auxiliary simulations performed without the thermal conduction have shown that the diamond shock would be unstable if the thermal conduction is neglected, the hydrodynamic instability heavily perturbing the flow structure at the nozzle exit." Analyzing the N-vav ciission svuthesized from the warodvuaic model. as described iu Sect. 3.1.. ," Analyzing the X-ray emission synthesized from the hydrodynamic model, as described in Sect. \ref{Synthesis of X-ray emission}," we investigated both the morphology aud spectral properties f the svuthetic N-rav sources., we investigated both the morphology and spectral properties of the synthetic X-ray sources. The N-rav emission from ie modeled jet consists of two main features: a quasi-stationary source associated with the diamoud shock at re jet base and a moving source associated with the shock at the head of the jet., The X-ray emission from the modeled jet consists of two main features: a quasi-stationary source associated with the diamond shock at the jet base and a moving source associated with the shock at the head of the jet. The latter is a trausieut eafure we are not interested aud does not influeuce ιο evolution of the diamouc shock at the base of the jet: therefore we will not discuss its properties m the ollowiug., The latter is a transient feature we are not interested and does not influence the evolution of the diamond shock at the base of the jet; therefore we will not discuss its properties in the following. " The X-av hnuuinositv of the diamond shock is £xx5«1077 ore aud is stationary over z100 yrs,"," The X-ray luminosity of the diamond shock is $L_{\rm X}\approx 5\times 10^{29}$ erg and is stationary over $\approx 100$ yrs." This value is sinülar to that observed for ΠΠ 151 that is almost stationary in about 8 vears., This value is similar to that observed for HH 154 that is almost stationary in about $8$ years. By comparing the total dux derived from the moclel with the specific rif aud arf respouse of cach data-sct. we have verified that the degraded QE of the iustriuneut iu the time baseline analyzed affects the svuthesized couut rate for less than 7%.," By comparing the total flux derived from the model with the specific rmf and arf response of each data-set, we have verified that the degraded QE of the instrument in the time baseline analyzed affects the synthesized count rate for less than $7\%$." This confiniis that the source fux can be assumed coustaut over 8 vrs. within the Poisson CLYOLS.," This confirms that the source flux can be assumed constant over $8$ yrs, within the Poisson errors." The melt upper paucl in Fie., The right upper panel in Fig. Lo shows the svuthetic N-vrayv cluission arising frou the shock iuteerated along he line-ofsielt., \ref{mappa} shows the synthetic X-ray emission arising from the shock integrated along the line-of-sight. Most of the cussion originates just diud the shock iu a bright and compact knot with eimperatire Z2:8<10° IK. The knot is uounded by a diffuse region clongated along the jet axis. characterized w lower temperatures (Dz1.2«4109 K).," Most of the emission originates just behind the shock in a bright and compact knot with temperature $T\approx 8\times 10^6$ K. The knot is surrounded by a diffuse region elongated along the jet axis, characterized by lower temperatures $T\approx 1-2\times 10^6$ K)." Figure 5 shows the profiles of deusity and temperature along the jet axis in the region where the diamond shock foris., Figure \ref{mod_prof} shows the profiles of density and temperature along the jet axis in the region where the diamond shock forms. We found that the spectrum svuthesized frou the wdrodyvuamuc model. as explained iu Sect. 3.1. ," We found that the spectrum synthesized from the hydrodynamic model, as explained in Sect. \ref{Synthesis of X-ray emission}," can fitted with one isothermal component which is compatible with that derived from the three data-scts of Chandra., can be fitted with one isothermal component which is compatible with that derived from the three data-sets of Chandra. We rescaled the svuthetic X-ray image shown in Fie., We rescaled the synthetic X-ray image shown in Fig. to the Chandra/ACIS pixel size (last. panels in Fie. Lj)., to the Chandra/ACIS pixel size (last panels in Fig. \ref{mappa-X-bin}) ). The cussion within the nozzle is assumed to be totally absorbed., The emission within the nozzle is assumed to be totally absorbed. We found that the spatial scales of the N-ray chutting diamond shock at the same spatial resolution of Chandra are consistent with the size of the III 151 N-rav cutting source: a svuthetic N-rayv source of a few arcsec at the base of the jet consistiug of a bright poiut-like component surrounded by a faint aud clongated compoucut along the jet axis., We found that the spatial scales of the X-ray emitting diamond shock at the same spatial resolution of Chandra are consistent with the size of the HH 154 X-ray emitting source: a synthetic X-ray source of a few arcsec at the base of the jet consisting of a bright point-like component surrounded by a faint and elongated component along the jet axis. In Fig., In Fig. " 6 we compare the smoothed 2001 nuage with a bin size 0.25"" (left paucl) with the N-rav source derived from the model at its maxim spatial resolution. 0.011"". (right pancl)."," \ref{contour} we compare the smoothed 2001 image with a bin size $0.25''$ (left panel) with the X-ray source derived from the model at its maximum spatial resolution, $0.014''$, (right panel)." The 2001 image coutour Is superimposed ou the modeled source., The 2001 image contour is superimposed on the modeled source. The analysis of the observations of III 151 in Έπος different epochs with Chandra reveals a faint aud clongated X-ray source displaced by 0.51 arcsec (Ballyetal.2003)) from the L1551 55 protostar (the driving source of the jet) along the jet axis., The analysis of the observations of HH 154 in three different epochs with Chandra reveals a faint and elongated X-ray source displaced by $0.5-1$ arcsec \citealt{bfr03}) ) from the L1551 5 protostar (the driving source of the jet) along the jet axis. The source appears to be quasi-stationary over a time base of zSvis without appreciable proper motion aud variability of X-rav lununosity aud of temperature., The source appears to be quasi-stationary over a time base of $\approx 8$yrs without appreciable proper motion and variability of X-ray luminosity and of temperature. The morphological analysis shows that the N-vav source consists of a bright stationary component with temperature T27«10° Is surrounded by an clougated cooler compoucut extended. in the direction away from the driving source. with temperatures To<τς109 Ik. Very recently Sclincideretal.(2011) aualvzed the same data-sets finding simular observational results in terms of N-ray Iunuinosity. spectral parameters. and morphology. independently showing the robustuess of the derived parameters that forma the basis of our conrparison with a simulation of the jet based on detailed hydrodynamic models.," The morphological analysis shows that the X-ray source consists of a bright stationary component with temperature $T > 7\times 10^{6}$ K surrounded by an elongated cooler component extended in the direction away from the driving source, with temperatures $T < 7 \times 10^{6}$ K. Very recently \citet{sgs11} analyzed the same data-sets finding similar observational results in terms of X-ray luminosity, spectral parameters, and morphology, independently showing the robustness of the derived parameters that form the basis of our comparison with a simulation of the jet based on detailed hydrodynamic models." As shown in Bonitoetal.(2008).. the N-ray source is not perfectly aligned. with the optical jet observed im ΠΠ 151 (see Fig.," As shown in \citet{bff08}, the X-ray source is not perfectly aligned with the optical jet observed in HH 154 (see Fig." 13 in Bonitoetal. 2008))., 13 in \citealt{bff08}) ). " Iu fact the UST tages of Fridluudetal.(2005) show that the optical jet from TIT 151 is along PA.z251"" (see also Pvoctal. 2002)). while from the N-rav data we derive a DAoz270°."," In fact the HST images of \citet{fld05} show that the optical jet from HH 154 is along $P.A.\approx254^{\circ}$ (see also \citealt{phk02}) ), while from the X-ray data we derive a $P.A.\approx270^{\circ}$." Bonitoetal.(2010a) sueeested that an ejection direction varving in time could explain the nisalieumieut between the N-rav source aud the optical jet., \citet{bom10} suggested that an ejection direction varying in time could explain the misalignment between the X-ray source and the optical jet. Since the jet driving source. L1551 IRS5. is known to be a binary system (Diegiug&Cohen 19853). a jet precession could be induced due to the presence of the colupahiou star.," Since the jet driving source, L1551 IRS5, is known to be a binary system \citealt{bc85}) ), a jet precession could be induced due to the presence of the companion star." The absorption cohunu density derived from the analysis of the three data-sets is too low if compared witli the 150 mae of absorption of L1551 55. confirming the results of Ballyetal.(2003). aud Favataetal. (2006).," The absorption column density derived from the analysis of the three data-sets is too low if compared with the 150 mag of absorption of L1551 5, confirming the results of \cite{bfr03} and \cite{fbm06}." . This fact together with the evident displacement of 07.51” of the source. from L1551 55 aud the lack of temporal variation m the N-vay flux aud spectral properties suggest that the N-rav onmüssiou detected iu the three epochs uuiunubiguouslv arises from the jet aud cannot be of stellar origin., This fact together with the evident displacement of $0''.5 - 1''$ of the source from L1551 5 and the lack of temporal variation in the X-ray flux and spectral properties suggest that the X-ray emission detected in the three epochs unambiguously arises from the jet and cannot be of stellar origin. The obscrvatious suggest therefore that the N-ray enission of IIT 151 originates in a standing shock located at the base of the jet. Bonitoetal. (2010a)..," The observations suggest therefore that the X-ray emission of HH 154 originates in a standing shock located at the base of the jet. \citet{bom10}, ," by analyzing the N-ray eunission arising from a pulsed jet model. have discussed the possibility to produce a staudiug slock at the base of the jet as a result of multiple self-interactions," by analyzing the X-ray emission arising from a pulsed jet model, have discussed the possibility to produce a standing shock at the base of the jet as a result of multiple self-interactions" causally connected.,causally connected. We will assume that this is the accretion disc., We will assume that this is the accretion disc. In the previous section we determined that for AIR. 2251-178 the delay between the optical and the J and L-band light curves is very short., In the previous section we determined that for MR 2251-178 the delay between the optical and the J and H-band light curves is very short. This is consistent with the Ilux-Ilux. plots presented in Figure 3., This is consistent with the flux-flux plots presented in Figure 3. All the near-H1. bands also show linear correlations with the B-banel us albeit with nearly Lat slopes., All the near-IR bands also show linear correlations with the B-band flux albeit with nearly flat slopes. These linear relations can be interpreted as being due to nearly simultaneous variation in the optical and near-H bands., These linear relations can be interpreted as being due to nearly simultaneous variation in the optical and near-IR bands. Hence. we can assume that the near-LH1 Hux is also being produced in the accretion disc.," Hence, we can assume that the near-IR flux is also being produced in the accretion disc." We need to understand. the different slopes. however.," We need to understand the different slopes, however." Assuming the simple mocel described above. for a constant albedo we would. expect that the same of the incident X-ray [lux will be thermalised at each radius. with 1e incident Hux being x2% for large 41.," Assuming the simple model described above, for a constant albedo we would expect that the same of the incident X-ray flux will be thermalised at each radius, with the incident flux being $\propto R^{-3}$ for large $R$." This heating ux will be added to the gravitational energy. released at cach radius. which is also x47.," This heating flux will be added to the gravitational energy released at each radius, which is also $\propto R^{-3}$." Hence. we can expect wt the reprocessed N-ray. flux should. remain zürlv constant with racii (1.0. as a function of wavelengths).," Hence, we can expect that the reprocessed X-ray flux should remain fairly constant with radii (i.e., as a function of wavelengths)." However. our observations show that while the D-band flux nearly. cloubled during the observational campaign. the V-xuxd presented a Lux increment. and the near-LR. bands show less than variation.," However, our observations show that while the B-band flux nearly doubled during the observational campaign, the V-band presented a flux increment, and the near-IR bands show less than variation." One possible explanation is a wavelength dependent albedo., One possible explanation is a wavelength dependent albedo. Another possibility is that the variation in the near-H1t is hiehly diluted by another near-LR component. like the emission from a dusty torus.," Another possibility is that the variation in the near-IR is highly diluted by another near-IR component, like the emission from a dusty torus." ]t is interesting to notice that the linear relations seen between the optical anc near-LR bands for MIU 2251-178 break for low and high B-bancl Buxes. while they hold [or 7.51075XfgHM erngs/s/em?/A.," It is interesting to notice that the linear relations seen between the optical and near-IR bands for MR 2251-178 break for low and high B-band fluxes, while they hold for $7.5\times10^{-15} \la f_{B} \la 10^{-14}$ $^2$." " Outside this range. an ""excess"" of emission appears. which can be interpreted as a new component to the near-IH1t emission."," Outside this range, an “excess” of emission appears, which can be interpreted as a new component to the near-IR emission." Llowever. while the new component at low D-band fluxes seems to be present only in HE and Ix. the “new” component at high D-band Iluxes is clearly visible in all near-L1t. bancs.," However, while the “new” component at low B-band fluxes seems to be present only in H and K, the “new” component at high B-band fluxes is clearly visible in all near-IR bands." This might indicate that the near-H1t excess at low B-banel κος is due to the presence of a dusty torus. since it is expected that the emission [from this component peaks somewhere in the mid-IHlt.," This might indicate that the near-IR excess at low B-band fluxes is due to the presence of a dusty torus, since it is expected that the emission from this component peaks somewhere in the mid-IR." Phe excess at high D-band Huxes is consistent with the cliflerent variability trends seen in the fourth vear of monitoring. as already conimented in Section 5.1.," The excess at high B-band fluxes is consistent with the different variability trends seen in the fourth year of monitoring, as already commented in Section 5.1." This might correspond to a new component of ncar-LR emission. like an outburst in the outer parts of the accretion disc. for example.," This might correspond to a new component of near-IR emission, like an outburst in the outer parts of the accretion disc, for example." For NGC 3783 the situation is quite dillerent due to the clclays already cliscussecl in Section 5.2., For NGC 3783 the situation is quite different due to the delays already discussed in Section 5.2. In Figure 3 it can be seen that some linearity is present in the Dux-Iux plots. but with large scatter for all near-L1t bands.," In Figure 3 it can be seen that some linearity is present in the flux-flux plots, but with large scatter for all near-IR bands." In fact. two regimes are present: in the first vear of monitoring the slope of the correlations in all bands are positive due to the consistent Hux decline observed during this period: in the second and third. vear of monitoring the Ilux-Ilux. slopes change [rom being slightly positive in the J-band to slightly negative in the Ix-band.," In fact, two regimes are present: in the first year of monitoring the slope of the correlations in all bands are positive due to the consistent flux decline observed during this period; in the second and third year of monitoring the flux-flux slopes change from being slightly positive in the J-band to slightly negative in the K-band." This is because of the anti-correlation in the light curves around. ALJD ~45201560. 4600το. and 483594950. where the B-hancl light curve presents a Hux decline while the near-LR. light curves show a Ilux rise.," This is because of the anti-correlation in the light curves around MJD $\sim 4520-4560$, $4600-4670$, and $4835-4950$, where the B-band light curve presents a flux decline while the near-IR light curves show a flux rise." Since the delay. becomes larger at longer wavelengths. the strongest anti-correlation is seen in the Ix-band.," Since the delay becomes larger at longer wavelengths, the strongest anti-correlation is seen in the K-band." We constructed delaved. Hux-Ilux. plots of the B-band versus the J and Ll bands. meaning pairs of photometric data where the ποσα. points corresponded to the time of the B-band observation plus a delay.," We constructed delayed flux-flux plots of the B-band versus the J and H bands, meaning pairs of photometric data where the near-IR points corresponded to the time of the B-band observation plus a delay." For the J-band cilferent delays were tried. because of the very broad. peak seen in the cross-correlation plot shown in Figure 2. which could be due to the presence of more than one emitting region. as we already. have cliscussed.," For the J-band different delays were tried because of the very broad peak seen in the cross-correlation plot shown in Figure 2, which could be due to the presence of more than one emitting region, as we already have discussed." For the H-band we tried delays, For the H-band we tried delays assume the outer gap does not exist. we have estimated in section 3 that the fraction of spin-down power carried away by pairs is about 0.1.,"assume the outer gap does not exist, we have estimated in section 3 that the fraction of spin-down power carried away by pairs is about 0.1." Using table 1 and assuming IR as the inverse Compton soft photons. we can estimate that the number of MSPs for 47 Tuc ancl Terzan-5 are ~50 and 7245 respectively.," Using table 1 and assuming IR as the inverse Compton soft photons, we can estimate that the number of MSPs for 47 Tuc and Terzan-5 are $\sim$ 50 and $\sim$ 245 respectively." Although the inverse Compton scattering can explain the Fermi data of both clusters verv well. we cannot distinguish from the data scattering on which photons. i.e. optical. IB and relic. produce this gamma-ray Πας.," Although the inverse Compton scattering can explain the Fermi data of both clusters very well, we cannot distinguish from the data scattering on which photons, i.e. optical, IR and relic, produce this gamma-ray flux." For 47 Tuc all three cases are equally possible., For 47 Tuc all three cases are equally possible. For Terzan 5 the scattering on ealactic infrared photons ancl optical photons can be possible candidates., For Terzan 5 the scattering on galactic infrared photons and optical photons can be possible candidates. Ii (his section we will explore the constraints for the model in derived from other energy bands., In this section we will explore the constraints for the model in derived from other energy bands. " The inverse Compton scattering cooling time is given bv Τομ74XLotsTipLs. where 5,5 is the Lorentz [actor of the relativistic electron/positron pairs in units of 10? and ieyo is the energy density of soft photon in units of LOZerg/em."," The inverse Compton scattering cooling time is given by $\tau_{cooling}\sim 4\times 10^{14} \gamma_{w5}^{-1}w_{-12}^{-1}\rm s$, where $\gamma_{w5}$ is the Lorentz factor of the relativistic electron/positron pairs in units of $10^5$ and $w_{-12}$ is the energy density of soft photon in units of $10^{-12} \rm erg/cm^3$." The diffusion time of these pairs over (he distance d is given bv Ty~10!HPDats. where d is in units of pc and D; is the diffusion coefficient in units of 107em?/s.," The diffusion time of these pairs over the distance $d$ is given by $\tau_d \sim 10^{11} d^2 D_{26}^{-1} \rm s$, where $d$ is in units of pc and $D_{26}$ is the diffusion coefficient in units of $10^{26}\rm cm^2/s$." Therefore the diffusion radius is estimated as [rom the equality Tooting=7; and is given by since (he total IC photon spectrum trom (he GC is given by where T is given by Eq.(19). therefore (he photon spectral index is —1.5 (see Dlunenthal Gould 1970).," Therefore the diffusion radius is estimated as from the equality $\tau_{cooling}=\tau_{d}$ and is given by Since the total IC photon spectrum from the GC is given by where $\frac{dN}{dE_e}$ is given by Eq.(19), therefore the photon spectral index is $\sim -1.5$ (see Blumenthal Gould 1970)." " Ilere doje/de, is the IC cillerential cross-section which in the", Here $d\sigma_{IC}/d\epsilon_\gamma$ is the IC differential cross-section which in the When (he viscositv is present. the primitive equations have been (he object of much attention. on the mathematical side.,"When the viscosity is present, the primitive equations have been the object of much attention, on the mathematical side." See the original articles 2.7]. and the review articles about the mathematical theory of the PEs with viscosity appearing in {?) and in an updated form in |?]:: see also the articles [?.?.7]..," See the original articles \cite{LTW92a, LTW92b}, and the review articles about the mathematical theory of the PEs with viscosity appearing in \cite{TZ04} and in an updated form in \cite{PTZ08}; see also the articles \cite{CT07, Ko06, Ko07}." For the physical background on primitive equations. see e.g. |?7] or |?]..," For the physical background on primitive equations, see e.g. \cite{P87} or \cite{WP05}." In the absence of viscosity. little progress has been made on the analvsis of the primitive equations since the negative result of Oliger and Sundstrómm [?]. showing that these equations are not well-posed. for any set of local boundary conditions.," In the absence of viscosity, little progress has been made on the analysis of the primitive equations since the negative result of Oliger and Sundströmm \cite{OS78} showing that these equations are not well-posed for any set of local boundary conditions." However. the determination of suitable boundary conditions for the primitive equations is a very important problem for limitedarea models: see e.g. a discussion in |?]..," However, the determination of suitable boundary conditions for the primitive equations is a very important problem for limitedarea models; see e.g. a discussion in \cite{WPT97}. ." stellar flux.,stellar flux. ThisΤε corresponds to a iuean photosphevic of 1 to 100 nibar depending ou the assuned ietallicity of the atmosphere (Figure 1))., This$T_{eff}$ corresponds to a mean photospheric of 1 to 100 mbar depending on the assumed metallicity of the atmosphere (Figure \ref{chem_plot}) ). Because CJ136b is known to have an eccentric orbit. we incorporated the effects of non-sxuchironous rotation and tfine-wiunviug distance frou the host star iuto the SPARC model.," Because GJ436b is known to have an eccentric orbit, we incorporated the effects of non-synchronous rotation and time-varying distance from the host star into the SPARC model." " The most probable rotation rate for C136) was determined using the following pseudo-svuchronous rotation relationship preseuted iu ?:: where D,rot isthe planetary rotation rate. Dp ds the orbita period of the planet. aud € ds the eccentricity of the planetary orbit."," The most probable rotation rate for GJ436b was determined using the following pseudo-synchronous rotation relationship presented in \citet{hut81}: where $P_{rot}$ isthe planetary rotation rate, $P_{orb}$ is the orbital period of the planet, and $e$ is the eccentricity of the planetary orbit." In all cases considered here the obliquity of the planet is assumed o be zero., In all cases considered here the obliquity of the planet is assumed to be zero. The time-varving distance of the planetwith respect to its host star. r(f). is determined using dEeplers equation (7) and used to update the incident flux on the planet at each radiative timestep.," The time-varying distance of the planetwith respect to its host star, $r(t)$, is determined using Kepler's equation \citep{mur99} and used to update the incident flux on the planet at each radiative timestep." A ciagram of CUIbis orbit is preseuted iu Figure 2.., A diagram of GJ43b's orbit is presented in Figure \ref{orbit_fig}. . To test the inpact of pseudo-svuchronousrotation aud time-varving stellar insolation. additional simulations for the 1« aud \ solar imetallicitv cases were performec assundne svuchronous rotation and zero eccentricity.," To test the impact of pseudo-synchronousrotation and time-varying stellar insolation, additional simulations for the $\times$ and $\times$ solar metallicity cases were performed assuming synchronous rotation and zero eccentricity." Tn our models. for computational efficieucy. the radiative timestep used to update the radiative Huxes ix longer than the timestep used to update he dyvnamics.," In our models, for computational efficiency, the radiative timestep used to update the radiative fluxes is longer than the timestep used to update the dynamics." Cenerally. as we imereased the uetallicitv of the atinosphiere. progressively shorter radiative and dynamical tunesteps were needed Oo nmautain stabilitv.," Generally, as we increased the metallicity of the atmosphere, progressively shorter radiative and dynamical timesteps were needed to maintain stability." For the 1l aud 34 solar uetallicitv cases a dviauuic timestep of 25 s aud a radiative timestep of 200 s were used., For the $\times$ and $\times$ solar metallicity cases a dynamic timestep of 25 s and a radiative timestep of 200 s were used. The and s solar metallicity cases required a dvuauiic iuestep of 20 s and a radiative timestep of 100 s while the 50 solar case required a dvuauiic nuestep of 15 s and a radiative timestep of GU s. Timestepping iu our sinauulations i$ accomplished hrough a third-order Adams-Bashforth scheme (2).., The $\times$ and $\times$ solar metallicity cases required a dynamic timestep of 20 s and a radiative timestep of 100 s while the $\times$ solar case required a dynamic timestep of 15 s and a radiative timestep of 60 s. Timestepping in our simulations is accomplished through a third-order Adams-Bashforth scheme \citep{dur91}. We applied a fourth-order Shapiro filter iu the iorizontal direction to both velocity compoucuts and the potential tempcrature over a timescale equivalent to twice the dvuamical timestep iu order to reduce simall scale erid noise while munimally affecting the plysical structure of the wind aud temperature fields at the large scale., We applied a fourth-order Shapiro filter in the horizontal direction to both velocity components and the potential temperature over a timescale equivalent to twice the dynamical timestep in order to reduce small scale grid noise while minimally affecting the physical structure of the wind and temperature fields at the large scale. We integrated. cach of our models until the velocities reached a stable configuration., We integrated each of our models until the velocities reached a stable configuration. Figure 3 show the root mean square (RAIS) velocity as a function of pressure and simulated tine. calculated according to: where the inteeral is a elobal (horizoutal) integral over the elobe. A is the horizontal area of the globe. « is the cast-west wind speed. and eds the north-south wind speed.," Figure \ref{vrms_plot} show the root mean square (RMS) velocity as a function of pressure and simulated time, calculated according to: where the integral is a global (horizontal) integral over the globe, $A$ is the horizontal area of the globe, $u$ is the east-west wind speed, and $v$ is the north-south wind speed." The high-frequency variations in the RAIS velocity. seen in the upper levels of both the 1« and 50s solar cases are largelv due to variation iu the luckeut stellar flux associated with the eccentric orbi of CEI36b., The high-frequency variations in the RMS velocity seen in the upper levels of both the $\times$ and $\times$ solar cases are largely due to variation in the incident stellar flux associated with the eccentric orbit of GJ436b. Notice that. iu the observable atinosplere (pressures less than 100 mbar). the orbit-averaged winds become essentially steady within ~2500 Earth davs for solar ietallicity aud 1000 Earth days for 50< solar metallicity.," Notice that, in the observable atmosphere (pressures less than 100 mbar), the orbit-averaged winds become essentially steady within $\sim$ 2500 Earth days for solar metallicity and $\sim$ 1000 Earth days for $\times$ solar metallicity." RMS wind speeds typically reach ~1 kan ! at plotosphere levels., RMS wind speeds typically reach $\sim$ 1 km $^{-1}$ at photosphere levels. Αν further increases in wind speeds will be small and confined to pressure well below the mean photosphere so as not to affect anv svuthetic observations derived from our siuaulations., Any further increases in wind speeds will be small and confined to pressure well below the mean photosphere so as not to affect any synthetic observations derived from our simulations. As outlined in ? the energy available for the production of winds is limited larecly by the elobal available teutial energw within the atinosphere and to some extent cucrey losses due to the Shapiro filter which acts as a livperviscosity., As outlined in \citet{sho09} the energy available for the production of winds is limited largely by the global available potential energy within the atmosphere and to some extent energy losses due to the Shapiro filter which acts as a hyperviscosity. A full discussion of the energetics of our simulated GII36b-like atmosphere is left for a future paper., A full discussion of the energetics of our simulated GJ436b-like atmosphere is left for a future paper. " The following sectious overview the key results from the study of GJ£36bs atinosphierie circulation at νι ὃν, 10. 30. and 50s solar metallicity."," The following sections overview the key results from the study of GJ436b's atmospheric circulation at $\times$ , $\times$ , $\times$ , $\times$ , and $\times$ solar metallicity." Both the thermal structure and winds in these siauulations have a strong dependence on the assumed composition of the atinosphiere for GJ136b., Both the thermal structure and winds in these simulations have a strong dependence on the assumed composition of the atmosphere for GJ436b. Additionally.theoretical light curves aud. spectra," Additionally,theoretical light curves and spectra" ealaxy should terminate its stellar growth. as well as growth of the black hole.,"galaxy should terminate its stellar growth, as well as growth of the black hole." The final appearance of a galaxy is thus significantly allected by its central black hole., The final appearance of a galaxy is thus significantly affected by its central black hole. How far the gas is ejected depends on how long the unobsceured. quasar phase lasts and what the surrounding gas mass and density is: whether for example the galaxy is in a group or cluster., How far the gas is ejected depends on how long the unobscured quasar phase lasts and what the surrounding gas mass and density is; whether for example the galaxy is in a group or cluster. Phe most massive black holes will be in the most. massive galaxies and may last longest in the unobscurecl quasar phase., The most massive black holes will be in the most massive galaxies and may last longest in the unobscured quasar phase. They might also be surrounded by a hot intragroup mecium which could prevent much of the hotter space-filling phase from being ejected., They might also be surrounded by a hot intragroup medium which could prevent much of the hotter space-filling phase from being ejected. Lf a surrounding hot. phase is a necessary ingredient for a radio source then such. objects might be more likely to be radio galaxies., If a surrounding hot phase is a necessary ingredient for a radio source then such objects might be more likely to be radio galaxies. During the ejection phase the quasar might be classed as a BAL and later it might be seen to be surrounded. by extended metal-rich filaments. depending on the velocity of ejection of the cold. eas.," During the ejection phase the quasar might be classed as a BAL and later it might be seen to be surrounded by extended metal-rich filaments, depending on the velocity of ejection of the cold gas." The metal-rich gas. if mixed with surrounding hot intracluster eas. will enhance the local metallicity. providing one source for the extensive metallicity eracients found. by X-ray spectroscopy. around. many cD ealaxies in clusters (Pukazawa ct al 1994).," The metal-rich gas, if mixed with surrounding hot intracluster gas, will enhance the local metallicity, providing one source for the extensive metallicity gradients found by X-ray spectroscopy around many cD galaxies in clusters (Fukazawa et al 1994)." Finally. it is noted that the model requires a significant rower output in the form of a wind associated. with the erowth of black holes.," Finally, it is noted that the model requires a significant power output in the form of a wind associated with the growth of black holes." This wind power is cissipatec as reat in the surrounding medium., This wind power is dissipated as heat in the surrounding medium. Lo may have à marked elfect on surrounding intracluster gas (IEnsslin et al 1998: Wu. Fabian Nulsen 1999). possibly contributing to he heating required to change the X-ray luminosity relation. LyxZ2. from the predicted one with a~2 to the observed one with a~3. The estimates of Wu et al (1999) indicate that it will also heat the general intergalactic medium to a temperature of ~I0Ix at 1] 2.," It may have a marked effect on surrounding intracluster gas (Ensslin et al 1998; Wu, Fabian Nulsen 1999), possibly contributing to the heating required to change the X-ray luminosity--temperature relation, $L_{\rm x}\propto T_{\rm x}^\alpha$, from the predicted one with $\alpha\sim 2$ to the observed one with $\alpha\sim 3.$ The estimates of Wu et al (1999) indicate that it will also heat the general intergalactic medium to a temperature of $\sim 10^7\K$ at $z\sim 1-2$ ." 1n summary. the growth of both massive black holes and ealactic bulges is a highly obsceured. and. related. process. best observed directly in the hard N-rav. band and indirectLy. through radiation of the absorbed. energy. in the sub-nin band.," In summary, the growth of both massive black holes and galactic bulges is a highly obscured, and related, process, best observed directly in the hard X-ray band and indirectly, through radiation of the absorbed energy, in the sub-mm band." L thank the referee for comments and Phe Roval Society [or support., I thank the referee for comments and The Royal Society for support. relative velocity ds typically smaller than the surface escape velocity of the embryo durug the clubrvo erowth.,relative velocity is typically smaller than the surface escape velocity of the embryo during the embryo growth. If the orbital euergv of a body is sufficiently reduced by the atimospheric eas drag. the body is captured by the emibrvo.," If the orbital energy of a body is sufficiently reduced by the atmospheric gas drag, the body is captured by the embryo." The asin radius r of bodies captured at distance Rois given (Inaba&Ikoina2003) where fay(AL/BALIYO ds the reduced. IBI radius of the embrvo audο=cha;," The maximum radius $r$ of bodies captured at distance $R_{\rm e}$ is given by \citep{inaba_ikoma03} where $h_M = (M/3M_*)^{1/3}$ is the reduced Hill radius of the embryo and $\tilde e = e/h_M$." Equation (8)) is derived under the two-body approximation., Equation \ref{eq:atm_cap}) ) is derived under the two-body approximation. Tanigawa&Ohtsuli(2010) confirmed that Equation (8)) is valid iuthe case where the body effects are iucluded., \citet{tanigawa10} confirmed that Equation \ref{eq:atm_cap}) ) is valid inthe case where the three-body effects are included. Equation (8)) means that AR. is the effective collisional radius of an embrwvo for bodies with radius r., Equation \ref{eq:atm_cap}) ) means that $R_{\rm e}$ is the effective collisional radius of an embryo for bodies with radius $r$. The enhanced radius of the eiirvo with atmosphere is thus derived from Eqs. (6)) (51) , The enhanced radius of the embryo with atmosphere is thus derived from Eqs. \ref{eq:atm_dens}) \ref{eq:atm_cap}) ) as where The enhancement factor A.R eiven |x Equation (9)) is shown in Fie. 2..," as where The enhancement factor $R_{\rm e}/R$ given by Equation \ref{eq:Re}) ) is shown in Fig. \ref{fig:enhanced_radius}," where the power-law density profile eiven by Equation (6)) is compared with a niore realistic profile given by Inaba&Dsoma (2003)., where the power-law density profile given by Equation \ref{eq:atm_dens}) ) is compared with a more realistic profile given by \citet{inaba_ikoma03}. ". As we discuss later. planetary embryos mainly erow through collisions with plauetesinials of the initial size or with racsnients of radius roc θα, The euhancenmienut factor calculated with Equation (9)) reproduces we the more realistic one for kui-sézed or arecr plauetesinals. but Equation (9)) significauth overestimates RAR foy fragments."," As we discuss later, planetary embryos mainly grow through collisions with planetesimals of the initial size or with fragments of radius $r \sim 10$ m. The enhancement factor calculated with Equation \ref{eq:Re}) ) reproduces well the more realistic one for km-sized or larger planetesimals, but Equation \ref{eq:Re}) ) significantly overestimates $R_{\rm e}/R$ for fragments." However. since the accretion rate due to collision with such fragimieuts has a weak dependence ou the cuhancement factor CRA Ry): soc Equation (30)3). this discrepancy produces insignificant errors.," However, since the accretion rate due to collision with such fragments has a weak dependence on the enhancement factor $\propto (R_{\rm e}/R)^{1/2}$ ; see Equation \ref{eq:pcol_low}) )), this discrepancy produces insignificant errors." " Planetary enmibrvos can erow until they have accreted all plauetesinals within their feeding ZOOS,", Planetary embryos can grow until they have accreted all planetesimals within their feeding zones. " The width of a feeding zone is given by the orbital separation of enibrvos. πο]AL.Ea, where bcLO ds (I&okubo&Tda2000."," The width of a feeding zone is given by the orbital separation of embryos, $\tilde b (2M/3M_*)^{1/3} a$, where $\tilde b \simeq 10$ is \citep{kokubo00,kokubo02}." " 2002).. WANT Wass Or ""jsolatiou lass” is ALA,=Iwπα”ΟΛΗ,TOMEBIND."," The maximum mass or “isolation mass” is $M_{\rm iso} = 2 \pi a^2 (2M_{\rm iso}/3M_*)^{1/3}\tilde b \Sigma_{\rm s,0}$." It cau be expressed as where AL). is the Earth Lass and AL. is the solar mass., It can be expressed as where $M_{\oplus}$ is the Earth mass and $M_\sun$ is the solar mass. The planetary enibrvo lass approaches the isolation nass if fragmentation is ignored (Ixokubo&Ida2000. 2002)..," The planetary embryo mass approaches the isolation mass if fragmentation is ignored \citep{kokubo00,kokubo02}. ." Ilowever. if fraeiieutation is included. the embryo mass cau reach onlv about Mars nüuass for a MMSN| disk (Ixobavashietal. 2010)..," However, if fragmentation is included, the embryo mass can reach only about Mars mass for a MMSN disk \citep{kobayashi+10}. ." The desired ellipse paramecrs E—(ry.yopyya\J cuter the least-squares fit non-linearly. hence some iterative scheme (or Markov chain. Bridleetal. (2002))) is required to determine the values that mect the constrait (17)).,"The desired ellipse parameters ${\bf E}=\{x_0, y_0, \mu, \eta_+, \eta_\times\}$ enter the least-squares fit non-linearly, hence some iterative scheme (or Markov chain, \citet{Bridle}) ) is required to determine the values that meet the constraint \ref{mb0}) )." For a chosen E. the determination of hhas the rapid solution (11)).," For a chosen ${\bf E}$, the determination of has the rapid solution \ref{sumpix}) )." If the curreut estimate. Ey vields a ὂμ that does not imect the circularity condition. the Newtou-Raphsou iteration would be The derivative db/dE follows from noting the effect of a sinall change 9E to the basis of i: Tere (αι. is thegenerator for the transformation inclicated by Ath parameter of E either translation. dilation. or shear.," If the current estimate ${\bf E}_0$ yields a $\boldb_0$ that does not meet the circularity condition, the Newton-Raphson iteration would be The derivative $d\boldb / d{\bf E}$ follows from noting the effect of a small change $\delta{\bf E}$ to the basis of : Here ${\bf G}_k$ is the for the transformation indicated by $k$ th parameter of ${\bf E}$ —either translation, dilation, or shear." These matrices are fixed by the choice of basis functions {ey}., These matrices are fixed by the choice of basis functions $\{\psi_i\}$. These alterations to the basis-function values can be propagated through the solution (113) to eive the perturbation tob: The matrix db/dE is apparent from this last equation., These alterations to the basis-function values can be propagated through the solution \ref{sumpix}) ) to give the perturbation to: The matrix $d\boldb / d{\bf E}$ is apparent from this last equation. " Tere we have taken he generator matrices Gy, to cach be NNX the vector B now must be. in general. augiuneued to infinite cimeusiou. aud we also take @ to he o&N."," Here we have taken the generator matrices ${\bf G}_k$ to each be $N\times\infty$ ; the vector $\hboldbeta$ now must be, in general, augmented to infinite dimension, and we also take $\hboldalpha$ to be $\infty\times N$." Note that the pareuthesized portion of the solutiou (19)) would vanish if uot for the distinction between the truncated and infe-dinenusioual versions of acadG.. siuce the first [IN clemenuts of 8Aby are zero.," Note that the parenthesized portion of the solution \ref{dbde1}) ) would vanish if not for the distinction between the truncated and infinite-dimensional versions of and, since the first $N$ elements of $\hboldbeta - \hboldalpha \boldb_0$ are zero." " Likewise.κ we could sot the initial⋅⋅⋅ aτὰ,⋀↕−≽ of the final term to ideutitv if not for the truucation. in which case the transformation would become the verv simple 6b=(Goby)-6E (with some abuse of notation here)."," Likewise we could set the initial $\boldalpha^{-1} \hboldalpha^T$ of the final term to identity if not for the truncation, in which case the transformation would become the very simple $\delta\boldb = ({\bf G}^T\boldb_0)\cdot \delta{\bf E}$ (with some abuse of notation here)." Since we are using db/dE oulv to help us iterate the solution for E. we could use this simple approximation. or extend to some order bevoud NV using(19).," Since we are using $d\boldb/d{\bf E}$ only to help us iterate the solution for ${\bf E}$, we could use this simple approximation, or extend to some order beyond $N$ using." . We use the Causs-LaeucrreOo decomposition iu our shape measurements., We use the Gauss-Laguerre decomposition in our shape measurements. These are the eigeufunctions of the 2-dimensional quanti liaxinonic oscillator. and are most compactly expressed as complex functions indexed by two integers p.q=0: The elliptical-basis versions are taken to be Note we have tweaked the normalizations so that the flux is rather than making the functions orthonormal.," These are the eigenfunctions of the 2-dimensional quantum harmonic oscillator, and are most compactly expressed as complex functions indexed by two integers $p,q \ge 0$: The elliptical-basis versions are taken to be Note we have tweaked the normalizations so that the flux is rather than making the functions orthonormal." The Catss-Laeucire (GL)functions are still. however. a complete and orthogonalset over the plane.," The Gauss-Laguerre (GL)functions are still, however, a complete and orthogonalset over the plane." " The functions are equivalent to the ""polar shapelets” of Masseyetal.(200L)..", The functions are equivalent to the “polar shapelets” of \citet{Massey}.. The useful advice proviceck by the referee Fabio CGovernato is gratefully acknowledged. too.,"The useful advice provided by the referee Fabio Governato is gratefully acknowledged, too." equation (29)) and equation (40)) (taking Mp=0).,equation \ref{hdel}) ) and equation \ref{gdel}) ) (taking $\dot{M}_D = 0$ ). We can define a halllight radius ry). within which the energy radiated per unit time by the disk is one half of the total power of the disk. ie. Lypplrj, in the disk is The total power of an accretion disk is ος=Mp(1—E)."," From equation \ref{mcL12}) ), for a non-accretion disk magnetically coupled to a black hole, $r_{1/2}$ can be solved from Similarly, for a standard accretion disk, the energy radiated per unit time from the region inside a circle of radius $r>r_{ms}$ in the disk is The total power of an accretion disk is ${\cal L}_{acc} = \dot{M}_D \left(1- E_{ms}^+\right)\,$." " Thus. the hall-Hight radius of a standard accretion disk. whichis defined by έςrye)=d£, can be solved from where f is give by equation (15n) of PageanclThorne(1974)."," Thus, the half-light radius of a standard accretion disk, whichis defined by ${\cal L}_{acc}(3\sigma$ peak radio emission in the vicinity $\rm <6\,arcsec$ ) of X-ray sources." This method further identifies 7 X-rayradio matches., This method further identifies 7 X-ray/radio matches. Given the surface densities of the radio and the X-ray source catalogues the probability of fincüng by chance a 36; radio source within Garcsec from an X-ray. position is estimated to be x1 per cent.," Given the surface densities of the radio and the X-ray source catalogues the probability of finding by chance a $3\sigma$ radio source within $\rm 6\,arcsec$ from an X-ray position is estimated to be $\approx1$ per cent." Redshift measurements are available for 18 hard. X-ray selected sources brighter than 7?z22 mmage., Redshift measurements are available for 18 hard X-ray selected sources brighter than $R\approx22$ mag. In addition to these spectroscopic redshifts. for X-ray sources with optica ancl near-infrared: (NUR) photometry in at least 4+ bancs ancl relatively hard X-ray. spectral properties. LR=»0.4 (corresponding to observed column densities in excess. of ]07em7: P= L3) we also estimate photometric redshifts using galaxy templates and methods outlined in. Sullivan et al. (," In addition to these spectroscopic redshifts, for X-ray sources with optical and near-infrared (NIR) photometry in at least 4 bands and relatively hard X-ray spectral properties, $\rm HR>-0.4$ (corresponding to observed column densities in excess of $\rm 10^{21}\, cm^{-2}$; $\Gamma=1.7$ ) we also estimate photometric redshifts using galaxy templates and methods outlined in Sullivan et al. (" 2004).,2004). Phese sources have colours suggesting tha wily optical emission is dominatedbv light from the hos galaxy rather than the central AGN. thus allowing templates o) normal galaxies to be used (see section ??7: Bareer et al.," These sources have colours suggesting that their optical emission is dominatedby light from the host galaxy rather than the central AGN, thus allowing templates for normal galaxies to be used (see section \ref{results}; Barger et al." 2002. 2003: Mobasher et al.," 2002, 2003; Mobasher et al." 2004: Gandhi et al., 2004; Gandhi et al. 2004)., 2004). Comparing zí5 with ts. for the 5 sources with (i) Htc— O.4. (i) at least 4-banc photometry and. (iii) available spectroscopy we estimate the accuracy of our method to be 62)ο© OL ," Comparing $z_{phot}$ with $z_{spec}$ for the 5 sources with (i) $\rm HR>-0.4$ , (ii) at least 4-band photometry and (iii) available spectroscopy we estimate the accuracy of our method to be $| \delta z|/z_{spec}\approx 0.1$ ." Although the statistics are »»or the above result. indicates that templates for normal, Although the statistics are poor the above result indicates that templates for normal the scattering. was not explicitly. justified.,"the scattering, was not explicitly justified." “Phe purpose of this paper is to quantitatively assess the validity of the ήν model in. view., The purpose of this paper is to quantitatively assess the validity of the BGK model in view. We show that all. pitch angles scatter at roughly comparable rates. so that the neglect of the pitch angles dependence (made by Cary Feldman 1977: Levinson Eichler 1992. Pistinner et al.," We show that all pitch angles scatter at roughly comparable rates, so that the neglect of the pitch angles dependence (made by Gary Feldman 1977; Levinson Eichler 1992, Pistinner et al." 1996) is quantitatively valid., 1996) is quantitatively valid. The structure of this paper is: ln ?? we consider the governing equations for collision dominated ancl whistler dominated plasma., The structure of this paper is: In \ref{sec:gov} we consider the governing equations for collision dominated and whistler dominated plasma. In ?? we obtain the formal expression for the electron distribution function first in the absence of whistlers and then in the presence of quasilinear situated whistlers., In \ref{sec:steady} we obtain the formal expression for the electron distribution function first in the absence of whistlers and then in the presence of quasilinear situated whistlers. In ?? we obtain the critical condition. [ου whistlers excitation by a collision dominated: plasma., In \ref{sec:wis} we obtain the critical condition for whistlers excitation by a collision dominated plasma. We then discuss the consisteney of the small scale plasma turbulence theory. ane show that. olf-asxis whistlers are required for significant heat Hux inhibition and that they are excited by the required amount.," We then discuss the consistency of the small scale plasma turbulence theory, and show that off-axis whistlers are required for significant heat flux inhibition and that they are excited by the required amount." Phe expression for the heat Εικ vector is considered in 27.., The expression for the heat flux vector is considered in \ref{sec:heat}. We summarize our conclusions in 7?.., We summarize our conclusions in \ref{sec:con}. This section outlines the governing equations that ead το the heat Εαν., This section outlines the governing equations that lead to the heat flux. The discussion starts with collision dominated: plasma theory., The discussion starts with collision dominated plasma theory. I0 concentrates on the assumptions made in deriving the inhibited heat. Hux. in xwticular. the assumption ofsFale. which raises the question of kinetic stability of the plasma.," It concentrates on the assumptions made in deriving the inhibited heat flux, in particular, the assumption of, which raises the question of kinetic stability of the plasma." WWinctic plasma instabilities can lead to a plasma »ervaded. by stochastic electromagnetic fields., Kinetic plasma instabilities can lead to a plasma pervaded by stochastic electromagnetic fields. These fields may scatter particles faster than binary collisions., These fields may scatter particles faster than binary collisions. To account for a kinetic instability saturation. a set of governing equations that describe this phenomena is required.," To account for a kinetic instability saturation, a set of governing equations that describe this phenomena is required." An electron-ion. plasma. irrespective of whether the plasma is collision or collective phenomena dominated. can be deseribed by two Boltzmann or Fokker-Planck equations (BEPE).," An electron-ion plasma, irrespective of whether the plasma is collision or collective phenomena dominated, can be described by two Boltzmann or Fokker-Planck equations (BFPE)." For sake of brevity we shall assume that. the solution to the ion BEPE is given. and. consider only the solution to the electron. DEPE.," For sake of brevity we shall assume that the solution to the ion BFPE is given, and consider only the solution to the electron BFPE." " The electron. DEPE (ος. Dlandford Eichler LOST) reads: where « f. g. ce. D. “Let 6. FQ are (he electrons distribution function. the EU.cosine of the pitch angle. the electron. speed. the magnetic field magnitude. the self consistent DC electric field the electron scattering rate (collision frequency)τν, and the alline length along the magnetic field lines respectively."," The electron BFPE (e.g. Blandford Eichler 1987) reads: where $f$ , $\mu$, $v$, $B$, $E^{DC}_{\parallel}$, $\nu$, $l_{\parallel}$ are the electrons distribution function, the cosine of the pitch angle, the electron speed, the magnetic field magnitude, the self consistent DC electric field the electron scattering rate (collision frequency), and the affine length along the magnetic field lines respectively." Several assumptions have been mace in writing eq. 1::, Several assumptions have been made in writing eq. \ref{eq:drift_kin}: These assumptions are justified in the context of clusters of galaxies. where the large scale hydrodynamical timescale and the collisional timescale are. both long compared to the plasma timescales. the scale length of the magnetic field is enormous compared to particle gvroraclii. and the whistler phase velocity is small compared. to the electron. thermal velocity.," These assumptions are justified in the context of clusters of galaxies, where the large scale hydrodynamical timescale and the collisional timescale are both long compared to the plasma timescales, the scale length of the magnetic field is enormous compared to particle gyroradii, and the whistler phase velocity is small compared to the electron thermal velocity." For completeness we elaborate brielly on each of these assumptions in ??.., For completeness we elaborate briefly on each of these assumptions in \ref{sec:first_appe}. Classical astrophysical plasmas have traditionally been assumed to be thermal i.e. collision dominated., Classical astrophysical plasmas have traditionally been assumed to be thermal i.e. collision dominated. Thus. the Spitzer Llarrm (1953) results are traditionally applied to model them.," Thus, the Spitzer Härrm (1953) results are traditionally applied to model them." With eq., With eq. 1 one readily. reproduces the Spitzer Ilàrrm (1953) results (within a factor of five: cf.," \ref{eq:drift_kin} one readily reproduces the Spitzer Härrm (1953) results (within a factor of five; cf." Table LL and eq., Table III and eq. 36 in Spitzer Πάνα as energy exchange is ignored in eq., 36 in Spitzer Härrm as energy exchange is ignored in eq. 1) along a single magnetic field line., 1) along a single magnetic field line. Toward that goal one only need assume that Coulomb forces (collision dominated. plasma) vield: where and with Y. kg. ome. wy Νο and Ημ) the gas temperature. the Boltzmann constant. the electron. mass. the electron. plasma frequency. the Debye number. and the Coulomb logarithm respectively.," Toward that goal one only need assume that Coulomb forces (collision dominated plasma) yield: where and with $T$, $k_{B}$, $m_e$, $\omega_{p}$, $N_{D}$ and $\ln (\Lambda_{coul})$ the gas temperature, the Boltzmann constant, the electron mass, the electron plasma frequency, the Debye number, and the Coulomb logarithm respectively." To obtain significant electron. heat-Dux. inhibition by whistlers. whistler-cleetron scattering must be as fast as ion-electron scattering.," To obtain significant electron heat-flux inhibition by whistlers, whistler-electron scattering must be as fast as ion-electron scattering." Thus. the time scale for establishing steady state on microscopic scales is at least as [ast as that when whistlers are absent. and we mav assume that a modified steady state is formed.," Thus, the time scale for establishing steady state on microscopic scales is at least as fast as that when whistlers are absent, and we may assume that a modified steady state is formed." Under such a situation eq., Under such a situation eq. 1.describes the evolution of the electron distribution function but. with the following important mocification. where," \ref{eq:drift_kin} describes the evolution of the electron distribution function but, with the following important modification, where" signals are no longer prominent in the leftover residuals.,signals are no longer prominent in the leftover residuals. We conclude that detecting precession in the radial velocity data of a star within a binary svstem may be an indication that there is an unresolved third star., We conclude that detecting precession in the radial velocity data of a star within a binary system may be an indication that there is an unresolved third star. We discussed the case of v-Octantis which is a close binary svstemi (2.55 AU) composed of a Ix-type star. (y- Octantis A) and a fainter companion (v-Octantis 13)., We discussed the case of $\nu$ -Octantis which is a close binary system $2.55$ AU) composed of a K-type star $\nu$ -Octantis A) and a fainter companion $\nu$ -Octantis B). Raclia velocity data analysis showed a signal at 417 dav which was identified as a planet at 1.2 AU of v-Octantis A. However. we showed that the racial velocity data currently impliec retrograde precession of about O.S6°/vr for this binary svstem.," Radial velocity data analysis showed a signal at $417$ day which was identified as a planet at $1.2$ AU of $\nu$ -Octantis A. However, we showed that the radial velocity data currently implied retrograde precession of about $-0.86^\circ$ /yr for this binary system." We suggested that this may indicate that z-Octantis D is actually a double star which could. explain a signa similar to that. previously. associated. with a planet., We suggested that this may indicate that $\nu$ -Octantis B is actually a double star which could explain a signal similar to that previously associated with a planet. At the moment we cannot vet. decide that thereported. planet of v-Octantis A is simply an artifact caused by v-Octantis B being a double star., At the moment we cannot yet decide that thereported planet of $\nu$ -Octantis A is simply an artifact caused by $\nu$ -Octantis B being a double star. In order to distinguish between the two hypothesis (planet or double star). more radial velocity data for v-Octantis is needed. so that we can better constrain the main binary precession rate.," In order to distinguish between the two hypothesis (planet or double star), more radial velocity data for $\nu$ -Octantis is needed, so that we can better constrain the main binary's precession rate." Moreover. the planet hypothesis could s.be compatible with retrograde precession of the v-Octantis binary i£ we could. prove the existence of stable orbits around v-Octantis A. with semi-major axis ratio a=O47 and inclined more than 45° with respect to the v-Octantis binary”.," Moreover, the planet hypothesis could be compatible with retrograde precession of the $\nu$ -Octantis binary if we could prove the existence of stable orbits around $\nu$ -Octantis A, with semi-major axis ratio $\alpha=0.47$ and inclined more than $45^\circ$ with respect to the $\nu$ -Octantis ." . We acknowledge financial support from. FC'L-Portugal (erant ωςοτιςΑν/098528/2008)., We acknowledge financial support from FCT-Portugal (grant PTDC/CTE-AST/098528/2008). and temperature as a fraction of the photospheric temperature of thestar.,and temperature as a fraction of the photospheric temperature of the. .. First of all. we improved P and Το from the spectroscopic solution. after we had the photometric data and preliminary parameters from JKTEBOP.," First of all, we improved $P$ and $T_0$ from the spectroscopic solution, after we had the photometric data and preliminary parameters from JKTEBOP." This was possible thanks to the PHOEBE's ability of working on several light curves anc both RV curves simuItaneously., This was possible thanks to the PHOEBE's ability of working on several light curves and both RV curves simultaneously. Later. we kept them fixed and fitted for temperatures. gravitational potentials. inclinatior and quantities obtained. from the spectroscopic. orbit.," Later, we kept them fixed and fitted for temperatures, gravitational potentials, inclination and quantities obtained from the spectroscopic orbit." " Spots were added later ""manually"" by putting their parameters anc inspecting the light curve by eye."," Spots were added later ""manually"" by putting their parameters and inspecting the light curve by eye." The light curve mimics ellipsoidal variations. but a model with two spots. one oi each component. both seen around eclipses. better fits the observations.," The light curve mimics ellipsoidal variations, but a model with two spots, one on each component, both seen around eclipses, better fits the observations." If the shape of the variation were caused by tidally distorted stars. their radii would be much larger and thus eclipses would be much wider.," If the shape of the variation were caused by tidally distorted stars, their radii would be much larger and thus eclipses would be much wider." Also. a closer inspection reveals an asymmetry between the out-of-eclipse variations.," Also, a closer inspection reveals an asymmetry between the out-of-eclipse variations." In the last stage of modelling we set all parameters free once again to let them converge onto their final values., In the last stage of modelling we set all parameters free once again to let them converge onto their final values. In our analysis we used the square-root limb-darkening law (Diaz-Cordovez&Gimenez1992) with the coefficients automatically interpolated by PHEOEBE from the van Hamme LD tables (vanHamme1993)., In our analysis we used the square-root limb-darkening law \citep{dia92} with the coefficients automatically interpolated by PHEOEBE from the van Hamme LD tables \citep{vHa93}. . The albedos for both components were held fixed at the value of 0.5 as is appropriate for convective envelopes., The albedos for both components were held fixed at the value of 0.5 as is appropriate for convective envelopes. The gravity. brightening coefficient was set to 0.32 — the classical value obtained by Lucy(1967)., The gravity brightening coefficient was set to 0.32 – the classical value obtained by \citet{luc67}. . It is common knowledge that it is hard to reliably estimate temperatures of eclipsing binary components., It is common knowledge that it is hard to reliably estimate temperatures of eclipsing binary components. The depth of the eclipse depends not only on temperatures. but also inclination. stellar radii and the spots? configuration. and the ratio of the eclipse depths can give only the ratio of effective temperatures.," The depth of the eclipse depends not only on temperatures, but also inclination, stellar radii and the spots' configuration, and the ratio of the eclipse depths can give only the ratio of effective temperatures." Thus. to compute the stars” temperatures precisely. one must have very precise starting. values.," Thus, to compute the stars' temperatures precisely, one must have very precise starting values." PHOEBE enables one to separately compute the flux from every component in every band., PHOEBE enables one to separately compute the flux from every component in every band. with the V and / light curves. we computed the V—7 colour for each star and used them with the empirical colour-temperature calibration from Casagrandeetal.(2006)..," with the $V$ and $I$ light curves, we computed the $V-I$ colour for each star and used them with the empirical colour-temperature calibration from \citet{cas06}." In this way we obtained a starting point for the temperature fitting., In this way we obtained a starting point for the temperature fitting. This presumably should have produced reliable values of the temperatures with relatively small formal errors. typically about 50 K. The idea that lays behind this approach ts described by Pria&Zwitter(2005.2006) or Kallrath&Milone and is based on the calculation of the so called — a time- or phase-dependent value that can be associated with a colour index of the whole system (that is why two or more light curves are required).," This presumably should have produced reliable values of the temperatures with relatively small formal errors, typically about 50 K. The idea that lays behind this approach is described by \citet{prs05,prs06} or \citet{kal09} and is based on the calculation of the so called – a time- or phase-dependent value that can be associated with a colour index of the whole system (that is why two or more light curves are required)." The discussion however does not include the influence of systematic uncertainties (see below) or spots., The discussion however does not include the influence of systematic uncertainties (see below) or spots. The method itself is known but was not widely used on spotted systems. which is why more attention at this point is required.," The method itself is known but was not widely used on spotted systems, which is why more attention at this point is required." However. the biggest contribution to the final error budget of temperatures in our case comes from the imperfect absolute magnitude calibration.," However, the biggest contribution to the final error budget of temperatures in our case comes from the imperfect absolute magnitude calibration." The uncertainty of V-IL. at the level of 0.07 mag. led to an error of about 200 K in every component's temperature.," The uncertainty of $V-I$, at the level of 0.07 mag, led to an error of about 200 K in every component's temperature." One should keep in mind that this is actually the uncertainty of the absolute scale of temperatures. while the ratio is very well constrained.," One should keep in mind that this is actually the uncertainty of the absolute scale of temperatures, while the ratio is very well constrained." We noticed that a change of any components temperature by 5-10 K results in an eclipse depth variation that is noticeable with our photometry., We noticed that a change of any component's temperature by 5-10 K results in an eclipse depth variation that is noticeable with our photometry. We also noticed that temperature variations at a level of about 200 K have a small influence on the derived radii and increase their final uncertainties by about 25 per cent (from 0.004 to 0.005)., We also noticed that temperature variations at a level of about 200 K have a small influence on the derived radii and increase their final uncertainties by about 25 per cent (from 0.004 to 0.005). Additionally. note that the V—/ colour does not change significantly even when one uses completely improbable starting values of the temperatures for the fitting.," Additionally, note that the $V-I$ colour does not change significantly even when one uses completely improbable starting values of the temperatures for the fitting." The final set of absolute physical and radiative parameters is listed in Table 3.., The final set of absolute physical and radiative parameters is listed in Table \ref{tab_par_04}. We managed to obtain a very good level of precision in masses and radi (about 0.6%))., We managed to obtain a very good level of precision in masses and radii (about ). The resulting flux ratio in the V. band is 0.790+0.015. which agrees with the value from TODCOR. but is more accurate.," The resulting flux ratio in the $V$ band is $0.790\pm0.015$, which agrees with the value from TODCOR, but is more accurate." (V—I) values are corrected for the reddening (see below)., $(V-I)$ values are corrected for the reddening (see below). Note that the absolute values and their uncertainties were not taken from PHOEBE. but were calculated by a procedure called JKTABSDIM. which ts available together with JKTEBOP.," Note that the absolute values and their uncertainties were not taken from PHOEBE, but were calculated by a procedure called JKTABSDIM, which is available together with JKTEBOP." " It provides photometric properties (like absolute magnitudes) and distances by calculating Mj, on the basis of temperature. applying various bolometric corrections (Besseletal.1998; to calculate absolute"," It provides photometric properties (like absolute magnitudes) and distances by calculating $M_{bol}$ on the basis of temperature, applying various bolometric corrections \citep{bes98,flo96,gir02} to calculate absolute" Note that when we centroid spectral features to find their separation. both cllect (i) (shifting) and clleet (ii) (instrumental profile (LP) distortion)ga effectively ‘stretch’ the spectrum.,"Note that when we centroid spectral features to find their separation, both effect (i) (shifting) and effect (ii) (instrumental profile (IP) distortion) effectively `stretch' the spectrum." For the sample. this should lead to systematically positive values of Aafa.," For the sample, this should lead to systematically positive values of $\da$." That is. atmospheric dispersion effects cannot explain the average negative value of Aafa seen in the QSO cata.," That is, atmospheric dispersion effects cannot explain the average negative value of $\da$ seen in the QSO data." Removing these elfects [rom our data would make the results significant., Removing these effects from our data would make the results significant. Although there is no obvious correlation between zoo and£ as would be expected in this scenario (see Fig., Although there is no obvious correlation between $\da$ and $\xi$ as would be expected in this scenario (see Fig. 6). the potential effect is quantified in our analvsis below.," 6), the potential effect is quantified in our analysis below." For all objects which were observed. without the use of an image rotator. we have used the observational parameters reported in the image header files to find average values of £ (sce Fig.," For all objects which were observed without the use of an image rotator, we have used the observational parameters reported in the image header files to find average values of $\xi$ (see Fig." 6). temperature. pressure and relative humidity for each object.," 6), temperature, pressure and relative humidity for each object." This allows us to correct for the stretching of the spectrum implied by equation 6..., This allows us to correct for the stretching of the spectrum implied by equation \ref{eq:angsep}. We have re-caleulated Aafo in the same manner as described in MOla and we plot the results in Fig., We have re-calculated $\da$ in the same manner as described in M01a and we plot the results in Fig. 7., 7. For several QSOs. only a single image header (i.e. for one of the QSO exposures out of a series) was available.," For several QSOs, only a single image header (i.e. for one of the QSO exposures out of a series) was available." In these cases we have added: (in. (quadrature) an error of 0.9«10.7., In these cases we have added (in quadrature) an error of $0.9 \times 10^{-5}$. This is an average value determined by calculating Aafa for several values of the zenith distance for those objects concerned. aid. corresponds to an uncertainty in the average£ of about 420°., This is an average value determined by calculating $\da$ for several values of the zenith distance for those objects concerned and corresponds to an uncertainty in the average $\xi$ of about $\pm 20^{\circ}$. We have also tested. the ellect of the IP. distortions (elfect (ii) above) on z;Na/a., We have also tested the effect of the IP distortions (effect (ii) above) on $\da$. We generated high SNR. single component absorption spectra (with Aafa= 0) for several redshifts.," We generated high SNR, single component absorption spectra (with $\da = 0$ ) for several redshifts." We included different combinations of transitions in the different spectra so as to make a representative estimate for both samples of QSO data (particularly the sample which contains many combinations of different: transitions)., We included different combinations of transitions in the different spectra so as to make a representative estimate for both samples of QSO data (particularly the sample which contains many combinations of different transitions). A wavelength. dependent PSE was constructed. using the following procedure., A wavelength dependent PSF was constructed using the following procedure. We assume that the seeing (taken as 8S) and tracking error (taken as (225) generate Gaussian profiles across the slit ane that a wavelength. Ay falls at its centre., We assume that the seeing (taken as 8) and tracking error (taken as 25) generate Gaussian profiles across the slit and that a wavelength $\lambda_0$ falls at its centre. Other wavelengths. are refracted to dillerent parts of the slit. depending on the, Other wavelengths are refracted to different parts of the slit depending on the region from those obtained with ALICE-MIDAS aud with VISTA data-set of intensities.,region from those obtained with ALICE-MIDAS and with VISTA data-set of intensities. In his case. the values of the gracdieui vary from —0.006 dex/kpe to —0.18 dex/kpe (see Table 1.," In this case, the values of the gradient vary from $-0.006$ dex/kpc to $-0.18$ dex/kpc (see Table 1)." Tlese values a 'e slightly larger thai those deternined for other barrec late-type galaxies., These values a re slightly larger than those determined for other barred late-type galaxies. Agai. the values of the sope obtainec with he most/less external regions are very sinilar to hose obtained with the fitting.," Again, the values of the slope obtained with the most/less external regions are very similar to those obtained with the fitting." " On the cottra""v. he slope deter:dined [rom the most/less netallic 'eglous a'e very large."," On the contrary, the slope determined from the most/less metallic regions are very large." This valte could not ye realistic and the nain reason for such a steep gradieut is that the less uetallic region. U1262. is ucM te most externalo 1e.," This value could not be realistic and the main reason for such a steep gradient is that the less metallic region, U42c2, is not the most external one." The differences in abuiclances yetweell he regions is of almost 0.5 dex bu with less than 1 kpc in separation., The differences in abundances between the regions is of almost $0.5$ dex but with less than $1$ kpc in separation. Mor'eover. {le most uetallic region jas the lowest S/N. When aotler region is COLsiclerec. a gradient of —0.15 dex/kpe is obtaiued. which is more similar to the rest o. je values.," Moreover, the most metallic region has the lowest S/N. When another region is considered, a gradient of $-0.15$ dex/kpc is obtained, which is more similar to the rest of the values." Athough i should be taken with care clue o the s1uall numbero ‘region involved. a metallicity at averaged cisances cali be obtained as well :isa gradient.," Although it should be taken with care due to the small number of region involved, a metallicity at averaged distances can be obtained as well as a gradient." Valtes from —0.02 to —0.11 dex/kpe are obained. which are only slightly smaller tlau those obtainecLwith all the regiMis.," Values from $-0.02$ to $-0.14$ dex/kpc are obtained, which are only slightly smaller than those obtained with all the regions." An average eraclieit of —0.17 is obtained fro all the values in Table 1. with a «ispersion of 0.06.," An average gradient of $-0.17$ is obtained from all the values in Table 1, with a dispersion of $0.06$." Iu a investigation like this there could be a lot of sources of uncertainties., In a investigation like this there could be a lot of sources of uncertainties. Some of trem could be related to uncertainties in the clisauce dletermination to the galaxy itsell., Some of them could be related to uncertainties in the distance determination to the galaxy itself. Normally. dislances are very difficult to obtain when no pritjary candles are considered.," Normally, distances are very difficult to obtain when no primary candles are considered." This is the case for all tle galaxies in this sample., This is the case for all the galaxies in this sample. The distance used Iere were those from Hidalgo-Cránunez (2001). normally based ou secondary indicators.," The distance used here were those from Hidalgo-Gámmez (2004), normally based on secondary indicators." Distance determiiations cau change the value of the eracient if the new determination dillers greatly. from the old oue., Distance determinations can change the value of the gradient if the new determination differs greatly from the old one. Iu. general. the cdistances provided wx NED/NASA are very similar to those reported in. Hidaeo-Ciáiminez (2001) for tlie galaxies in the sauple.," In general, the distances provided by NED/NASA are very similar to those reported in Hidalgo-Gámmez (2004) for the galaxies in the sample." The ouly important difference is ou the clistarce of UGC 5296. ane the gradient. chaiges from —0.6 dex/kpe to —0.15 dex/kpe. meanwile for the rest of the galaxies the dilfereuces in the eraclient determiuationa'e sinaller than the ncertalnities.," The only important difference is on the distance of UGC 5296, and the gradient changes from $-0.6$ dex/kpc to $-0.45$ dex/kpc, meanwhile for the rest of the galaxies the differences in the gradient determination are smaller than the uncertainties." Therefore. the steep gradients in tlese galaxies are LOL απο LO WYIOL[n]ο cistauce determiallons.," Therefore, the steep gradients in these galaxies are not due to wrong distance determinations." Also. the galactocent‘ic distances migh have iuflueuce O1 eslope of the abundance. bi1 not1 this case as 1idicated by the results of the gracdieut determied at. fixed distances.," Also, the galactocentric distances might have influence on the slope of the abundance, but not in this case as indicated by the results of the gradient determined at fixed distances." Probabls. tlie argest source of certainty in the sloyes obtained iu this investigation is the abundance deteunilation.," Probably, the largest source of uncertainty in the slopes obtained in this investigation is the abundance determination." As they c:ol |ye caleulated wihi the staucard methocl (e.g. Osterbrock 1989). the abundaice value itself 1ig| be very uncertain.," As they cannot be calculated with the standard method (e.g. Osterbrock 1989), the abundance value itself might be very uncertain." As described in paper L four different semi empirical 1netιο» were used iu he abundauce deterulnatiou.," As described in paper I, four different semi empirical methods were used in the abundance determination." Moreover. a weightec-average value of he abtuucance was obtainecl for each region.," Moreover, a weighted-average value of the abundance was obtained for each region." Thereore. the gradients determined with such metallicity should be very reliable.," Therefore, the gradients determined with such metallicity should be very reliable." Moreover. those regious which are suspected uot to be a normal," Moreover, those regions which are suspected not to be a normal" The discovery of strong gravitational lensing in Q09572-561 (Walsh et al.L979) opened up the vast possibility {ο use strong lens svstems in the study of cosmology and astroplivsics.,The discovery of strong gravitational lensing in Q0957+561 (Walsh et al.1979) opened up the vast possibility to use strong lens systems in the study of cosmology and astrophysics. Up to now. strong lensing has developed into an important. astrophysical tool for probing," Up to now, strong lensing has developed into an important astrophysical tool for probing" is that the turbulence SCS mocel is pushed to its limit in the WLILAL because of the relatively high Mach numbers in the Dow.,is that the turbulence SGS model is pushed to its limit in the WHIM because of the relatively high Mach numbers in the flow. For this reason. the result in the WLIILM has to be confirmed with a SGS model that does not suller from such constraints ," For this reason, the result in the WHIM has to be confirmed with a SGS model that does not suffer from such constraints ." Using data from a cosmological hydrodynamic simulation. present an in-depth analysis of the vorticity and divergence fields in the intergalactic medium.," Using data from a cosmological hydrodynamic simulation, present an in-depth analysis of the vorticity and divergence fields in the intergalactic medium." The rationale behind their analysis is similar to ours. except that they infer turbulence properties [rom the derivative of the resolved velocity field.," The rationale behind their analysis is similar to ours, except that they infer turbulence properties from the derivative of the resolved velocity field." Moreover. they consider dvnamical equations for the modulus of the vorticity and the divergence.," Moreover, they consider dynamical equations for the modulus of the vorticity and the divergence." " OF particular importance is the rate of change of the divergence. which is generalised to a co-moving coordinate system: where e is the time-dependent cosmological scale factor. D/Di=W/E|aτο.V is the material derivative in co-moving coordinates. C is the gravitational constant. pau is the local dark matter density. Qu, is the cosmological mean density parameter of Ρανο] and dark matter. respectively. and df=fea is the Llubble parameter."," Of particular importance is the rate of change of the divergence, which is generalised to a co-moving coordinate system: where $a$ is the time-dependent cosmological scale factor, $\DD/\DD t=\partial/\partial t + a^{-1}\bmath{v}\cdot\bmath{\nabla}$ is the material derivative in co-moving coordinates, $G$ is the gravitational constant, $\rho_{\rm dm}$ is the local dark matter density, $\Omega_{\rm m}$ is the cosmological mean density parameter of baryonic and dark matter, respectively, and $H=\dot{a}/a$ is the Hubble parameter." " This is the same as in?) (their equation 3). with only the gravity terms (in the second line of equation 19)) slightly. rearranged. aud noting that. for the components of the rate of strain tensor. 25,=[52 "," This is the same as in (their equation 3), with only the gravity terms (in the second line of equation \ref{eq:zhudiv}) ) slightly rearranged, and noting that, for the components of the rate of strain tensor, $2 S_{ij}S_{ij} = |S|^2$ ." The advantage of the filtering approach outlined in Section 2.2. is that we can casily include SGS terms. in particular. turbulent pressure terms.," The advantage of the filtering approach outlined in Section \ref{sgs} is that we can easily include SGS terms, in particular, turbulent pressure terms." “Phe SCS model cleseribecl in Section 2.2. allows for a direct computation of the turbulent. pressure that is associated with the grid scale: pr=2/3peu., The SGS model described in Section \ref{sgs} allows for a direct computation of the turbulent pressure that is associated with the grid scale: $p_{\rm t} = 2/3\ \rho e_{\mathrm{t}}$. Since the divergence equation is derived from the momentum equation. in which the turbulent pressure is simply added to the thermal pressure. it follows that the filtered version of the divergence equation is readily obtained from equation (19)) by substituting p with p|pi everywhere: and by considering filtered quantities (we dropped the hats for brevity).," Since the divergence equation is derived from the momentum equation, in which the turbulent pressure is simply added to the thermal pressure, it follows that the filtered version of the divergence equation is readily obtained from equation \ref{eq:zhudiv}) ) by substituting $p$ with $p + p_{\mathrm t}$ everywhere: and by considering filtered quantities (we dropped the hats for brevity)." The trace-free part of the turbulence stress tensor is neglected in the above equation., The trace-free part of the turbulence stress tensor is neglected in the above equation. The expression on the right-hand specifies the net negative compression rate of a fluid. parcel., The expression on the right-hand specifies the net negative compression rate of a fluid parcel. Phe sell-eravity term on the very right stems [rom the Poisson equation for the gravitational potential and tends to decrease the divergence., The self-gravity term on the very right stems from the Poisson equation for the gravitational potential and tends to decrease the divergence. To understand. the meaning of the various ternis in equation (20)). we consider different limiting cases: Neglecting the effects. of pressure gradients. that are unaligned with the density. eradients ancl comparing the limiting cases (ii) and (ii). we see that the term 1/2pooIs7) in a fully resolved. simulation ids equivalent to Vp if the Yow is fDiltered. on the largest. scale. of the system.," To understand the meaning of the various terms in equation \ref{eq:cosmodiv}) ), we consider different limiting cases: Neglecting the effects of pressure gradients that are unaligned with the density gradients and comparing the limiting cases (ii) and (iii), we see that the term $1/2\ \rho(\omega^2-|S|^{2})$ in a fully resolved simulation is equivalent to $-\nabla^{2}p_{\rm t}$ if the flow is filtered on the largest scale of the system." In a darge eddy simulation. we have an intermediate case. where part of the effect. of turbulence is captured by the vorticity and the rate of strain of the resolved. flow. while the turbulent pressure at. the eric scale. accounts for numerically unresolved: turbulence.," In a large eddy simulation, we have an intermediate case, where part of the effect of turbulence is captured by the vorticity and the rate of strain of the resolved flow, while the turbulent pressure at the grid scale accounts for numerically unresolved turbulence." Lf wo |S]. numerically resolved. turbulence counteracts the gravitational contraction of the eas.," If $\omega>|S|$ , numerically resolved turbulence counteracts the gravitational contraction of the gas." The turbulent pressure of unresolved: velocity Luctuations counteracts self-gravity if V7p«UO. respectively.," The turbulent pressure of unresolved velocity fluctuations counteracts self-gravity if $\nabla^{2}p_{\rm t}<0$, respectively." The relative contribution of Ja depends on the grid scale., The relative contribution of $p_{\rm t}$ depends on the grid scale. ]t is important that. by its very definition. the urbulent pressure is a quantity(7).," It is important that, by its very definition, the turbulent pressure is a quantity." .. investigate the scale-dependence of the turbulent pressure w integrating the spectrum of the kinetic energy. density or all wave numbers greater than then a certain wave number (corresponding to a particular length scale)., investigate the scale-dependence of the turbulent pressure by integrating the spectrum of the kinetic energy density for all wave numbers greater than then a certain wave number (corresponding to a particular length scale). Since he resulting turbulent. pressure spectrum is rather flat. no clear distinction is made between the integral turbulent oessure of the resolved. How. and the turbulent pressure of velocity Hücetuations below the grid. scale.," Since the resulting turbulent pressure spectrum is rather flat, no clear distinction is made between the integral turbulent pressure of the resolved flow and the turbulent pressure of velocity fluctuations below the grid scale." “Phe advantage of our approach is that we can investigate both resolved urbulenee anc SCS turbulence. elfects., The advantage of our approach is that we can investigate both resolved turbulence and SGS turbulence effects. In. Fig. 9..," In Fig. \ref{2dpdf-support}," we show the mass-weighted correlation diagrams of 1/2ρίωτsp) and Vp., we show the mass-weighted correlation diagrams of $1/2\ \rho(\omega^2-|S|^{2})$ and $-\nabla^{2}p_{\rm t}$. Both for the WLIIINM and the ICM. hese quantities are roughly correlated.," Both for the WHIM and the ICM, these quantities are roughly correlated." This is expected. oeause SOS. turbulence is. produced. by. the interactions with turbulent velocity [üctuations on the smallest resolved ength scales. which are probed by w and [9].," This is expected, because SGS turbulence is produced by the interactions with turbulent velocity fluctuations on the smallest resolved length scales, which are probed by $\omega$ and $|S|$." However. the non-local nature of the SGS turbulence energy (see equation 102). implies that there is no simple algebraic relationship otween the resolved: and unresolved: turbulent pressures.," However, the non-local nature of the SGS turbulence energy (see equation \ref{eq:etsum}) ), implies that there is no simple algebraic relationship between the resolved and unresolved turbulent pressures." This becomes manifest in the large scatter of the correlation diagrams., This becomes manifest in the large scatter of the correlation diagrams. Consequently. the SCS model is essential for he computation of the support by the turbulent pressure. V7.," Consequently, the SGS model is essential for the computation of the support by the turbulent pressure, $-\nabla^{2}p_{\rm t}$." Compared to a given value of the resolved turbulent oessure (corresponding to a horizontal cut. through the wo-dimensional distribution). Vpi istvpically an order of magnitude smaller.," Compared to a given value of the resolved turbulent pressure (corresponding to a horizontal cut through the two-dimensional distribution), $-\nabla^{2}p_{\rm t}$ istypically an order of magnitude smaller." Locally. |however.the contribution rom SGS turbulence can become comparable to or even," Locally, however,the contribution from SGS turbulence can become comparable to or even" Blazars are a special class of active galactic nuclei (AGN) exhibiting a spectral energy distribution (SED) that is strongly dominated by nonthermal emission across a wide range of wavelengths. from radio waves to gamma rays. and rapid. large-amplitude variability.,"Blazars are a special class of active galactic nuclei (AGN) exhibiting a spectral energy distribution (SED) that is strongly dominated by nonthermal emission across a wide range of wavelengths, from radio waves to gamma rays, and rapid, large-amplitude variability." The source of this emission ts presumably the relativistic jet emitted at a narrow angle to the line of sight to the IIn high-peaked BL Lac objects (HBLs) the SED shows a double hump structure as the most notable feature with the first hump in the UV- to X-ray regime and the second hump in the gamma-ray regime., The source of this emission is presumably the relativistic jet emitted at a narrow angle to the line of sight to the In high-peaked BL Lac objects (HBLs) the SED shows a double hump structure as the most notable feature with the first hump in the UV- to X-ray regime and the second hump in the gamma-ray regime. Indeed. a substantial fraction of the known nearby HBLs have already been discovered with Cherenkov telescopes like H.E.S.S.. MAGIC or VERITAS.," Indeed, a substantial fraction of the known nearby HBLs have already been discovered with Cherenkov telescopes like H.E.S.S., MAGIC or VERITAS." The origin of the first hump is mostly undisputed: nonthermal. relativistic electrons in the jet are emitting synchrotron radiation.," The origin of the first hump is mostly undisputed: nonthermal, relativistic electrons in the jet are emitting synchrotron radiation." The origin of the second hump ts still controversially debated., The origin of the second hump is still controversially debated. Up to now two kinds of models are discussed: leptonic (e.g.?) and hadronic (e.g.2) ones. which are mostly applied for other subclasses of AAnother important feature of AGNs in general and HBLs in particular is their strong variability.," Up to now two kinds of models are discussed: leptonic \citep[e.g.][]{maraschi92} and hadronic \citep[e.g.][]{mannheim93} ones, which are mostly applied for other subclasses of Another important feature of AGNs in general and HBLs in particular is their strong variability." The dynamical timescale may range from minutes to years., The dynamical timescale may range from minutes to years. This requires complex models. which obviously have to include time dependence. but this gives us also the chance to understand the mechanisms that drive AGNs.," This requires complex models, which obviously have to include time dependence, but this gives us also the chance to understand the mechanisms that drive AGNs." We will apply a self-consistent leptonic model to new data observed for the source.. because those are the ones favoured for The source HBL has been discovered as a candidate BL Lae object on the basis of Its X-ray emission and has been identified with the X-ray source (??)..," We will apply a self-consistent leptonic model to new data observed for the source, because those are the ones favoured for The source HBL has been discovered as a candidate BL Lac object on the basis of its X-ray emission and has been identified with the X-ray source \citep{wilson79,ledden81}." For the first time. has been observed at VHE energies using the MAGIC telescope in January 2005 (?) and later from VERITAS (?)..," For the first time, has been observed at VHE energies using the MAGIC telescope in January 2005 \citep{magic1218} and later from VERITAS \citep{veritas1218}." Coverage of the optical/X-ray regime 1s provided by BeppoSAX (?) and SWIFT (?).. unfortunately the data are not always simultaneous.," Coverage of the optical/X-ray regime is provided by BeppoSAX \citep{beppo05} and SWIFT \citep{swift07}, unfortunately the data are not always simultaneous." During the observations from December 2008 to April 2009 VERITAS also observed showing a time-variability (?).., During the observations from December 2008 to April 2009 VERITAS also observed showing a time-variability \citep{veritas2010}. The observations fromthe MAGIC telescope have previously been modelled by ?.., The observations fromthe MAGIC telescope have previously been modelled by \citet{michl1218}. ? claim that their new observations exhibiting variability challenge the previous models., \citet{veritas2010} claim that their new observations exhibiting variability challenge the previous models. We will show that a timedependent model using a self-consistent treatment of electron acceleration is able to model the new VERITAS We present the kinetic equation. which we solve numerically. describing the synchrotron-self Compton emission (Sect. 2)).," We will show that a timedependent model using a self-consistent treatment of electron acceleration is able to model the new VERITAS We present the kinetic equation, which we solve numerically, describing the synchrotron-self Compton emission (Sect. \ref{sec:model}) )." In Sect., In Sect. 3 we apply our code to1215-3205... taking the VERITAS data into account and give a set of physical parameters for the most acceptable fit.," \ref{sec:results} we apply our code to, taking the VERITAS data into account and give a set of physical parameters for the most acceptable fit." Finally. we discuss our results in the light of particle acceleration theory and the multiwavelength features.," Finally, we discuss our results in the light of particle acceleration theory and the multiwavelength features." Here we will give a brief description of the model used. for a complete overview see (??).. W," Here we will give a brief description of the model used, for a complete overview see \citep{weidinger2010a, weidinger2010b}." wWe start with the relativistic Vlasov equation (seee.g.?) in the one dimensional diffusion approximation (e.g.2).. here the relativistic approximation p=yme is used.," We start with the relativistic Vlasov equation \citep[see e.g.][]{schlick02} in the one dimensional diffusion approximation \citep[e.g.][]{schlickeiser84}, here the relativistic approximation $p\approx \gamma m c$ is used." This kinetic equation will then be solved time-dependently in two spatially different zones. the smaller acceleration zone and the radiation zone. which are assumed to be spherical and homogeneous.," This kinetic equation will then be solved time-dependently in two spatially different zones, the smaller acceleration zone and the radiation zone, which are assumed to be spherical and homogeneous." Both contain isotropically distributed electrons and a randomly oriented magnetic field as common for these models., Both contain isotropically distributed electrons and a randomly oriented magnetic field as common for these models. All calculations are made in the rest frame of the EElectrons entering the acceleration zone (radius Rae) from the upstream of the jet are continuously accelerated through diffusive shock acceleration., All calculations are made in the rest frame of the Electrons entering the acceleration zone (radius $R_{\text{acc}}$ ) from the upstream of the jet are continuously accelerated through diffusive shock acceleration. This extends the model of ? with a stochastic part., This extends the model of \citet{kirk98} with a stochastic part. The energy gain due to the acceleration is balanced by radiative (synchrotron) and escape losses. the latter scaling with £4;=Πλο with 7=10 as an empirical factor reflecting the diffusive nature of particle loss.," The energy gain due to the acceleration is balanced by radiative (synchrotron) and escape losses, the latter scaling with $t_{\text{esc}}= \eta R_{\text{acc}}/c$ with $\eta=10$ as an empirical factor reflecting the diffusive nature of particle loss." Escaping electrons completely enter the radiation zone (radius Ry) downstream of the acceleration HHere the electrons are suffering synchrotron losses as in the acceleration zone and also inverse-Compton losses. but they do not undergo acceleration.," Escaping electrons completely enter the radiation zone (radius $R_{\text{rad}}$ ) downstream of the acceleration Here the electrons are suffering synchrotron losses as in the acceleration zone and also inverse-Compton losses, but they do not undergo acceleration." Pair production and other contributions do not alter the SED in typical SSC conditions and are neglected (?).., Pair production and other contributions do not alter the SED in typical SSC conditions and are neglected \citep{boettcher02}. . The SED in the observer’s frame is, The SED in the observer's frame is In the limit of τι>>A. which is probably the appropriate limit for an application (o the crust of voung neutron stars. this reduces to the approximate form also in agreement with the general results of the above two-component model (eq.,"In the limit of $\tau_v >> {2 \pi \over \ \Omega_{\rm s}}$, which is probably the appropriate limit for an application to the crust of young neutron stars, this reduces to the approximate form also in agreement with the general results of the above two-component model (Eq." 12). for €=1. as expected in that limit where the effect of the vortex radial displacement max be neglected (hence vortex relaxation behaves as normal fluid. approximately.," 12), for $\xi=1$, as expected in that limit where the effect of the vortex radial displacement may be neglected thence vortex relaxation behaves as normal fluid, approximately." The dynamical relaxation time 7p. in presence of pinning. might be as well deduced [rom the time behavior of the vortex motion. over many successive pinning/unpinung cvcles.," The dynamical relaxation time $\tau_{\rm P}$, in presence of pinning, might be as well deduced from the time behavior of the vortex motion, over many successive pinning/unpinning cycles." " We are again assuming Tp>>/,. as argued above."," We are again assuming $\tau_{\rm P} >> t_{\rm c}$, as argued above." As depicted in Fig., As depicted in Fig. la. the radial position of vortex. in (the pinned case. describes ai exponential-like rise in (he diagram over a period £/.. as predicted by Eq.," 1a, the radial position of vortex, in the pinned case, describes an exponential-like rise in the radial-position--time diagram over a period $\xi t_{\rm c}$, as predicted by Eq." 14 initially for the case of no pinning. Iollowed by a flat portion extended for another period of time (1—£V...," 14 initially for the case of no pinning, followed by a flat portion extended for another period of time $(1 -\xi) t_{\rm c}$." This pattern would be (hen repeated. with the evcle time ἐς. until the final position is reached. corresponding to an assumed final lrequeney of the superfluid.," This pattern would be then repeated, with the cycle time $t_{\rm c}$, until the final position is reached, corresponding to an assumed final frequency of the superfluid." In comparison to 7j which is defined as the lime constant associated wilh an exponential fit to the curve (ie..," In comparison to $\tau_{\rm D}$ which is defined as the time constant associated with an exponential fit to the curve (ie.," the ΠιοΙον in Eq., the function in Eq. 14 } described by each vortex in the case of no pinning. rp. would be likewise the (ime constant associated wilh an exponential fit (o the whole curve representing the overall motion of each vortex.," 14 ) described by each vortex in the case of no pinning, $\tau_{\rm P}$ would be likewise the time constant associated with an exponential fit to the whole curve representing the overall motion of each vortex." " As indicated earlier. for a long term and/or steady state consideration as that ol deducing a relaxation time scale (tp>> /,) for a superfluid in presence of pinning.a the vortices plav the same and equal role: the distinction between. pinned and uipinned populations is but an instantaneous fact."," As indicated earlier, for a long term and/or steady state consideration as that of deducing a relaxation time scale $\tau_{\rm P} >> t_{\rm c}$ ) for a superfluid in presence of pinning, the vortices play the same and equal role; the distinction between pinned and unpinned populations is but an instantaneous fact." IIence. in the linear approximation which makes it also possible to proceed further analvtically. simple geometrical considerations (hen eive (Fig.," Hence, in the linear approximation which makes it also possible to proceed further analytically, simple geometrical considerations then give (Fig." Lh) also in agreement wilh the earlier approximate result as in Eq., 1b) also in agreement with the earlier approximate result as in Eq. 21., 21. other subclusters.,other subclusters. The instantaneous gas removal discussed in this paper is an extreme form of the more gradual expulsion occurring in nature., The instantaneous gas removal discussed in this paper is an extreme form of the more gradual expulsion occurring in nature. As a result. the described weak effect of gas expulsion should be even weaker in real subelusters.," As a result, the described weak effect of gas expulsion should be even weaker in real subclusters." It seems that gas expulsion plays a negligible role on the length scales of the compaet stellar aggregates in star-forming regions., It seems that gas expulsion plays a negligible role on the length scales of the compact stellar aggregates in star-forming regions. However. the regions between subclusters may still be gas-dominated. implying that feedback could prevent the further merging of subclusters and thereby inhibit their hierarchical growth.," However, the regions between subclusters may still be gas-dominated, implying that feedback could prevent the further merging of subclusters and thereby inhibit their hierarchical growth." The length scale on which the subclusters will have merged and have become gas-poor depends on the moment at which feedback starts., The length scale on which the subclusters will have merged and have become gas-poor depends on the moment at which feedback starts. For the MST break distance and corresponding length scale that is used in most of this paper. the subclusters are gus-poor irrespective of time.," For the MST break distance and corresponding length scale that is used in most of this paper, the subclusters are gas-poor irrespective of time." However. there should be a break distance at which a notable time-evolution of the gas fraction appears.," However, there should be a break distance at which a notable time-evolution of the gas fraction appears." By comparing the subcluster gas fractions for different break distances. we find that at the end of the simulation (after one free-fall time). the subclusters have become gas-poor (ifa?«0.1) on a length scale of about 0.1—0.2 pe.," By comparing the subcluster gas fractions for different break distances, we find that at the end of the simulation (after one free-fall time), the subclusters have become gas-poor $\langle f_{\rm gas}\rangle<0.1$ ) on a length scale of about 0.1–0.2 pc." This length scale will increase further with the number of free-fall times that are completed before the onset ofremoval., This length scale will increase further with the number of free-fall times that are completed before the onset of. In turn. this increases the spatial extent over which the subclusters are allowed to merge before gas expulsion. which implies that the most massive bound structure is inversely related to the free-fall time.," In turn, this increases the spatial extent over which the subclusters are allowed to merge before gas expulsion, which implies that the most massive bound structure is inversely related to the free-fall time." " The free-fall time is related to the density as fipXpHr which implies that the time of the onset of feedback finiS associated with a density pry that has a free-fall time equal to fij.For a given density spectrum ofsubclusters (seeeg.1). only those subclusters with densities.punXty, have the opportunity to undergo the collapse and shrinkage that we tind in the simulations."," The free-fall time is related to the density as $t_{\rm ff}\propto\rho^{-1/2}$, which implies that the time of the onset of feedback $t_{\rm fb}$is associated with a density $\rho_{\rm fb}$ that has a free-fall time equal to $t_{\rm fb}$.For a given density spectrum ofsubclusters \citep[see e.g.][]{bressert10}, only those subclusters with densities $\rho\gg \rho_{\rm fb}\propto t_{\rm fb}^{-2}$ have the opportunity to undergo the collapse and shrinkage that we find in the simulations." The CFE increases with the fraction of subclusters that forms in these density peaks., The CFE increases with the fraction of subclusters that forms in these density peaks. As subclusters merge. üccrete gas and shrink. the density of the stellar structure further increases (See Sect. 3)).," As subclusters merge, accrete gas and shrink, the density of the stellar structure further increases (see Sect. \ref{sec:results}) )." Each free-fall time. more subclusters evolve into the density regime where p>y. also on larger length scales.," Each free-fall time, more subclusters evolve into the density regime where $\rho\gg \rho_{\rm fb}$, also on larger length scales." This means that the length scales on which star-forming regions produce virialised stellar systems that are insensitive to gas expulsion are larger in dense sites of star formation than in sparse ones., This means that the length scales on which star-forming regions produce virialised stellar systems that are insensitive to gas expulsion are larger in dense sites of star formation than in sparse ones. The resulting dense clusters are also less susceptible to disruptive tidal effects from their environment. which potentially further increases their survival chances.," The resulting dense clusters are also less susceptible to disruptive tidal effects from their environment, which potentially further increases their survival chances." As a result. the CFE should increase with density.," As a result, the CFE should increase with density." Through the Schmidt-Kennicutt law (22).. this suggests a relation between the CFE and the star formation rate per unit volume psp or per unit surface area 2 sig.," Through the Schmidt-Kennicutt law \citep{schmidt59,kennicutt98b}, this suggests a relation between the CFE and the star formation rate per unit volume $\rho_{\rm SFR}$ or per unit surface area $\Sigma_{\rm SFR}$ ." Indeed. first observational indicationsfor such a relation have been found by ?.. ‘ ?.. and recently also by ‘ ?.. who obtain: CFE*xπμ.E27}.," Indeed, first observational indicationsfor such a relation have been found by \citet{larsen00b}, , \citet{larsen04b}, , and recently also by \citet{goddard10}, , who obtain ${\rm CFE}\propto\Sigma_{\rm SFR}^{0.24}$." A relation, A relation A relation+, A relation where: c=1.62076x107!+8.502I07yi! and —0.228442+ 0.000242.,where: $c=1.62076 \times 10^{-10} \pm 8.502 \times 10 ^{-14} yr^{-1}$ and $d = -0.228442 \pm 0.000242$ . The slope of the linear relation. c. represents the preset= rate of injection of plutinos from the 2:3 mean motion resonance Into the Centaur zone.," The slope of the linear relation, $c$, represents the present rate of injection of plutinos from the 2:3 mean motion resonance into the Centaur zone." The present number of escaped plutinos in the Centaur population can be calculated by differentiating Eq., The present number of escaped plutinos in the Centaur population can be calculated by differentiating Eq. " 2: /No/df= where we have assumed that V, is constant during an interval of time dr.", 2: $dN_C / dt = c N_p $ where we have assumed that $N_p$ is constant during an interval of time $dt$. " Then. in order to calculate the present number of plutino-Centaurs we take dt=ἰς and now assume that N,, is constant during the lifetime of plutino-Centaurs."," Then, in order to calculate the present number of plutino-Centaurs we take $dt = l_C$ and now assume that $N_p$ is constant during the lifetime of plutino-Centaurs." where /c 1s the mean lifetime in the Centaur zone., where $l_C$ is the mean lifetime in the Centaur zone. Taking from de Elíaa et al. (2008)), Taking from de a et al. \cite{deelia08}) ) the present number of plutinos with radius R>1 km as Nj~105-10°: the rate of injection of plutinos with radius greater than | km to the Centaur zone will be between 1.6 to 16 plutinos every 100 years., the present number of plutinos with radius $R > 1$ km as $N_p \sim 10^8 - 10^9$; the rate of injection of plutinos with radius greater than 1 km to the Centaur zone will be between 1.6 to 16 plutinos every 100 years. This is between 250 and 25 times less tha the rate of injection of SDOs to the Centaur zone obtained by Di Sisto Brunini (2007))., This is between 250 and 25 times less than the rate of injection of SDOs to the Centaur zone obtained by Di Sisto Brunini \cite{Disisto07}) ). Then the present number of plutino-Centaurs with radius greater of 1 km would be betwee 1.8x105—10%., Then the present number of plutino-Centaurs with radius greater of 1 km would be between $1.8 \times 10^{6} - 1.8 \times 10^{7}$. Di Sisto Brunini (2007)) estimated a number of Centaurs with R>| km coming from the SD of ~2.8x105. the Centaurs coming from plutinos would represent a fractio of less than 6% of the total Centaur population.," Di Sisto Brunini \cite{Disisto07}) ) estimated a number of Centaurs with $R>1$ km coming from the SD of $\sim 2.8 \times 10^8$, then Centaurs coming from plutinos would represent a fraction of less than $6 \%$ of the total Centaur population." That ts to say that the plutino population is a secondary source of Centaurs. comparable to the contribution of the low eccentricity transneptunian objects according to the estimations of Levison Duncan (1997)) of 1.2x 107.," That is to say that the plutino population is a secondary source of Centaurs, comparable to the contribution of the low eccentricity transneptunian objects according to the estimations of Levison Duncan \cite{Levison97}) ) of $1.2 \times 10^7$ ." activity is not strongly correlated with mass for !Xesini.,activity is not strongly correlated with mass for $^{-1} \le v\sin i$. This holds even when we only consider objects will radiative core and (hus (he potential to operate a solar-tvpe. rotationallv. driven dvnamo.," This holds even when we only consider objects with radiative core and thus the potential to operate a solar-type, rotationally driven dynamo." It is also important to note that the distribution of rotational velocities for the non-active stars (not contained in Fig. 7)), It is also important to note that the distribution of rotational velocities for the non-active stars (not contained in Fig. \ref{f8}) ) is imdistinguishable from the active stars: they cover the full range from «5 (o |. with a accumulation between 10 and ss.!.," is indistinguishable from the active stars; they cover the full range from $<5$ to $^{-1}$, with a accumulation between 10 and $^{-1}$." Moreover. among the four slowest rotators in our sample with ! (shown as upper limits in Fig. 7)).," Moreover, among the four slowest rotators in our sample with $v\sin i <5$ $^{-1}$ (shown as upper limits in Fig. \ref{f8}) )," there is only one object with an activity level significantly below the range of datapoints for the faster rotators., there is only one object with an activity level significantly below the range of datapoints for the faster rotators. Thus. by aud laree the rolalion-aclivily correlation derived from Πα emission is flat in our sample.," Thus, by and large the rotation-activity correlation derived from $\alpha$ emission is flat in our sample." These results can be compared phenomenologically with rotation-activitv studies based on X-ray data., These results can be compared phenomenologically with rotation-activity studies based on X-ray data. delaReza&Pinzon(2004) find that stars in TWA. DPMG. and TII are roughly comparable to T Tauri stus in the ONC in terms of their ταν properties.," \citet{2004AJ....128.1812D} find that stars in TWA, BPMG, and TH are roughly comparable to T Tauri stars in the ONC in terms of their X-ray properties." The activity in (he ONC has been studied in detail in the COUP project (e.g.etal. 2004)..," The activity in the ONC has been studied in detail in the COUP project \citep[e.g.][]{2003ApJ...582..398F,2004AJ....127.3537S}." " Both in the COUP data and in the sample of de (2004).. there is no strong correlation between L,/L,, aud rotation period."," Both in the COUP data and in the sample of \citet{2004AJ....128.1812D}, there is no strong correlation between $L_x / L_\mathrm{bol}$ and rotation period." The rotation/activity relationship appears to be flat over a wide range of periods. interpreted as saturation with some indication for supersaturation. Le.a decline of activity. for the fastest rotators.," The rotation/activity relationship appears to be flat over a wide range of periods, interpreted as saturation with some indication for supersaturation, i.e.a decline of activity for the fastest rotators." This is verv similar to what we observe in Ho., This is very similar to what we observe in $\alpha$. The (wo ultralast rotators in Fig., The two ultrafast rotators in Fig. 7 appear to have below average activity levels. which might be interpreted as supersaturation.," \ref{f8} appear to have below average activity levels, which might be interpreted as supersaturation." The two additional ullvalast rotators not plotted in Fig., The two additional ultrafast rotators not plotted in Fig. 7 have no measurable activity level. (hus confirming this (trend.," \ref{f8} have no measurable activity level, thus confirming this trend." However. since we have ouly very. few datapoints at hieh rotational velocities. this should be treated with caution.," However, since we have only very few datapoints at high rotational velocities, this should be treated with caution." Still. it is interesting to note that the four ulirafast rotators are objects with radiative core. mavbe implying that supersaturaticΕν might be associated to the presence of a solar-twpe dynanmo.," Still, it is interesting to note that the four ultrafast rotators are objects with radiative core, maybe implying that supersaturation might be associated to the presence of a solar-type dynamo." It is well established that field stars show a mostly linear relationship between rotatic1 and relative X-ray luminosity (Randich2000).., It is well established that field stars show a mostly linear relationship between rotation and relative X-ray luminosity \citep{2000ASPC..198..401R}. In voung open clusters like 22391. 22602. and the Pleiades with ages ranging from 30 to MMwvr. an intermediate situation is seen. with many objects in (he saturated regime and an addiüonal linear part 1996)..," In young open clusters like 2391, 2602, and the Pleiades with ages ranging from 30 to Myr, an intermediate situation is seen, with many objects in the saturated regime and an additional linear part \citep[e.g.][]{1996ApJS..106..489P}." A hint of a linear relation might also be seen in the sample of post T Tauri Lindroos stars with ages between 10 and MMwyr analvzed by Hnélamoοἱal.(2004).., A hint of a linear relation might also be seen in the sample of post T Tauri Lindroos stars with ages between 10 and Myr analyzed by \citet{2004A&A...428..953H}. Linear correlations between X-ray flux and rotation rate have additionally been found [or voung stars in Taurus (Stelzer&Neuhauser2001)., Linear correlations between X-ray flux and rotation rate have additionally been found for young stars in Taurus \citep{2001A&A...377..538S}. . Stassunetal.(2004) argued that the l[umrear part of the rotation/activity correlation in the ONC may be hidden in the objects Dor which no periods have been measured., \citet{2004AJ....127.3537S} argued that the linear part of the rotation/activity correlation in the ONC may be hidden in the objects for which no periods have been measured. However. studies of magnetic activity al very. voung ages are problematic. because accretion additionally affects bot X-ray and Ila Iuminosities. which in principle requires (he strict separation of accretors [rom non-accretors.," However, studies of magnetic activity at very young ages are problematic, because accretion additionally affects both X-ray and $\alpha$ luminosities, which in principle requires the strict separation of accretors from non-accretors." Our IIa luminosity vs. esin/ plot does not reveal a strong indication for a linear regime in the, Our $\alpha$ luminosity vs. $v\sin i$ plot does not reveal a strong indication for a linear regime in the The pulsation properties of Cepheids are tightly correlated to their fundamental parameters. such as mass and luminosity. which makes them valuable tools for distance measurements and cosmology.,"The pulsation properties of Cepheids are tightly correlated to their fundamental parameters, such as mass and luminosity, which makes them valuable tools for distance measurements and cosmology." Cepheids are also powerful probes of stellar evolution thanks to the coupling of stellar evolution and stellar pulsation models. both constraining the internal structure of these stars (e.g.222)..," Cepheids are also powerful probes of stellar evolution thanks to the coupling of stellar evolution and stellar pulsation models, both constraining the internal structure of these stars \citep[e.g.][]{Hofmeister1964, Cox1966, Christy1966}." However. mass predictions using each method do not agree. ? found that stellar evolution models predict Cepheids have higher masses than do stellar pulsation models for the same effective temperature and luminosity.," However, mass predictions using each method do not agree, \cite{Stobie1969} found that stellar evolution models predict Cepheids have higher masses than do stellar pulsation models for the same effective temperature and luminosity." This Cepheid mass discrepaney has been a challenge for stellar evolution and pulsation theory for the past 40 years., This Cepheid mass discrepancy has been a challenge for stellar evolution and pulsation theory for the past $40$ years. ? showed that the mass discrepancy. defined as the mass difference relative to the predicted stellar evolution mass. ts approximately 40%.," \cite{Cox1980} showed that the mass discrepancy, defined as the mass difference relative to the predicted stellar evolution mass, is approximately $40\%$ ." ? claimed that the updated ? opacities provide a resolution to the mass discrepancy., \cite{Moskalik1992} claimed that the updated \cite{Iglesias1990} opacities provide a resolution to the mass discrepancy. However. the current status of the Cepheid mass discrepancy is 17+5% (2222)..," However, the current status of the Cepheid mass discrepancy is $17 \pm 5\%$ \citep{Keller2002, Caputo2005, Keller2006, Keller2008}." Furthermore. there is evidence that the mass discrepancy ts a function of both mass (?) and metallicity (?)..," Furthermore, there is evidence that the mass discrepancy is a function of both mass \citep{Caputo2005} and metallicity \citep{Keller2006}." Dynamic masses have been determined for four Galactic Cepheids that are in binary systems: SU Cyg (?).. V350 Ser (2).. S Mus (?).. and Polaris (2)..," Dynamic masses have been determined for four Galactic Cepheids that are in binary systems: SU Cyg \citep{Evans1990}, V350 Sgr \citep{Evans1997}, S Mus \citep{Evans2006}, and Polaris \citep{Evans2008}." The dyamic masses are all lower than masses predicted using stellar evolution theory and consistent with stellar pulsation models., The dynamic masses are all lower than masses predicted using stellar evolution theory and consistent with stellar pulsation models. Furthermore. ? determine the mass of the Large Magellanic Cloud Cepheid OGLE-LMC-CEP0227. which ts in an eclipsing binary system. to a precision of 1% and find that it agrees with the mass predicted by stellar pulsation.," Furthermore, \cite{Pietrzynski2010} determine the mass of the Large Magellanic Cloud Cepheid OGLE-LMC-CEP0227, which is in an eclipsing binary system, to a precision of $1\%$ and find that it agrees with the mass predicted by stellar pulsation." ? model the evolution of this Cepheid and find agreement with the dynamic mass when extra mixing is included., \cite{Cassisi2011} model the evolution of this Cepheid and find agreement with the dynamic mass when extra mixing is included. These results suggest that there are physics missing in the stellar evolution calculations., These results suggest that there are physics missing in the stellar evolution calculations. The two most likely solutions to the mass discrepancy are convective core overshooting in a Cepheid’s main-sequence progenitor (?) and. mass loss during the Cepheid stage of evolution (?).., The two most likely solutions to the mass discrepancy are convective core overshooting in a Cepheid's main-sequence progenitor \citep{Chiosi1992} and mass loss during the Cepheid stage of evolution \citep{Bono2006}. Convective core overshooting during main sequence evolution mixes extra hydrogen into the core., Convective core overshooting during main sequence evolution mixes extra hydrogen into the core. This leads to a more massive post-main sequence helium core. hence to a more luminous Cepheid or conversely to a less massive Cepheid for the same luminosity if overshooting is not included in the stellar evolution models.," This leads to a more massive post-main sequence helium core, hence to a more luminous Cepheid or conversely to a less massive Cepheid for the same luminosity if overshooting is not included in the stellar evolution models." Overshooting Is also required to explain observations of eclipsing binary stars (e.g.22).. 6 Cephei stars (?) and massive B-type stars (?)..," Overshooting is also required to explain observations of eclipsing binary stars \citep[e.g.][]{Sandberg2010, Clausen2010}, $\beta$ Cephei stars \citep{Lovekin2010} and massive B-type stars \citep{Brott2011}." On the other hand. mass loss during the Cepheid stage of evolution acts to reduce the stellar mass without affecting the stellar luminosity.," On the other hand, mass loss during the Cepheid stage of evolution acts to reduce the stellar mass without affecting the stellar luminosity." ?. determined mass-loss rates of 10? to 1075Msyr! from IRAS observations., \cite{Deasy1988} determined mass-loss rates of $10^{-9}$ to $10^{-8}~M_\odot~\rm{yr}^{-1}$ from IRAS observations. More recently ?.andreferencestherein observed infrared excess in nearby Galactic Cepheids from interferometric observations. while Spitzer observations also detected infrared excesses (???).," More recently \citet[][and references therein]{Merand2007} observed infrared excess in nearby Galactic Cepheids from interferometric observations, while Spitzer observations also detected infrared excesses \citep{Marengo2010, Marengo2011, Barmby2010}." ", ?? modeled the infrared excess in Large Magellanic Cloud Cepheids in the OGLE-III (?) and SAGE (?) surveys."," \cite{Neilson2009b, Neilson2010} modeled the infrared excess in Large Magellanic Cloud Cepheids in the OGLE-III \citep{Soszynski2008} and SAGE \citep{Meixner2006} surveys." In these works. the observed infrared excess was modeled by a dusty wind. suggesting that Cepheids may be undergoing significant mass loss.," In these works, the observed infrared excess was modeled by a dusty wind, suggesting that Cepheids may be undergoing significant mass loss." From a theoretical perspective. ?? developed a prescription for pulsation-driven mass loss in Cepheids.," From a theoretical perspective, \cite{Neilson2008, Neilson2009} developed a prescription for pulsation-driven mass loss in Cepheids." They predicted mass-loss rates up to 107Μαyr!., They predicted mass-loss rates up to $10^{-7}~M_\odot~\rm{yr}^{-1}$. While this evidence suggests Cepheid mass loss is important. 1t remained unclear whether enough mass is lost during the Cepheid stage of stellar evolution to account for the measured Cepheid mass discrepancy.," While this evidence suggests Cepheid mass loss is important, it remained unclear whether enough mass is lost during the Cepheid stage of stellar evolution to account for the measured Cepheid mass discrepancy." The purpose of this work ts to test whether pulsation-driven mass loss in Cepheids is an important contributor towards solving the Cepheid mass discrepancy., The purpose of this work is to test whether pulsation-driven mass loss in Cepheids is an important contributor towards solving the Cepheid mass discrepancy. In the next section. we estimate the order-of-magnitude change in mass that may occur during the Cepheid stage of evolution due to mass loss based on the ? prescription.," In the next section, we estimate the order-of-magnitude change in mass that may occur during the Cepheid stage of evolution due to mass loss based on the \cite{Neilson2008} prescription." In Sect. ??..," In Sect. \ref{sem}," we compute detailed stellar evolution models to explore the role of mass loss and convective core overshooting., we compute detailed stellar evolution models to explore the role of mass loss and convective core overshooting. In Sect. ??..," In Sect. \ref{dis}," we summarize our results., we summarize our results. We estimate the amount of mass loss during the Cepheid stage of evolution. where we assume the Cepheid lifetime ts equivalent to the heltum-burning timescale Ty. for à given stellar mass.," We estimate the amount of mass loss during the Cepheid stage of evolution, where we assume the Cepheid lifetime is equivalent to the helium-burning timescale $\tau_{\rm{He}}$ for a given stellar mass." We compute an average Cepheid mass-loss rate by assuming that theCepheid instability strip is infinitesimally thin., We compute an average Cepheid mass-loss rate by assuming that theCepheid instability strip is infinitesimally thin. Thus. for a given mass and luminosity there is only one value for the pulsation period. amplitude of luminosity," Thus, for a given mass and luminosity there is only one value for the pulsation period, amplitude of luminosity" x.,$x$. The radial velocities of particles are predicted. by equation (13)) using simulated gas velocily after (he establishment of the quasi-steady flow (/0=70)., The radial velocities of particles are predicted by equation \ref{eq:turb}) ) using simulated gas velocity after the establishment of the quasi-steady flow $t \Omega = 70$ ). Since the eas velocity. is influenced by remnant turbulence. which has variations dependent on y ancl z. the predicted radial velocities have the maximums and the minimums.," Since the gas velocity is influenced by remnant turbulence, which has variations dependent on $y$ and $z$, the predicted radial velocities have the maximums and the minimums." Figure 4dd shows that the turbulent fluctuations are sufficiently small compared with the systematic angular velocity change due to the modulation of the pressure profile., Figure \ref{fig:eta-puy}d d shows that the turbulent fluctuations are sufficiently small compared with the systematic angular velocity change due to the modulation of the pressure profile. In Figure 4dd. the max/min of radial aaplitude of turbulent. velocity. 0. is plotted.," In Figure \ref{fig:eta-puy}d d, the max/min of radial amplitude of turbulent velocity, $v_{\rm t}$, is plotted." The amount of e is smaller than (hose of e; except in the region οx0., The amount of $v_{\rm t}$ is smaller than those of $v_{\rm f}$ except in the region $\left| v_{\rm f} \right| \approx 0$. Thus. ey represents the (vpical radial velocitw of particles Chat is induced by head/tail angular wind in the absence of turbulence.," Thus, $v_{\rm f}$ represents the typical radial velocity of particles that is induced by head/tail angular wind in the absence of turbulence." " Also plotted by dots are the actual particle radial velocities in the simulation result. e, which are concentrated near the super/sub-heplerian boundary."," Also plotted by dots are the actual particle radial velocities in the simulation result, $v_{x}$ , which are concentrated near the super/sub-Keplerian boundary." The data are taken al /Q=10. but il stays essentially the same alter the MIRI saturation at /Q~40.," The data are taken at $t\Omega=70$, but it stays essentially the same after the MRI saturation at $t\Omega\simeq40$." In the radial regions where the maximum ry ds negalive. eas rotation is sub-Ilxeplerian for all y ancl z.," In the radial regions where the maximum $v_{\rm f}$ is negative, gas rotation is sub-Keplerian for all $y$ and $z$." In such radial locations. all the particles lose their angular momentum by the drag due to the slower angular wind aud migrate inwarcl.," In such radial locations, all the particles lose their angular momentum by the drag due to the slower angular wind and migrate inward." Conversely. in (he regions where the minimum vy is positive. all (he particles migrate outward.," Conversely, in the regions where the minimum $v_{\rm f}$ is positive, all the particles migrate outward." In the middle of the stable zone (|r/I7|2 0.5). the gas flow is hardly changed.," In the middle of the stable zone $\left|x/H\right| \gtrsim 0.5$ ), the gas flow is hardly changed." The value of e;~—0.02e; corresponds to (the infall speed due to global. pressure gradient under the initial condition., The value of $v_{\rm f} \sim -0.02c_{s}$ corresponds to the infall speed due to global pressure gradient under the initial condition. The particles are concentrated to the zone where both mine]<0 and πανί>0 are satisfied. which is situated around 7/11~0.4.," The particles are concentrated to the zone where both $v_{\rm f}] < 0$ and $v_{\rm f}] > 0$ are satisfied, which is situated around $x/H \sim 0.4$." " The zone satisfvine the (wo inequalities is rather narrow in cz. and the difference between the maximum and the minimum v, in (his zone is small. resulting in hieh concentration of the dust particles at the outer-edge οἱ the super-Ixeplerian zone as shown in Figure tec. Because ef(opο)< Lin most of the regions except for the dust concentration zone. ancl the width of the dust concentration zone is small. (he effects of turbulence do not significantly expand the dust concentration zone."," The zone satisfying the two inequalities is rather narrow in $x$, and the difference between the maximum and the minimum $v_{\rm f}$ in this zone is small, resulting in high concentration of the dust particles at the outer-edge of the super-Keplerian zone as shown in Figure \ref{fig:eta-puy}c c. Because $\left| v_{\rm t}/(v_{\rm f} + v_{\rm t}) \right| \ll 1$ in most of the regions except for the dust concentration zone, and the width of the dust concentration zone is small, the effects of turbulence do not significantly expand the dust concentration zone." In Figure 5aa. we plot the time variation of the maximum number of particles per grid.," In Figure \ref{fig:eta-clump}a a, we plot the time variation of the maximum number of particles per grid." The more or less monotonic increase leads to the peak density of more than 1.000 (times the initial density for ο=50.," The more or less monotonic increase leads to the peak density of more than 1,000 times the initial density for $t\Omega \gtrsim 50$." We will show that the same clump grows in density while keeping ils identity. which is needed for subsequent gravitational instability.," We will show that the same clump grows in density while keeping its identity, which is needed for subsequent gravitational instability." " We pick up a particular time /, during the period when (he number of dust particles in the densest grid in the whole region increase monotonicallv or is saturated.", We pick up a particular time $t_c$ during the period when the number of dust particles in the densest grid in the whole region increase monotonically or is saturated. Then. we search for the cell which has the largest number of particles in it.," Then, we search for the cell which has the largest number of particles in it." This cell is identified as (he center of the most prominent clump that is composed of a number of cells., This cell is identified as the center of the most prominent clump that is composed of a number of cells. " The ID numbers of the AN, particles in this cell of the highest density al /=/, are recorded aud their motions are traced in Gime (also backward in time if necessary).", The ID numbers of the $N_c$ particles in this cell of the highest density at $t = t_c$ are recorded and their motions are traced in time (also backward in time if necessary). To determine anew position of the center of (he same chunp at different times. we inspect the cells within 5 exid cdistauce (0.0577) from," To determine anew position of the center of the same clump at different times, we inspect the cells within 5 grid distance $0.05H$ ) from" (Table 3).,(Table 3). All these rates ave frou theoretical estimates in BRUSLIB (Aikawactal.2005) inaking use of experimental masses (Audi.Wapstra.&Thibault2003)., All these rates are from theoretical estimates in BRUSLIB \citep{Aika2005} making use of experimental masses \citep{Audi2003}. . Oi test calculations with the (a.p) rates replaced by those in the REACLIB compilation (Rauscherctal.2002) are in reasonable aereciment (within factor of a few) with our standard case (seealsoWanajoetal. 2004)).," Our test calculations with the $(n, p)$ rates replaced by those in the REACLIB compilation \citep{Raus2002} are in reasonable agreement (within factor of a few) with our standard case \citep[see also][]{Wana2009}." . We fud a remarkable change iu the p-abundauces with Aoc110 by a factor of 10 with only a factor of 2 variation on P Nita.pyre 'o (Figure 16 aud Table 3).," We find a remarkable change in the p-abundances with $A \sim 110$ by a factor of 10 with only a factor of 2 variation on $^{56}$ $(n, p)^{56}$ Co (Figure 16 and Table 3)." This demonstrates that the (69.p) reaction on the first (9.p)- “Ni plays a key role for tho progress of uuclear flows.," This demonstrates that the $(n, p)$ reaction on the first $(n, p)$ $^{56}$ Ni plays a key role for the progress of nuclear flows." It should be noted that a smaller rate leads to more efficient p-processiug as can be seen in the bottom paucl of Figure 16 aud in Table 3 (see fuas and elias)., It should be noted that a smaller rate leads to more efficient $\nu$ p-processing as can be seen in the bottom panel of Figure 16 and in Table 3 (see $f_\mathrm{max}$ and $A_\mathrm{max}$ ). The reason can be explained as follows: Figure 17 extends the nuclear flows in Figure 15., The reason can be explained as follows: Figure 17 extends the nuclear flows in Figure 15. " We find that the rp-process path proceeds through eveu-eveu Z=JN isotopes aud deviates from Mo (Z=N 12) toward Z(5.p) is generally faster than (7.p) aud (0.5) and thus iu a quasi equilibrium.," In particular, the flow strength of radiative proton capture during $\nu$ p-processing $T_9 = 3-1.5$ ) is mostly determined from proton separation energies, where $(p, \gamma) \leftrightarrow (\gamma, p)$ is generally faster than $(n, p)$ and $(n, \gamma)$ and thus in a quasi equilibrium." This explains the concentration of abundances ou eveu-Z isotopes m Figures 8 (left panel: in particular for Zx50). 9. 15. 17. aud 18.," This explains the concentration of abundances on $Z$ isotopes in Figures 8 (left panel; in particular for $Z \le 50$ ), 9, 15, 17, and 18." " There are a umber of isotopes without measure masses in the compilation of Audi.Wapstra.&Thibault(2003). for LO€ZxbU (denoted bv open circles in Figures 17 aud LS). including the parent nuclei of light p-unelei. του, 9?Mo. and οΠα, Pru"," There are a number of isotopes without measured masses in the compilation of \citet{Audi2003} for $40 \le Z \le 50$ (denoted by open circles in Figures 17 and 18), including the parent nuclei of light p-nuclei, $^{84}$ Sr, $^{92, 94}$ Mo, and $^{96, 98}$ Ru." "etetal. noted that the mumeasured masses of ""Tiu ane PRL (ic. the proton separation energy of Rb) on the N=Ld isotones are crucial for determining the ratio of 92N[o /?Ao. Recently Weberetal.(2008) obtained precisio- nieasurenients of a munuber of nuclear masses along the mp-process patloway. ποιοιο those of ""Iu aud ΟΠ], "," \citet{Prue2006} noted that the unmeasured masses of $^{92}$ Ru and $^{93}$ Rh (i.e., the proton separation energy of $^{93}$ Rh) on the $N=48$ isotones are crucial for determining the ratio of $^{92}$ $^{94}$ Mo. Recently, \citet{Webe2008} obtained precision measurements of a number of nuclear masses along the $\nu$ p-process pathway, including those of $^{92}$ Ru and $^{93}$ Rh." Here. we present the nucleosvuthetie result with inclusion of there new masses. denoted by star sviubols in Figure 21. with our standard imiodel (first lines in Table 1 and 3).," Here, we present the nucleosynthetic result with inclusion of there new masses, denoted by star symbols in Figure 21, with our standard model (first lines in Table 1 and 3)." We confirm the suppression of the flow throug1 V Mo(p.5) Te CN=15: seo Figure 17). which has bee1 reported in Weberet(2008)..," We confirm the suppression of the flow through $^{87}$ $(p, \gamma)^{88}$ Tc $N=45$; see Figure 17), which has been reported in \citet{Webe2008}." " This leads to a factor of three enhancement ofal. “Sr aud a factor of two reduction of YY, which are however not p-isotopes (aud with snall production factors)."," This leads to a factor of three enhancement of $^{87}$ Sr and a factor of two reduction of $^{89}$ Y, which are however not p-isotopes (and with small production factors)." " The other p-abuudances. iucludiug of ""29 NAIo, ave almost unchanged. as reported ii etal.(2008) aud in Fiskeretal.(20091."," The other p-abundances, including of $^{92, 94}$ Mo, are almost unchanged, as reported in \citet{Webe2008} and in \citet{Fisk2009}." " Our calculations of sensitivity tests for all other tuumeasured masses on the rp-process path show that the mass of ""Zr (or the proton separation enerev of SND) ou N=2 plavs au important role for production of a light p-unclei !Sr.", Our calculations of sensitivity tests for all other unmeasured masses on the $\nu$ p-process path show that the mass of $^{82}$ Zr (or the proton separation energy of $^{83}$ Nb) on $N=42$ plays an important role for production of a light p-nuclei $^{84}$ Sr. The others have ouly minor roles for the scusitivity tests with variations of up to +1 MeV on the unclear masses., The others have only minor roles for the sensitivity tests with variations of up to $\pm 1$ MeV on the nuclear masses. We find in Figure 22 that a 1.0 MeV reduction of the “?Zr mass (equivalent to a reduction of the proton separation energy of ΝΟ) leads to a reduction of the !Sr abuudauce by a factor of two (uiddle panel)., We find in Figure 22 that a 1.0 MeV reduction of the $^{82}$ Zr mass (equivalent to a reduction of the proton separation energy of $^{83}$ Nb) leads to a reduction of the $^{84}$ Sr abundance by a factor of two (middle panel). An increase of tle “277 ass has no effect on the p-abuudauces., An increase of the $^{82}$ Zr mass has no effect on the p-abundances. " This is particularly important when we consider the role of the rp-process to the solar inventory of most jivsterious p-uuclei. ?Mo aud P!Mo. As cau be seen iu Figure 22 (bottom panel: aud in other simular figures). the production factors of ??Mo and ""Mo. are always substantially smaller than the neighboring psotopes. imn particular. “!Sy (sce Figures 6 aud 7)."," This is particularly important when we consider the role of the $\nu$ p-process to the solar inventory of most mysterious p-nuclei, $^{92}$Mo and $^{94}$ Mo. As can be seen in Figure 22 (bottom panel; and in other similar figures), the production factors of $^{92}$ Mo and $^{94}$ Mo are always substantially smaller than the neighboring p-isotopes, in particular, $^{84}$ Sr (see Figures 6 and 7)." A reduction of the “tSy would iu part reduce this laree gap., A reduction of the $^{84}$ Sr would in part reduce this large gap. Note that the experimental mass of Nb in Audi.Wapstra.&Thibault involves a large uncertainty (315 keV)., Note that the experimental mass of $^{93}$ Nb in \citet{Audi2003} involves a large uncertainty (315 keV). Future precision measurements of both “Zr aud “Nb are thus liehly desired., Future precision measurements of both $^{82}$ Zr and $^{83}$ Nb are thus highly desired. Tn the previous sections Lo and 5) we fud that uncertainties iun beth the supernova cdyvuunuics," In the previous sections 4 and 5), we find that uncertainties in both the supernova dynamics" scaling properties inherent in the formulation of the problem.,scaling properties inherent in the formulation of the problem. The formulation of the radiative transfer problem. the model assumptions and the scaling properties are described in detail by Ivezi¢ Elitzur (1907).," The formulation of the radiative transfer problem, the model assumptions and the scaling properties are described in detail by Ivezić Elitzur \cite{IE97}) )." Therefore. we give only a brief discussion here.," Therefore, we give only a brief discussion here." The problem under consideration is a spherically symmetric dust envelope with a dust free inner cavity surrounding a central source of radiation., The problem under consideration is a spherically symmetric dust envelope with a dust free inner cavity surrounding a central source of radiation. This geometry is not restricted to the dust shell of a single star., This geometry is not restricted to the dust shell of a single star. It can as well describe a dust envelope around a group of stars aa binary) or even around a galactic nucleus., It can as well describe a dust envelope around a group of stars a binary) or even around a galactic nucleus. The radial dependence of the dust density between the inner and outer boundary can be chosen arbitrarily., The radial dependence of the dust density between the inner and outer boundary can be chosen arbitrarily. " To arrive at a scale invariant formulation two assumptions are introduced: 1) the grains are in radiative equilibrium with the radiation field. and i1) the location of the inner boundary +, of the dust envelope ts controlled by a fixed temperature T of the grains at +."," To arrive at a scale invariant formulation two assumptions are introduced: i) the grains are in radiative equilibrium with the radiation field, and ii) the location of the inner boundary $r_1$ of the dust envelope is controlled by a fixed temperature $T_1$ of the grains at $r_1$." Due to radiative equilibrium this temperature is determined by the energy flux at 4. which in tun is controlled by the energy flux from the central source via the radiative transfer through the dusty envelope.," Due to radiative equilibrium this temperature is determined by the energy flux at $r_1$, which in turn is controlled by the energy flux from the central source via the radiative transfer through the dusty envelope." Then prescribing the dust temperature at 4 1s equivalent to specifying the bolometric flux at the inner boundary. and the only relevant property of the input radiation is its spectral shape (Ivezié Elitzur 1997)).," Then prescribing the dust temperature at $r_1$ is equivalent to specifying the bolometric flux at the inner boundary, and the only relevant property of the input radiation is its spectral shape (Ivezić Elitzur \cite{IE97}) )." Similarly. if the overall optical οπιepth of the dust envelope at some reference wavelength s prescribed. only dimensionless. normalized. distributions οescribing the spatial variation of the dust density and the wavelength dependence of the grain optical properties enter nto the problem.," Similarly, if the overall optical depth of the dust envelope at some reference wavelength is prescribed, only dimensionless, normalized distributions describing the spatial variation of the dust density and the wavelength dependence of the grain optical properties enter into the problem." " This formulation of the radiative transfer problem for a ""Susty envelope is well suited for model fits of IR observations. because it minimizes the number of independent model parameters."," This formulation of the radiative transfer problem for a dusty envelope is well suited for model fits of IR observations, because it minimizes the number of independent model parameters." The input consists of: For a given set of parameters. iteratively determines the radiation. field and the dust temperature distribution. by solving an integral equation for the energy density. which is derived from a formal integration of the radiative transfer equation.," The input consists of: For a given set of parameters, iteratively determines the radiation field and the dust temperature distribution by solving an integral equation for the energy density, which is derived from a formal integration of the radiative transfer equation." For a prescribed radial grid the numerical integrations of radial funetions are transformed into multiplications with a matrix of weight factors determined purely by the geometry., For a prescribed radial grid the numerical integrations of radial functions are transformed into multiplications with a matrix of weight factors determined purely by the geometry. Then. the energy density at every point is determined by matrix inversion. which avoids iterations over the energy density itself and allows a direct solution of the pure scattering problem.," Then, the energy density at every point is determined by matrix inversion, which avoids iterations over the energy density itself and allows a direct solution of the pure scattering problem." Typically fewer than 30 grid points are needed to achieve a relative error of flux conservation of less than1%., Typically fewer than 30 grid points are needed to achieve a relative error of flux conservation of less than. . The number of points used in angular integrations 1s 2-3 times the number of radial grid points. and the build-in wavelength grid has 98 points in the range from 0.01ju to 3.6 em (see Appendix C in Ivezié Elitzur 1997)).," The number of points used in angular integrations is 2–3 times the number of radial grid points, and the build–in wavelength grid has 98 points in the range from $0.01\,{\rm\mu m}$ to 3.6 cm (see Appendix C in Ivezić Elitzur \cite{IE97}) )." The distributed version of the code provides a variety of quantities of interest including the monochromatic fluxes and the spatial intensity distribution at wavelengths selected by the user. but not the corresponding visibilities.," The distributed version of the code provides a variety of quantities of interest including the monochromatic fluxes and the spatial intensity distribution at wavelengths selected by the user, but not the corresponding visibilities." Since we want to employ the visibilities obtained from our high spatial resolution measurements as constraints for the radiative transfer models. we have supplemented the code with routines for the calculation of synthetic visibility functions.," Since we want to employ the visibilities obtained from our high spatial resolution measurements as constraints for the radiative transfer models, we have supplemented the code with routines for the calculation of synthetic visibility functions." An important ingredient for the radiative transfer modeling of circumstellar dust shells around evolved stars is the spectral energy distribution (SED)., An important ingredient for the radiative transfer modeling of circumstellar dust shells around evolved stars is the spectral energy distribution (SED). Due to the variability of Μιας and OH/IR stars. the SED of such objects ideally has to be determined from coeval observations covering all wavelengths of interest.," Due to the variability of Miras and OH/IR stars, the SED of such objects ideally has to be determined from coeval observations covering all wavelengths of interest." Unfortunately. no such coeval photometric data set for the wavelength region from A~μια to Ac20s 1s available in the literature for2290.," Unfortunately, no such coeval photometric data set for the wavelength region from $\lambda \approx 1\,{\rm\mu m}$ to $\lambda \ge 20\,{\rm\mu m}$ is available in the literature for." ". Thus. we have to define a ""composite"" SED. which is derived from observations made by different authors at different epochs. but at about the same photometric phase (Griffin 1993))."," Thus, we have to define a `composite' SED, which is derived from observations made by different authors at different epochs, but at about the same photometric phase (Griffin \cite{Grif93}) )." From the infrared photometry of available i1 the literature. we selected those publications which specity the date of observation and present the fluxes in tabulated form. either in physical units JJy) or in magnitudes with given conversion factors (at least as a reference).," From the infrared photometry of available in the literature, we selected those publications which specify the date of observation and present the fluxes in tabulated form, either in physical units Jy) or in magnitudes with given conversion factors (at least as a reference)." Table | lists the references. the date and phase of observation anc the wavelengths.," Table \ref{IR-obstab} lists the references, the date and phase of observation and the wavelengths." The phases were determined from the perioc P= 1121d and the epoch of maximum. JD = 244 4860.5. which has been derived from the monitoring of the OH maser emission by Herman Habing (1985)).," The phases were determined from the period $P = 1424$ d and the epoch of maximum, JD = 244 4860.8, which has been derived from the monitoring of the OH maser emission by Herman Habing \cite{HerHab85}) )." Engels et ((1983)) determined periods of OH/IR stars from infrared observations and found that the periods and phases are in agreement for objects in common with the sample Herman Habing (1985))., Engels et \cite{EKSS83}) ) determined periods of OH/IR stars from infrared observations and found that the periods and phases are in agreement for objects in common with the sample Herman Habing \cite{HerHab85}) ). "The orbits of three stars are found at low significance of 68.3—95.4%,, i.e. the astrometric data contains very little or no orbital signal.","The orbits of three stars are found at low significance of $68.3-95.4$, i.e. the astrometric data contains very little or no orbital signal." As we have shown by simulation (cf., As we have shown by simulation (cf. "Sect. 3.8.1)),","Sect. \ref{sec:simulation}) )," orbital solutions at this significance level are prone to large biases., orbital solutions at this significance level are prone to large biases. " Therefore, the solution parameters shall not be considered valid in these cases."," Therefore, the solution parameters shall not be considered valid in these cases." The formal solution of the fitting procedure is given for completeness in Tables 7 and 8.., The formal solution of the fitting procedure is given for completeness in Tables \ref{tab:sol2sigma} and \ref{tab:mass2sigma}. The analysis of 17 objects yields orbits with significance below 1-σ., The analysis of 17 objects yields orbits with significance below $\sigma$. " Because the astrometric data does not contain orbital information, the derived result is physically meaningless and only a mathematical solution."," Because the astrometric data does not contain orbital information, the derived result is physically meaningless and only a mathematical solution." Therefore we do not list the solution parameters., Therefore we do not list the solution parameters. Table 10 shows the targets and their basic parameters., Table \ref{tab:insignificantOrbits} shows the targets and their basic parameters. Two characteristics can be observed that impede the astrometric orbit detection., Two characteristics can be observed that impede the astrometric orbit detection. " In the one case, applicable to HD 65430 and HD 167665, the orbital coverage is poor and the orbit is not detected although the expected signal is large compared to the instrument precision."," In the one case, applicable to HD 65430 and HD 167665, the orbital coverage is poor and the orbit is not detected although the expected signal is large compared to the instrument precision." " In the other case, for instance for GJ 595, HD 13189, and HD 140913, the minimum orbital signature given by asini is very small compared to the instrument precision."," In the other case, for instance for GJ 595, HD 13189, and HD 140913, the minimum orbital signature given by $a \sin i$ is very small compared to the instrument precision." The companions of six stars have maximum mass M»yp-tim above 0.63Μο. which does not represent a considerable constraint of the system.," The companions of six stars have maximum mass $M_{2,\mathrm{up-lim}}$ above $0.63\,M_{\odot}$, which does not represent a considerable constraint of the system." Nine companions have upper mass-limits of Μουρ=0.11—0.63Μο and thus in the M-dwarf mass range.," Nine companions have upper mass-limits of $M_{2,\mathrm{up-lim}} = 0.11 - 0.63\,M_{\odot}$ and thus in the M-dwarf mass range." " Finally, the mass of the companion of HD 137510 is confined between M»sini=22.7M, and Μορ.πι=64.4M;."," Finally, the mass of the companion of HD 137510 is confined between $M_2 \sin i = 22.7\,M_J$ and $M_{2,\mathrm{up-lim}} = 64.4\,M_J$." " Therefore, we find that has to be a brown dwarf."," Therefore, we find that has to be a brown dwarf." " This detection became possible, because of the confidence we gained on the capability of Hipparcos to detect astrometric orbital motion."," This detection became possible, because of the confidence we gained on the capability of Hipparcos to detect astrometric orbital motion." " Using a simpler argument, ? derived an upper mass-limit of 94M;, which was not stringent enough to prove the substellar nature of the companion."," Using a simpler argument, \citet{Endl:2004uq} derived an upper mass-limit of $94\,M_J$, which was not stringent enough to prove the substellar nature of the companion." " This sample also contains38529,, for which ? found the orbit inclination of the outer companion and derived its mass of My=17.6M; using astrometry."," This sample also contains, for which \cite{Benedict:2010ph} found the orbit inclination of the outer companion and derived its mass of $M_2 = 17.6\,M_J$ using astrometry." " Our analysis made use of the radial velocity orbit given by ?,, but fails to detect a significant orbit, although the Hipparcos precision of 1.6 mas is in the range of the orbit size (a— mas)."," Our analysis made use of the radial velocity orbit given by \cite{Benedict:2010ph}, but fails to detect a significant orbit, although the Hipparcos precision of 1.6 mas is in the range of the orbit size $a=1.05 \pm 0.06$ mas)." " However, the Hipparcos orbit coverage is poor at 0.4, which can explain the non-detection."," However, the Hipparcos orbit coverage is poor at 0.4, which can explain the non-detection." The recent compilation of close companions to Sun-like stars with minimum masses of 10—80M; by ? lists 39 objects.," The recent compilation of close companions to Sun-like stars with minimum masses of $10-80\,M_J$ by \cite{Sozzetti:2010nx} lists 39 objects." " With the discovery of 9 new companions, we increase the known number of such objects by about 20 %.. Ten companions in the ? list are probably stars."," With the discovery of 9 new companions, we increase the known number of such objects by about 20 Ten companions in the \cite{Sozzetti:2010nx} list are probably stars." We confirm the stellar nature, We confirm the stellar nature " We also define the cumulative number of SNe, I’, as I(t) is used as an indicator of the dust production in SNe (Section 5.3))."," We also define the cumulative number of SNe, $\Gamma$, as $\Gamma (t)$ is used as an indicator of the dust production in SNe (Section \ref{subsec:origin}) )." We present the results calculated by the framework described above., We present the results calculated by the framework described above. We concentrate on the parameter ranges relevant for the central star formation in II Zw 40., We concentrate on the parameter ranges relevant for the central star formation in II Zw 40. " As shown later, ngo~10? ccm? and Μο~3x10* MM, fit the radio SED if such a young age 3 Myr as indicated by the optical observations (see Introduction) is adopted."," As shown later, $n_\mathrm{H0}\sim 10^5$ $^{-3}$ and $M_0\sim 3\times 10^6$ $_{\sun}$ fit the radio SED if such a young age $\sim 3$ Myr as indicated by the optical observations (see Introduction) is adopted." " The radio luminosity is almost proportional to Mo, so the constraint on Mo is rather severe."," The radio luminosity is almost proportional to $M_0$, so the constraint on $M_0$ is rather severe." " Thus, we mainly investigate the case of Mo=3x106M."," Thus, we mainly investigate the case of $M_0=3\times 10^6~\mathrm{M}_{\sun}$." " For the density, we examine nuo=3x 10*, 10°, and 3x10? cm?."," For the density, we examine $n_\mathrm{H0}=3\times 10^4$ , $10^5$ , and $3\times 10^5$ $^{-3}$." " In reffig:nH,i, , weshowthekeyquantities(ng, ri, Nion, and I) as functions of time."," In \\ref{fig:nH_ri}, we show the key quantities $n_\mathrm{H}$, $r_\mathrm{i}$, ${N}_\mathrm{ion}$, and $\Gamma$ ) as functions of time." The ionized region radius r; monotonically increases and the density ny decreases until {~3 Myr because of the pressure-driven expansion and the increase of Nion., The ionized region radius $r_{\rm i}$ monotonically increases and the density $n_\mathrm{H}$ decreases until $t\sim 3$ Myr because of the pressure-driven expansion and the increase of ${N}_{\rm ion}$. " After that, the expansion stops because Nion decreases."," After that, the expansion stops because $N_\mathrm{ion}$ decreases." The initial SFR is (0)=esr.Mo/tac2.2(egr/0.1)(Mo/3x109Mc)(nno/3em~3)1/?Mg yr!.," The initial SFR is $\psi (0)=\epsilon_\mathrm{SF}M_0/ t_\mathrm{ff}\simeq 2.2(\epsilon_\mathrm{SF}/0.1) (M_0/3\times 10^6~\mathrm{M}_{\sun}) (n_\mathrm{H0}/3\times 10^5~\mathrm{cm}^{-3})^{1/2}~ \mathrm{M}_{\sun}~\mathrm{yr}^{-1}$ ." The SFR measured by the Ho luminosity is roughly ~1 yr (vanZeeetal.1998;Vanzi 2008)..," The SFR measured by the $\alpha$ luminosity is roughly $\sim 1~\mathrm{M}_{\sun}$ $^{-1}$ \citep{vanzee98,vanzi08}. ." " Since the MeSFR exponentially! decays on a time-scale of ig/espg~lA(ege/0.1) (ngo/10?cm-?)-U? Myr in our models, we obtain the SFR averaged for 3 Myr as ~0.91Me yr! (ngo.=10? cm? is assumed), which is near to the value obtained from the Ho line."," Since the SFR exponentially decays on a time-scale of $\tff/\epsilon_\mathrm{SF}\sim 1.4 (\epsilon_\mathrm{SF}/0.1)^{-1} (n_\mathrm{H0}/10^5~\mathrm{cm}^{-3})^{-1/2}$ Myr in our models, we obtain the SFR averaged for 3 Myr as $\sim 0.91~\mathrm{M}_{\sun}$ $^{-1}$ $n_\mathrm{H0}=10^5$ $^{-3}$ is assumed), which is near to the value obtained from the $\alpha$ line." " As shown later, the SFR assumed also reproduces the interferometric radio continuum flux."," As shown later, the SFR assumed also reproduces the interferometric radio continuum flux." " For the stellar mass, Buckalew,Kobulnicky,&Dufour(2005) derived 6.3x10° from a stellar spectral synthesis model (Starburst99;LeithererMeetal.1999) with a Salpeter IMF of stellar mass range 1— and a metallicity of 1/5 solar."," For the stellar mass, \citet{buckalew05} derived $6.3\times 10^{6}~\mathrm{M}_{\sun}$ from a stellar spectral synthesis model \citep[Starburst 99;][]{leitherer99} with a Salpeter IMF of stellar mass range 1--120 $\mathrm{M}_{\sun}$ and a metallicity of 1/5 solar." Vanzietal.(2008) derived 1.7xMe106 with the same spectral synthesis model but with a Kroupa IMF., \citet{vanzi08} derived $1.7\times 10^6~\mathrm{M}_{\sun}$ with the same spectral synthesis model but with a Kroupa IMF. " Mg,Our stellar mass (Mo~3x10° Mo) is bracketed by those two results, which means that our stellar mass is consistent with those in the literature within the uncertainty in the IMF."," Our stellar mass $M_0\sim 3\times 10^6~\mathrm{M}_{\sun}$ ) is bracketed by those two results, which means that our stellar mass is consistent with those in the literature within the uncertainty in the IMF." The evolution of Γ is used for the discussion of dust production by SNe in Section 5.3.., The evolution of $\Gamma$ is used for the discussion of dust production by SNe in Section \ref{subsec:origin}. " I' rapidly increases after £=3 Myr, when the first SNe occur."," $\Gamma$ rapidly increases after $t=3$ Myr, when the first SNe occur." " In Figure 3aa, we show the radio SEDs at t=1, 3, and MMyr with nuo=10° cm? and Mo=3x10° Mo."," In Figure \ref{fig:sed_age}a a, we show the radio SEDs at $t=1$, 3, and Myr with $n_\mathrm{H0}=10^5$ $^{-3}$ and $M_0=3\times 10^6~\mathrm{M}_{\sun}$ ." " As the age becomes older, the peak shifts to lower frequencies, because the free-free optical depth becomes smaller as the rregion expands."," As the age becomes older, the peak shifts to lower frequencies, because the free-free optical depth becomes smaller as the region expands." " At t=1 and 3 Myr, the emission is completely dominated by free-free emission, and at t=5Myr, the synchrotron component begins to contribute to the emission and the spectrum slope changes."," At $t=1$ and 3 Myr, the emission is completely dominated by free–free emission, and at $t=5~\mathrm{Myr}$, the synchrotron component begins to contribute to the emission and the spectrum slope changes." " For comparison, the VLA ‘matched’ data whose (u,v) coverage is restricted to baselines greater than 20kA ssensitive to structures smaller than 4 arcsec) are adopted (three triangles in fluxes f ge))asrepresentativeromthecentralstar— reffig:sed,formingregion."," For comparison, the VLA `matched' data whose $(u,\, v)$ coverage is restricted to baselines greater than $\lambda$ sensitive to structures smaller than 4 arcsec) are adopted (three triangles in \\ref{fig:sed_age}) ) as representative fluxes from the central star-forming region." The density strongly affects the frequency at which the flux peaks because free—free absorption is sensitive to the density., The density strongly affects the frequency at which the flux peaks because free–free absorption is sensitive to the density. " In gebb, weshowtheSE f orvariousinitialdensities(nguo) with reffig:sedaMo=3x10°M."," In \\ref{fig:sed_age}b b, we show the SEDs for various initial densities $n_\mathrm{H0}$ ) with $M_0=3\times 10^6~\mathrm{M}_{\sun}$." We observe that Dsatt=3Mthe peak position of the SED is indeed sensitive to the density., We observe that the peak position of the SED is indeed sensitive to the density. The rising spectrum of the matched data(triangles)is consistent with free—free absorption., The rising spectrum of the matched data(triangles)is consistent with free–free absorption. It is possible to search for the best-fit valuesof Mo and ngo for each age., It is possible to search for the best-fit valuesof $M_0$ and $n_\mathrm{H0}$ for each age. " The matched VLA data are adopted (threetriangles in reffig:sedage)) forthex? fitting (one degree of freedom), since our models are applicable to the central star-forming region."," The matched VLA data are adopted (threetriangles in \\ref{fig:sed_age}) ) for the $\chi^2$ fitting (one degree of freedom), since our models are applicable to the central star-forming region." The best-fit solutions are shown in Table 3 and, The best-fit solutions are shown in Table \ref{tab:fit} and inetallicity throughout this work.,metallicity throughout this work. " We express inetallicitv im terms of the munber of oxvecn atoms to hwdrogen atoins in the gas component of a ealaxy, normalised to the dimensionless quantity Z=124log(O/H)."," We express metallicity in terms of the number of oxygen atoms to hydrogen atoms in the gas component of a galaxy, normalised to the dimensionless quantity $Z = 12+\textnormal{log(O/H)}$." The current determination of the solar oxveen abundance m these units is Z.—8.69 (AllendePrietoctal.2001:Asplundctal. 2009).," The current determination of the solar oxygen abundance in these units is $Z_{\textnormal{\astrosun}} = 8.69$ \citep{AP01,A09}." ". Following Mannuceioetal(2010). total stellar masses are taken directly from the SDSS-DR7 catalogue, and corrected from a Ixroupa to a Chabrier IMF by dividing by a factor of 1.06."," Following \citet{M10}, total stellar masses are taken directly from the SDSS-DR7 catalogue, and corrected from a Kroupa to a Chabrier IMF by dividing by a factor of 1.06." " Cleansing the sample of galaxies with: a) uncertam estimates of M. in the catalogue, b) emission lines that have too low signal-to-noise (SNR) for accurate Z oestinates. c) estimates of Z from the two diagnostics used that differ by more than 0.25 dex (see below). reduces the sample to a total of 120.491 galaxies."," Cleansing the sample of galaxies with: a) uncertain estimates of $M_{*}$ in the catalogue, b) emission lines that have too low signal-to-noise (SNR) for accurate $Z$ estimates, c) estimates of $Z$ from the two diagnostics used that differ by more than 0.25 dex (see below), reduces the sample to a total of 120,491 galaxies." " SFRs were measured from the Ha emission line flux, corrected for dust extinction."," SFRs were measured from the $\alpha$ emission line flux, corrected for dust extinction." The correctedHa flux from each galaxy was converted to huninosity using L=F.x4xD?κ10τν where the distance D to the source was derived from the galaxy5 redshift. and 10 is the factor used to nonrmnalise SDSS fluxes to wits of ergs Lan 7.," The corrected$\alpha$ flux from each galaxy was converted to luminosity using $L=F_{\textnormal{c}}\times 4\pi D^{2}\times 10^{-17}$ , where the distance $D$ to the source was derived from the galaxy's redshift, and $10^{-17}$ is the factor used to normalise SDSS fluxes to units of ergs $^{-1}$ $^{-2}$." " Star formation rate was then determined using the fixed conversion from Ixennicutt(1998).. which assulnes a Case B recombination, an electron temperature of 10! K aud a Salpeter IMF."," Star formation rate was then determined using the fixed conversion from \citet{K98}, which assumes a case B recombination, an electron temperature of $10^{4}\:$ K and a Salpeter IMF." This value was then also corrected to a Chabrier IMF by dividing by 1.7., This value was then also corrected to a Chabrier IMF by dividing by 1.7. " The observed Ha flux is corrected for external dust extinction using where the Ha optical depth 7j, can be determined using the waveleugth-independent relation A,=1.08674 (Calzetti1994).", The observed $\alpha$ flux is corrected for external dust extinction using where the $\alpha$ optical depth $\tau_{\textnormal{H}\alpha}$ can be determined using the wavelength-independent relation $A_{\lambda}=1.086\tau_{\lambda}$ \citep{C94}. ". An estimate of Ag, can be obtained from the Bahner decrement B=Fa3,(Ho)/F5,(H2) and the following equation: where 2.86 1s the intrinsic Bahner decrement for a case B recombination with electron density 2,=100em? and electron temperature 7;— 10!K (Osterbrock 1959)..", An estimate of $A_{\textnormal{H}\alpha}$ can be obtained from the Balmer decrement $B=F_{\textnormal{obs}}(\textnormal{H}\alpha)/F_{\textnormal{obs}}(\textnormal{H}\beta)$ and the following equation: where 2.86 is the intrinsic Balmer decrement for a case B recombination with electron density $n_{e}=100 \textnormal{cm}^{-3}$ and electron temperature $T_{e}=10^{4}$ K \citep{O89}. . These values are, These values are when combining the BCDs with MOPEX.,when combining the BCDs with MOPEX. Both of the reduction methods gave the same results to well within uncertainties., Both of the reduction methods gave the same results to well within uncertainties. Each Gemini NIRI J-band image was set to the World Co-ordinate System using stars in the field with good 2MASS J-band detections (?).., Each Gemini NIRI $J$ -band image was set to the World Co-ordinate System using stars in the field with good 2MASS $J$ -band detections \citep{2MASS}. " We used the SExtractor task to detect all point sources in the final stacked image with a flux >36 above deviations in the local background, and computed the motions of these objects in RA and Dec between the two epochs (Figure 1)."," We used the SExtractor task to detect all point sources in the final stacked image with a flux $\ge3\,\sigma$ above deviations in the local background, and computed the motions of these objects in RA and Dec between the two epochs (Figure 1)." We also show in Figure 1 the 1σ and 3c scatter of the distribution of all the measurements (excluding the white dwarf).," We also show in Figure 1 the $1\,\sigma$ and $3\,\sigma$ scatter of the distribution of all the measurements (excluding the white dwarf)." The instrumental magnitude of each detected source was corrected to apparent magnitude using stars in the field with 2MASS J-band fluxes (?).., The instrumental magnitude of each detected source was corrected to apparent magnitude using stars in the field with 2MASS $J$ -band fluxes \citep{2MASS}. " To calculate the 3σ completeness limit of these data, we inserted a total of 10,000 fake stars into each image at a variety of magnitudes from J—1924, and attempted to recover them using SExtractor."," To calculate the $3\,\sigma$ completeness limit of these data, we inserted a total of 10,000 fake stars into each image at a variety of magnitudes from $J = 19 - 24$, and attempted to recover them using SExtractor." Figure 2 shows the fraction of implanted stars recovered as a function of their brightness at each epoch., Figure 2 shows the fraction of implanted stars recovered as a function of their brightness at each epoch. The number of implanted stars recovered is always less than of those injected as some stars are lost behind or within the wings of other real or implanted stars., The number of implanted stars recovered is always less than of those injected as some stars are lost behind or within the wings of other real or implanted stars. The fake stars were inserted at the same positions in images., The fake stars were inserted at the same positions in images. " However, each implanted star may not necessarily be recovered in both images, especially towards the completeness limit, in which case it would not be available for a proper motion measurement."," However, each implanted star may not necessarily be recovered in both images, especially towards the completeness limit, in which case it would not be available for a proper motion measurement." The curve with the star markers takes this into account., The curve with the star markers takes this into account. We performed aperture photometry on the mosaicked IRAC images using standard IRAF tools., We performed aperture photometry on the mosaicked IRAC images using standard IRAF tools. A full description is given in ?.., A full description is given in \citet{Carolyn}. " Briefly, we adopted an aperture size of 2.5 pixels, and subsequently corrected to an aperture size of 10 pixels."," Briefly, we adopted an aperture size of 2.5 pixels, and subsequently corrected to an aperture size of 10 pixels." " using corrections of 1.190, 1.199, 1.211 and 1.295 for channels 1—4 respectively. ?.."," using corrections of 1.190, 1.199, 1.211 and 1.295 for channels $1-4$ respectively. \citet{iraccal}." are extrapolated toward hieher densities.,are extrapolated toward higher densities. The mixing length and helium are recalibrated {ο the solar data viekling a=1.731 and Y=0.272. respectively.," The mixing length and helium are recalibrated to the solar data yielding $\alpha =1.731$ and $Y=0.272$, respectively." The lxuruez(1998) and Alexander&Ferguson(1994) opacities are very similar except for log( D)«3.6. where the effects of molecules become important.," The \citet{kur98} and \citet{ale94} opacities are very similar except for $\log$ $<$ 3.6, where the effects of molecules become important." The opacities of Alexander&Ferguson.(1994) are increasinglv larger lor logCD) «3.6 in comparison to the Ixurucz.(1998). opacity data., The opacities of \citet{ale94} are increasingly larger for $\log$ $<$ 3.6 in comparison to the \citet{kur98} opacity data. The lower Ixurucz.(1993) opacities in the outermost lavers lead (o a hotter star. which evolves more rapidly.," The lower \citet{kur98} opacities in the outermost layers lead to a hotter star, which evolves more rapidly." We compare our reference models to models using the latestopacity calculations of Allardοἱal.(2001) as the short-dashed line in Figure 4.., We compare our reference models to models using the latestopacity calculations of \citet{all01} as the short-dashed line in Figure \ref{opacfig}. Figure 4. shows the comparison between a calculation emploving the so-called “dusty” opacities that include the affects of dust grains on the opacities to the reference calculation.," Figure \ref{opacfig} shows the comparison between a calculation employing the so-called ""dusty"" opacities that include the affects of dust grains on the opacities to the reference calculation." The “dustw opacity table fully covers (he low temperature regine under investigation here.," The ""dusty"" opacity table fully covers the low temperature regime under investigation here." The solar calibration vields a=L767 and Y=0.272., The solar calibration yields $\alpha =1.767$ and $Y=0.272$. We also caleulate LDB ages using the so-called “condensed” opacities of Allardetal.(2001) that remove grains [rom the opacity since they condense out of the photosphere.," We also calculate LDB ages using the so-called ""condensed"" opacities of \citet{all01} that remove grains from the opacity since they condense out of the photosphere." " Since the models are never cool enough for grain formation. neither the ""dusty opacities or condensed"" opaciüies appreciably affect the LDB ages."," Since the models are never cool enough for grain formation, neither the ""dusty"" opacities or ""condensed"" opacities appreciably affect the LDB ages." The opacity tables presented so far have qualitatively similar structure., The opacity tables presented so far have qualitatively similar structure. The opacities have a maxinum al log(T)—4.4 due to hydrogen ionization and sharply decrease toward cooler temperatures with a minimum at log( T)23.3., The opacities have a maximum at $\log$ (T)=4.4 due to hydrogen ionization and sharply decrease toward cooler temperatures with a minimum at $\log$ $\sim$ 3.3. The opacities begin to increase toward even cooler temperatures due to the formation of molecules and collision-induced absorption., The opacities begin to increase toward even cooler temperatures due to the formation of molecules and collision-induced absorption. Also. (here is an overall increase in the opacities toward higher density.," Also, there is an overall increase in the opacities toward higher density." Following advances in more conplete line lists. (he overall opacity tends to increase.," Following advances in more complete line lists, the overall opacity tends to increase." In order (o study the impact of higher opacities and the possibility of a change in the «qualitative shape to the opacity data. we create an opacily table that is identical to the reference calculation opacities for temperatures greater (han log(D)—4.0.," In order to study the impact of higher opacities and the possibility of a change in the qualitative shape to the opacity data, we create an opacity table that is identical to the reference calculation opacities for temperatures greater than $\log$ (T)=4.0." For temperatures less than log(T)—4.0. the opacities al [ixed density are extrapolated Coward lower temperatures al a constant value given bv the opacily value at logCD)—4.0 lor the corresponding density.," For temperatures less than $\log$ (T)=4.0, the opacities at fixed density are extrapolated toward lower temperatures at a constant value given by the opacity value at $\log$ (T)=4.0 for the corresponding density." Thus. the only structure kept is (he increase in opacity for increasing density.," Thus, the only structure kept is the increase in opacity for increasing density." The dot-dashed line in Figure 4. shows the resulting LDB ages using the extreme high opacitv table described in the preceding paragraph and a solu-calibrated a=2.096 and )—02T1., The dot-dashed line in Figure \ref{opacfig} shows the resulting LDB ages using the extreme high opacity table described in the preceding paragraph and a solar-calibrated $\alpha =2.096$ and $Y=0.271$. The higher opacities do increase (he superaciabalic temperature gradient. which results in cooler stars.," The higher opacities do increase the superadiabatic temperature gradient, which results in cooler stars." However. there is only a modest increase in the LDD ages.," However, there is only a modest increase in the LDB ages." The opacilies are currently. high enough thatthe stars are strongly convective all the wav to the atmosphere boundary point., The opacities are currently high enough thatthe stars are strongly convective all the way to the atmosphere boundary point. In the opposite opacity extreme. we calculate LDB ages lor a zero-metallicity opacity (Stabler.Palla.&Salpeter 1936).," In the opposite opacity extreme, we calculate LDB ages for a zero-metallicity opacity \citep{sta86}. ." . The solar calibration results in a=1.50 and Y= 0.271., The solar calibration results in $\alpha =1.50$ and $Y=0.271$ . the equation of motion. then the stabilizing value of dust particle eccentricity is usually suffiicicutly: hieh to ect the particle close to oue of the planets during a loug time span.,"the equation of motion, then the stabilizing value of dust particle eccentricity is usually sufficiently high to get the particle close to one of the planets during a long time span." As a consequence. eravitation of the planet can change orbit of the particle and cancel the stabilization process.," As a consequence, gravitation of the planet can change orbit of the particle and cancel the stabilization process." We investigated orbital evolution of a dust erain uncer the action of iuterstellar eas flow., We investigated orbital evolution of a dust grain under the action of interstellar gas flow. We preseuted secular time derivatives of the eraivs orbital eleiíieuts for arbitrary orieutatiou of the orbit with respect to fje velocity vecOr of the interstellar gas; which is à generaization of several results presented in EKackka et al. (," We presented secular time derivatives of the grain's orbital elements for arbitrary orientation of the orbit with respect to the velocity vector of the interstellar gas, which is a generalization of several results presented in Klačkka et al. (" 204Da).,2009a). The secular time derivatives wore ¢erived using asstniptious that he acceleration caused by the interstellar eas flow is small in coniparison with eravitation of a central object (he Sun). eccentricity of fιο orbit is not cose to 1 ancl he speed of the dust particle is 10all in comparison witli he," The secular time derivatives were derived using assumptions that the acceleration caused by the interstellar gas flow is small in comparison with gravitation of a central object (the Sun), eccentricity of the orbit is not close to 1 and the speed of the dust particle is small in comparison with the" are linuted o near solar metallicity.,are limited to near solar metallicity. At the same time. realistic galaxy modeling requires inetallicities rauegiug your 1.76 for the most metal-poor galaxy kuown 115 (Aloisietal. 2003).. to supersolar values. 1ieasured for at least for some giant elliptical galaxies (C'asusoetal. 1996).," At the same time, realistic galaxy modeling requires metallicities ranging from $-$ 1.76 for the most metal-poor galaxy known 18 \citep{alo03}, to supersolar values, measured for at least for some giant elliptical galaxies \citep{cas96}." . The properties of the most prominent near-IR spectral libraries available in the literature are sunuuarized iu refPblILibRew.., The properties of the most prominent near-IR spectral libraries available in the literature are summarized in \\ref{TblLibRev}. For a review of the earlier work see Merrill&Rideway(1979)., For a review of the earlier work see \citet{mer79}. This suunuuuv shows that despite the sizable quantity of available stellar spectra. up until now there was no wniform near-IR dataset with ligh signal-to-noise and resohition. covering the cutire range of spectral classes. Duuuinositv. and metallicity necessary to carry out evolutionary population svuthesis in the near-IR.," This summary shows that despite the sizable quantity of available stellar spectra, up until now there was no uniform near-IR dataset with high signal-to-noise and resolution, covering the entire range of spectral classes, luminosity, and metallicity necessary to carry out evolutionary population synthesis in the near-IR." The deficit of some types of stars such as metal-poor super elauts is understandable in the context of the Milkv. Wavy star formation history. but the lack of 10auv other types is rectifiable.," The deficit of some types of stars such as metal-poor super giants is understandable in the context of the Milky Way star formation history, but the lack of many other types is rectifiable." We concentrate ou metal features that have equivaleut widths in a typical starburst galaxy larser than as they can be measured reliably iu spectra with signal-to-noise ratios of ~30-50 (Eneclhbracht1997 )., We concentrate on metal features that have equivalent widths in a typical starburst galaxy larger than – as they can be measured reliably in spectra with signal-to-noise ratios of $\sim$ 30-50 \citep{eng97}. . A second application of our library. albeit no less important. is the analysis of individua stars hidden behind Απ 10 mae of visual extinction.," A second application of our library, albeit no less important, is the analysis of individual stars hidden behind $_V$$\geq$ 10 mag of visual extinction." A typical case for such a population is represeuted by the Arches cluster miciuber starss in the Calactic Center region (Nagatactal.1993)., A typical case for such a population is represented by the Arches cluster member starss in the Galactic Center region \citep{nag93}. . Tere we describe the observations aud the siuuple of an eimipirical near-IR stellar library that 15is clesigned to iicet the requirements of population svuthesis., Here we describe the observations and the sample of an empirical near-IR stellar library that is designed to meet the requirements of population synthesis. The nain advantage i comparison with previous work is the expaucded netallicity COVCLALC., The main advantage in comparison with previous work is the expanded metallicity coverage. We also present a few laenostics methods to derive parameters of individual stars., We also present a few diagnostics methods to derive parameters of individual stars. The evolutionary population model will be published in a subsequent paper., The evolutionary population model will be published in a subsequent paper. The next section describes the observations aud the data reduction technique., The next section describes the observations and the data reduction technique. 33 stuumarizes the sample selection., 3 summarizes the sample selection. Spectral indices are defined in LL. and some diagnostic applications for parameters of individual stars are considered in 55.," Spectral indices are defined in 4, and some diagnostic applications for parameters of individual stars are considered in 5." In 66., In 6. we eive the sTuuduary., we give the summary. The near-IR spectra were taken frou: 1995 to 1999 imainly at the Steward Observatory 2.311 Dok telescope ou Witt Peak., The near-IR spectra were taken from 1995 to 1999 mainly at the Steward Observatory 2.3m Bok telescope on Kitt Peak. Some stars were observed at the original [51i MALT and at the Steward Observatory 1.551à d[uiper telescope., Some stars were observed at the original 4.5m MMT and at the Steward Observatory 1.55m Kuiper telescope. We used FSpec (Willisetal.1993).. a cryogenic long slit near-IR spectrometer utilizing a NICAIOS3 oe56x256 array (INozlowskiotal.1993).," We used FSpec \citep{wil93}, a cryogenic long slit near-IR spectrometer utilizing a NICMOS3 256x256 array \citep{koz93}." .. The majority. of the stars wore observed with a 600 lunes 1 erating. corresponding to a spectral resolution 22000-3000.," The majority of the stars were observed with a 600 lines $^{-1}$ grating, corresponding to a spectral resolution $R$$\approx$ 2000-3000." This is the hiehest useful spectral resolution for studies of stellar populations in external galaxies where the intrinsic velocity dispersion simooths out the iutegrated spectra., This is the highest useful spectral resolution for studies of stellar populations in external galaxies where the intrinsic velocity dispersion smooths out the integrated spectra. The rest were observed with a 300 lines + grating and 1000-1500., The rest were observed with a 300 lines $^{-1}$ grating and $R$$\approx$ 1000-1500. The slit widths were 2.1 aresec at the 2:311. 1.2 arcsec at the MANIT. iux 3ο aresec at the 1.5511. The plate scales were 1.2. 0.6. and 1.8 arcsec |. respectively.," The slit widths were 2.4 arcsec at the 2.3m, 1.2 arcsec at the MMT, and 3.6 arcsec at the 1.55m. The plate scales were 1.2, 0.6, and 1.8 arcsec $^{-1}$, respectively." " The limited plivsical size of the ucar- array required the acquisition of spectra at 10-12 erating positions. corresponding to different ceutral waveleneths (A,.) to cover the entire 77 and A atmosphere windows with sufficient overlap."," The limited physical size of the near-IR array required the acquisition of spectra at 10-12 grating positions, corresponding to different central wavelengths $\lambda_c$ ) to cover the entire $H$ and $K$ atmospheric windows with sufficient overlap." Usually. one of the following two combinatious of À. was used: 1.51. 1.62. 1.70. 2.06. 2.13. 2.19. 2.215. 2.31. 2.37. 2.12 pon. or 1.50. 1.57. L.61. 1.71. 2.05. 2.10. 2.15. 2.20. 2.25. 2.30. 2.35. 2.10 jnu. The log of observations is eiven in Table 2..," Usually, one of the following two combinations of $\lambda_c$ was used: 1.54, 1.62, 1.70, 2.06, 2.13, 2.19, 2.245, 2,31, 2.37, 2.42 $\,\rm\mu m$, or 1.50, 1.57, 1.64, 1.71, 2.05, 2.10, 2.15, 2.20, 2.25, 2.30, 2.35, 2.40 $\,\rm\mu m.$ The log of observations is given in Table \ref{TblObsLog}." The observing strategv for a single settiug included. uodding the telescope to obtain spectra at | (at the MAIT) or 6 (at the 2.2311 aud 1.551 telescopes) differcut positions aloug the slit. aud integrating at cach position for 3Pa—20 seconds. depending ou the appareut brightuess of the object and the sky background.," The observing strategy for a single setting included nodding the telescope to obtain spectra at 4 (at the MMT) or 6 (at the 2.3m and 1.55m telescopes) different positions along the slit, and integrating at each position for $3-20$ seconds, depending on the apparent brightness of the object and the sky background." This was necessary in order to: (1) carry out the sky emission subtraction and account for the sky background variations by having a sky takeu just before aud after the science exposures: (41) nuüprove the pixel sampling. flat fielding. and bad pixel correction by haviug the object placed on nultiple positions ou the array.," This was necessary in order to: (i) carry out the sky emission subtraction and account for the sky background variations by having a sky taken just before and after the science exposures; (ii) improve the pixel sampling, flat fielding, and bad pixel correction by having the object placed on multiple positions on the array." Next. we repeated the same procedure for a ostandard star at similar adiruaass (airiass difference <00.1-0.15) to correct for the atmospheric absorption.," Next, we repeated the same procedure for a standard star at similar airmass (airmass difference $\leq$ 0.1-0.15) to correct for the atmospheric absorption." Then we changed the erating setting. obtained a sequence of 16 spectra of the standard. moved he telescope back to the object.," Then we changed the grating setting, obtained a sequence of $4-6$ spectra of the standard, moved the telescope back to the object," "The tables in this appendix show the mean flux measured for each spectral line used to evaluate the metallicities, according to the different procedures mentioned on the paper.","The tables in this appendix show the mean flux measured for each spectral line used to evaluate the metallicities, according to the different procedures mentioned on the paper." Slits flagged with a ”'” were removed from our analysis due the underlying Balmer absorption.," Slits flagged with a $^\dag$ "" were removed from our analysis due the underlying Balmer absorption." Galaxy clusters constitute the largest bound structures in the Universe. with their masses up to M.~1015 and outskirts extending out to sizes R~ afew Mpes.,"Galaxy clusters constitute the largest bound structures in the Universe, with their masses up to $M\sim 10^{15}\, M_{\odot}$ and outskirts extending out to sizes $R\sim$ a few Mpcs." These set the between the intergalactic environment keyed to the cosmology at large. and the confined intracluster plasma (ICP).," These set the between the intergalactic environment keyed to the cosmology at large, and the confined intracluster plasma (ICP)." The latter pervades the clusters at temperatures kpT«xGM/R~5 keV and number densities 5.~107* οι. and so emits copious X-ray powers mainly by thermal Bremsstrahlung (seeSarazin 1988).," The latter pervades the clusters at temperatures $k_B T\propto GM/R\sim 5$ keV and number densities $n\sim 10^{-3}$ $^{-3}$, and so emits copious X-ray powers mainly by thermal Bremsstrahlung \citep[see][]{Sarazin1988}." . The ICP coexists with the gravitationally dominant dark matter (DM) component in the baryonic fraction Η/Μ close to the cosmic value 0.16. and the two build up together from accretion across the cluster boundary.," The ICP coexists with the gravitationally dominant dark matter (DM) component in the baryonic fraction $m/M$ close to the cosmic value $0.16$, and the two build up together from accretion across the cluster boundary." The build up comprises an early collapse of the cluster body. tailing off into a secular development of the outskirts by smooth accretion and minor mergers (seeZhaoetal.2003;Diemandetal.2007:Vass2008;Navarro 2010).," The build up comprises an early collapse of the cluster body, tailing off into a secular development of the outskirts by smooth accretion and minor mergers \citep[see][]{Zhao2003, Diemand2007, Vass2008, Navarro2010}." . In radius. the body ranges out to 7~7-5» where the slope of the DM density run n(r) equals —2: the adjoining outskirts extend out to the current virial radius R with steepening density.," In radius, the body ranges out to $r\sim r_{-2}$ where the slope of the DM density run $n(r)$ equals $-2$; the adjoining outskirts extend out to the current virial radius $R$ with steepening density." In time. the transition is marked by the redshift z;: thereafter Fo» stays put while R grows larger in a quasi-static. self-gravitating DM equilibrium (describedthroughtheJeansequa-tion.seeLapi&Cavaliere 2009a).. to imply for the standard concentration parameter c=Δ/ς observed values c=3.5Hz/H(zas) in terms of the Hubble parameter A(z).," In time, the transition is marked by the redshift $z_t$; thereafter $r_{-2}$ stays put while $R$ grows larger in a quasi-static, self-gravitating DM equilibrium \citep[described through the Jeans equation, see ][]{Lapi2009a}, to imply for the standard concentration parameter $c\equiv R/r_{-2}$ observed values $c\approx 3.5\, H(z_t)/H(z_{\rm obs})$ in terms of the Hubble parameter $H(z)$." In the following we adopt the standard flat cosmology (see 2009)., In the following we adopt the standard flat cosmology \citep[see][]{Dunkley2009}. ". So values of c ranging from 3 to 10 correspond for zi,=0—0.2 to or to dynamical cluster ages τι~0.2--3."," So values of $c$ ranging from $3$ to $10$ correspond for $z_{\rm obs}\approx 0-0.2$ to or to dynamical cluster ages $z_t\sim 0.2-3$." The concentration can be directly if laboriously probed with gravitational lensing (seeBroadhurstetal.2008:Lapi&Cavaliere 2009b)..," The concentration can be directly if laboriously probed with gravitational lensing \citep[see][]{Broadhurst2008, Lapi2009b}." Secular accretion of DM goes along with inflow of intergalactic gas., Secular accretion of DM goes along with inflow of intergalactic gas. The ensuing ICP equilibrium is amenable to the powerful yet simple description provided by the (SM:seeCavaliereetal.2009.hereafterCLFFO9)., The ensuing ICP equilibrium is amenable to the powerful yet simple description provided by the \citep[SM; see][hereafter CLFF09]{Cavaliere2009}. . Clearly. inflows into the cluster outskirts are exposed to the cosmological grip.," Clearly, inflows into the cluster outskirts are exposed to the cosmological grip." This 15 the focus of the present paper., This is the focus of the present paper. " The SM expresses in full the hydrostatic equilibrium (HE) of the ICP in terms of DM gravity and of the ""entropy? /n77."," The SM expresses in full the hydrostatic equilibrium (HE) of the ICP in terms of DM gravity and of the `entropy' $k\equiv k_BT/n^{2/3}$ ." In its basic form. the latter's run may be represented as consistent out to r=R/2 with recent analyses of wide cluster samples (Cavagnoloetal.2009:Pratt2010).," In its basic form, the latter's run may be represented as consistent out to $r\approx R/2$ with recent analyses of wide cluster samples \citep{Cavagnolo2009, Pratt2010}." ". This embodies two ICP parameters: the central level &, and the outer powerlaw slope e.", This embodies two ICP parameters: the central level $k_c$ and the outer powerlaw slope $a$. The former is set at a basal level Κι.~10 keV em? by intermittent entropy injections by central AGN feedback (e.g..Cavaliereetal.2002;Valageas&Silk1999;Wual.2000;McNamara&Nulsen 2007): the ensuing quasi- condition corresponds to cool core morphologies (CC:Molendi&Pizzolato 2001).. featuring a limited central temperature dip and generally large concentrations c=6—10. as discussed by CLFFO9.," The former is set at a basal level $k_c\sim 10$ keV $^2$ by intermittent entropy injections by central AGN feedback \citep[e.g.,][]{Cavaliere2002, Valageas1999, Wu2000, McNamara2007}; the ensuing quasi-stable condition corresponds to cool core morphologies \citep[CC; see][]{Molendi2001}, , featuring a limited central temperature dip and generally large concentrations $c\approx 6-10$, as discussed by CLFF09." " On the other hand. &, may be enhanced up to several 10” keV em? by deep mergers (e.g..McCarthyetal.2007;Marke-vitch&Vikhlinin 2007).. frequent during the cluster youth: these events give rise to non cool core (CC) clusters. featuring generally low concentrations ο=3-5 and a central temperature plateau. scarred in some instances by imprints from recently stalled blastwaves (seediscussionsbyFusco-Femiano2009;Rossetti&Molendi 2010)."," On the other hand, $k_c$ may be enhanced up to several $10^2$ keV $^2$ by deep mergers \citep[e.g.,][]{McCarthy2007, Markevitch2007}, frequent during the cluster youth; these events give rise to non cool core (NCC) clusters, featuring generally low concentrations $c\approx 3-5$ and a central temperature plateau, scarred in some instances by imprints from recently stalled blastwaves \citep[see discussions by][]{Fusco2009, Rossetti2010}." . The second term in Eq. (, The second term in Eq. ( 1) describes the powerlaw outward rise expected from the scale-free stratification of the entropy continuously produced by the boundary accretion shock. while the cluster grows larger byslow accretion.,"1) describes the powerlaw outward rise expected from the scale-free stratification of the entropy continuously produced by the boundary accretion shock, while the cluster grows larger byslow accretion." The slope ag at r.=R with standard values around | has been derived by CLFFO9 from the shock jumps and the adjoining HE maintained by thermal pressure. to read," The slope $a_R$ at $r\approx R$ with standard values around $1$ has been derived by CLFF09 from the shock jumps and the adjoining HE maintained by thermal pressure, to read" "Compared to many other spectrographs and despite a comfortably large sky aperture, HERMES really is ahigh-resolution spectrograph.","Compared to many other spectrographs and despite a comfortably large sky aperture, HERMES really is ahigh-resolution spectrograph." In Fig., In Fig. " 17 (bottom panel) spectral resolution is shown as derived from the measured line widths on a spectrum of thorium, argon, and neon emission lines."," \ref{fig:resolution} (bottom panel) spectral resolution is shown as derived from the measured line widths on a spectrum of thorium, argon, and neon emission lines." " In LRF mode, spectral resolving power R==A/AA amounts to 0000 (4.8 km/s)."," In LRF mode, spectral resolving power $R$ $\lambda/\Delta\lambda$ amounts to 000 (4.8 km/s)." " This value is higher than the value of 0000, calculated from a ZEMAX model for a 2.15-arcsec rectangular slit."," This value is higher than the value of 000, calculated from a ZEMAX model for a 2.15-arcsec rectangular slit." " In HRF mode we measure R== 0000 (3.5 km/s), higher than the calculated value of 0000, proving the excellent image quality of the spectrograph optics."," In HRF mode we measure $R$ 000 (3.5 km/s), higher than the calculated value of 000, proving the excellent image quality of the spectrograph optics." " The anamorphic magnification of the spectrograph makes the sampling drop along the spectral orders (Fig. 17,,"," The anamorphic magnification of the spectrograph makes the sampling drop along the spectral orders (Fig. \ref{fig:resolution}," top panel), top panel). " For HRF, sampling decreases from 2.7 to 2 pixels per resolution element, and this explains the drop in HRF resolution with X-pixel coordinate."," For HRF, sampling decreases from 2.7 to 2 pixels per resolution element, and this explains the drop in HRF resolution with X-pixel coordinate." " Only for the lowest sampling values does the image quality of the optics start becoming relevant, causing a small loss in resolution."," Only for the lowest sampling values does the image quality of the optics start becoming relevant, causing a small loss in resolution." This effect is not noticeable for LRF because of much higher sampling 33.1 pixels)., This effect is not noticeable for LRF because of much higher sampling 3.1 pixels). Fig., Fig. " 18 shows the accurate sampling in a detailed part of the spectrum with two Ο2 lines, both for HRF and LRF."," \ref{fig:O2plot} shows the accurate sampling in a detailed part of the spectrum with two $_{2}$ lines, both for HRF and LRF." Fig., Fig. 19 shows a larger part of two more illustrative spectra (Procyon and Polaris)., \ref{fig:spectrum} shows a larger part of two more illustrative spectra (Procyon and Polaris). Fig., Fig. 20 shows the efficiency at blaze peak for measurements under excellent observing conditions., \ref{fig:efficiency} shows the efficiency at blaze peak for measurements under excellent observing conditions. " Unfortunately, according to the histogram in Fig."," Unfortunately, according to the histogram in Fig." 4 median observations only reach of these values., \ref{fig:flux_histogram} median observations only reach of these values. The complete system including spectrograph and telescope has a maximum throughput of for HRF and for LRF around nnm., The complete system including spectrograph and telescope has a maximum throughput of for HRF and for LRF around nm. " Taking out telescope losses (estimated to be for three reflections), these numbers leave us with a peak efficiency for the spectrograph alone of around and 20%,, outperforming"," Taking out telescope losses (estimated to be for three reflections), these numbers leave us with a peak efficiency for the spectrograph alone of around and , outperforming" magnification matrix.,magnification matrix. We choose coordinates such that the origin of the source plane (y=0) is on the caustic., We choose coordinates such that the origin of the source plane $(\bby = \bmo)$ is on the caustic. In addition. we require that the origin of the lens plane (x=0) maps to the origin of the source plane.," In addition, we require that the origin of the lens plane $(\bx = \bmo)$ maps to the origin of the source plane." We are interested in sources that lic near the caustic point (y=0). which give rise to lensed images near the critical point (x=0).," We are interested in sources that lie near the caustic point $\bby = \bmo$ ), which give rise to lensed images near the critical point $\bx = \bmo$ )." In this case. we may expand the lens potential in a Tavlor series about the point x=0.," In this case, we may expand the lens potential in a Taylor series about the point $\bx = \bmo$." We then find that the inverse magnification matrix at x=0 is eiven by where The subseripts indicate partial derivatives of c with respect to x., We then find that the inverse magnification matrix at $\bx = \bmo$ is given by where The subscripts indicate partial derivatives of $\psi$ with respect to $\bx$ . Note that c has no linear part (since y=0 when x— (0)., Note that $\psi$ has no linear part (since $\bby=\bmo$ when $\bx=\bmo$ ). For y20 to be acaustic point. we must have (1.26)(1.26).££— 0.," For $\bby = \bmo$ to be acaustic point, we must have $(1-2\ha)(1-2\hc) - \hb^2 = 0$ ." In addition. at least one of (124) (126)|. and 67 must be non-zero (Pettersetal.2001.p.249)..," In addition, at least one of $(1-2\ha)$, $(1-2\hc)$, and $\hb^2$ must be non-zero \citep[p.~349]{Petters_book}." Consequently. (1.26) and 1.26) cannot both vanish.," Consequently, $(1-2\ha)$ and $(1-2\hc)$ cannot both vanish." Without loss of generalitv. we assume that 1.24z0.," Without loss of generality, we assume that $1-2\ha \neq 0$." " We now introduce the orthogonal matrix (seePettersetal.2001.p.344) which ciagonalizes Oy/Ox|,."," We now introduce the orthogonal matrix \citep[see][p.~344]{Petters_book} which diagonalizes $\left. \partial \bby / \partial \bx \right|_{\bmo}$." We then define new orthogonal coordinates by Note that the coordinate changes are the in the lens and source planes., We then define new orthogonal coordinates by Note that the coordinate changes are the in the lens and source planes. Phe advantage of using the same transformation in both the lens and source planes is that the lens equation takes the simple form and that the inverse magnification can be written as The old and new coordinate svstems in the source and image planes are shown in Figure L.., The advantage of using the same transformation in both the lens and source planes is that the lens equation takes the simple form and that the inverse magnification can be written as The old and new coordinate systems in the source and image planes are shown in Figure \ref{fig:u-theta-def}. Since the caustic in the source plane maps to the eritical curve in the image plane. the origin of the (61.65) frame is determined from that of the (9j.im) frame.," Since the caustic in the source plane maps to the critical curve in the image plane, the origin of the $(\theta_1, \theta_2)$ frame is determined from that of the $(u_1, u_2)$ frame." The orientation of the (61.009) axes is determined by the matrix ME. and is not necessarily related to the tangent to the critical curve.," The orientation of the $(\theta_1, \theta_2)$ axes is determined by the matrix ${\bf M}$, and is not necessarily related to the tangent to the critical curve." Using the local orthogonal coordinates u and 9. Pettersetal.(2001.p.346). showed that xθ is a folderitical point if ane only if the following conditions hold For à cusp. the third condition above is replaced by the requirements tha Note in particular that σου(0)=0 for a cusp while ¢222(0)=0 for a fold: this indicates that these two cases must be treatecl separately.," Using the local orthogonal coordinates $\bu$ and $\bt$, \citet[p.~346]{Petters_book} showed that $\bx = \bmo$ is a foldcritical point if and only if the following conditions hold For a cusp, the third condition above is replaced by the requirements that Note in particular that $\psi_{222} (\bmo) = 0$ for a cusp while $\psi_{222} (\bmo) \neq 0$ for a fold; this indicates that these two cases must be treated separately." We are interested in obtaining the positions. magnifications and time delavs of images near critical points.," We are interested in obtaining the positions, magnifications and time delays of images near critical points." Since these quantities depend only on the behavior of the lens potential near a fold or cusp point. we can expand. 0(8) in a Tavlor series about the point @=0.," Since these quantities depend only on the behavior of the lens potential near a fold or cusp point, we can expand $\psi(\bt)$ in a Taylor series about the point $\bt = \bmo$." To obtain all the quantities of interest to leading order. we must expand the lens potential to fourth order in 0 (Pettersetal.2001.pp.346341): where the cocllicicnts [Aονf.g.....rt are partial derivatives of the potential evaluated at the origin.," To obtain all the quantities of interest to leading order, we must expand the lens potential to fourth order in $\bt$ \citep[pp.~346--347]{Petters_book}: where the coefficients $\{K, e, f, g, \ldots, r\}$ are partial derivatives of the potential evaluated at the origin." Lensing observables are independent of a constant term in the potential. so we have not included one.," Lensing observables are independent of a constant term in the potential, so we have not included one." Since @=0 maps to u=0. anv linear terms in the potential must vanish.," Since $\bt=\bmo$ maps to $\bu=\bmo$, any linear terms in the potential must vanish." " In the second order terms. the coellicients of the 0,65 and 65 terms are set to0 and 1/2. respectively. in order to ensure that the point 0= is a critical point (seeAppendixALofIxeetonctal. 2005)."," In the second order terms, the coefficients of the $\theta_1 \theta_2$ and $\theta_2^2$ terms are set to$0$ and $1/2$ , respectively, in order to ensure that the point $\bt = 0$ is a critical point \citep[see Appendix A1 of][]{Keeton-fold}. ." . In this section. we use perturbation theory (e.g..Bellman1966). to derive an analytic relationbetween the time delays in," In this section, we use perturbation theory \citep[e.g.,][]{Bellman_pert} to derive an analytic relationbetween the time delays in" from initially verv wide svstems. which avoided AIT but then during the DII formation a precisely placed natal kick may Gehten the binary.,"from initially very wide systems, which avoided MT but then during the BH formation a precisely placed natal kick may tighten the binary." However. the possibility of such an event is very small. and moreover i( is not vet clear if most massive DIIs receive anv kicks at all.," However, the possibility of such an event is very small, and moreover it is not yet clear if most massive BHs receive any kicks at all." In fact. Nelemans. Tauris van den Ileuvel (1999) found that spatial velocities of binaries harboring Dll. are easily explained by (he symmetrical SN mass ejection and without any significant natal kick accompanying BIL formation.," In fact, Nelemans, Tauris van den Heuvel (1999) found that spatial velocities of binaries harboring BH, are easily explained by the symmetrical SN mass ejection and without any significant natal kick accompanying BH formation." We consider the low spatial velocity of GRS 19154-105 (45=—3z10 kkm !). as the first observational evidence that the most massive DII are formed without any kicks imparted on the svstem. and (hus no accompanying Nass ejection nor SN explosion.," We consider the low spatial velocity of GRS 1915+105 $\gamma = -3 \pm 10$ km $^{-1}$ ), as the first observational evidence that the most massive BH are formed without any kicks imparted on the system, and thus no accompanying mass ejection nor SN explosion." This is just a reasonable extrapolation of the findings of Nelemans et al. (, This is just a reasonable extrapolation of the findings of Nelemans et al. ( 1999) which is consistent with theoretical modeling of SN/core collapse evenls by Frver (1999); NS are formed in asymmetric SN explosions. while intermediate massive DII are lormecl through partial fall back accompanied by almost svimimetric SN and receive either a small or no kick at all. while the most massive DII are formed in direct collapse with no SN nor natal kick.,"1999) which is consistent with theoretical modeling of SN/core collapse events by Fryer (1999); NS are formed in asymmetric SN explosions, while intermediate massive BH are formed through partial fall back accompanied by almost symmetric SN and receive either a small or no kick at all, while the most massive BH are formed in direct collapse with no SN nor natal kick." We conclude that existence of a massive DIL in GRS 1915+105 implies that the currently used wind mass loss rates. both for H- and He-vich stars. are possibly overestimated by [actor of ~2 for very massive stars.," We conclude that existence of a massive BH in GRS 1915+105 implies that the currently used wind mass loss rates, both for H- and He-rich stars, are possibly overestimated by factor of $\sim 2$ for very massive stars." Moreover. our models reproduce the observed properties of GRS 19154-105. only if we allow for direct DII formation. with no acconmpanving SN explosion.," Moreover, our models reproduce the observed properties of GRS 1915+105, only if we allow for direct BH formation, with no accompanying SN explosion." Our results also suggest that the directly. formed. DII do not receive any. natal kicks., Our results also suggest that the directly formed BH do not receive any natal kicks. If we agree on the possibilitv of the direct collapse of a massive star at the end of its nuclear lifetime. and also if we allow for change of wind mass loss rates within observational bounds. we [ind (hat evolution ancl formation of GRS 19154-105 can be well understood within the current. framework of stellar single aud. binary. evolution.," If we agree on the possibility of the direct collapse of a massive star at the end of its nuclear lifetime, and also if we allow for change of wind mass loss rates within observational bounds, we find that evolution and formation of GRS 1915+105 can be well understood within the current framework of stellar single and binary evolution." We would like to thank Michal Rozvezka. Ron Taam. Vicky INXalogera. Ron Webbink. Natasha Ivanova. Janusz Ziolkowski and Fred Rasio for comments on (his project.," We would like to thank Michal Rozyczka, Ron Taam, Vicky Kalogera, Ron Webbink, Natasha Ivanova, Janusz kowski and Fred Rasio for comments on this project." We acknowledge support from ABN through grant 5P03D01120., We acknowledge support from KBN through grant 5P03D01120. not by Bondi-Hoyle accretion.,not by Bondi-Hoyle accretion. " The difference becomes apparent if one compares our simulations to those of ?,, who start with initial conditions very similar to ours, but do not include radiative feedback."," The difference becomes apparent if one compares our simulations to those of \cite{2005MNRAS.360....2D}, who start with initial conditions very similar to ours, but do not include radiative feedback." " In their simulations, after 0.5tg they find no stars larger than 1 Mo because all the gas has fragmented to small masses, while in our simulations we have 10 Mo stars after a similar time."," In their simulations, after $0.5 t_{\rm ff}$ they find no stars larger than $\sim 1$ $\msun$ because all the gas has fragmented to small masses, while in our simulations we have $10$ $M_\odot$ stars after a similar time." Figure 2. shows the properties of the star particles formed in the simulations as a function of time., Figure \ref{stars} shows the properties of the star particles formed in the simulations as a function of time. " To show all the runs on the same plot, we have normalized the time by £g, but in physical units the High X simulation evolves about 3 times faster than the others."," To show all the runs on the same plot, we have normalized the time by $t_{\text{ff}}$, but in physical units the High $\Sigma$ simulation evolves about 3 times faster than the others." " The top panel shows the total mass in stars, which is quite similar across all the runs."," The top panel shows the total mass in stars, which is quite similar across all the runs." " This is to be expected, because the star formation rate is set by the global properties of the flow, which are essentially independent of radiative effects."," This is to be expected, because the star formation rate is set by the global properties of the flow, which are essentially independent of radiative effects." " The middle panel shows fmax, the fraction of the total stellar mass that is in the most massive star."," The middle panel shows $f_{\text{max}}$, the fraction of the total stellar mass that is in the most massive star." " There is a period around 0.3£g where the Solar run levels off, but this appears to be a temporary phenomenon."," There is a period around $0.3 t_{\text{ff}}$ where the Solar run levels off, but this appears to be a temporary phenomenon." " By 0.5tg, fmax is very similar across all the runs."," By $0.5 t_{\text{ff}}$, $f_{\max}$ is very similar across all the runs." " Overall, there appears to be little difference between the runs, either in the total mass converted to stars or in the fraction of that mass that ends up in the most massive star."," Overall, there appears to be little difference between the runs, either in the total mass converted to stars or in the fraction of that mass that ends up in the most massive star." The bottom panel of Figure 2 shows the total luminosity of all the stars in the simulation., The bottom panel of Figure \ref{stars} shows the total luminosity of all the stars in the simulation. The value of 10* Lo we find is typical of observed massive protostars (e.g. ?))., The value of $10^4$ $L_{\odot}$ we find is typical of observed massive protostars (e.g. \cite{2007prpl.conf..197C}) ). " Here, we can see a difference between the High X run and the others - because of the higher accretion rates, the total luminosity is higher in the High X run, although the difference decreases with time as the stars become more massive and more of the radiant output comes in the form of nuclear luminosity."," Here, we can see a difference between the High $\Sigma$ run and the others - because of the higher accretion rates, the total luminosity is higher in the High $\Sigma$ run, although the difference decreases with time as the stars become more massive and more of the radiant output comes in the form of nuclear luminosity." " The nuclear luminosity is never dominant, however, and thus the luminosity as a function of time is roughly flat after about 0.2£g, even though we are forming more starsand the stars are growing more massive."," The nuclear luminosity is never dominant, however, and thus the luminosity as a function of time is roughly flat after about $0.2 t_{\text{ff}}$, even though we are forming more starsand the stars are growing more massive." We will make use of the luminosity averaged after over 0.2t¢ to 0.5tg in Section 4 below., We will make use of the luminosity averaged after over $0.2 t_{\text{ff}}$ to $0.5 t_{\text{ff}}$ in Section \ref{discussion} below. " Figure3 shows the cumulative mass distribution of the stars in the four runs - that is, for each value of m, the shows the fraction of the total stellar mass than in is stars with masses greater than m. Visually, there appears to be little difference between the curves, particularly for the X=2 g cm? runs."," Figure \ref{cmfs} shows the cumulative mass distribution of the stars in the four runs - that is, for each value of $m$, the y-axis shows the fraction of the total stellar mass than in is stars with masses greater than $m.$ Visually, there appears to be little difference between the curves, particularly for the $\Sigma = 2$ g $^{-2}$ runs." " To test whether the initial mass function is indeed the same in the different runs, we have performed two-sided Kolmogorov-Smirnov (K-S) tests between each pair of distributions."," To test whether the initial mass function is indeed the same in the different runs, we have performed two-sided Kolmogorov-Smirnov (K-S) tests between each pair of distributions." The results are shown in Table 2.., The results are shown in Table \ref{ks}. " At the level, we cannot reject the null hypothesis that the three 5=2 g cm? have the same underlying initial mass function."," At the level, we cannot reject the null hypothesis that the three $\Sigma = 2$ g $^{-2}$ have the same underlying initial mass function." " The High X distribution, on the other had, does seem to be statistically different from the others."," The High $\Sigma$ distribution, on the other had, does seem to be statistically different from the others." " In contrast to the minor effect reported here, ? found that isothermal runs fragmented completely differently from radiative ones, and KCKMIO found a major difference in fragmentation between runs with low and high surface density."," In contrast to the minor effect reported here, \cite{2007ApJ...656..959K} found that isothermal runs fragmented completely differently from radiative ones, and KCKM10 found a major difference in fragmentation between runs with low and high surface density." " To summarize, the differences in the fragmentation of all of our runs are minor."," To summarize, the differences in the fragmentation of all of our runs are minor." " To the extent that there are significant differences, they are due to changes in the surface density, rather than to changes in the metallicity."," To the extent that there are significant differences, they are due to changes in the surface density, rather than to changes in the metallicity." " At least within the range of parameters considered here, metallicity appears to have little effect on either the temperature or the fragmentation of molecular gas."," At least within the range of parameters considered here, metallicity appears to have little effect on either the temperature or the fragmentation of molecular gas." 'The above simulations suggest that metallicity plays little role in thefragmentation of star-forming gas., The above simulations suggest that metallicity plays little role in thefragmentation of star-forming gas. " To understand why, consider a simple model system like the initial conditions above: a core of gas and dust with radius R., mass M, surface density X=M/nrR2, and a power law density profile p(r)οςr—*e."," To understand why, consider a simple model system like the initial conditions above: a core of gas and dust with radius $R_c$, mass $M$ , surface density $\Sigma = M / \pi R_c^2$, and a power law density profile $\rho(r) \propto r^{-k_\rho}$." " We would like to understand what happens to the temperature of this core once stars have started to form, so we will place a point source of luminosity L in the center to represent the combined radiant output of the central collection of stars."," We would like to understand what happens to the temperature of this core once stars have started to form, so we will place a point source of luminosity $L$ in the center to represent the combined radiant output of the central collection of stars." We assume that the dust opacity follows a power law in the far IR regime: where the subscript “0” refers to an arbitrary reference value and is the dust-to-gas mass ratio relative to solar.," We assume that the dust opacity follows a power law in the far IR regime: where the subscript $0$ "" refers to an arbitrary reference value and $\delta$ is the dust-to-gas mass ratio relative to solar." " The T in 6this equation is the dust temperature, which we assume is identical to the radiation temperature."," The $T$ in this equation is the dust temperature, which we assume is identical to the radiation temperature." " We will adopt the dust opacity model of ?,, forwhich kp= cm? g! at Ag=100 uim and f= 2; however, we have verified that using the opacities of ? (as used by"," We will adopt the dust opacity model of \cite{2001ApJ...548..296W}, , forwhich $\kappa_0 = 0.27$ $^2$ $^{-1}$ at $\lambda_0 = 100$ $ \mu \text{m}$ and $\beta = 2$ ; however, we have verified that using the opacities of \cite{2003A&A...410..611S} (as used by" momentum. po and. follow their phase-space trajectories.,momentum $p_0$ and follow their phase-space trajectories. We assume the constant particle injection to continue in time after the initial time {ος=0., We assume the constant particle injection to continue in time after the initial time $t_0 = 0$. As some particles escape From the acceleration process by crossing the escape boundary. placed far behind the shock we use the trajectory splitting. procedure to keep the total amount of particles involved in simulations constant (cl, As some particles escape from the acceleration process by crossing the escape boundary placed far behind the shock we use the trajectory splitting procedure to keep the total amount of particles involved in simulations constant (cf. Wirk Schneider 1987b: Ostrowski 1991)., Kirk Schneider 1987b; Ostrowski 1991). " Here we put the boundary at the distance Gre,/l|dry."," Here we put the boundary at the distance $6\kappa_{2,n}/U_2 + 4 r_{g,2}$." We checked by simulations that any further increase of this distance does not influence the results in any noticeable wav., We checked by simulations that any further increase of this distance does not influence the results in any noticeable way. For every shock crossing. the particle weight factor multiplied by the inverse of the particle velocity normal to the shock (= particle density) is added to the respective time anc momentum bin of the spectrum. as measured in the shock normal rest frame.," For every shock crossing, the particle weight factor multiplied by the inverse of the particle velocity normal to the shock $\equiv$ particle density) is added to the respective time and momentum bin of the spectrum, as measured in the shock normal rest frame." As one considers a Continuous injection in all instants alter fy. in order to obtain the particle spectrum at some time Fi>fo. one has to add to particle density in à bin p; at f; the densities in this momentum bin for all the earlier times.," As one considers a continuous injection in all instants after $t_0$, in order to obtain the particle spectrum at some time $t_j > t_0$, one has to add to particle density in a bin $p_i$ at $t_j$ the densities in this momentum bin for all the earlier times." The resulting particle spectra are represented as power-law functions with the squared exponential cut-off in momentum In this formula three parameters are to be fitted: the normalization constant zl. the spectral index for the stationary solution a. and the momentum cut-olfp. (Fig.," The resulting particle spectra are represented as power-law functions with the squared exponential cut-off in momentum In this formula three parameters are to be fitted: the normalization constant $A$, the spectral index for the stationary solution $\alpha$, and the momentum cut-off $p_c$ (Fig." 2: for details of the fitting procedure see Appendix A)., 2; for details of the fitting procedure see Appendix A). In the simulations. due to our. proportional to momentuni. scaling of the respective quantities. the derived acceleration time scale (2.3) must be also proportional to p. and thus to rj(p)/e.," In the simulations, due to our, proportional to momentum, scaling of the respective quantities, the derived acceleration time scale (2.3) must be also proportional to $p$, and thus to $r_g(p)/c$." Therefore. this time scale measured in units ΟΕ Cor re(pd fe) is momentum independent and can be easily scaled to any momentum.," Therefore, this time scale measured in units of $r_g(p_c)/c$ (or $r_e(p_c) /c$ ) is momentum independent and can be easily scaled to any momentum." The parameter Ti gives the value ofthe acceleration time scale in units of ∣⋅↴⊽⊥∠⋅⊳↙⋯∡∶↙∣∣⋮↴⊽⊥∠⋅⊳∐↕⋖⊾∖⇁⋜↧↓⋯⊾∪⇂↙≴⋯⋊⊽∣⋜∐⋜↧↓≻⋜," The parameter $T_r$ gives the value ofthe acceleration time scale in units of $r_{e,1}/c$, $T_{acc}^{(c)} = T_r \, r_{e,1}/c$." ⊔⋅↿⊔⇍⊔↓⋜⊔⋅ ⊳⇁⊔↴⊳⇁ ⊳∖ ⋅⊳⇁⊔ ⋠ ↿⊲↓⊔↓⋖⋅∣∣⊀↓⊳∖∠⇂⋖⋅↓⋰↓∖⇁⋖⋅∠⇂∐⋅∪⊔↓↿↓⊔⋅↓⋅⋖⋅⊳∖↓≻⋖⋅≼∼↿⊲↓∖⇁∢⋅∖⇁⋜↧⇂⋯⋅≱∖∪⇂∎∣↗⋯∶ where we consider the advanced phase of. acceleration (ρεX» po).," The value of $T_{acc,i}^{(c)}$ at a particular time $t_i$ is derived from the respective values of $p_{c,i}$: where we consider the advanced phase of acceleration $p_{c,i} \gg p_0$ )." As in our simulations p.-x/( the condition (peipesA)fper« Lis not required to hold in equation (3.5).," As in our simulations $p_c \propto t$ the condition $(p_{c,i}-p_{c,i-1})/p_{c,i} \ll 1$ is not required to hold in equation (3.5)." Therefore. with all scales proportional to the particle momentunm. the formula. (3.5).2r reduces to quedον=f; and the parameter 7; tends to a constant (Fig.," Therefore, with all scales proportional to the particle momentum, the formula (3.5) reduces to $T_{acc,i}^{(c)} = t_i$ and the parameter $T_r$ tends to a constant (Fig." 3)., 3). The extension of the simulated. spectra over several decades. in particle energy allows to avoid problems with the initial conditions ancl decrease the relative error of the derived time scale by averaging over a larger number of instantaneous 5545.," The extension of the simulated spectra over several decades in particle energy allows to avoid problems with the initial conditions and decrease the relative error of the derived time scale by averaging over a larger number of instantaneous $T_{acc,i}$." For a given relativistic shock velocity particle anisotropy in the shock depends on the mean magnetic field. inclination to the shock normal and the form of turbulent field., For a given relativistic shock velocity particle anisotropy in the shock depends on the mean magnetic field inclination to the shock normal and the form of turbulent field. Below. we describe the results of simulations performed in order to understand the time dependence of the acceleration process in various conditions.," Below, we describe the results of simulations performed in order to understand the time dependence of the acceleration process in various conditions." " ln order to do that. we consider shock waves propagating with velocities C, = 0.3. 0.5. 0.7 and 0.9 of the velocity of light. and the magnetic field inclinations inclucing the euasi-parallel. oblique sub-Iuminal ancl oblique super-Iuminal configurations."," In order to do that, we consider shock waves propagating with velocities $U_1$ = $0.3$, $0.5$, $0.7$ and $0.9$ of the velocity of light, and the magnetic field inclinations including the quasi-parallel, oblique sub-luminal and oblique super-luminal configurations." In all these cases we investigate the role of varving magnitude of turbulence characterized here by the value of Af or by the ratio of the cillusion cocllicient across the mean field and that along the field. &i584 .," In all these cases we investigate the role of varying magnitude of turbulence characterized here by the value of $\Delta t$ or by the ratio of the diffusion coefficient across the mean field and that along the field, $\kappa_\perp / \kappa_\parallel$ ." The relation between these parameters [or AQ=10 is presented at Fig.," The relation between these parameters for $\Delta \Omega = 10^\circ$ is presented at Fig." 4. where - at 2M>0.01 ," 4, where - at $\Delta t > 0.01$ " using the Mg IX ddiagnostic line ratio are also given.,using the Mg IX diagnostic line ratio are also given. The error bar on (he points at 1.3 and 1.6/4. are estimated here from the scatter in the points on Figure 8 of Wilhelmetal.(1998)., The error bar on the points at 1.3 and $1.6R_{\sun}$ are estimated here from the scatter in the points on Figure 8 of \citet{wilhelm98}. . These authors use the atomic physics data of Ixeenanοἱal.(1984). to derive a temperature ratio. which is consistent wilh coronal hole temperatures determined by other authors (e.g.DoschekFeldman1977:Doscheketal. 2001).," These authors use the atomic physics data of \citet{keenan84} to derive a temperature ratio, which is consistent with coronal hole temperatures determined by other authors \citep[e.g.][]{doschek77,doschek01}." . More recent ealeulations in R-matrix and distorted wave approximations sumnmarzed by Landietal.(2001) give temperatures significantly hieher or lower respectively. and ave likely due to inaccuracies in these atomic data.," More recent calculations in R-matrix and distorted wave approximations summarized by \citet{landi01} give temperatures significantly higher or lower respectively, and are likely due to inaccuracies in these atomic data." We base our coronal hole temperatures on works such as Doschek&Feldman(1971) and Doschekal.(2001) where the ionization balance is the principal temperature diagnostic. ancl on the O VI observations of Davidetal.(1998).. whose electron temperature diagnostic depends on much less controversial atomic physics.," We base our coronal hole temperatures on works such as \citet{doschek77} and \citet{doschek01} where the ionization balance is the principal temperature diagnostic, and on the O VI observations of \citet{david98}, whose electron temperature diagnostic depends on much less controversial atomic physics." Even if the absolute temperatures measured by Wilhelmοἱal.(1998) cannot be interpreted with confidence. as (hey state in their paper. al least (he maximum variation of the electron temperature with distance from (he solar surface can be constrained by their observations.," Even if the absolute temperatures measured by \citet{wilhelm98} cannot be interpreted with confidence, as they state in their paper, at least the maximum variation of the electron temperature with distance from the solar surface can be constrained by their observations." Figure 6 shows the electron temperature profiles resulting from using the maximum collisionless energv. (transfer in. Figure 5 and. differing initial flow speeds. with the highest temperatures resulting Ilrom the slowest initial speeds since more time 1s available for the plasma electron to be heated and the rate of temperature decrease due to adiabatic expansion is lower.," Figure 6 shows the electron temperature profiles resulting from using the maximum collisionless energy transfer in Figure 5 and differing initial flow speeds, with the highest temperatures resulting from the slowest initial speeds since more time is available for the plasma electron to be heated and the rate of temperature decrease due to adiabatic expansion is lower." Figures T. 8. and 9 show the evolution of the ionization balances of O. Si. and Fe with heliocentric distance.," Figures 7, 8, and 9 show the evolution of the ionization balances of O, Si, and Fe with heliocentric distance." In each case the flow starts at a density of 105 electrons 7 and a temperature of 9x10? IX. The initial flow speed is 20 kins +1 and the electron-ion equilibration yarameter is 5=5;ieM;a;feelferd(ως>/μυς)un0.5., In each case the flow starts at a density of $10^8$ electrons $^{-3}$ and a temperature of $9\times 10^5$ K. The initial flow speed is 20 km $^{-1}$ and the electron-ion equilibration parameter is $\gamma ^{\prime}=\gamma _iM_i/\omega Afq^2\left(\omega ^2/k^2v_{iy}^2\right) = 0.5$. Increased ionization Commences al around 1.58... m response to the onset of ion evelotvon heating al this location. aud charge states freeze in between 2 and 2.5.i..2 at the values found in situ by Ulvsses )..," Increased ionization commences at around $1.5R_{\sun}$, in response to the onset of ion cyclotron heating at this location, and charge states freeze in between 2 and $2.5R_{\sun}$ at the values found in situ by Ulysses \citep{geiss95,ko97}." The resulting ionization balances are given in Tables 1-4 for C. O. Mg. Si and Fe respectively.," The resulting ionization balances are given in Tables 1-4 for C, O, Mg, Si and Fe respectively." " From (he C and O ionization balances in Table 1. it is clear than only [or values of the parameter ο)=(5;M;/cAJq*)Gefhs,y~0.5 and initial wind speeds of 10-20 does sufficient electron heating occur to bring the modelled charge states into agreement with those observed."," From the C and O ionization balances in Table 1, it is clear than only for values of the parameter $\gamma ^{\prime}=\left(\gamma _iM_i/\omega Afq^2\right) \left(\omega /kv_{iy}\right)^2\simeq 0.5$ and initial wind speeds of 10-20 does sufficient electron heating occur to bring the modelled charge states into agreement with those observed." Tables 2-4 verify that these conclusions do not change when other, Tables 2-4 verify that these conclusions do not change when other The evolution of a representative strongly buckling simulation. shown in Fie. 2..,"The evolution of a representative strongly buckling simulation, shown in Fig. \ref{fig:fig2}," produced a bar by /2750. which then buckled stronglv at /7100.," produced a bar by $t\simeq 50$, which then buckled strongly at $t\simeq 100$." Despite the strong buckling. the bar is weakened but not destroved.," Despite the strong buckling, the bar is weakened but not destroyed." As is well known. the process of bar formation drives a redistribution of angular momentum. leading to an increase in (he central densitv.," As is well known, the process of bar formation drives a redistribution of angular momentum, leading to an increase in the central density." This process is largely complete by the time the bar buckles: the buckling instability does not aller significantly the scale length or (he mass of the inner Sérrsic component., This process is largely complete by the time the bar buckles: the buckling instability does not alter significantly the scale length or the mass of the inner Sérrsic component. " However. it is interesting that at buckling. 2; changes [rom ny~1 (o njον1.5: thus buckling may contribute to the scatter of my, around the exponential value observed in the bulges of real intermediate-tvpe galaxies."," However, it is interesting that at buckling, $n_b$ changes from $n_b \simeq 1$ to $n_b \simeq 1.5$: thus buckling may contribute to the scatter of $n_b$ around the exponential value observed in the bulges of real intermediate-type galaxies." ) and 3 metal abundances (Z=0.5.1.0.5.0 in solar units retrieved from ?)).,"$^{-3}$ ) and 3 metal abundances $\zeta = 0.2, 1.0, 5.0$ in solar units retrieved from \citealt{Anders1989GeCOA}) )." Both densities and metal abundances span larger ranges than those obtained from high spectral resolution X-ray observations., Both densities and metal abundances span larger ranges than those obtained from high spectral resolution X-ray observations. We focused our analysis on a large space of parameters for two main reasons., We focused our analysis on a large space of parameters for two main reasons. Probably the most important is that current high spectral. resolution X-ray observations of CTTSs are limited. to a very small sample of very close and bright CTTSs., Probably the most important is that current high spectral resolution X-ray observations of CTTSs are limited to a very small sample of very close and bright CTTSs. These stars are older and accrete to a lower rate than typical CTTSs and it is most likely that physical and chemical properties of the corresponding accretion stream may differ too., These stars are older and accrete to a lower rate than typical CTTSs and it is most likely that physical and chemical properties of the corresponding accretion stream may differ too. " Indeed. ? and ? estimated pre-shock densities ra.=10'—105care, while pre-shockdensities derived from X-ray data are n,=10!!—10"" cae."," Indeed, \cite{Bary2008ApJ} and \cite{Martin1996ApJ} estimated pre-shock densities $n_{\rm acc}=10^{12}-10^{13}~cm^{-3}$, while pre-shockdensities derived from X-ray data are $n_{\rm acc}=10^{11}-10^{12}~cm^{-3}$ ." Moreover. densities and metal abundances are measured from the spatially integrated emission 1cluding both the coronal and the aceretior component.," Moreover, densities and metal abundances are measured from the spatially integrated emission including both the coronal and the accretion component." Typical coronal densities Ga.<10! cjr) are much lower than densities expected in the accretion stream and metal abundaces are lower than photospheric abundances observed in young stars (?).., Typical coronal densities $n_{e}<10^{10}~cm^{-3}$ ) are much lower than densities expected in the accretion stream and metal abundances are lower than photospheric abundances observed in young stars \citep{Telleschi2007A&A}. Therefore. both accretion stream densities and abundances derived from X-ray observations could be underestimated.," Therefore, both accretion stream densities and abundances derived from X-ray observations could be underestimated." A heuristic model that assumes the strong shock approximation (?).. stationary conditions and radiative cooling has been previously used to describe accretion shock physics in CTTSs (??) and to derive mass accretion rates from the X-ray emission (2)..," A heuristic model that assumes the strong shock approximation \citep{Zeldovich1967book}, stationary conditions and radiative cooling has been previously used to describe accretion shock physics in CTTSs \citep{Lamzin1998ARep, Calvet1998ApJ} and to derive mass accretion rates from the X-ray emission \citep{Argiroffi2007A&A}." " This model provides post-shock region characteristics: where 45, and zs, are the post-shock velocity and density. Hace and Agee are the stream pre-shock velocity and density. Tao. IS the crossing time of the accreting material through the post-shock zone (which is expected to be equal to the radiative cooling time r4. Tp, is thepost-shock temperature. and /,, is the thickness of the post-shock zone. and where the radiative cooling function has been approximated as 1.6x107PZT-7 erg s! em? (eg. 2)."," This model provides post-shock region characteristics: where $u_{\rm ps}$ and $n_{\rm ps}$ are the post-shock velocity and density, $u_{\rm acc}$ and $n_{\rm acc}$ are the stream pre-shock velocity and density, $\tau_{\rm cross}$ is the crossing time of the accreting material through the post-shock zone (which is expected to be equal to the radiative cooling time $\tau_{\rm cool}$ ), $T_{\rm ps}$ is thepost-shock temperature, and $l_{\rm ps}$ is the thickness of the post-shock zone, and where the radiative cooling function has been approximated as $\Lambda(T)\approx 1.6 \times 10^{-19} \zeta T^{-1/2}$ erg $^{-1}$ $^{3}$ (e.g. \citealt{Orlando2005A&A}) )." Table | reports the ranges of values of all the relevant physical parameters of the simulations explored here., Table \ref{tab:Par_space} reports the ranges of values of all the relevant physical parameters of the simulations explored here. " The first three rows report the three independent parameters of our analysis (re. density. velocity. and metalabundance of the stream). whereas the following rows report the parameters derived from the independent ones. namely the post-shock temperature 7, (Eq. 5))."," The first three rows report the three independent parameters of our analysis (i.e. density, velocity, and metalabundance of the stream), whereas the following rows report the parameters derived from the independent ones, namely the post-shock temperature $T_{\rm ps}$ (Eq. \ref{eqn:posttemp}) )," the radiative cooling tme To. (Eq. 6)).," the radiative cooling time $\tau_{\rm cross}$ (Eq. \ref{eqn:taucool}) )," the slab thickness ἐς (Eq., the slab thickness $l_{\rm ps}$ (Eq. 9. and Fig. 1)).," \ref{eqn:lslab} and Fig. \ref{fig:cartoon}) )," the ram pressure of the accretion stream Py=Piectfzue- the sinking of the slab in the chromosphere μι (1.8. the distance of the base of the slab from the transition region between the chromosphere and the stellar corona. see Fig. 1)).," the ram pressure of the accretion stream $P_{\rm ram}=\rho_{\rm acc} u_{\rm acc}^2$, the sinking of the slab in the chromosphere $h_{\rm sink}$ (i.e. the distance of the base of the slab from the transition region between the chromosphere and the stellar corona, see Fig. \ref{fig:cartoon}) )," " and theplasma parameter of the post-shock zone B=P,/(87/87). where the magnetic field strength is assumed to be B~| kG (which ts the orderof magnitude of the field strengths derived from observations of CTTSs; ?))."," and theplasma parameter of the post-shock zone $\beta=P_{\rm ram}/(B^2/8\pi)$, where the magnetic field strength is assumed to be $B\sim 1$ kG (which is the orderof magnitude of the field strengths derived from observations of CTTSs; \citealt{Johns-Krull2007ApJ}) )." Note that the plasma 6 is «| for most of the accretion streams considered in this work (thus justifying the low-8 assumption of our model) except for 5 cases. where P1-2 for the magnetic field assumed).," Note that the plasma $\beta$ is $\ll 1$ for most of the accretion streams considered in this work (thus justifying the $\beta$ assumption of our model) except for 5 cases, where $\beta \sim 1-2$ (for the magnetic field assumed)." On the other hand. showed that. forB~|—5. the evolution of radiative shocks in 2D MHD models (thus including an explicit description of the ambient magnetic field) is analogous to that described by 1-D hydrodynamic models. although the amplitude of oscillations is smaller and the frequency higher than those predicted by 1-D models.," On the other hand, \cite{Orlando2009A&A} showed that, for $\beta \sim 1-5$, the evolution of radiative shocks in 2D MHD models (thus including an explicit description of the ambient magnetic field) is analogous to that described by 1-D hydrodynamic models, although the amplitude of oscillations is smaller and the frequency higher than those predicted by 1-D models." For the 30 different cases analyzed here. the duration of the simulations ranges from 100 to 19000 s. The duration of each simulation was set much longer than the initial transient effect. at the impact of the stream onto the chromosphere. and to include a large number(at least three) of oscillation periods of the post-shock zone (see Paper D.," For the 30 different cases analyzed here, the duration of the simulations ranges from 100 to 19000 s. The duration of each simulation was set much longer than the initial transient effect, at the impact of the stream onto the chromosphere, and to include a large number(at least three) of oscillation periods of the post-shock zone (see Paper I)." For each simulation. we synthesize the X-ray luminosity (Lx) in the [0.5—8.0] keV energy band and in the resonance lines of two He-like tons. namely the at 21.60 (Loygy) and the at 13.45 (Lneix). which ean be measured with the high resolution spectrographs on board the and satellites.," For each simulation, we synthesize the X-ray luminosity $L_{\rm X}$ ) in the $[0.5-8.0]$ keV energy band and in the resonance lines of two He-like ions, namely the at 21.60 $L_{\rm OVII}$ ) and the at 13.45 $L_{\rm NeIX}$ ), which can be measured with the high resolution spectrographs on board the and satellites." In particular:, In particular: Drandletal.(2006) of the prototwpe starburst NGC 1714.,\citet{bra06} of the prototype starburst NGC 7714. Figure 1 illustrates composite spectra (hat arise [rom different mixtures of the Markarian 231 and NGC 7714 spectra. [rom pure starburst al the top through starburst contributions of75%...50%... and to pure AGN at the bottom.," Figure 1 illustrates composite spectra that arise from different mixtures of the Markarian 231 and NGC 7714 spectra, from pure starburst at the top through starburst contributions of, and to pure AGN at the bottom." Spectra are normalized to the peak which is between μην and 7.9m. depending on the composite.," Spectra are normalized to the peak which is between $\mu$ m and $\mu$ m, depending on the composite." The decreasing equivalent width of the PAIL features is evident as the starburst contribution lessens., The decreasing equivalent width of the PAH features is evident as the starburst contribution lessens. This is shown quantitatively in Figure 2. which tracks the equivalent width (EW) in the rest lrame of the 6.2;an feature as a function of the starburst contribution.," This is shown quantitatively in Figure 2, which tracks the equivalent width (EW) in the rest frame of the $\mu$ m feature as a function of the starburst contribution." " This EW is measured by fitting a single Gaussian profile to the G.2y;an feature ancl using the underlying “continuum” defined between 5.54 and 0011. For pure starbursts. much of this continuum"" maa actually be extended wings of the 7.7;an PAIL complex. but measuring the 6.2;an feature in this wav provides a consistent measurement of its strength."," This EW is measured by fitting a single Gaussian profile to the $\mu$ m feature and using the underlying ""continuum"" defined between $\mu$ m and $\mu$ m. For pure starbursts, much of this ""continuum"" may actually be extended wings of the $\mu$ m PAH complex, but measuring the $\mu$ m feature in this way provides a consistent measurement of its strength." " The “pure starbursts"" in our sample generally have rest frame equivalent widths for the G.2yan feature greater than 0.5;au. indicating that the starburst contribution exceeds of the mid-infrared. laminosity."," The ""pure starbursts"" in our sample generally have rest frame equivalent widths for the $\mu$ m feature greater than $\mu$ m, indicating that the starburst contribution exceeds of the mid-infrared luminosity." However. equivalent widths for the ULIRGs are generally less than this value. implving an AGN contribution to the underlving continuum.," However, equivalent widths for the ULIRGs are generally less than this value, implying an AGN contribution to the underlying continuum." " For the ULIRGs. a simple measure of pL, (7.7m) could overestimate the starburst Iuminosity."," For the ULIRGs, a simple measure of $\nu$ $_{\nu}$ $\mu$ m) could overestimate the starburst luminosity." " For this reason. we determine a zL, μη) for the starburst component of ULIRGs by using the published luminosities of the total PAIL features μαι) (Imanishiοἱal.2007:Sargsvanelal.2008) or L(6.2jm--11.2jm) (Farrahetal.2007)."," For this reason, we determine a $\nu$ $_{\nu}$ $\mu$ m) for the starburst component of ULIRGs by using the published luminosities of the total PAH features $\mu$ m) \citep{ima07,sar08} or $\mu$ $\mu$ m) \citep{far07}." . Such luminosities are measured only for the PAI] emission feature and do not include any continuum contribution from the AGN., Such luminosities are measured only for the PAH emission feature and do not include any continuum contribution from the AGN. " Luminosities of these features are related to the Inminosity of our PAIL parameter VL ATT um)) using empirical transformations which have been determined by measuring vf, (cram). μη). and 1.38ym)} for the brightest 69 pure starbursts in Table 1. (Sargsvan et al.."," Luminosities of these features are related to the luminosity of our PAH parameter $\nu$ $_{\nu}$ ) using empirical transformations which have been determined by measuring $\nu$ $_{\nu}$ $\mu$ m), $\mu$ m), and $\mu$ m) for the brightest 69 pure starbursts in Table 1 (Sargsyan et al.," in preparation)., in preparation). " These transformations eive that vL,,(7.7 um)) = £15) um)) and vL,.(7.7 ΠΕ 11.349).", These transformations give that $\nu$ $_{\nu}$ ) = $\pm$ 15) ) and $\nu$ $_{\nu}$ ) = $\pm$ 6) $\mu$ $\mu$ m). " Using these transformations. the equivalent pL, ΠΠ for ULIRGs are listed in Table 1."," Using these transformations, the equivalent $\nu$ $_{\nu}$ $\mu$ m) for ULIRGs are listed in Table 1." "We report new observations of the debris disc around 110647, 5506) using theHerschel Space Observatory (Pilbrattetal.2010).","We report new observations of the debris disc around 10647, 506) using the Space Observatory \citep{pilbratt2010}." ". The observations form part of a larger Key Programme (KP), viz.DUNES!,"," The observations form part of a larger Key Programme (KP), viz.," ", which is described in more detail by Eiroaetal.(2010).", which is described in more detail by \citet{eiroa2010}. ". Here, we give a brief summary to put the contents of this Letter into context."," Here, we give a brief summary to put the contents of this Letter into context." " The DUNES KP is a sensitivity limited study with the goal of discovering and characterising extra-solar analogues of the Edgeworth-Kuiper Belt (EKB) in an unbiased, statistical sample of nearby F, G and K main-sequence stars."," The DUNES KP is a sensitivity limited study with the goal of discovering and characterising extra-solar analogues of the Edgeworth-Kuiper Belt (EKB) in an unbiased, statistical sample of nearby F, G and K main-sequence stars." " The sample is volume limited, with distances ppc, and spans a broad range of stellar ages, from ,00.1 to roughly 10GGyr."," The sample is volume limited, with distances pc, and spans a broad range of stellar ages, from 0.1 to roughly Gyr." " In addition to the object of the present study Eri)), a number of M- and A-type stars will be observed in collaboration with the DEBRIS-KP team (Matthewsetal.2010),, implying that the whole sample covers a decade in stellar mass from 0.2 to msun."," In addition to the object of the present study ), a number of M- and A-type stars will be observed in collaboration with the DEBRIS-KP team \citep{matthews2010}, implying that the whole sample covers a decade in stellar mass from 0.2 to ." . The PACS (Poglitschetal.2010) observations at aaim at the detection of the stellar photospheres down to the confusion noise with a signal to noise ratio (S/N) of at least 5., The PACS \citep{poglitsch2010} observations at aim at the detection of the stellar photospheres down to the confusion noise with a signal to noise ratio (S/N) of at least 5. " Together with observations in the other bands, this will lead to an unprecedented characterisation of discs and"," Together with observations in the other bands, this will lead to an unprecedented characterisation of discs and" reduce the proportion of WR runaways?,reduce the proportion of WR runaways? To test this proposition we use the analytic formulae provided by Tauris Takens (1998) for the effect of a given kick magnitude and direction on the companion's velocity., To test this proposition we use the analytic formulae provided by Tauris Takens (1998) for the effect of a given kick magnitude and direction on the companion's velocity. To quantify the effects of kicks we also need to know (or guess) a suitable distribution of parameters for systems immediately before the first SN., To quantify the effects of kicks we also need to know (or guess) a suitable distribution of parameters for systems immediately before the first SN. This in turn depends on the nature of mass transfer., This in turn depends on the nature of mass transfer. Whilst there are initial parameter distributions for binaries which are widely used. the masses and periods immediately before the SN depend critically on a number of rather less well-known evolution-based quantities. including the amount of matter which may be accreted during RLOF and the efficiency of common envelope mass loss.," Whilst there are initial parameter distributions for binaries which are widely used, the masses and periods immediately before the SN depend critically on a number of rather less well-known evolution-based quantities, including the amount of matter which may be accreted during RLOF and the efficiency of common envelope mass loss." Fig., Fig. 2 shows Monte Carlo simulations of sets of 50000 systems with varying assumptions about input systems and kicks., 2 shows Monte Carlo simulations of sets of 50000 systems with varying assumptions about input systems and kicks. In all cases we assume an isotropic distribution of Kick directions and a Maxwellian distribution of kick velocities with mean 450kms (Lyne Lorimer 1994: Lorimer. Bailes Harrison 1997). and that the initial binary population has mass ratio g and period P distributed according to P(g)eIl. P(P)eL/P with primary masses appropriate to a Salpeter IMF.," In all cases we assume an isotropic distribution of kick directions and a Maxwellian distribution of kick velocities with mean $450 \,{\rm kms}^{-1}$ (Lyne Lorimer 1994; Lorimer, Bailes Harrison 1997), and that the initial binary population has mass ratio $q$ and period $P$ distributed according to $P(q) \propto 1$, $P(P) \propto 1/P$ with primary masses appropriate to a Salpeter IMF." Observations of massive stars suggest that the initial binary fraction is high. quite possibly close to 100 (Mason et al.," Observations of massive stars suggest that the initial binary fraction is high, quite possibly close to 100 (Mason et al." 1998). though the binary fraction amongst runaways is much lower.," 1998), though the binary fraction amongst runaways is much lower." Therefore we consider an initial population composed solely of binaries., Therefore we consider an initial population composed solely of binaries. Initially-single stars are highly unlikely to become runaways by either method. so the effect of their inclusion would be to lower the runaway fractions of both O and WR stars.," Initially-single stars are highly unlikely to become runaways by either method, so the effect of their inclusion would be to lower the runaway fractions of both O and WR stars." A further consideration is the appropriate metallicity., A further consideration is the appropriate metallicity. With the recent work of Apslund et al. , With the recent work of Apslund et al. ( 2005). it now seems apparent that the rue solar metallicity is similar to that of the solar neighborhood. i.e. closer to 0.01 that 0.02. the usually assumed ‘solar value when models are calculated.,"2005), it now seems apparent that the true solar metallicity is similar to that of the solar neighborhood, i.e. closer to $0.01$ that $0.02$, the usually assumed 'solar' value when models are calculated." It is likely that runaway O stars originate Tom systems with a range of metallicities. of which 0.02 is towards he higher end (Daflon et al.," It is likely that runaway O stars originate from systems with a range of metallicities, of which $0.02$ is towards the higher end (Daflon et al." 2001)., 2001). Many of the regions in which WR stars are common have metallicities which are close to the old value of solar metallicity (Nayarro et al., Many of the regions in which WR stars are common have metallicities which are close to the old value of solar metallicity (Najarro et al. 2004). due to the greater ikelihood of forming such stars at higher Z. In order to allow comparison with previous studies. we run our initial caleulations assuming Z =0.02.," 2004), due to the greater likelihood of forming such stars at higher Z. In order to allow comparison with previous studies, we run our initial calculations assuming Z $= 0.02$." " However. we consider in addition the lower value of metallicity. which is also close to the metallicity of the LMC, and it should be borne in mind that the true Galactic value most likely results from a range between the two."," However, we consider in addition the lower value of metallicity, which is also close to the metallicity of the LMC, and it should be borne in mind that the true Galactic value most likely results from a range between the two." For panel of Fig., For panel of Fig. 2 we assume a simple model of binary interaction without stellar wind mass loss in which all systems with initial periods below 3000 days interact. systems with initial q less than 0.6 or period greater than 200 days come into contact (Pols 1994) and others have stable mass transfer.," 2 we assume a simple model of binary interaction without stellar wind mass loss in which all systems with initial periods below 3000 days interact, systems with initial $q$ less than 0.6 or period greater than 200 days come into contact (Pols 1994) and others have stable mass transfer." For stable mass transfer we assume RLOF is conservative. the primarys initial mass Mjj and post-RLOF mass Mjy are related by and the post-RLOF period related to the initial period by (van den Heuvel et al.," For stable mass transfer we assume RLOF is conservative, the primary's initial mass $M_{\rm 1,i}$ and post-RLOF mass $M_{\rm 1,p}$ are related by and the post-RLOF period related to the initial period by (van den Heuvel et al." 2000)., 2000). For contact systems we assume the primary is stripped to its core as before. the secondary’s mass remains constant and the period is determined by the energy argument of Webbink (1984). ∖↖∣↧∁⇂⊾∁∖↖∁↾⋡∙∣∣∖⊽∁∏⊂⊲∟⋯∣↴∁∣⋅↭⋡∙⋯↳∪↘⋯∣↴∁↭⋅∃≺↕∃↑↴∙∣∣↧∣∁↾∸∣∣⋅∶↭↭∶≻⋅ ," For contact systems we assume the primary is stripped to its core as before, the secondary's mass remains constant and the period is determined by the energy argument of Webbink (1984), where we take $\eta_{\rm CE}$ to be 1.0 and $\lambda$ to be 0.5 (Pfahl et al." , 2002). The ratio of the Roche lobe radius of the primary to the separation. rey. is taken to be (Eggleton 1983).," The ratio of the Roche lobe radius of the primary to the separation, $r_{\rm L1}$, is taken to be (Eggleton 1983)." Systems are considered to merge during common envelope evolution if the secondary would overflow its Roche Lobe at the post-CE separation and masses given above., Systems are considered to merge during common envelope evolution if the secondary would overflow its Roche Lobe at the post-CE separation and masses given above. In order to calculate the relative observed populations of WR and O stars we also need to have an idea ofthe time each star spends in these phases. both when it is runaway and when it is not.," In order to calculate the relative observed populations of WR and O stars we also need to have an idea of the time each star spends in these phases, both when it is runaway and when it is not." For the toy model we assume that post-RLOF. pre-SN primaries spend 10° years ina WR-like phase. and. for other stars. those above 17M. have an O phase of 4x10° years and above 28M.. have a WR phase of 10° years.," For the toy model we assume that post-RLOF, pre-SN primaries spend $10^{6}$ years in a WR-like phase, and, for other stars, those above $17 \, \msun$ have an O phase of $4 {\rm x} 10^{6} \,$ years and above $28 \, \msun$ have a WR phase of $10^{6} \,$ years." If they have accreted significantly. these mass limits are likely lowered somewhat (Dray Tout 2005).," If they have accreted significantly, these mass limits are likely lowered somewhat (Dray Tout 2005)." The mass lost in the SN explosion is calculated from the pre-SN core mass-remnant mass fit of Portinari. Chiosi Bressan (1998) to the SN models of Woosley Weaver (1995) at Z =0.02.," The mass lost in the SN explosion is calculated from the pre-SN core mass-remnant mass fit of Portinari, Chiosi Bressan (1998) to the SN models of Woosley Weaver (1995) at Z $= 0.02$." For cores of over [SM we assume direct collapse to a BH with no SN (Fryer 1999) and hence no Kick.," For cores of over $15 \, \msun$ we assume direct collapse to a BH with no SN (Fryer 1999) and hence no kick." In panelsb to we take pre-SN parameters from. the evolutionary models of Dray Tout (2005) for binaries at Z = 0.02., In panels to we take pre-SN parameters from the evolutionary models of Dray Tout (2005) for binaries at Z = $0.02$. We use the non-conservative RLOF set of models for which an accreting star can only accept ten percent of its own mass in accretion during an episode of RLOF., We use the non-conservative RLOF set of models for which an accreting star can only accept ten percent of its own mass in accretion during an episode of RLOF. These models do not follow post-contact systems. so for those we assume that the primary is stripped down to its core mass. the secondary stays roughly the same mass as at the start of contact. and the period is governed by equation 3 as for the previous models.," These models do not follow post-contact systems, so for those we assume that the primary is stripped down to its core mass, the secondary stays roughly the same mass as at the start of contact, and the period is governed by equation 3 as for the previous models." " The pre-SN radius and post-SN lifetime of post-contact secondaries are then estimated from single stars of the corresponding mass, since in the majority of cases it has accreted only a small amount."," The pre-SN radius and post-SN lifetime of post-contact secondaries are then estimated from single stars of the corresponding mass, since in the majority of cases it has accreted only a small amount." Parameters of noninteracting systems are also taken from single star models (Dray Tout 2003)., Parameters of noninteracting systems are also taken from single star models (Dray Tout 2003). Under the assumptions used here. mergers are a frequent result of common envelope evolution.," Under the assumptions used here, mergers are a frequent result of common envelope evolution." Unless the merger process itself involves significant asymmetric mass loss. the stars thus formed will not be runaway.," Unless the merger process itself involves significant asymmetric mass loss, the stars thus formed will not be runaway." Their subsequent evolution is likely also to differ from that of a normally-formed single star at their new mass., Their subsequent evolution is likely also to differ from that of a normally-formed single star at their new mass. One might expect them to be rapidly-rotating and have non-ZAMS abundance profiles., One might expect them to be rapidly-rotating and have non-ZAMS abundance profiles. However it is notable that many Blue Straggler stars have low rates of rotation. even though most scenarios for their creation involve mergers or significant amounts of accretion (Leonard Livio 1995. Schónnberner Napiwotzki 1994).," However it is notable that many Blue Straggler stars have low rates of rotation, even though most scenarios for their creation involve mergers or significant amounts of accretion (Leonard Livio 1995, Schönnberner Napiwotzki 1994)." Probably merger products evolve more similarly to secondaries which have undergone accretion than to ZAMS stars., Probably merger products evolve more similarly to secondaries which have undergone accretion than to ZAMS stars. We calculate the O and WR lifetimes of these stars. therefore. by reference to post-accretion secondary models of the corresponding mass.," We calculate the O and WR lifetimes of these stars, therefore, by reference to post-accretion secondary models of the corresponding mass." Tt should be noted that these may not have exactly the same composition. so this comparison is relatively approximate: however. it is probably closer than assuming lifetimes appropriate toa ZAMS star of the new mass.," It should be noted that these may not have exactly the same composition, so this comparison is relatively approximate; however, it is probably closer than assuming lifetimes appropriate to a ZAMS star of the new mass." Systems for which the SN explosion prompts a merger of the new NS and its companion (mainly via the Kick direction being such that the binary is significantly hardened to the point that the new periastron distance is less than the radius of the companion. rather than by direct collision) are fairly uncommon. happening to around | of systems which reach the SN stage.," Systems for which the SN explosion prompts a merger of the new NS and its companion (mainly via the kick direction being such that the binary is significantly hardened to the point that the new periastron distance is less than the radius of the companion, rather than by direct collision) are fairly uncommon, happening to around 1 of systems which reach the SN stage." In this case a Thorne-Zyytkow object is formed (e.g. Podsiadlowski. Cannon Rees 1993).," In this case a Thorne-Żyytkow object is formed (e.g. Podsiadlowski, Cannon Rees 1995)." For systems which remain bound and close after the, For systems which remain bound and close after the "A line-by-line code was used to calculate the opacities for the different gases, assuming a homogeneous mixing of all the different species present in the atmosphere.","A line-by-line code was used to calculate the opacities for the different gases, assuming a homogeneous mixing of all the different species present in the atmosphere." We used a Voigt profile for the individual lines and applied a line wing cut-off of 30 οσα”! to simulate a sub-Lorentzian line profile (e.g.?).., We used a Voigt profile for the individual lines and applied a line wing cut-off of 30 $^{-1}$ to simulate a sub-Lorentzian line profile \citep[e.g.][]{baileyandkedziora11}. This gives rise to a lower continuum and more pronounced absorption features than GJ1214b model results presented elsewhere., This gives rise to a lower continuum and more pronounced absorption features than GJ1214b model results presented elsewhere. " We have chosen to generate three models to make a qualitative study of the atmosphere of GJ1214b, and we have overplotted these models on the observed transmission spectrum shown in Fig. 6."," We have chosen to generate three models to make a qualitative study of the atmosphere of GJ1214b, and we have overplotted these models on the observed transmission spectrum shown in Fig. \ref{fig:tspec0}." " The models were matched to the mean of the measured radius ratios between 0.7 um and 1 um. The first model, the green (dash-dotted) line in Fig. 6,,"," The models were matched to the mean of the measured radius ratios between 0.7 $\mu$ m and 1 $\mu$ m. The first model, the green (dash-dotted) line in Fig. \ref{fig:tspec0}," is for a (geometrically) thick atmosphere with a solar composition and no cloud layers., is for a (geometrically) thick atmosphere with a solar composition and no cloud layers. The concentrations of water and methane are 3-107., The concentrations of water and methane are $\cdot$ $^{-4}$. " The dominant hydrogen gives rise to a high atmospheric scale height, as can be seen by the strong molecular features in the near infrared."," The dominant hydrogen gives rise to a high atmospheric scale height, as can be seen by the strong molecular features in the near infrared." Fig., Fig. " 6 indicates that a solar metallicity atmosphere gives features that are too strong compared to our measurements, resulting in a Y? of 26.7."," \ref{fig:tspec0} indicates that a solar metallicity atmosphere gives features that are too strong compared to our measurements, resulting in a $\chi^2$ of 26.7." " The second model, the red (dashed) line in the figure, is for an atmosphere with a sub-solar metallicity, and includes a grey cloud layer at a pressure of 0.5 bar."," The second model, the red (dashed) line in the figure, is for an atmosphere with a sub-solar metallicity, and includes a grey cloud layer at a pressure of 0.5 bar." The concentrations of, The concentrations of ~0.1 M. 100 Irasunopolskvetal.2011 (Crutcher2005:Troland&Crutcher2008)) A]enetal.2003:Galli dissipation effects.," $\sim 0.1$ $_{\odot}$ $\sim 100$ \citealt{krasnopolsky_etal_2011} \citealt{crutcher_2005, troland_crutcher_2008}) \citealt{allen_etal_2003, galli_etal_2006, price_bate_2007, hennebelle_fromang_2008, mellon_li_2008}) dissipation effects." " The AD. which was first discussed in this context bv Mostel&Spitzer (1956).. has been extensively investigated since then (οον, SpitzerLOGS:Fatuzzo&Adams2002:Zweibel 2002))."," The AD, which was first discussed in this context by \citet{mestel_spitzer_1956}, , has been extensively investigated since then (e.g., \citealt{spitzer_1968, nakano_tademaru_1972, mouschovias_1976, mouschovias_1977, mouschovias_1979, nakano_nakamura_1978, shu_1983, lizano_shu_1989, fiedler_mouschovias_1992, fiedler_mouschovias_1993, li_etal_2008, fatuzzo_adams_2002, zweibel_2002}) )." In principle. AD allows maeuctic flux to be redistributed during the collapse in low ionization regious as the result of the differential motion between the ionized and the neutral eus.," In principle, AD allows magnetic flux to be redistributed during the collapse in low ionization regions as the result of the differential motion between the ionized and the neutral gas." ons Towever. for realistic levels of core magnetization and ionization. recent work has shown that AD does not secu to be sufficient to weaken the maeuetic braking in order to allow rotationally supported disks to form.," However, for realistic levels of core magnetization and ionization, recent work has shown that AD does not seem to be sufficient to weaken the magnetic braking in order to allow rotationally supported disks to form." Iu sole cases. the maeuetic braking has been found to be even chhanced by AD (Mellon&Li 2011).," In some cases, the magnetic braking has been found to be even enhanced by AD \citep{mellon_li_2009, krasnopolsky_konigl_2002, basu_mouschovias_1995, hosking_whitworth_2004, duffin_pudritz_2009, li_etal_2011}." . These findings motivated Krasuopolskyetal.(2010). (see also Lietal. 20111) to examine whether Olunic clissipation could be effective in weakening the magnetic braking., These findings motivated \citet{krasnopolsky_etal_2010} (see also \citealt{li_etal_2011}) ) to examine whether Ohmic dissipation could be effective in weakening the magnetic braking. They claimed that in order to euable the formation of persistent. rotationally supported disks during the protostellarass accretion phase a highlychhanced resistivity. or “lyper-resistivity 4)102? ," They claimed that in order to enable the formation of persistent, rotationally supported disks during the protostellarmass accretion phase a highlyenhanced resistivity, or “hyper-resistivity” $\eta \gtrsim 10^{19}$ " We have discovered emission lines in far-UV spectra of the DO white dwarfKPD0005+5106.,We have discovered emission lines in far-UV spectra of the DO white dwarf. . This is the first detection of photospheric emission lines in this spectral range of any hot white dwarf., This is the first detection of photospheric emission lines in this spectral range of any hot white dwarf. Provencal (2005) discovered low-ionisation emission lines in UV spectra of two relatively cool (Teg KK) He-rich white dwarfs (spectral type DQ)., Provencal (2005) discovered low-ionisation emission lines in UV spectra of two relatively cool $\approx$ K) He-rich white dwarfs (spectral type DQ). " It was shown, however, that they are chromospheric in origin."," It was shown, however, that they are chromospheric in origin." TheCaX lines are the highest ionisation stage of any element identified in any stellar photosphere., The lines are the highest ionisation stage of any element identified in any stellar photosphere. Our discovery also represents the first identification of calcium in hot (pre-) WDs., Our discovery also represents the first identification of calcium in hot (pre-) WDs. The Ca abundance in iis in the range times solar, The Ca abundance in is in the range times solar. A more precise determination from the emission lines is not possible., A more precise determination from the emission lines is not possible. A comparison of this result with predictions from radiative levitation/gravitational diffusion equilibrium theory is difficult because aand oof aare outside of the range considered by Chayer (1995; their 220)., A comparison of this result with predictions from radiative levitation/gravitational diffusion equilibrium theory is difficult because and of are outside of the range considered by Chayer (1995; their 20). " For the closest parameters -211300000KK, 277) a huge overabundance is predicted (2500 times solar)."," For the closest parameters K, 7) a huge overabundance is predicted (2500 times solar)." Our estimate for iis smaller (6.2-6.5) which would result in an even higher overabundance., Our estimate for is smaller (6.2–6.5) which would result in an even higher overabundance. " On the other hand it is impossible to make a solid estimate for the effect of the higher KK) on the behaviour of the Ca equilibrium abundance, because the dominant ionisation stage in lisxr, while it is in the hottest Chayer model KK, 277.5)."," On the other hand it is impossible to make a solid estimate for the effect of the higher K) on the behaviour of the Ca equilibrium abundance, because the dominant ionisation stage in is, while it is in the hottest Chayer model K, 7.5)." " Looking at the behaviour of other elements (S, Ar) namely how their equilibrium abundance changes when their (respective isoelectronic) ionisation stages increase (with increasing ΊΤε)), it is suggestive that the Ca abundance at KK is lower than at KK, but not by orders of magnitude."," Looking at the behaviour of other elements (S, Ar), namely how their equilibrium abundance changes when their (respective isoelectronic) ionisation stages increase (with increasing ), it is suggestive that the Ca abundance at K is lower than at K, but not by orders of magnitude." " Although detailed calculations are required for a definitive statement, we conclude that the atmosphere of iis probably not in levitation/diffusion equilibrium."," Although detailed calculations are required for a definitive statement, we conclude that the atmosphere of is probably not in levitation/diffusion equilibrium." " This is confirmed by the diffusion/mass-loss calculations of Unglaub Bues (2000) which suggest that hhas yet to cross the wind-limit on its evolutionary track, meaning that mass-loss is large enough to prevent both gravitational settling and the accumulation of radiatively supported heavy elements."," This is confirmed by the diffusion/mass-loss calculations of Unglaub Bues (2000) which suggest that has yet to cross the wind-limit on its evolutionary track, meaning that mass-loss is large enough to prevent both gravitational settling and the accumulation of radiatively supported heavy elements." " In this case, lis not a descendant of the PG1159 stars."," In this case, is not a descendant of the PG1159 stars." An evolutionary link to the He-dominated central stars of spectral type O(He) and to the RCrB stars has been suggested (Werner 2008)., An evolutionary link to the He-dominated central stars of spectral type O(He) and to the RCrB stars has been suggested (Werner 2008). " If unaffected by diffusion processes, then the photospheric composition of iis the consequence of previous evolutionary phases."," If unaffected by diffusion processes, then the photospheric composition of is the consequence of previous evolutionary phases." " In contrast, the presence of Ca in the atmospheres of cooler white dwarfs (spectral types DAZ and DBZ, with low-ionisation optical Ca absorption lines) requires on-going accretion of circumstellar matter, because gravitational settling rapidly removes heavy elements from the photosphere KKoester Wilken 2006)."," In contrast, the presence of Ca in the atmospheres of cooler white dwarfs (spectral types DAZ and DBZ, with low-ionisation optical Ca absorption lines) requires on-going accretion of circumstellar matter, because gravitational settling rapidly removes heavy elements from the photosphere Koester Wilken 2006)." " The non-detection of the Ad 1137, llines in the hottest PG1159 stars is explained by undetectably weak absorption line features in the models."," The non-detection of the $\lambda\lambda$ 1137, lines in the hottest PG1159 stars is explained by undetectably weak absorption line features in the models." " Another line pair (AA 1462, AA)) is possibly present in absorption in aand suggests a roughly solar Ca abundance."," Another line pair $\lambda\lambda$ 1462, ) is possibly present in absorption in and suggests a roughly solar Ca abundance." " The only other object in which we discovered the Ad 1137, eemission lines is the [WCE]-type central star 22371."," The only other object in which we discovered the $\lambda\lambda$ 1137, emission lines is the [WCE]-type central star 2371." This corroborates the extraordinarily high effective temperature ofthis object., This corroborates the extraordinarily high effective temperature ofthis object. Superclusters of ealaxies represeut the largest known conglomerations «X both visible aud dark matter in the universe (IaBiukovetal.1998).,Superclusters of galaxies represent the largest known conglomerations of both visible and dark matter in the universe \citep{kal98}. ". Given the complex 1norphologies of superclusters (c.g.deLappareut.Celler.&IIchra1986:al.2000:Diiukwateret 2001)... as well as their huge scale (ο,ο,,Zuccaetal.1993:Eimastoct2001) and potential alguiment within the loca universe (Tullyetal.1992)... superclusters pose unique challenges for sccnarios of the erowth of aud inter-relationship leTween structures on al scales; such as the hierarchical structure formation picture (Bauehetal.2000:Motl2t08)."," Given the complex morphologies of superclusters \citep[e.g.,][]{del86,hay86,wes95,bar98,bar00,dri04}, as well as their huge scale \citep[e.g.,][]{zuc93,ein01} and potential alignment within the local universe \citep{tul92}, superclusters pose unique challenges for scenarios of the growth of and inter-relationship between structures on all scales, such as the hierarchical structure formation picture \citep{bau00,mot04}." Detailed studies of the supercluster environment require extensive redshift information over larec areas of the sky. παρug both the iutra- aud iuter-cluster regions (Dardellietal.2000)... Wide-field.," Detailed studies of the supercluster environment require extensive redshift information over large areas of the sky, sampling both the intra- and inter-cluster regions \citep{bar00}. Wide-field," iulti-hber spectrographlis are ideally suited o this task. as they pαι three-dinieuslonal xobiug of structures on uegaparsecHH scales.," multi-fiber spectrographs are ideally suited to this task, as they permit three-dimensional probing of structures on megaparsec scales." The range of structures identified as superchisters varies widely in terms of norpholoey aud sizc, The range of structures identified as superclusters varies widely in terms of morphology and size. On he one hand there are superclusters coutainiug just a few major galaxy custers connected by long spiralrich salaxw filaiecits., On the one hand there are superclusters containing just a few major galaxy clusters connected by long spiral-rich galaxy filaments. Two such examples are the Coma Supoercluser (Cregorv&Thomp-West.Joues.&Forman1995) and the 1cΑΝ Disces-Perseus Supercluser (Tlavues&Cüoviulli1956:Chamarausetal. 1990).," Two such examples are the Coma Supercluster \citep{gre78,del86,wes95} and the nearby Pisces-Perseus Supercluster \citep{hay86,cha90}." . Iu coutrast. «Xther structures are perhaps more readily cliiracterized w the presence of rich clusters. frou the few in the Hercules Superchster (Barmby&Ihchia1998) to those containine ou the order of twenty uajor clusters. as iu fre case of the Shilev supercluster (e.g...Bardelietal.2000:Quintajaetal.2000:Diiukwateret1999.200 1).," In contrast, other structures are perhaps more readily characterized by the presence of rich clusters, from the few in the Hercules Supercluster \citep{bar98} to those containing on the order of twenty major clusters, as in the case of the Shapley supercluster \citep[e.g.,][]{bar00,qui00,dri99,dri04}." . In these atter cases. there is evicently a rich variev of substructure present iu fhese large-scale eutities.," In these latter cases, there is evidently a rich variety of substructure present in these large-scale entities." Finally. Tullyetal.(1992) have found tha the superclusters within the local universe exhivit a pronounced tendeucy to align within the preferred plane of the Vireo Su]xvYeluster. represeutiug a structure ou the scale of —0.1c.," Finally, \citet{tul92} have found that the superclusters within the local universe exhibit a pronounced tendency to align within the preferred plane of the Virgo Supercluster, representing a structure on the scale of $\sim$ 0.1c." " Originally noted by Shiiplev (1935) as exlubiting ""a considerable departure from uuiforii distribution.” the IHorologimmu-Roeticulum Supercluster (IRS) is now recognized as one of the largest superclusters in the local universe (Luceyetal.19823:Zucca1993:Einastoetal.2001).. containing more than twenty Abell clusters (AbellCorwin&Olowin1989.hereafterACO).."," Originally noted by Shapley (1935) as exhibiting “a considerable departure from uniform distribution,” the Horologium-Reticulum Supercluster (HRS) is now recognized as one of the largest superclusters in the local universe \citep{luc83, zuc93, ein01}, containing more than twenty Abell clusters \citep[][hereafter ACO]{aco89}." " The IIRS covers au area of the «kv in excess of LOO square degrees. centered at approximately à=0319"",8— —507002"" citepzuct3.."," The HRS covers an area of the sky in excess of 100 square degrees, centered at approximately $\alpha = 03^h19^m, \delta = $ $-$ \\citep{zuc93}." Ta fact. iu terms of mass concentrations within 200 AIpe. the TRS stands as second only to the Shapley supercluster (ITudsonuetal.1999:Linastoctal.2001).," In fact, in terms of mass concentrations within 200 Mpc, the HRS stands as second only to the Shapley supercluster \citep{hud99,ein01}." . It is of imterest to note that while the Shapley supercluster lies witlin the preferred. plane discussed by Tullyetal.(1992).. the IIRS lies more than 150 Mpc outside of that plane.," It is of interest to note that while the Shapley supercluster lies within the preferred plane discussed by \citet{tul92}, the HRS lies more than 150 Mpc outside of that plane." Recent studies in the URS have focused exclusively upon the rich clusters in the region., Recent studies in the HRS have focused exclusively upon the rich clusters in the region. EKatgertet suunuuize the redshift inforination from the ESO Nearby Abell Clusters Survey (ENACS). which investigated ACO cluster cores throughout the IIRS (specifically A3093.. A3108. ΑΟ. A3I12. ÀS128.. ABLLL and A3158).," \citet{kat98} summarize the redshift information from the ESO Nearby Abell Clusters Survey (ENACS), which investigated ACO cluster cores throughout the HRS (specifically A3093, A3108, A3111, A3112, A3128, A3144, and A3158)." Roseetal.(2002) examined the imereing double-cluster system A3I25/A3128. which is located in the Southeast portion of the IRS.," \citet{ros02} examined the merging double-cluster system A3125/A3128, which is located in the Southeast portion of the HRS." This multiswaveleugth study revealed a nunuber of rapidly infalliuge eroups and flauenuts. which were accelerated by the URS potential.," This multi-wavelength study revealed a number of rapidly infalling groups and filaments, which were accelerated by the HRS potential." " The results from their observations nuplv that the TRS coutains evolving substructures on a wide range of nass scales,", The results from their observations imply that the HRS contains evolving substructures on a wide range of mass scales. To date. no studies lave been carried out that concentrate upon the dynamical state of the IIRS euviromneut outside of the rich clusters.," To date, no studies have been carried out that concentrate upon the dynamical state of the HRS environment outside of the rich clusters." To remedy this situation for the IIRS. we have initiated a wide-field. spectroscopic study of the iuter-cluster regions. and the initial results of our study are presented here.," To remedy this situation for the HRS, we have initiated a wide-field, spectroscopic study of the inter-cluster regions, and the initial results of our study are presented here." Specifically. we report here on the largest scale spatialkinematic features found in our data.," Specifically, we report here on the largest scale spatial-kinematic features found in our data." Iu 22. we describe the redshift sample. from the ealaxy sclection to the determination of optical redshifts.," In 2, we describe the redshift sample, from the galaxy selection to the determination of optical redshifts." The four primary results of the studs. all relating to large-scale kinematic features in the IIRS. are presented in 33.," The four primary results of the study, all relating to large-scale kinematic features in the HRS, are presented in 3." In li we compare our results from the IIRS with studies of the Shapley Supercluster. the largest," In 4 we compare our results from the HRS with studies of the Shapley Supercluster, the largest" expected spectral evolution.,expected spectral evolution. The implication is that the mass-radius relation derived in Steiner et al. (, The implication is that the mass-radius relation derived in Steiner et al. ( 2010) would shift to higher radii as a result of using the more reliable “long” PRE bursts. and thus farther away from our derived upper limits.,"2010) would shift to higher radii as a result of using the more reliable “long” PRE bursts, and thus farther away from our derived upper limits." A smaller hydrogen fraction at the photosphere in wwould increase the R. limits and make them consistent with the theoretical calculations and the mass-radius curve from Steiner et al. (, A smaller hydrogen fraction at the photosphere in would increase the $R_\infty$ limits and make them consistent with the theoretical calculations and the mass-radius curve from Steiner et al. ( 2010).,2010). " We can get an impression of what the upper limit on R4. would be for an atmosphere with a reduced hydrogen fraction by first looking at the extreme case of the pure helium atmosphere. and its derived upper limit of 21.5 km for log,)(g)=14.3 (see Figure 5))."," We can get an impression of what the upper limit on $R_\infty$ would be for an atmosphere with a reduced hydrogen fraction by first looking at the extreme case of the pure helium atmosphere, and its derived upper limit of $21.5$ km for $\log_{10}(g)=14.3$ (see Figure \ref{fig:mr}) )." Such an upper limit is consistent with theoretical calculations and the results from Steiner et al. (, Such an upper limit is consistent with theoretical calculations and the results from Steiner et al. ( 2010).,2010). We can go one step farther and estimate the hydrogen fraction we would require to have such a consistency with previous results using Equation 19.., We can go one step farther and estimate the hydrogen fraction we would require to have such a consistency with previous results using Equation \ref{eq:rinflim}. " Assuming a surface gravity of log,(g)=14.3. an upper limit on R4. of ~16 km or more would be required."," Assuming a surface gravity of $\log_{10}(g)=14.3$, an upper limit on $R_\infty$ of $\sim$ 16 km or more would be required." " Using values for Fjjj; and A averaged across the solar H/He model fits with log,;(g)=14.3. we estimate that a hydrogen fraction of X~0.5 or less would be needed."," Using values for $F_{\rm Edd}$ and $A$ averaged across the solar H/He model fits with $\log_{10}(g)=14.3$, we estimate that a hydrogen fraction of $X\approx0.5$ or less would be needed." We are assuming that such a spectral model would not differ too greatly in shape from the solar H/He models., We are assuming that such a spectral model would not differ too greatly in shape from the solar H/He models. Galloway et al. (, Galloway et al. ( 2004) find that the theoretical variations in. burst properties with persistent flux between ignition models with X=0.7 and X=0.5 are largely indistinguishable.,2004) find that the theoretical variations in burst properties with persistent flux between ignition models with X=0.7 and X=0.5 are largely indistinguishable. However. more burst lighteurve simulations would be necessary to establish whether agreement with observed lighteurves ts still possible with a reduced accreted hydrogen fraction.," However, more burst lightcurve simulations would be necessary to establish whether agreement with observed lightcurves is still possible with a reduced accreted hydrogen fraction." " Given that the upper limit on R4, depends on the color correction as (via A in equation 19)). even a small increase in the fivalue of f; would yield a ~22% increase in the upper limit on A4."," Given that the upper limit on $R_{\infty}$ depends on the color correction as $f_c^4$ (via $A$ in equation \ref{eq:rinflim}) ), even a small increase in the value of $f_c$ would yield a $\sim22\%$ increase in the upper limit on $R_{\infty}$." Furthermore. Suleimanov et al. (," Furthermore, Suleimanov et al. (" "2011b) discuss large color correction factors of f,= 1.6-1.8 (cf.",2011b) discuss large color correction factors of $f_c=1.6$ $1.8$ (cf. also Suleimanov Poutanen 2006) possibly arising from a spreading layer associated with accretion onto the neutron star equator., also Suleimanov Poutanen 2006) possibly arising from a spreading layer associated with accretion onto the neutron star equator. Perhaps in ssomething similar is happening. although the increase in color correction required is not as large.," Perhaps in something similar is happening, although the increase in color correction required is not as large." " It is worth noting that changing the visible area. for example by blocking one hemisphere of the neutron star with the accretion disk during the burst. does not change the inferred limits on radius because the limit on Rj is independent of the anisotropy factor £, (isotropic emission from only half the area is equivalent to setting £5= 2)."," It is worth noting that changing the visible area, for example by blocking one hemisphere of the neutron star with the accretion disk during the burst, does not change the inferred limits on radius because the limit on $R_\infty$ is independent of the anisotropy factor $\xi_b$ (isotropic emission from only half the area is equivalent to setting $\xi_b=2$ )." There are several points to keep in mind when looking at our derived constraints on M and Α., There are several points to keep in mind when looking at our derived constraints on $M$ and $R$ . First. the constraints are only partly self-consistent in the sense that the lightcurve model used to fit the data does not have the same gravity as the derived M. and R.," First, the constraints are only partly self-consistent in the sense that the lightcurve model used to fit the data does not have the same gravity as the derived $M$ and $R$." Heger et al. (, Heger et al. ( 2007) (and Woosley et al.,2007) (and Woosley et al. 2004) used a specific choice of gravity in their X-ray burst simulations., 2004) used a specific choice of gravity in their X-ray burst simulations. " As we argue in §4. the lightcurve probably does not depend too sensitively on gravity. but additional simulations are needed to check this. and to calculate the uncertainty in the predicted model flux which enters in equation (5)) relating f, and {ες"," As we argue in 4, the lightcurve probably does not depend too sensitively on gravity, but additional simulations are needed to check this, and to calculate the uncertainty in the predicted model flux which enters in equation \ref{eq:fczcorr}) ) relating $f_c$ and $1+z$." On the other hand. for the comparison to spectral models. in Figure 5.. the upper limits on Ry. represented by the solid colored curves. are placed in such a way as to coincide with the appropriate curve of constant surface gravity. consistent with the atmosphere spectral models used to derive those upper limits.," On the other hand, for the comparison to spectral models, in Figure \ref{fig:mr}, the upper limits on $R_{\infty}$, represented by the solid colored curves, are placed in such a way as to coincide with the appropriate curve of constant surface gravity, consistent with the atmosphere spectral models used to derive those upper limits." A second issue is that the upper limit on Α. from the spectral models is based on fitting the initial part of the cooling tail only., A second issue is that the upper limit on $R_\infty$ from the spectral models is based on fitting the initial part of the cooling tail only. We found that at first the slope of K with flux agrees well with the theoretical models of f..., We found that at first the slope of $K^{-1/4}$ with flux agrees well with the theoretical models of $f_c$. In the latter part of the burst. however. at lower fluxes. the agreement breaks down.," In the latter part of the burst, however, at lower fluxes, the agreement breaks down." For ΕΠ<0.2-0.3. K!* increases with decreasing flux. but more rapidly than expected based on the predicted f. values. particularly those given by the solar metallicity models.," For $F/F_{\rm Edd}\lesssim 0.2-0.3$, $K^{-1/4}$ increases with decreasing flux, but more rapidly than expected based on the predicted $f_c$ values, particularly those given by the solar metallicity models." Some other explanation is required for the rapid increase in. f£. and corresponding decrease in blackbody normalization in the tail of the burst., Some other explanation is required for the rapid increase in $f_c$ and corresponding decrease in blackbody normalization in the tail of the burst. " In ""t Zand et al. (", In 't Zand et al. ( 2009) suggest that this decrease could be due to incorrect subtraction of the persistent emission. in particular. the subtraction of a thermal component that comes from the neutron star surface during accretion which ts no longer present during the burst.,"2009) suggest that this decrease could be due to incorrect subtraction of the persistent emission, in particular, the subtraction of a thermal component that comes from the neutron star surface during accretion which is no longer present during the burst." Van Paradis Lewin (1986) pointed out that this effect should become important during the tail of the burst. when the burst flux becomes comparable to that of the accretion.," Van Paradijs Lewin (1986) pointed out that this effect should become important during the tail of the burst, when the burst flux becomes comparable to that of the accretion." Looking at Figure 3.. the observations and the low metallicity (solar metallicity) models begin to deviate at fluxes below MS«107 Cz10% s) compared to the persistent flux of 2.1«107s7!..," Looking at Figure \ref{fig:fit}, the observations and the low metallicity (solar metallicity) models begin to deviate at fluxes below $\sim 5\times10^{-9}$ $\gtrsim 10^{-8}$ ) compared to the persistent flux of $2.1\times10^{-9}$." The disagreement between the observations and models begins sooner following the burst peak for solar metallicity than for low metallicity models because the former have a depression in 7. at low fluxes ΕΠ&0.3 (see Figure 3)) arising from absorption edges in. partially-ionized Fe (Suleimanov et al.," The disagreement between the observations and models begins sooner following the burst peak for solar metallicity than for low metallicity models because the former have a depression in $f_c$ at low fluxes $F/F_{\rm Edd}\lesssim 0.3$ (see Figure \ref{fig:fit}) ), arising from absorption edges in partially-ionized Fe (Suleimanov et al." 2011b)., 2011b). There is no sign of such a dip in the observations of1826—24., There is no sign of such a dip in the observations of. . This suggests a low metallicity in the photosphere. contrasting with the conclusions of Galloway et al. (," This suggests a low metallicity in the photosphere, contrasting with the conclusions of Galloway et al. (" 2004) and Heger et al. (,2004) and Heger et al. ( 2007) who argued that the metallicity was solar. based on burst lighteurves and energetics.,"2007) who argued that the metallicity was solar, based on burst lightcurves and energetics." A way to reconcile these disparate results is to consider the possibility that Fe. whose presence has a significant influence on the spectrum but not on the burst energetics. may be absent from the atmosphere during bursts.," A way to reconcile these disparate results is to consider the possibility that Fe, whose presence has a significant influence on the spectrum but not on the burst energetics, may be absent from the atmosphere during bursts." If aceretion halts during the burst. then Fe will rapidly sink through the atmosphere (Bildsten. Chang. Paerels 2003).," If accretion halts during the burst, then Fe will rapidly sink through the atmosphere (Bildsten, Chang, Paerels 2003)." On the other hand. since bursts from aare all sub-Eddington. aecretion may continue during the burst. resupplying Fe to the photosphere.," On the other hand, since bursts from are all sub-Eddington, accretion may continue during the burst, resupplying Fe to the photosphere." Furthermore. while disk accretion only deposits mass near the equator. the accreted mass spreads faster latitudinally Cz0.1s: Inogamov Sunyaev 1999; Piro Bildsten 2007) than the timescale for Fe to sink through the atmosphere of ~I s. Proton spallation could also destroy a substantial amount of the accreted Fe (Bildsten. Chang. Paerels 2003).," Furthermore, while disk accretion only deposits mass near the equator, the accreted mass spreads faster latitudinally $\lesssim0.1\,$ s; Inogamov Sunyaev 1999; Piro Bildsten 2007) than the timescale for Fe to sink through the atmosphere of $\sim1\,$ s. Proton spallation could also destroy a substantial amount of the accreted Fe (Bildsten, Chang, Paerels 2003)." It should be noted that X-ray bursts produce à wide range of elements in their ashes which could significantly alter the spectrum., It should be noted that X-ray bursts produce a wide range of elements in their ashes which could significantly alter the spectrum. However. mixing of burned material to the photosphere is thought not to occur due to the substantial entropy barrier (Joss 1977; Weinberg. Bildsten. Schatz 2006).," However, mixing of burned material to the photosphere is thought not to occur due to the substantial entropy barrier (Joss 1977; Weinberg, Bildsten, Schatz 2006)." Another important unresolved issue 1s the changing spectral normalization K with accretion rate., Another important unresolved issue is the changing spectral normalization $K$ with accretion rate. The blackbody normalization K is z20% smaller for the 4.07 hr recurrence time bursts than the 5.74 hr recurrence time bursts., The blackbody normalization $K$ is $\approx 20$ smaller for the 4.07 hr recurrence time bursts than the 5.74 hr recurrence time bursts. We cannot explain this difference by changing the composition at the photosphere and therefore changing f; (see discussion in $5.3)., We cannot explain this difference by changing the composition at the photosphere and therefore changing $f_c$ (see discussion in 5.3). .. Also. it seems unlikely that a major change in composition would occur with only a ~50% change in accretion rate and smaller change in. burst energy andlightcurves.," Also, it seems unlikely that a major change in composition would occur with only a $\approx 50$ change in accretion rate and smaller change in burst energy andlightcurves." As mentioned previously in $6. Suleimanov et al. (," As mentioned previously in 6, Suleimanov et al. (" 201Ib) discuss large color correction factors associated with accretion onto the neutron star equator. which they suggest accounts for the variations in measured K. for the,"2011b) discuss large color correction factors associated with accretion onto the neutron star equator, which they suggest accounts for the variations in measured $K$ for the" band. which has a very small central depth due to its intrinsic broadness.,"band, which has a very small central depth due to its intrinsic broadness." The hypothesis that iis a diffuse interstellar band carrier has been very attractive on spectroscopic grounds alone — no previously proposed carrier has come so close to providing a wavelength match to any set of the diffuse bands., The hypothesis that is a diffuse interstellar band carrier has been very attractive on spectroscopic grounds alone — no previously proposed carrier has come so close to providing a wavelength match to any set of the diffuse bands. There are strong chemical arguments against this hypothesis: chemical models (Ruffleetal.1999) are unable to reproduce the necessary abundance ofC;.. even with the most favorable assumptions.," There are strong chemical arguments against this hypothesis: chemical models \citep{ruffle} are unable to reproduce the necessary abundance of, even with the most favorable assumptions." This is due in large part to the destruction of bby hydrogen atoms. which has been recently confirmed to proceed with a fast rate coefficient (Barckholtz.Snow.andBierbaum 2001).," This is due in large part to the destruction of by hydrogen atoms, which has been recently confirmed to proceed with a fast rate coefficient \citep{bierbaum}." . In spite of these chemical arguments. the approximate coincidence between the aand DIB wavelengths has been too close to ignore. given the uncertainties inherent in the previously available laboratory and astronomical work.," In spite of these chemical arguments, the approximate coincidence between the and DIB wavelengths has been too close to ignore, given the uncertainties inherent in the previously available laboratory and astronomical work." Armed with the spectroscopic constants of ffrom Lakinetal.(2000) and our improved sample of DIB observations. however. it is now clear that Πας the stringent tests enabled by high resolution spectroscopy.," Armed with the spectroscopic constants of from \citet{lakin} and our improved sample of DIB observations, however, it is now clear that fails the stringent tests enabled by high resolution spectroscopy." The origin band does not match A6270 in wavelength or profile. and there is no sign of the higher-lying ()'=3/2 component.," The origin band does not match $\lambda$ 6270 in wavelength or profile, and there is no sign of the higher-lying $\Omega''$ =3/2 component." The 1] band is way off in wavelength from A5610 (— 2 A)) and also does not agree with the profile of the DIB., The $1^1_0$ band is way off in wavelength from $\lambda$ 5610 $\sim$ 2 ) and also does not agree with the profile of the DIB. The DIB attributed to the 2! band turns out to be a stellar line., The DIB attributed to the $2^1_0$ band turns out to be a stellar line. The 3) band does not match A6065 in wavelength or profile., The $3^1_0$ band does not match $\lambda$ 6065 in wavelength or profile. " Finally. the DIBs attributed to the 173, band (A4964) and the origin band (46270) do not vary together in intensity. and therefore do not share a common carrier."," Finally, the DIBs attributed to the $1^2_03^1_0$ band $\lambda$ 4964) and the origin band $\lambda$ 6270) do not vary together in intensity, and therefore do not share a common carrier." Close as the wavelength match appeared to be at first sight. there now seems to be no evidence to support the hypothesis that iis a carrier of the diffuse interstellar bands.," Close as the wavelength match appeared to be at first sight, there now seems to be no evidence to support the hypothesis that is a carrier of the diffuse interstellar bands." The authors thank J. P. Maier and his research group for providing their laboratory data in advance of publication., The authors thank J. P. Maier and his research group for providing their laboratory data in advance of publication. This work has made use of the NASA Astrophysies Data Service. as well as the SIMBAD database at the Centre de Donnéees astronomiques de Strasbourg.," This work has made use of the NASA Astrophysics Data Service, as well as the SIMBAD database at the Centre de Donnéees astronomiques de Strasbourg." This work has been supported by NSF grant PHYS-972269] and NASA grant NAGS-4070., This work has been supported by NSF grant PHYS-9722691 and NASA grant NAG5-4070. hhas been supported by the Fannie and John Hertz Foundation., has been supported by the Fannie and John Hertz Foundation. It is now known that the history of cosmic star formation and luminous AGN activity track each other rather well. both showing a dramatic decline between z2 and the presentday. (Franceschinietal.1999).,"It is now known that the history of cosmic star formation and luminous AGN activity track each other rather well, both showing a dramatic decline between $z \sim 2$ and the presentday \citep{franceschini99}." . Their legacy. the prevalence of massive black holes today and (he proportionality between black hole mass and the mass of their host galaxy spheroids (Merritt&Ferrarese2001).. is most easily explained if the formation of the two components was coeval. i.e. (he black hole was built up by accretion of the same eas (hat rapidly formed the stars of the spheroid.," Their legacy, the prevalence of massive black holes today \citep{yu02} and the proportionality between black hole mass and the mass of their host galaxy spheroids \citep{merritt01}, is most easily explained if the formation of the two components was coeval, i.e. the black hole was built up by accretion of the same gas that rapidly formed the stars of the spheroid." During this formation episode. (he average bolometrie luminosity of the stellar component is expected to exceed that emitted by the AGN bv a [actor of a few (Pageοἱal.2001a)..," During this formation episode, the average bolometric luminosity of the stellar component is expected to exceed that emitted by the AGN by a factor of a few \citep{page01sci}." Under such circumstances. a large fraction of stellar mass must have built up around the AGN that dominate the accretion power of the Universe. because these were responsible for the majority of present day. black hole mass.," Under such circumstances, a large fraction of stellar mass must have built up around the AGN that dominate the accretion power of the Universe, because these were responsible for the majority of present day black hole mass." " The bulk of the comoving luminositv density was produced by objects wilh luminosities close to the break huminositv £,. on account of the AGN Iuminosity funcetion at any reclshilt being characterised bv a broken power law (Pageetal.1997:Bovle2000)."," The bulk of the comoving luminosity density was produced by objects with luminosities close to the break luminosity $L_{*}$, on account of the AGN luminosity function at any redshift being characterised by a broken power law \citep{page97,boyle00}." .. While the X-rav background is chiefly produced by AGN at 2< (eg.Dargeretal.2001).. the Iuminositv density of AGN was at its peak between z=1 and =3 (Pageet 2001).," While the X-ray background is chiefly produced by AGN at $z<2$ \citep[e.g.][]{barger01}, the luminosity density of AGN was at its peak between $z=1$ and $z=3$ \citep{page97,miyaji01}." ". Therefore coeval black hole / stellar bulge formation would imply that a large traction of the Universe's star formation took place around AGN with | \dot{m_1}$ despite $m_2 0) but there are not any spatial variations., The wave is in the propagating domain in the internal part of the loop $k_{\mathrm i}^2 >0$ ) but there are not any spatial variations. For realistic values of k.R=(xRy/L the pressure perturbation and the divergence of the displacement field are zero for all practical purposes., For realistic values of $k_z R = (\pi R)/L $ the pressure perturbation and the divergence of the displacement field are zero for all practical purposes. The kink mode is to a high degree of accuracy an incompressible wave with very small magnetic pressure perturbations., The kink mode is to a high degree of accuracy an incompressible wave with very small magnetic pressure perturbations. " Apart from &, the wave quantities are continuous at r= R.", Apart from $\xi_{\varphi}$ the wave quantities are continuous at $r= R$ . &£. varies in à discontinuous manner at 7r=R with opposite values at R. and R.., $\xi_{\varphi}$ varies in a discontinuous manner at $r=R$ with opposite values at $R_<$ and $R_>$. This discontinuous behaviour is due to the change of sign of the factor «—ως when we move from the interior to the exterior of the loop., This discontinuous behaviour is due to the change of sign of the factor $\omega^2 - \omega_{\mathrm A}^2$ when we move from the interior to the exterior of the loop. The behaviour of £. creates strong shear layers which might undergo Kelvin-Helmholtz type instabilities as shown by Terradasetal.(2005)., The behaviour of $\xi_{\varphi}$ creates strong shear layers which might undergo Kelvin-Helmholtz type instabilities as shown by \cite{Terradas2008}. So far we have described the properties of modes that involve non-zero total pressure (Pz 0)., So far we have described the properties of modes that involve non-zero total pressure $P'\neq 0$ ). However. if the medium is uniform the system of equations given by (1)) also allows pure incompressible Alfvénn waves.," However, if the medium is uniform the system of equations given by \ref{MHDwavesNoPressure1}) ) also allows pure incompressible Alfvénn waves." They are only driven by magnetic tension. their eigenfrequency is simply €)=wa and the total pressure. P’. is equal to zero.," They are only driven by magnetic tension, their eigenfrequency is simply $\omega=\omega_{\mathrm A}$ and the total pressure, $P'$, is equal to zero." To have such modes the displacement has to satisfy V-£=0., To have such modes the displacement has to satisfy $\nabla \cdot \vec{\xi} =0$. In cylindrical coordinates this means that. If we prescribe the radial dependence of one of the components of the displacement. we can easily calculate the other component from the previous equation.," In cylindrical coordinates this means that, If we prescribe the radial dependence of one of the components of the displacement, we can easily calculate the other component from the previous equation." " The case m=0 is à particular solution that represents torsional Alfvénn waves (€,=0. &-v arbitrary). but equation (22)) can be solved for any azimuthal wavenumber 7i."," The case $m=0$ is a particular solution that represents torsional Alfvénn waves $\xi_r=0$, $\xi_\varphi$ arbitrary), but equation \ref{Alfincompress}) ) can be solved for any azimuthal wavenumber $m$." Let us concentrate on 1=| and the homogeneous loop model., Let us concentrate on $m=1$ and the homogeneous loop model. Now we can have two different incompressible Alfvénn waves., Now we can have two different incompressible Alfvénn waves. One inside oscillating at the frequency c; and another outside oscillating at wa.., One inside oscillating at the frequency $\omega_{\mathrm {Ai}}$ and another outside oscillating at $\omega_{\mathrm {Ae}}$. However. it is Important to note that in such a configuration the radial displacement of the internal and external Alfvénn waves has to vanish at r=R (otherwise the continuity of the radial component is not guaranteed). 1.9. the modes are localised in regions of constant Alfvénn frequency.," However, it is important to note that in such a configuration the radial displacement of the internal and external Alfvénn waves has to vanish at $r=R$ (otherwise the continuity of the radial component is not guaranteed), i.e. the modes are localised in regions of constant Alfvénn frequency." This means that an internal incompressible Alfvénn wave is unable to laterally displace the full tube (it cannot displace the tube boundary). although it is able to produce an incompressible motion of the loop axis at its surroundings (for mi= I).," This means that an internal incompressible Alfvénn wave is unable to laterally displace the full tube (it cannot displace the tube boundary), although it is able to produce an incompressible motion of the loop axis at its surroundings (for $m=1$ )." Since these pure incompressible Alfvénn waves do not move the whole tube hereafter we will focus again on the kink solutions with P'£z0., Since these pure incompressible Alfvénn waves do not move the whole tube hereafter we will focus again on the kink solutions with $P'\neq 0$. Contrary to the incompressible Alfvénn waves these waves (with Pz0) are able to connect the internal and external medium and to produce a coherent motion of the system because of their mixed nature., Contrary to the incompressible Alfvénn waves these waves (with $P'\neq 0$ ) are able to connect the internal and external medium and to produce a coherent motion of the system because of their mixed nature. The fact that P is small but different from zero plays a fundamental role in the mixed properties of these kink waves., The fact that $P'$ is small but different from zero plays a fundamental role in the mixed properties of these kink waves. The analytic expressions (21)) (P#0) have been obtained in the limit A-R<<1., The analytic expressions \ref{SolutionsNoPr2}) ) $P'\neq 0$ ) have been obtained in the limit $k_z R << 1$. It is straightforward to solve the dispersion relation (15)) and calculate the spatial solutions (14))., It is straightforward to solve the dispersion relation \ref{DRNoPr1}) ) and calculate the spatial solutions \ref{SolutionsNoPr1}) ). This allows us to determine how the analytical expressions. are modified by effects due to a finite radius., This allows us to determine how the analytical expressions are modified by effects due to a finite radius. In Figure | the eigenfunctions of three loops with different radi are represented., In Figure \ref{eigen} the eigenfunctions of three loops with different radii are represented. It is clear that the spatial profile is well described by the approximated solutions in the TT limit given. by equations (21))., It is clear that the spatial profile is well described by the approximated solutions in the TT limit given by equations \ref{SolutionsNoPr2}) ). The radial and azimuthal components. are constant inside the loop. the azimuthal component has the expected jump at r=R. while the total pressure grows linearly with the radius.," The radial and azimuthal components are constant inside the loop, the azimuthal component has the expected jump at $r=R$, while the total pressure grows linearly with the radius." Increasing R results m an increase of the total pressure. and thus compressibility. since this magnitude is proportional to (Κ.Δ.," Increasing $R$ results in an increase of the total pressure, and thus compressibility, since this magnitude is proportional to $(k_zR)^2$." Interestingly. for fat loops (see the case R/L= 0.1) the TT approximations of the eigenfunctions are still quite valid.," Interestingly, for fat loops (see the case $R/L=0.1$ ) the TT approximations of the eigenfunctions are still quite valid." An analysis of the forces (not shown here) indicates that. even for thick loops. the tension dominates over the magnetic pressure gradient.," An analysis of the forces (not shown here) indicates that, even for thick loops, the tension dominates over the magnetic pressure gradient." In this subsection we remove the discontinuous variation of density from its internal valuep top. by a continuous variation in à non-uniform layer [R—//2.R+//2].," In this subsection we remove the discontinuous variation of density from its internal value $\rho_{\mathrm i}$ to $\rho_{\mathrm e}$ by a continuous variation in a non-uniform layer $[R - l/2 , R + l/2]$." A fully non-uniform equilibrium state corresponds to /=2R., A fully non-uniform equilibrium state corresponds to $l= 2 R$. When the jump in € Is replaced by a continuous variation of wa new physics is introduced in the system., When the jump in $\omega_{\mathrm A}$ is replaced by a continuous variation of $\omega_{\mathrm A}$ new physics is introduced in the system. The continuous variation of wa has the important effect that the kink MHD wave. which has its frequency in the Alfvénn continuum. interacts with local Alfvénn continuum waves and gets damped.," The continuous variation of $\omega_{\mathrm A}$ has the important effect that the kink MHD wave, which has its frequency in the Alfvénn continuum, interacts with local Alfvénn continuum waves and gets damped." This resonant damping is traslated in a complex frequency (and complex eigenfunction)., This resonant damping is translated in a complex frequency (and complex eigenfunction). In the present paper damped global eigenmodes that are coupled to resonant Alfvénn waves in a non-uniform equilibrium state shall be computed by two methods., In the present paper damped global eigenmodes that are coupled to resonant Alfvénn waves in a non-uniform equilibrium state shall be computed by two methods. The first method is to use a numerical code that integrates the resistive MHD equations in the whole volume of the equilibrium state to determine a selected mode or part of the resistive spectrum of the system (seeforexampleVanDoorsselaereetal..2004:Arregui2005;Terradas 2006).," The first method is to use a numerical code that integrates the resistive MHD equations in the whole volume of the equilibrium state to determine a selected mode or part of the resistive spectrum of the system \citep[see for example][]{VanDoorsselaere2004, Arregui2005,Terradas2006}." . The second method was introduced by Tirry&Goossens (1996).., The second method was introduced by \cite{Tirry1996}. . It circumvents the numerical integration of the non-ideal MHD equations and only requiresnumerical integration (or closed analytical solutions) of the linear ideal MHD equations., It circumvents the numerical integration of the non-ideal MHD equations and only requiresnumerical integration (or closed analytical solutions) of the linear ideal MHD equations. The method relies on the fact that dissipation is important only in a narrow layer around the resonant point where the real part of the frequency of quasi-mode equals the local, The method relies on the fact that dissipation is important only in a narrow layer around the resonant point where the real part of the frequency of quasi-mode equals the local year of monitoring one to two dozen white dwarfs is significant.,year of monitoring one to two dozen white dwarfs is significant. " Altough we do not have the knowledge needed to assess the likelihood of transits by rings or moons, the discovery that exoplanets commonly have properties that were unexpected leads us to consider a range of possibilities for planets orbiting white dwarts."," Altough we do not have the knowledge needed to assess the likelihood of transits by rings or moons, the discovery that exoplanets commonly have properties that were unexpected leads us to consider a range of possibilities for planets orbiting white dwarfs." " The considerations above show that, 7 white dwarfs tend to be orbited by close-in planets, and ivf these planets have rings and/or moons, there is a chance thatKepler will discover them by monitoring a modest number of white dwarfs."," The considerations above show that, ` white dwarfs tend to be orbited by close-in planets, and ` these planets have rings and/or moons, there is a chance that will discover them by monitoring a modest number of white dwarfs." An all-sky survey with the sensitivity ofKepler would cither discover such systems or definitively rule them out., An all–sky survey with the sensitivity of would either discover such systems or definitively rule them out. Consider the possibility that white dwarfs host both asteroid systems and close-in planets with rings and/or moons., Consider the possibility that white dwarfs host both asteroid systems and close-in planets with rings and/or moons. Dynamical stability arguments place constraints on the number of planets and on the linear dimensions of the system of moons orbiting each., Dynamical stability arguments place constraints on the number of close-in planets and on the linear dimensions of the system of moons orbiting each. " Unless, therefore, the asteroid systems are deficient in large asteroids relative to what we might expect based on the solar system, transits by asteroids should provide the dominant signal."," Unless, therefore, the asteroid systems are deficient in large asteroids relative to what we might expect based on the solar system, transits by asteroids should provide the dominant signal." The continuous monitoring of white dwarfs can lead to significant scientific results in addition to those associated with asteroids., The continuous monitoring of white dwarfs can lead to significant scientific results in addition to those associated with asteroids. " If coherent oscillations are present in these stars, astroseismic analysis would reveal these modes at amplitudes of 16 ppm (3o) in just one month of data on a 15th magnitude star, and 4.6 ppm (3c) in one year."," If coherent oscillations are present in these stars, astroseismic analysis would reveal these modes at amplitudes of 16 ppm $3 \sigma$ ) in just one month of data on a 15th magnitude star, and 4.6 ppm $3 \sigma$ ) in one year." These are 10-30 times (or more) lower than any ground-based photometry has achieved., These are 10-30 times (or more) lower than any ground-based photometry has achieved. At these low levels new pulsating classes could well be discovered., At these low levels new pulsating classes could well be discovered. We thank the anonymous referee for very helpful suggestions which have helped us clarity the discussion and analysis presented in this paper., We thank the anonymous referee for very helpful suggestions which have helped us clarify the discussion and analysis presented in this paper. " Alcock. C.. Fristrom, C. C.. Siegelman, R. 1986, ApJ. 302. 462 Barnes, J. W.. Fortney, J. 22004.ApJ.. 616. 1193 Barnes, J. 22004, Ph.D. Thesis, Farihi. J.. Jura, Μ.. Zuckerman, 22009, ApJ. 694, 805"," Alcock, C., Fristrom, C. C., Siegelman, R. 1986, ApJ, 302, 462 Barnes, J. W., Fortney, J. 2004, 616, 1193 Barnes, J. 2004, Ph.D. Thesis, Farihi, J., Jura, M., Zuckerman, 2009, ApJ, 694, 805" "Is admeasure of the overall amount oscillations i 11,",is a measure of the overall amount oscillations in $u$. The direct connection between the total variation ancl the overall amount of oscillations can be seen in the equivalent definition where each maxima is couuted positively twice and cach niünnmua counted negatively twice (SeeLaney 1998)., The direct connection between the total variation and the overall amount of oscillations can be seen in the equivalent definition where each maxima is counted positively twice and each minima counted negatively twice \citep[See][]{lan98}. . The formation of spurious oscillations will contribute new maxima aud minima aud the total variation will increase., The formation of spurious oscillations will contribute new maxima and minima and the total variation will increase. A flux assignment scheme is said to be TVD if which signifies that the overall amount of oscillations is bounded., A flux assignment scheme is said to be TVD if which signifies that the overall amount of oscillations is bounded. Iu linear fiux-assigunmieut schemes. the vou Neunaun linear stability condition requires that the Fourier modes remain bounded.," In linear flux-assignment schemes, the von Neumann linear stability condition requires that the Fourier modes remain bounded." Iu noulinear schemes. the TVD stability coudition requires that the total variation dinunishes.," In nonlinear schemes, the TVD stability condition requires that the total variation diminishes." We now describe a nonlinear second-order accurate TVD scheme which builds upon the first-order 1ionotone upwind scheme deseribed im the previous section., We now describe a nonlinear second-order accurate TVD scheme which builds upon the first-order monotone upwind scheme described in the previous section. " The secoud-order accurate fluxes Fr TEE cell boundaries are obtained by taking first-order fluxes FM, Boni the upwind scheme aud modifving it with a second order correction."," The second-order accurate fluxes $F_{n+1/2}^t$ at cell boundaries are obtained by taking first-order fluxes $F_{n+1/2}^{(1),t}$ from the upwind scheme and modifying it with a second order correction." First cousider the case where the advection velocity is positive., First consider the case where the advection velocity is positive. The first-order upwiud flux Pal» comes fron the averaged fiux FY in cell à.," The first-order upwind flux $F_{n+1/2}^{(1),t}$ comes from the averaged flux $F_n^t$ in cell $n$." We can define two second-order Hux corrections. using three local cell-ceutered fiuxes.," We can define two second-order flux corrections, using three local cell-centered fluxes." We use cell i aud the cells inuuediatelv left aud right of it., We use cell $n$ and the cells immediately left and right of it. If the advection velocity is negative. the first-order upwiud flux comes from the averaged flux Ftjj n cell |I.," If the advection velocity is negative, the first-order upwind flux comes from the averaged flux $F_{n+1}^t$ in cell $n+1$." Iu this case. the secouc-order fiux corrections. are based on cell 5»|l aud the cells directly adjacent to it.," In this case, the second-order flux corrections, are based on cell $n+1$ and the cells directly adjacent to it." Near extrema where the corrections have opposite signs. we dupose no secoud-order," Near extrema where the corrections have opposite signs, we impose no second-order" have the same slope at all variability time-scales ancl the time-scale dependence we observe in the sspectra would be produced. by the stronger variability. of a hard component at [frequencies of 3.10ο7 Lz.,have the same slope at all variability time-scales and the time-scale dependence we observe in the spectra would be produced by the stronger variability of a hard component at frequencies of $3 \times 10^{-4}-10^{-3}$ Hz. The spectrum of this additional component would then correspond. to the spectrum of the possible QPO detected in the PSD of aat L6.103 Hz (MarkowitzetaL., The spectrum of this additional component would then correspond to the spectrum of the possible QPO detected in the PSD of at $4.6\times 10 ^{-4}$ Hz \citep{markowitz}. 2007). The present data are insullicient to distinguish between an intrinsic hardening of the power law and the appearance of a separate variability component., The present data are insufficient to distinguish between an intrinsic hardening of the power law and the appearance of a separate variability component. We note however. that it is. unlikely that this possible hard component corresponds to the reflection component.," We note however, that it is unlikely that this possible hard component corresponds to the reflection component." Light travel times to the reflector will smooth short time-scale variability which is inconsistent with this hard component cisplavine (han the incident continuum., Light travel times to the reflector will smooth short time-scale variability which is inconsistent with this hard component displaying than the incident continuum. One interpretation of the change in slope of the sspectra with frequency is that. [luctuations on. dilferent time-scales originate in different regions. each one emitting a power law energy spectrum with its characteristic slope.," One interpretation of the change in slope of the spectra with frequency is that fluctuations on different time-scales originate in different regions, each one emitting a power law energy spectrum with its characteristic slope." Given that. for each observation. the absorption parameters of the sspectra at cilferent frequencies are similar. it is possible that all these emitting regions are covered bv the same (approximately constant) absorber.," Given that, for each observation, the absorption parameters of the spectra at different frequencies are similar, it is possible that all these emitting regions are covered by the same (approximately constant) absorber." " ""This configuration is expected if the power law component is emitted by a corona close to the central black hole. with absorbing material. such as à wind. in the line of sight to the centre."," This configuration is expected if the power law component is emitted by a corona close to the central black hole, with absorbing material, such as a wind, in the line of sight to the centre." The behaviour of the sspectrum can be understood in the context of propagating-Huctuation models. where the emitted. spectrum hardens towards the centre.," The behaviour of the spectrum can be understood in the context of propagating-fluctuation models, where the emitted spectrum hardens towards the centre." Propagating-Ductuation models relate the variability. to accretion rate Lluctuations. that are introduced. at. dillerent radii in the aecretion [low with a racdially-cepencdent characteristic time-scale. c.g. proportional to the local viscous time-scale.," Propagating-fluctuation models relate the variability to accretion rate fluctuations, that are introduced at different radii in the accretion flow with a radially-dependent characteristic time-scale, e.g. proportional to the local viscous time-scale." This. scenario was introduced by Lyubarskii(1997). to explain the wide range of variability time-scales present in the X-ray. light curves of accretion powered. systems. ancl explains several other variability properties (Arévalo&Uttlev.2006).," This scenario was introduced by \citet{lyubarskii} to explain the wide range of variability time-scales present in the X-ray light curves of accretion powered systems, and explains several other variability properties \citep{arevalo}." IXotovetal.(2001) have shown that if the emitted. energy spectrum hardens inward. then this model produces more high-frequeney power at higher energies and also time lags. where harder bands lag softer ones.," \citet{kotov} have shown that if the emitted energy spectrum hardens inward, then this model produces more high-frequency power at higher energies and also time lags, where harder bands lag softer ones." Churazovetal.(2001) note that a standard geometrically thin accretion disc cannot produce and »opagate short time-scale accretion rate f[Iuctuations due o its long characteristic time-scales., \citet{churazov} note that a standard geometrically thin accretion disc cannot produce and propagate short time-scale accretion rate fluctuations due to its long characteristic time-scales. A ecometrically thick accretion Low. however. can easily maintain and propagate hese rapid [auctuations.," A geometrically thick accretion flow, however, can easily maintain and propagate these rapid fluctuations." In their proposed configuration. the hermally-emitting ecometrically thin disc is sandwiched bv a thick accretion flow. which acts as an accreting corona. responsible for the Comptonised. X-ray emission. seen as he power law spectral component in ealactic black hole candidates and AGN.," In their proposed configuration, the thermally-emitting geometrically thin disc is sandwiched by a thick accretion flow, which acts as an accreting corona, responsible for the Comptonised X-ray emission seen as the power law spectral component in galactic black hole candidates and AGN." Therefore. a stable disc emission and lighly variable power law emission can coexist. where the variability arises from accretion. rate [Iuetuations in the corona.," Therefore, a stable disc emission and highly variable power law emission can coexist, where the variability arises from accretion rate fluctuations in the corona." Note that in a standard accretion How the crit velocity scales with the seale height squared. (LfRy. il the corona is 10 times thicker than the geometricallvy thin disc and its surface density is only 1 that of the thin disc. the accretion rate of both flows are comparable.," Note that in a standard accretion flow the drift velocity scales with the scale height squared, $(H/R)^2$, if the corona is 10 times thicker than the geometrically thin disc and its surface density is only 1 that of the thin disc, the accretion rate of both flows are comparable." This simple argument shows that even a tenuous corona can have a significant impact on the total accretion rate and so it is not unreasonable to think that it can produce most of the observed X-ray [lux variability in ACN., This simple argument shows that even a tenuous corona can have a significant impact on the total accretion rate and so it is not unreasonable to think that it can produce most of the observed X-ray flux variability in AGN. This interpretation. where fluctuations propagate inwards in the accretion How and the spectrum. hardens in the same direction. produces hard. lags (Ixotov.et.al.2001:Arévalo&Uttley.2006).. as observed in these data (MarkowitzetaL.," This interpretation, where fluctuations propagate inwards in the accretion flow and the spectrum hardens in the same direction, produces hard lags \citep{kotov, arevalo}, as observed in these data \citep{markowitz}." 2007). In this scenario. increasingly shorter variability. time-scales are. produced. closer to the centre. and therefore. the corresponding high-frequency sspectrum shows a harder energy spectrum. characteristic of its region of origin.," In this scenario, increasingly shorter variability time-scales are produced closer to the centre, and therefore, the corresponding high-frequency spectrum shows a harder energy spectrum, characteristic of its region of origin." The bottom panel displays the same colors for but only for pixels with detectable Ha emission.,The bottom panel displays the same colors for but only for pixels with detectable $\alpha$ emission. Note that the brightest pixels (above 23.5 mag arcsecs2) are the bluest pixels in either plot., Note that the brightest pixels (above 23.5 mag $^{-2}$ ) are the bluest pixels in either plot. " Ha pixels can occur in regions of high and low surface brightness, with the same distribution of color as other pixels."," $\alpha$ pixels can occur in regions of high and low surface brightness, with the same distribution of color as other pixels." " And, while Ha pixels are associated with some high surface brightness areas, the reverse is not true and, therefore, it is difficult to isolate star formation regions just from V band images as noted above."," And, while $\alpha$ pixels are associated with some high surface brightness areas, the reverse is not true and, therefore, it is difficult to isolate star formation regions just from $V$ band images as noted above." The increasing spread of color with fainter surface brightness is reflecting increasing error at low S/N levels., The increasing spread of color with fainter surface brightness is reflecting increasing error at low S/N levels. Even with this spread there is a weak correlation between pixel color and surface brightness such that the brightest pixels are the bluest., Even with this spread there is a weak correlation between pixel color and surface brightness such that the brightest pixels are the bluest. " While this is not surprising, and also true"," While this is not surprising, and also true" A rather surprising οσο. of local primordial non-CGaussianity on the large scale clustering properties of biased objects has been observed in various numerical studies over the last vears (Dalaletal.2008:Desjaccquesct09:Pillepichctal.2010:Grossiet 2009).,"A rather surprising effect of local primordial non-Gaussianity on the large scale clustering properties of biased objects has been observed in various numerical studies over the last years \citep{DalalEtal2008, DesjacquesSeljakIliev2009, PillepichPorcianiHahn2010, GrossiEtal2009}." .. These results attracted a ereat deal of attention as they showed that measurements of the power spectrum of galaxies ancl quasars from current data sets can lead to constraints on the local non-Gaussian parameter {νι Comparable to those of CMDB observations (Slosaretal.2008:Desjacques&Seljak201t Mb).," These results attracted a great deal of attention as they showed that measurements of the power spectrum of galaxies and quasars from current data sets can lead to constraints on the local non-Gaussian parameter $\fNL$ comparable to those of CMB observations \citep{SlosarEtal2008, DesjacquesSeljak2010B}." Previous work assumed that the main cHeet of primordial non-Gaussianity is limited to an extra contribution to the matter ancl galaxy bispectrum., Previous work assumed that the main effect of primordial non-Gaussianity is limited to an extra contribution to the matter and galaxy bispectrum. Still. even under such incorrect but. “conservative” assumption. it has been shown that future larec-volume redshift surveys will reach à sensitivity to a non-zero fx; comparable or »etter than the €MD bispecteum (Scoccimarroetal.2004:Sefusatti&Ixomatsu.2007 ).," Still, even under such incorrect but “conservative” assumption, it has been shown that future large-volume redshift surveys will reach a sensitivity to a non-zero $\fNL$ comparable or better than the CMB bispectrum \citep{ScoccimarroSefusattiZaldarriaga2004, SefusattiKomatsu2007}." . Vhe inclusion. of the non-Gaussian bias in the analysis of the galaxy bispectrum or. »etter. in a combined analysis of the power spectrum and rispectrtun. is desirable to reliably assess the potentiality of ortheoming surveys of the large scale structure.," The inclusion of the non-Gaussian bias in the analysis of the galaxy bispectrum or, better, in a combined analysis of the power spectrum and bispectrum, is desirable to reliably assess the potentiality of forthcoming surveys of the large scale structure." As a first step in this direction. we have measured he matter bispectrum for the main classes of triangle shape using a set of large-volume N-body simulations seeded with Gaussian ancl non-Ciaussian initial conditions of the local tvpe.," As a first step in this direction, we have measured the matter bispectrum for the main classes of triangle shape using a set of large-volume N-body simulations seeded with Gaussian and non-Gaussian initial conditions of the local type." . We focused on mildly. nonlinear. scales. 0025£&0.3hMpe presented a wide choice of triangular configurations of different shapes and. obtained a determination of the bispectrum with an overall errors of the order of 3-44.," We focused on mildly nonlinear scales, $0.02\lesssim k\lesssim 0.3\kMpc$, presented a wide choice of triangular configurations of different shapes and obtained a determination of the bispectrum with an overall errors of the order of $3$ $4\%$." Of. particular interest in this range of scales are the nonlinear corrections induced by gravitational instability. to non-Gaussian initial conditions as they generate an additional. non-Gaussian signal on top of the primordial component., Of particular interest in this range of scales are the nonlinear corrections induced by gravitational instability to non-Gaussian initial conditions as they generate an additional non-Gaussian signal on top of the primordial component. For a nonlinear parameter fy;= 100. we found that the amplitude of these corrections range from 3-4 for generic triangle configurations up to 20- 30% for “squeezed” configurations where we expect most of the signal for local non-Ciaussianity.," For a nonlinear parameter $\fNL=100$ , we found that the amplitude of these corrections range from $3$ $4\%$ for generic triangle configurations up to $20$ $30\%$ for “squeezed” configurations where we expect most of the signal for local non-Gaussianity." We quantified these corrections with the aid of the ratio anc the cdillerence between the non-Gaussian and the Gaussian. bispectrum., We quantified these corrections with the aid of the ratio and the difference between the non-Gaussian and the Gaussian bispectrum. Our set of eight different realizations of those moclels ensure that our results are robust to sampling variance., Our set of eight different realizations of those models ensure that our results are robust to sampling variance. We considered. simulations snapshots at redshift +=0. 1 and 2.," We considered simulations snapshots at redshift $z=0$, $1$ and $2$." Overall. we found that the magnitude of the correction induced. by non-Gaussian elfects is similar regardless the scale. and the redshift.," Overall, we found that the magnitude of the correction induced by non-Gaussian effects is similar regardless the scale and the redshift." This is due to a compensation between the primordial component that decreases with time on the one hand. and the contribution from. nonlinear structure growth that increases with time on the other hand.," This is due to a compensation between the primordial component that decreases with time on the one hand, and the contribution from nonlinear structure growth that increases with time on the other hand." We compared our results with the predictions. of Eulerian perturbation theory. both at. tree-level ancl one-loop (Sefusatti2009)," We compared our results with the predictions of Eulerian perturbation theory, both at tree-level and one-loop \citep{Sefusatti2009}." As expected. and similarly to what happens for Caussian initial conditions. the tree-level approximation fails at relatively large scales. &~0.05 - 0.1hAlpe* even at high redshift.," As expected, and similarly to what happens for Gaussian initial conditions, the tree-level approximation fails at relatively large scales, $k\sim0.05$ - $0.1\kMpc$, even at high redshift." " One-loop corrections extend. significantly the predictive power of perturbation theory down to mildly non-linear scales &—0.35Mpe* at redshift, z=1. similarly to the case of the power spectrum. analyzed byJeong&Ixomatsu(2006)."," One-loop corrections extend significantly the predictive power of perturbation theory down to mildly non-linear scales $k\sim 0.3\kMpc$ at redshift $z\gtrsim 1$, similarly to the case of the power spectrum analyzed \citet{JeongKomatsu2006}." ". They describe. in fact. the matter bispectrum measured in simulations at the few percent level. with an even better agreement with respect to the ""relative"" elfect of primordial non-Caussianity on the Gaussian. bispectrum."," They describe, in fact, the matter bispectrum measured in simulations at the few percent level, with an even better agreement with respect to the “relative” effect of primordial non-Gaussianity on the Gaussian bispectrum." Furthermore. they. also show a good qualitative agreement with simulations at recdshilt Zero.," Furthermore, they also show a good qualitative agreement with simulations at redshift zero." We thank Roman Seoccimarro and. Francis. Bernardeau or useful commoents., We thank Roman Scoccimarro and Francis Bernardeau for useful comments. IZ. aacknowledges support by the French Agence National de Ia Recherche (ANI) under grant DLANOT-1-212615 and by the European Commission under he Marie Curie Inter European Fellowship and he is grateful o the Institute for Theoretical Physies of the University of Zürrich. for hospitality curing the completion of this xoject., E. acknowledges support by the French Agence National de la Recherche (ANR) under grant BLAN07-1-212615 and by the European Commission under the Marie Curie Inter European Fellowship and he is grateful to the Institute for Theoretical Physics of the University of Zürrich for hospitality during the completion of this project. M. wwould like to thank the Institut de Physique 'Fhéoorique of CEA-Saclay for hospitality ancl acknowledges support from the Spanish Ministerio de Ciencia y Tecnologia (ALEC) through the Juan de la Clerva program., M. would like to thank the Institut de Physique Théoorique of CEA-Saclay for hospitality and acknowledges support from the Spanish Ministerio de Ciencia y Tecnologia (MEC) through the Juan de la Cierva program. V. wwould like tothank the Institut dAstrophysique de Paris or hospitality during the final stages of this work and he Swiss National Foundation (uncer contract No., V. would like tothank the Institut d'Astrophysique de Paris for hospitality during the final stages of this work and the Swiss National Foundation (under contract No. 200021-116696/1) for support., for support. The cooling time of X-rav emitting gas in the cores of many massive galaxies and galaxy clusters is much shorter than the HIubble. time.,The cooling time of X-ray emitting gas in the cores of many massive galaxies and galaxy clusters is much shorter than the Hubble time. In the absence of heat sources. the eas will cool and form stars.," In the absence of heat sources, the gas will cool and form stars." However. high-resolution X-rav spectroscopy of galaxies ancl clusters has shown that the rate at which gas cools to low temperatures 1s stenificanthy reduced compared to preliminary expectations (c.g.7777777) sugeesting that the gas is somehow being reheatect.," However, high-resolution X-ray spectroscopy of galaxies and clusters has shown that the rate at which gas cools to low temperatures is significantly reduced compared to preliminary expectations \citep[e.g.][]{peterson01,tamura01,xu02,sak,peterson03,kaastra04,peterson06} suggesting that the gas is somehow being reheated." Numerous possible heating mechanisms have been suggested. most notably energy injection by Active Galactic Nuclei (AGN) (e.g.2???) and the inward πας of thermal energv [rom large radii due to thermal conduction (e.g. 7777)..," Numerous possible heating mechanisms have been suggested, most notably energy injection by Active Galactic Nuclei (AGN) \citep[e.g.][]{bintab,tucker,cfq} and the inward flux of thermal energy from large radii due to thermal conduction \citep[e.g.][]{bregdav88,gaetz,zakamska03,pope05}." Quantifving these heating processes is dillicult cue our incomplete understanding of the microphvsies of the X-rav emitting plasma (see??.forexample)..," Quantifying these heating processes is difficult due our incomplete understanding of the microphysics of the X-ray emitting plasma \citep[see][for example]{cho03,parrish}." Nevertheless. due to its strong temperature dependence. thermal conduction alone probably cannot provide a general solution to the cooling Dow problem (e.g.??7)..," Nevertheless, due to its strong temperature dependence, thermal conduction alone probably cannot provide a general solution to the cooling flow problem \citep[e.g.][]{voigt04,pope06,guo}." ]nsteacd. it is generally assumed that energy input by a central AGN is predominantly responsible for reheating the gas.," Instead, it is generally assumed that energy input by a central AGN is predominantly responsible for reheating the gas." This is partly based on a wealth of observational evidence which indicates that racio GN. outllows. are trigecred in response to the thermal state of their environment (e.g.2???227727).," This is partly based on a wealth of observational evidence which indicates that radio AGN outflows are triggered in response to the thermal state of their environment \citep[e.g.][]{burns,best05,birzan,dunn05, best07,raff08,cav08,mittal}." HW true. this suggests that AGN activity is part of a negative feedback loop which may regulate properties of its environment.," If true, this suggests that AGN activity is part of a negative feedback loop which may regulate properties of its environment." Theoretical studies have also provided. complimentary evidence highlighting the importance of AGN feedback., Theoretical studies have also provided complimentary evidence highlighting the importance of AGN feedback. For example. implementations of AGN heating in semi-analytic models of galaxy formation have shown that. in principle. AGN can both reheat cooling Hows and explain the exponential ο at the bright end of the galaxy luminosity function (e.g.277?)..," For example, implementations of AGN heating in semi-analytic models of galaxy formation have shown that, in principle, AGN can both reheat cooling flows and explain the exponential cutoff at the bright end of the galaxy luminosity function \citep[e.g.][]{benson,croton05,bower06,short}." More recently. AGN heating has been shown to be fundamental in shaping the X-ray Iuminosity-temperature of massive galaxies (e.g.777).," More recently, AGN heating has been shown to be fundamental in shaping the X-ray luminosity-temperature of massive galaxies \citep[e.g.][]{puchwein,bower08,pope09}." Droadlv speaking. theoretical studies employ ACN heating as an input with which to control star formation rates and the X-rav [uminositv of the hot gas that," Broadly speaking, theoretical studies employ AGN heating as an input with which to control star formation rates and the X-ray luminosity of the hot gas that" Concerning the morphology of the ICM. we note that the rather spherically svuuuetric shape of the extended enussion. as compared to the completely cdlifferent uorphologv defined by the bright ellipticals aligned in a chain. argues against an origin of the eas in terms of halos of the chain galaxies. but rather for an association with the elobal eroup poteutial.,"Concerning the morphology of the IGM, we note that the rather spherically symmetric shape of the extended emission, as compared to the completely different morphology defined by the bright ellipticals aligned in a chain, argues against an origin of the gas in terms of halos of the chain galaxies, but rather for an association with the global group potential." The X-ray emission of the ICAL can be traced out to about 1 AIpe. which turus out to be about the virial radius of the eroup if we use the total mass value determined frou the N-rav observations aud the assmuption that the virial radius is approximately characterized by the region inside which the mean overdensity is a factor of 200 above the critical density of the universe (ee. Evrard et al.," The X-ray emission of the IGM can be traced out to about 1 Mpc, which turns out to be about the virial radius of the group if we use the total mass value determined from the X-ray observations and the assumption that the virial radius is approximately characterized by the region inside which the mean overdensity is a factor of 200 above the critical density of the universe (e.g., Evrard et al." 1996)., 1996). " The fairly spherically οποίας appearance of the eroups N-ray halo (except possibly for some faint outer extensions) taken together with the perfect consistency of the mass determined from the velocity dispersion aud the N-rav properties, aud the findines of Ledlow et al. ("," The fairly spherically symmetric appearance of the group's X-ray halo (except possibly for some faint outer extensions) taken together with the perfect consistency of the mass determined from the velocity dispersion and the X-ray properties, and the findings of Ledlow et al. (" 1996) that the ealaxy velocity distribution does not significantly deviate from) a Gaussian. implies that the matter in the eroup inside a radius of about 1 Alpe is most probably quite relaxed.,"1996) that the galaxy velocity distribution does not significantly deviate from a Gaussian, implies that the matter in the group inside a radius of about 1 Mpc is most probably quite relaxed." The position of the ceutral galaxy 3383 is found to be slightly off-set Yolu he center of the extended X-ray enission. and thus prestunably from the center of the dark. matter potential.," The position of the central galaxy 383 is found to be slightly off-set from the center of the extended X-ray emission, and thus presumably from the center of the dark matter potential." Such offsets of cD galaxies lave also been observed iun a number of other poor svstcms (6.8. TT. Neuuaun Dóhhriuger 1995: Fornax cluster. Ikebe et al.," Such off-sets of cD galaxies have also been observed in a number of other poor systems (e.g., 7, Neumann Böhhringer 1995; Fornax cluster, Ikebe et al." 1996) and some Abell clusters (e.g. Lazzati Clincarini 1998).," 1996) and some Abell clusters (e.g., Lazzati Chincarini 1998)." In Lazzati Clhinciniui (1998). this is traced back to a sialbuuplitude oscillation of the ¢D ealaxy around the bottom of the cluster potential.," In Lazzati Chincarini (1998), this is traced back to a small-amplitude oscillation of the cD galaxy around the bottom of the cluster potential." " The cooling time in the ceuter is f~2.71019. vr. ie. no large-scale"" cooling flow is expected to have developed."," The cooling time in the center is $t \simeq 2.7\,10^{10}$ yr, i.e. no `large-scale' cooling flow is expected to have developed." " Further. the enhanced N-ray. emission from the direction of 3382 is consistent with originating from a poiut ποιος,"," Further, the enhanced X-ray emission from the direction of 383 is consistent with originating from a point source." " We also note that although stroug low-ionizatiou optical eiuissiou lines have becu reported for some central ealaxies iu cluster cooling flows (οι, Cowie et al."," We also note that although strong low-ionization optical emission lines have been reported for some central galaxies in cluster cooling flows (e.g., Cowie et al." 1983. Deckman 1989. Crawford Fabian 1992). the morphology of the riug- or dixk-like e1uission line region iun 2383 (Owen et al.," 1983, Heckman 1989, Crawford Fabian 1992), the morphology of the ring- or disk-like emission line region in 383 (Owen et al." 1990. Fraix-Burnet et al.," 1990, Fraix-Burnet et al." 1991) does not areue for a counectiou to a cooling flow., 1991) does not argue for a connection to a cooling flow. Further. we fud the locus of NGC'E83 iu the enissiou line-ratio diagram [ST] vs. [NI] to Iv outside of the cclass T and ‘class IP. cooling flow nebulae of Deckman et al. (," Further, we find the locus of 383 in the emission line-ratio diagram [SII] vs. [NII] to ly outside of the `class I' and `class II' cooling flow nebulae of Heckman et al. (" 1989: see their Fig.,1989; see their Fig. 6). (, 6). ( This alone does not exclude the presence of a cooling flow. though. since not all of them are associated with cluission line nebulae.),"This alone does not exclude the presence of a cooling flow, though, since not all of them are associated with emission line nebulae.)" Although 331 is only a 1noderately bright radio galaxy. its jets could be studied in detail due to its proximity.," Although 31 is only a moderately bright radio galaxy, its jets could be studied in detail due to its proximity." Concerning the origin. morphology aud confinement of the jets. several models were explored (e... Blauclford TIcke 1978. Bridle et al.," Concerning the origin, morphology and confinement of the jets, several models were explored (e.g., Blandford Icke 1978, Bridle et al." 199. Bicknell 199L).," 1994, Bicknell 1994)." The gas density aux temperature derived for the X-ray eas allow a comparison with the pressure of the radio gas. and an assessinent of the confinement of the jet material.," The gas density and temperature derived for the X-ray gas allow a comparison with the pressure of the radio gas, and an assessment of the confinement of the jet material." Iu Fig., In Fig. 9 we compare the pressure of the radio cimittinego region as eiven iu Strom et al. (, \ref{pressure} we compare the pressure of the radio emitting region as given in Strom et al. ( 1983) aud Morganti et al.,1983) and Morganti et al. with he thermal pressure of the N-ray eas derived from the uu of density (Sect., with the thermal pressure of the X-ray gas derived from the run of density (Sect. 3.3) and a temperature of 15-15 keV. Whereas in the ceutral region (ie. within] 3383). here seems to be a stroug Overpressure of the radio eas (but note that there certainly is au additional contribution to thermal pressure frou lieher-density eas within the ealaxv). pressure equilibrium is reached at about 35 kpe (projected distance from the ceuter).," 3.3) and a temperature of $kT$ =1.5 keV. Whereas in the central region (i.e. within 383), there seems to be a strong overpressure of the radio gas (but note that there certainly is an additional contribution to thermal pressure from higher-density gas within the galaxy), pressure equilibrium is reached at about 35 kpc (projected distance from the center)." Further out the hermal pressure increasingly exceeds the nouthermal pressure., Further out the thermal pressure increasingly exceeds the nonthermal pressure. It is interesting to note that Bridle et al. (, It is interesting to note that Bridle et al. ( 1980) fined the expansion rate of the jets of 830°331 transverse to their leneth to decrease with increasing distance frou the radio core.,1980) find the expansion rate of the jets of 31 transverse to their length to decrease with increasing distance from the radio core. This mav be related to the relative increase of the thermal pressure of the ambient medium with increasing radius., This may be related to the relative increase of the thermal pressure of the ambient medium with increasing radius. While Bridle’s trend refers mainly to the presently, While Bridle's trend refers mainly to the presently ionizing background (Rauch. Haehnelt Stetuuetz 1997). although iu many other aspects this modelling shows considerable success iu reproducing observed characteristics of absorbers.,"ionizing background (Rauch, Haehnelt Steinmetz 1997), although in many other aspects this modelling shows considerable success in reproducing observed characteristics of absorbers." This data set is extended with equivalent high quality samples analysed from the spectra of QULOT|157 aud QI122|231. eivine coverage over the range 1.9«τες3.5: all are plotted in Figure 2. here excluding svsteiis within 5000 kins + of the cussion redshifts aud those not optically thin in the Lyman continuum as assessed from the corresponding Lyman region spectra.," This data set is extended with equivalent high quality samples analysed from the spectra of Q1107+487 and Q1422+231, giving coverage over the range $1.9 < z < 3.5$; all are plotted in Figure 2, here excluding systems within 5000 km $^{-1}$ of the emission redshifts and those not optically thin in the Lyman continuum as assessed from the corresponding Lyman region spectra." Contrary, Contrary cubes of the LiPASS 2lem southern sky survey (Barnesetal. 2001).,cubes of the HiPASS 21cm southern sky survey \cite{bar01}. . Phe angular resolution of the data is 15.5 aremin after the data have been eridded., The angular resolution of the data is 15.5 $arcmin$ after the data have been gridded. The ericd spacing in each cube is 4 are min and the spectrum usec is the nearest spectrum to the optical position., The grid spacing in each cube is 4 $arc$ $min$ and the spectrum used is the nearest spectrum to the optical position. The channel spacing is 13.2 kins and the velocity resolution is 27 Km os. after smoothing., The channel spacing is 13.2 $km$ $s^{-1}$ and the velocity resolution is 27 $km$ $s^{-1}$ after smoothing. There are 1024 channels. but we initially considered only velocities in the range 400-12000. An 5," There are 1024 channels, but we initially considered only velocities in the range 400-12000 $km$ $s^{-1}$." The lower limit was set to avoid local hyerogen. the upper limit by the proximity of the velocity eut-oll.," The lower limit was set to avoid local hydrogen, the upper limit by the proximity of the velocity cut-off." The typical noise Fluctuation in cach spectrum after smoothing is 0.006 Jv +., The typical noise fluctuation in each spectrum after smoothing is 0.006 Jy $^{-1}$. ‘Phe identification of sources in the EIE data is described below., The identification of sources in the HI data is described below. The automated. detection to well defined. selection criteria of images on. for example. CCD frames has become much more sophisticated over the last few vears (see for example (Bertin&Arnouts 1996))).," The automated detection to well defined selection criteria of images on, for example, CCD frames has become much more sophisticated over the last few years (see for example \cite{ber96}) )." Numerous computer packages exist to automatically select galaxies to well defined selection criteria. (isophotal size ancl magnitude for example)., Numerous computer packages exist to automatically select galaxies to well defined selection criteria (isophotal size and magnitude for example). This does not appear to be the case for HI detections vet. the two problems are very similar., This does not appear to be the case for HI detections yet the two problems are very similar. For example Ixilborn (2001) discusses an automated galaxy Binder for use on HiPASS data cubes. but then resorts to selection by eve.," For example Kilborn (2001) discusses an automated galaxy finder for use on HiPASS data cubes, but then resorts to selection by eye." In. none of the papers on blind. HIE surveys. we have come across. do we find an objective selection. criteria for LIL sources (Zwaanetal.1997:Schneider1998).," In none of the papers on blind HI surveys, we have come across, do we find an objective selection criteria for HI sources \cite{zwa97,sch98}." .. Phese papers supply information about the observing setup and the data reduction. but sav little about the detection of objects from. the spectra obtained.," These papers supply information about the observing setup and the data reduction, but say little about the detection of objects from the spectra obtained." In the main objects appear to be identified by eve and there is no explanation of the selection criteria except to sav (incorrectly) that there is some lower mass limit at each cüstance., In the main objects appear to be identified by eye and there is no explanation of the selection criteria except to say (incorrectly) that there is some lower mass limit at each distance. We have previously. been involved. with techniques for the detection of LSB galaxies in imaging data. (Phillipps&Davies1993:ctal.1994:Ixambas 2000).," We have previously been involved with techniques for the detection of LSB galaxies in imaging data \cite{phi93,dav94,kam00}." A number of vears ago it had become clear that LSB galaxies were very much underrepresented in optically (by eve) selected samples taken from imaging data., A number of years ago it had become clear that LSB galaxies were very much underrepresented in optically (by eye) selected samples taken from imaging data. The lesson learnt was that only when a full analysis of the selection process had been carried out. could vou then define. the sorts of galaxies vou would and would not be able to detect ((Disnev1976:Disnev&Phillipps1983:Davies1990).," The lesson learnt was that only when a full analysis of the selection process had been carried out could you then define the sorts of galaxies you would and would not be able to detect \cite{dis76,dis83,dav90}." . Carrving out deeper observations with better understood selection criteria has [ed to the detection of numerous LSB galaxies., Carrying out deeper observations with better understood selection criteria has led to the detection of numerous LSB galaxies. An optical image of a galaxy is detected against a systematically varying background level with the adcdition of random noise Luctuations., An optical image of a galaxy is detected against a systematically varying background level with the addition of random noise fluctuations. Detection of the LIE signal is very similar - the varving background is the base-line ripple anc in addition there are random noise Huctuations., Detection of the HI signal is very similar - the varying background is the base-line ripple and in addition there are random noise fluctuations. For optica image detection there is no well defined magnitude or size limit - sample selection is always a combination of magnitude and size., For optical image detection there is no well defined magnitude or size limit - sample selection is always a combination of magnitude and size. For example one can always think of a galaxy tha is bright enough to be part of a magnitude Iimited sample. but fails to get in because it is to laree (its surface brightness is less than or elose to the survey isophotal limit).," For example one can always think of a galaxy that is bright enough to be part of a magnitude limited sample, but fails to get in because it is to large (its surface brightness is less than or close to the survey isophotal limit)." In a similar way [large velocity width galaxies with low central intensities will be missed. or asigned to base line ripples even though they contain sullicient hydrogen. in total. to be detected in a mass limitecl survey.," In a similar way large velocity width galaxies with low central intensities will be missed or asigned to base line ripples even though they contain sufficient hydrogen, in total, to be detected in a 'mass limited' survey." In this section we describe how we have applied some of our previous techniques of surface photometry to the detection of LIE sources., In this section we describe how we have applied some of our previous techniques of surface photometry to the detection of HI sources. l]laving 2435 spectra to inspect was another strong motivation for emploving an automated. technique., Having 2435 spectra to inspect was another strong motivation for employing an automated technique. As mentioned. above there are two. important. [actors that inlluence our ability to detect “LU objects’ in HIE spectra., As mentioned above there are two important factors that influence our ability to detect 'HI objects' in HI spectra. The first is random noise the second is baseline Ductuations., The first is random noise the second is baseline fluctuations. The signal is the integral over the line width. so large signals can arise from large peak values and/or large velocity. widths.," The signal is the integral over the line width, so large signals can arise from large peak values and/or large velocity widths." The problem with identifving large velocity widths without arge peak values is that they can look the same as baseline uctuations (see also section 6 and figure 11))., The problem with identifying large velocity widths without large peak values is that they can look the same as baseline fluctuations (see also section 6 and figure \ref{fig:noise}) ). Lhe problem with the random noise is that the expectation (Gaussian) is one single channel 30 (σ is the standard. deviation of jo data values) Uuctuation in the 1000]. channels., The problem with the random noise is that the expectation (Gaussian) is one single channel $\sigma$ $\sigma$ is the standard deviation of the data values) fluctuation in the 1000+ channels. Thus 3o detections (see figure. 1)) are not reliable unless they wave sulliciently large. velocity widths. but even then. if 1ο velocity width is too [arge. they can resemble baseline uctuations.," Thus $\sigma$ detections (see figure \ref{fig:3sig}) ) are not reliable unless they have sufficiently large velocity widths, but even then, if the velocity width is too large, they can resemble baseline fluctuations." By hiding! simulated galaxies in real spectra -- became clear that an initial to detection was required. cause even 30 peak values with quite large velocity widths were not convincinglv dillerent to the noise.," By 'hiding' simulated galaxies in real spectra it became clear that an initial $\sigma$ detection was required, because even $\sigma$ peak values with quite large velocity widths were not convincingly different to the noise." So the initial object identifier was simply one of peak value at the ta evel., So the initial object identifier was simply one of peak value at the $\sigma$ level. At to we would expect one false detection in every 30 spectra or about SO false detections in the sample as a whole., At $\sigma$ we would expect one false detection in every 30 spectra or about 80 false detections in the sample as a whole. So the second requirement. was that the initial peak value detection. also hack a resolved! velocity width (figure. 2))., So the second requirement was that the initial peak value detection also had a 'resolved' velocity width (figure \ref{fig:4sig}) ). That is a velocity width greater than 27 Am s.+., That is a velocity width greater than 27 $km$ $s^{-1}$. With this criteria we would not expect any detections by chance (see also section 6 below)., With this criteria we would not expect any detections by chance (see also section 6 below). With these criteria the lowest signal to noise ratio for detection is about 10. a value that would be readily accepted in imaging data.," With these criteria the lowest signal to noise ratio for detection is about 10, a value that would be readily accepted in imaging data." Our selection. criteria does not lead. to an integrated Hux limited. sample (see above). so we will use the term ‘survey limits’ to indicate our two minimal selection criteria.," Our selection criteria does not lead to an integrated flux limited sample (see above), so we will use the term 'survey limits' to indicate our two minimal selection criteria." ‘This is analogous to what would be referred to (incorrectly) as the magnitude limit for à magnitude limited imaging survey sample., This is analogous to what would be referred to (incorrectly) as the magnitude limit for a magnitude limited imaging survey sample. There are two other points., There are two other points. Firstly. our selection criteria will lead. to the preferential selection of face-on. rather than edge-on. disc galaxies as these will have higher central intensities and narrower line profiles.," Firstly our selection criteria will lead to the preferential selection of face-on, rather than edge-on, disc galaxies as these will have higher central intensities and narrower line profiles." Secondly ‘spikes’ in the data like that illustrated in figure 2. are very similar in. velocity width but. lower in amplitude. to the confirmed. detection of an apparently. isolated. LIL cloud. by Ixilborn ct al. (," Secondly 'spikes' in the data like that illustrated in figure \ref{fig:4sig} are very similar in velocity width but, lower in amplitude, to the confirmed detection of an apparently isolated HI cloud by Kilborn et al. (" 2000).,2000). Given the noise in the data it is dillicult to measure the velocity width and [ux integral accurately., Given the noise in the data it is difficult to measure the velocity width and flux integral accurately. To minimise this problem we have cross-correclated the data with templates ancl used the best. fitting template to derive the central velocity. velocity width and flux integral.," To minimise this problem we have cross-correlated the data with templates and used the best fitting template to derive the central velocity, velocity width and flux integral." Inspection of a, Inspection of a when they were first accreted.,when they were first accreted. This fraction goes up to ST 93 per cent if we only consider substructures with more than 100 particles., This fraction goes up to $87$ $93$ per cent if we only consider substructures with more than $100$ particles. We now use our merging trees to study the of the subhalos in our simulations., We now use our merging trees to study the of the subhalos in our simulations. ?) has carried oul a similar analysis for dark matter halocs and has proposed an analytic expression for the mass accretion function based. on the extended: Press-Schechter formalism (?77)..," \citet{frank} has carried out a similar analysis for dark matter haloes and has proposed an analytic expression for the mass accretion function based on the extended Press-Schechter formalism \citep{ps,bond,bower}." Phis function was found to be in excellent agreement with the results of high-resolution A’-bocly simulations., This function was found to be in excellent agreement with the results of high-resolution $N$ -body simulations. Our aim is to study the mass accretion. function. for subhalos and. studs whether there is any dependence on mass or on environment., Our aim is to study the mass accretion function for subhalos and study whether there is any dependence on mass or on environment. We have selected. subhalos at. redshift ο=0 in two different mass ranges (210h+N and c10072 tM).," We have selected subhalos at redshift $z=0$ in two different mass ranges $\simeq 10^{11}\,h^{-1}{\rm M}_{\odot}$ and $\simeq 10^{12}\,h^{-1}{\rm M}_{\odot}$ )." 1n order to test for the ellects of environment. we selected on one hand subhalos that reside within the virial raclius of the massive clusters that formed in simulations Bl and B2 by the present dav. and on the other hand. subhalos located within the smaller haloes found in simulation M3.," In order to test for the effects of environment, we selected on one hand subhalos that reside within the virial radius of the massive clusters that formed in simulations $1$ and $2$ by the present day, and on the other hand subhalos located within the smaller haloes found in simulation $3$." ln the following. we will refer to the substructures in the clusters as and to the substructures inside the smaller haloes of M3 assubhalos.," In the following, we will refer to the substructures in the clusters as and to the substructures inside the smaller haloes of $M$ 3 as." . Note that since we have excluded from our analysis the main subhalo associated with the FOL group and. since on average the most massive substructure has a mass a few per cent of Aloo (see Fig. 4)), Note that since we have excluded from our analysis the main subhalo associated with the FOF group and since on average the most massive substructure has a mass a few per cent of $M_{200}$ (see Fig. \ref{fig:fig2}) ) we end up with very. few substructures selected from M3., we end up with very few substructures selected from $3$. In particular we have only 5 substructures with a mass 107!M. and 38 substructures with a mass ~1055IM...," In particular we have only $5$ substructures with a mass $\sim 10^{12}\,h^{-1}{\rm M}_{\odot}$ and $38$ substructures with a mass $\sim 10^{11}\,h^{-1}{\rm M}_{\odot}$." Phe corresponding numbers for the substructures selected: from simulations Bl and. B2 are 62 and 338., The corresponding numbers for the substructures selected from simulations $1$ and $2$ are $62$ and $338$. For cach of these samples. we build the mass accretion uistories as follows: we start from a particular subhalo at redshift z=0 and construct its merger tree as described in he previous section.," For each of these samples, we build the mass accretion histories as follows: we start from a particular subhalo at redshift $z=0$ and construct its merger tree as described in the previous section." At each redshift we track the history of the selected subhalo by linking it with its most. massive »rogenitor., At each redshift we track the history of the selected subhalo by linking it with its most massive progenitor. In Fig., In Fig. 9 we show a tvpical example of a mass accretion ustory [ου a subhalo with mass 210555tM. at redshift zero.," \ref{fig:fig7} we show a typical example of a mass accretion history for a subhalo with mass $2\times 10^{11}\,h^{-1}{\rm M}_{\odot}$ at redshift zero." In the lower panel. we show the mass accretion history of the subhalo and in the upper panel. the corresponding mass of the halo in which the subhalo resides at each redshift.," In the lower panel, we show the mass accretion history of the subhalo and in the upper panel, the corresponding mass of the halo in which the subhalo resides at each redshift." In this example. the subhalo was acereted onto a Larger halo at redshift ~1 (shown as a dotted line on the plot).," In this example, the subhalo was accreted onto a larger halo at redshift $\sim 1$ (shown as a dotted line on the plot)." For times prior to this event the substructure was a main subhalo. i.e. the subhalo corresponding to a FOR group. ane ils mass grew monotonically in time.," For times prior to this event the substructure was a main subhalo, i.e. the subhalo corresponding to a FOF group, and its mass grew monotonically in time." From now on. we wil refer to this event as the (ausos) Of the subhalo.," From now on, we will refer to this event as the $t_{\rm accr}$ ) of the subhalo." A few snapshots later. at redshift 0.8. the substructure and its host halo were accreted onto the main progenitor of the cluster (shown as a solid line on the plot).," A few snapshots later, at redshift $\sim 0.8$, the substructure and its host halo were accreted onto the main progenitor of the cluster (shown as a solid line on the plot)." After the subhalo is aceretecl. it sulfers significant tida μαripping ancldecreases in mass.," After the subhalo is accreted, it suffers significant tidal stripping and in mass." In this particular example. 1e final mass of the subhalo is 240 per cent of the value ad its accretion timo.," In this particular example, the final mass of the subhalo is $\simeq 40$ per cent of the value at its accretion time." We find that for 60 per cent of the subhalos in the rmμι mass bin and ~SO per cent of the subhalos in. the 1012 binqa the aceretion: event corresponds to the accretion: of the substructure onto the main progenitor of the cluster itself., We find that for $\sim 60$ per cent of the subhalos in the $10^{11}$ mass bin and $\sim 80$ per cent of the subhalos in the $10^{12}$ bin the accretion event corresponds to the accretion of the substructure onto the main progenitor of the cluster itself. For most of the rest. the time elapsed between these two events is fairly short.," For most of the rest, the time elapsed between these two events is fairly short." The results we will show later are essentially unchanged if. we adopt as definition of the, The results we will show later are essentially unchanged if we adopt as definition of the While quasars are amongst the most luminous sources in the Universe. being at cosmological distances ensures that their small angular size renders them unresolved. to modern telescopes.,"While quasars are amongst the most luminous sources in the Universe, being at cosmological distances ensures that their small angular size renders them unresolved to modern telescopes." While direct. imaging of the central engines of quasars is not. possible. more novel techniques are able to reveal the scales of structure of several prominent eatures e.g. reverberation mapping can reveal the size of he enveloping. Broad-Line Region: sce Peterson. (1998)]].," While direct imaging of the central engines of quasars is not possible, more novel techniques are able to reveal the scales of structure of several prominent features [e.g. reverberation mapping can reveal the size of the enveloping Broad-Line Region; see \citet{1998AdSpR..21...57P}] ]." CGravitational microlensing is one such method. occurring when the light from a distant. source is magnified. hy the oesence of stellar masses crossing the line of sight.," Gravitational microlensing is one such method, occurring when the light from a distant source is magnified by the presence of stellar masses crossing the line of sight." Within he Galaxy. where single or binary stars pass in front of more distant sources. microlensing has been used to great. elfect in studying the surface properties of distant stars. such as imb darkening (e.g.Ithie&Bennett1999).," Within the Galaxy, where single or binary stars pass in front of more distant sources, microlensing has been used to great effect in studying the surface properties of distant stars, such as limb darkening \citep[e.g.][]{Rhie:99}." . AMicrolensing also occurs in a cosmological context. where the light from a distant. quasar has been multiply imaged by a foreground. galaxy.," Microlensing also occurs in a cosmological context, where the light from a distant quasar has been multiply imaged by a foreground galaxy." As with the Galactic case. stars within the lensing galaxy which cross the line of sight o these images can induce substantial magnification ellects.," As with the Galactic case, stars within the lensing galaxy which cross the line of sight to these images can induce substantial magnification effects." " Unlike the Galactic case. the number of stars inlluencing a particular image can be many thousands. and hence he resultant pattern of magnification can be extremely complex (seeIxavser.Relsdal.&Stabell1986:Wambseganss.""czvnski.&ναι1990.for examples)."," Unlike the Galactic case, the number of stars influencing a particular image can be many thousands, and hence the resultant pattern of magnification can be extremely complex \citep[see][for examples]{1986A&A...166...36K,Wambsganss:1990b}." Regions within he quasar will respond differently to the magnilving stars. dependent upon their size ancl location. and hence the light Curve variations as the stars cross the line of sight encode he underlying quasar structure.," Regions within the quasar will respond differently to the magnifying stars, dependent upon their size and location, and hence the light curve variations as the stars cross the line of sight encode the underlying quasar structure." Understanding and. more importantly. deconvolving this encoding has been the focus of a substantial amount of study in recent vears. and. has included. the development of computational approaches to account for the gravitational lensing by a large population of sources (seeSchneider.Wochanek.&Wambseanss2006.forarecent review).," Understanding and, more importantly, deconvolving this encoding has been the focus of a substantial amount of study in recent years, and has included the development of computational approaches to account for the gravitational lensing by a large population of sources \citep[see][for a recent review]{2006glsw.book.....S}." . Microlensing has been used to study structure on a range of scales within quasars. both limiting the size of the central accretion disk (Yonebhara2001:Bateetal.2008:Blackburnect2010) and including the properties of the “hig blue bump”," Microlensing has been used to study structure on a range of scales within quasars, both limiting the size of the central accretion disk \citep{Yonehara:2001,Bate:2008,Pooley:2010} and including the properties of the “big blue bump”" size of a pixel.,size of a pixel. Phe polarisation detector noise is assumed to be 15 and 2 times that of the total power noise for NLAP and. Planck (see Puget. 1998 for a recent discussion of the polarisation characteristics of the Planck IET) respectively., The polarisation detector noise is assumed to be $1.5$ and $2$ times that of the total power noise for MAP and Planck (see Puget 1998 for a recent discussion of the polarisation characteristics of the Planck HFI) respectively. " In analvsing both satellites. we assume that Galactic emission is negligible (or subtractable to high accuracy) over a fraction f.i,=0.65 of the sky."," In analysing both satellites, we assume that Galactic emission is negligible (or subtractable to high accuracy) over a fraction $f_{sky}=0.65$ of the sky." " We assess the amplitude of the gravitational lensing corrections to C; by computing the reduced. X722 where C; is the eravitationally lensed power spectrum computed. from. equation. (5)). C5 is the unlensed linear power spectrum. and ACY is the variance of €, given as. for an observation with ΑΝ antennae ο dilferent sensitivities ancl Gaussian beam widths σεν. Pom--. The total noise level erg in equation (10) is the sum of the respective noise levels for each of the channels (ure ;,). and an elfective beam shape 6; is given by (Bond 1997). b;= For cosmic variance limited experiments. fas in equation (13)) is equal to the adopted: cut olf in an /( space."," We assess the amplitude of the gravitational lensing corrections to $C_\ell$ by computing the reduced $\hat\chi^2$, where $\wtilde C_\ell$ is the gravitationally lensed power spectrum computed from equation \ref{GLcl}) ), $C_\ell$ is the unlensed linear power spectrum, and $\Delta C_\ell$ is the variance of $C_\ell$ given as, for an observation with $N$ antennae of different sensitivities and Gaussian beam widths $\sigma_{b\l(i\r)},$ $i=1,...,N.$ The total noise level $w_{T,E}$ in equation (10) is the sum of the respective noise levels for each of the channels $w_{T,E\l(i\r)}$ ), and an effective beam shape $b_l$ is given by (Bond 1997), $b_\ell=w^{-1}_{T,E}\sum_i w_{T,E\l(i\r)} \exp\l[-\ell\l(\ell+1\r)\sigma^2_{b\l(i\r)}\r].$ For cosmic variance limited experiments, $\ell_{\rm max}$ in equation \ref{chi2}) ) is equal to the adopted cut off in an $\ell$ space." For the NLAP and. Planck satellite. we choose the value fas that maxinilzes C as eiven in Table 2. (see also figure 3).," For the MAP and Planck satellite, we choose the value $\ell_{\rm max}$ that maximizes $\hat \chi^2$ as given in Table \ref{tab1} (see also figure 3)." A value of $7 of order unity signifies that the lensing distortion is detectable in principle bv an experiment., A value of $\hat \chi^2$ of order unity signifies that the lensing distortion is detectable in principle by an experiment. In this Section we use this criterion as a rough measure of the detectability of gravitational lensing in he CAIB., In this Section we use this criterion as a rough measure of the detectability of gravitational lensing in the CMB. However. if we parameterize C by IN. cosmologicalo parameters. then values of X7 as low as Nfs Can lead to significant differences between: estimated: parameters.," However, if we parameterize $C_\ell$ by $N$ cosmological parameters, then values of $\hat \chi^2$ as low as $\sim N/\ell_{\rm max}$ can lead to significant differences between estimated parameters." The effect of lensing on Cosmological parameters is discussed. in more detail in Section 4.3., The effect of lensing on cosmological parameters is discussed in more detail in Section 4.3. Values of X7 are listed in ‘Table 2/— for various experimental setups., Values of $\hat \chi^2$ are listed in Table \ref{tab1} for various experimental setups. bor Cosmic variance limited observations. the reduced X7 values are. approximately proportional to the fourth. power of the mass spectrum normalisation amplitude ex(fy).," For cosmic variance limited observations, the reduced $\hat\chi^2$ values are approximately proportional to the fourth power of the mass spectrum normalisation amplitude $\sigma_8\l(t_0\r)$." For the normalisation required by the observed. present day cluster. abundance (equation. 2)). the gravitational ensing contributions to the CALB power spectra are small rut not negligible at the sensitivities of a Planck-tvpe experiment.," For the normalisation required by the observed present day cluster abundance (equation \ref{cluster}) ), the gravitational lensing contributions to the CMB power spectra are small but not negligible at the sensitivities of a Planck-type experiment." Since the lensing corrections depend. strongly on the amplitude of the mass Iluctuations at the relatively ügh redshifts. the detectability of lensing is sensitive to he parameters of the target model.," Since the lensing corrections depend strongly on the amplitude of the mass fluctuations at the relatively high redshifts, the detectability of lensing is sensitive to the parameters of the target model." Thus. the reduced. X7 values for the standard CDM. model listed in Table 2. for a anck-tvpe experiment. are much lower than those of the A-cominatec and open models listed in the table. which jwe higher values of e and lower perturbation growth rates at the present.," Thus, the reduced $\hat\chi^2$ values for the standard CDM model listed in Table \ref{tab1} for a Planck-type experiment are much lower than those of the $\Lambda$ -dominated and open models listed in the table, which have higher values of $\sigma_8$ and lower perturbation growth rates at the present." " Ciravitational lensing moclifies the ""clamping ail of the temperature power spectrum at high multipoles (Moetcealf ssilk 1998) and this ellect makes a significant contribution ο C in cosmic variance limited. experiments probing {μα2000.", Gravitational lensing modifies the `damping tail' of the temperature power spectrum at high multipoles (Metcalf Silk 1998) and this effect makes a significant contribution to $\hat\chi^2$ in cosmic variance limited experiments probing $\ell_{\rm max} \simgt 2000$. The cletectability of lensing is thus sensitive o the multipole range probed by an experiment. anc to he cosmological angle-distance relation: the effect of lensing is less easy to detect in a negatively curved. universe since he damping tail is pushed to higher multipoles and. power spectrum peaks are broader than in a spatially [lat universe., The detectability of lensing is thus sensitive to the multipole range probed by an experiment and to the cosmological angle-distance relation; the effect of lensing is less easy to detect in a negatively curved universe since the damping tail is pushed to higher multipoles and power spectrum peaks are broader than in a spatially flat universe. {ο use the relic photons to obtain reasonable fit to (he Fermi data and the scattering on relic photons provides a negligible effect because of very. high. density of IR. ancl optical photons in Terzan 5.,to use the relic photons to obtain reasonable fit to the Fermi data and the scattering on relic photons provides a negligible effect because of very high density of IR and optical photons in Terzan 5. On the other hand. the I or optical scattering can nicely reproduce (he experimental data as shown in Fig. 5..," On the other hand, the IR or optical scattering can nicely reproduce the experimental data as shown in Fig. \ref{Ter}." As Terzan 5 is located in a more complicated environment than 47 Tuc. in particular it is located very close to the Galactic plane (see Figure 1 in Kone et al.," As Terzan 5 is located in a more complicated environment than 47 Tuc, in particular it is located very close to the Galactic plane (see Figure 1 in Kong et al." 2010). this makes the estimation of ils 5—rav brightness profile much more intricatecl.," 2010), this makes the estimation of its $\gamma-$ ray brightness profile much more intricated." In view of this difliculty. we do not compare the spatial distribution computed from the model with the observation for Terzan 5.," In view of this difficulty, we do not compare the spatial distribution computed from the model with the observation for Terzan 5." We also apply our IC model to other clusters presented in the paper by Abdo et al. (, We also apply our IC model to other clusters presented in the paper by Abdo et al. ( 2010b).,2010b). The diffusion coefficients are the same as for 47 Tucanae ancl Terzan 5 for simplicity., The diffusion coefficients are the same as for 47 Tucanae and Terzan 5 for simplicity. Although the ICS of the τος photons in some GCs may also fit the Fermi data. as we have pointed oul in section 2.2 without another factor the millisecond pulsar ratio," Although the ICS of the relic photons in some GCs may also fit the Fermi data, as we have pointed out in section 2.2 without another factor the millisecond pulsar ratio" where the rate of discovery of real sources is: and the rate of discovery of bogus sources is: Note that P(discovery|real) is just theefficiency of discovery.,where the rate of discovery of real sources is: and the rate of discovery of bogus sources is: Note that $P({\rm discovery}|{\rm real})$ is just the of discovery. We expect in PTF (and other imaging surveys where detections are made on subtractions) that in any single subtraction R(real)., We expect in PTF (and other imaging surveys where detections are made on subtractions) that in any single subtraction $R({\rm bogus}) \gg R({\rm real})$ . " Roughly, in PTF, R(bogus)=1000xR(real)."," Roughly, in PTF, $R({\rm bogus}) \approx 1000 \times R({\rm real})$." " If discovery were done on just a single epoch then, P(discovery|real)=(1—FNR) and P(discovery|bogus)= FPR."," If discovery were done on just a single epoch then, $P({\rm discovery}|{\rm real}) = (1 - FNR)$ and $P({\rm discovery}|{\rm bogus}) = FPR$ ." " Following §2.1.1,, with FNRez 0.2 and FPRez0.1 this implies P=0.008; this is unacceptably low."," Following \ref{sec:rb}, with $FNR \approx$ 0.2 and $FPR \approx 0.1$ this implies ${\cal P} = 0.008$; this is unacceptably low." " If we adopt a more conservative cut (Fig 3)), with FNR= 0.4 and FPRz0.01, then P=0.06."," If we adopt a more conservative cut (Fig \ref{fig:rbroc}) ), with $FNR \approx$ 0.4 and $FPR \approx 0.01$, then ${\cal P} = 0.06$." " To keep P near unity (a high purity of discoveries to maximize followup resources), equation 2 requires that we create a detection classification scheme that satisfies P(discovery|real)P(discovery|bogus)."," To keep ${\cal P}$ near unity (a high purity of discoveries to maximize followup resources), equation \ref{eq:s} requires that we create a detection classification scheme that satisfies $P({\rm discovery}|{\rm real}) \gg P({\rm discovery}|{\rm bogus})$ ." " When multiple detections are required to cross a threshold for a discovery, then P(discovery) changes, and importantly, this probability changes differently for bogus events than real events."," When multiple detections are required to cross a threshold for a discovery, then $P({\rm discovery})$ changes, and importantly, this probability changes differently for bogus events than real events." " In the simple case where two observations are made and two good detections (i.e., high realbogus) required, then This assumes that the probability of getting the same classification value is the same for both epochs, which might be nominally expected in the case of a source with approximately constant flux and similar observing conditions."," In the simple case where two observations are made and two good detections (i.e., high realbogus) required, then This assumes that the probability of getting the same classification value is the same for both epochs, which might be nominally expected in the case of a source with approximately constant flux and similar observing conditions." " For a bogus source to be called a discovery, however, two bogus subtraction candidates must be both incorrectly identified as real and occur close on the sky."," For a bogus source to be called a discovery, however, two bogus subtraction candidates must be both incorrectly identified as real and occur close on the sky." " In PTF, we have found that the existence of a bogus candidate is (unfortunately) highly correlated with the existence of another bogus candidate near the same place on the sky at different times: that is, certain places on the sky will preferentially yield bad subtractions (due to a combination of poor astrometry, imperfections in the reference image, and proximity to bright stars or chip edges)."," In PTF, we have found that the existence of a bogus candidate is (unfortunately) highly correlated with the existence of another bogus candidate near the same place on the sky at different times: that is, certain places on the sky will preferentially yield bad subtractions (due to a combination of poor astrometry, imperfections in the reference image, and proximity to bright stars or chip edges)." " Ignoring correlations of realbogusvalues?,, we expect with the two-candidate requirement P=0.06 and P=0.78 for FNR=0.2 (FPR= 0.1) and FNR=0.4 (FPR= 0.01), respectively."," Ignoring correlations of realbogus, we expect with the two-candidate requirement ${\cal P}=0.06$ and ${\cal P}=0.78$ for $FNR = 0.2$ $FPR =0.1$ ) and $FNR = 0.4$ $FPR =0.01$ ), respectively." " This means for the 2-candidate discovery process that at purity, we are efficient in finding real sources."," This means for the 2-candidate discovery process that at purity, we are efficient in finding real sources." " In practice, the source-discovery process in PTF is complicated by the fact thatreal source brightnesses are changing in time (and so too the respective realbogus values)."," In practice, the source-discovery process in PTF is complicated by the fact thatreal source brightnesses are changing in time (and so too the respective realbogus values)." We were also wary of, We were also wary of where theparameter @isthemixing angle. Theincidentspin-upproton (pl) breaks 8iintoa valence quark anda valence diquark:,"with probabilities $(1-c_1^2)(1-P_{PM})$ times $\frac{4}{9}\sin^2\theta, \frac{2}{9} \sin^2\theta, \frac{2}{9}\sin^2\theta, \frac{1}{9}\sin^2\theta$ and $\cos^2\theta$, respectively and into a quark and an antiquark:" plausibly be expected.,plausibly be expected. Using the Subiuillineter Array (SALA) to observe the CO(3-2) transition. Wuehesetal.(2011) derived constraints on the turbulent linewidth in the atinosphere of the disks surrounding the T Tauri star TW Iva and the Herbig Ac star IID1632967.," Using the Submillimeter Array ) to observe the CO(3-2) transition, \citet{hughes11} derived constraints on the turbulent linewidth in the atmosphere of the disks surrounding the T Tauri star TW Hya and the Herbig Ae star HD." . For TW Ίνα they placed an upper lint to the turbulent velocity of ο<45^\circ$ defined by Gehrels et al. ( 2000).,2000). This result is robust against changes in the adopted prescription for Reo., This result is robust against changes in the adopted prescription for $R_{\rm form}$. Iu the lower panel of Fig. l..," In the lower panel of Fig. \ref{fig:gamma-cluster}," " we also show menn nass. redshift. aud angular radius Oj, correspoudiug to rq of such eanania-ray clusters brighter than a eiven flux."," we also show mean mass, redshift, and angular radius $\theta_{\rm vir}$ corresponding to $r_{\rm vir}$ of such gamma-ray clusters brighter than a given flux." " These quantities are AL~1012AZ... 2~0.05. aud Oa,~1° for clusters above the EGRET seusitivitv limit."," These quantities are $M \sim 10^{15}M_\odot$, $z \sim 0.05$, and $\theta_{\rm vir} \sim 1^\circ$ for clusters above the EGRET sensitivity limit." Considering the EGRET augular resolution. the typical radius of ~17 is consistent with the fact that a significant fraction of isotropic unidentified sources are indicated as possilly extended.," Considering the EGRET angular resolution, the typical radius of $\sim 1^\circ$ is consistent with the fact that a significant fraction of isotropic unidentified sources are indicated as possibly extended." It is predicted that amore than a few thousauds of ormiue clusters will be detected by future missions such as he GLAST (Gehrels Michelson 1999). and the improved angular resolution may reveal the extended profile or nearby eanunaray clusters with ligher statistical significance.," It is predicted that more than a few thousands of forming clusters will be detected by future missions such as the GLAST (Gehrels Michelson 1999), and the improved angular resolution may reveal the extended profile for nearby gamma-ray clusters with higher statistical significance." Another important prediction is that GLAST will observe the flattening of the log N-logF curve due to he cosmological effects compared with the expectation of a uniform source distribution in the Euclidean space (dotted line in the upper panel of Fig. 1)).," Another important prediction is that GLAST will observe the flattening of the $\log N$ $\log F$ curve due to the cosmological effects, compared with the expectation of a uniform source distribution in the Euclidean space (dotted line in the upper panel of Fig. \ref{fig:gamma-cluster}) )." Our formmlation also allows us to caleulate the ECRB flux aud spectrin as where (dn.f/de.) is the gamma-ray ΕΠ density that is related to the EGRB flux as, Our formulation also allows us to calculate the EGRB flux and spectrum as where $(dn_\gamma/d\epsilon_\gamma)$ is the gamma-ray number density that is related to the EGRB flux as "~10? ofequipartition"".. then electrons rapidly cool (by synchrotron emission) very close to the Jet base.","$\sim10^{-3}$ of, then electrons rapidly cool (by synchrotron emission) very close to the jet base." During the initial rapid cooling. most of the emission is in the X-ray band.," During the initial rapid cooling, most of the emission is in the X-ray band." Therefore. the flux at this band saturates to a constant value.," Therefore, the flux at this band saturates to a constant value." The rapid cooling implies that already close to the jet base. once the electrons cool below a critical energy. synchrotron emission becomes obscured. i.&.. <<εως.," The rapid cooling implies that already close to the jet base, once the electrons cool below a critical energy, synchrotron emission becomes obscured, i.e., $\nu_{peak} < \nu_{thick}$." " If no additional heating source exists. this situation1, continues along the jet: Le.. emission from electrons that propagate along the jet remains self absorbed."," If no additional heating source exists, this situation continues along the jet: i.e., emission from electrons that propagate along the jet remains self absorbed." At large radit the emission is mainly at the radio band. and thus the integrated spectrum shows a suppression of the flux at the radio band. whichnof accompanied by a similar suppression of the flux at the X-ray band.," At large radii the emission is mainly at the radio band, and thus the integrated spectrum shows a suppression of the flux at the radio band, which accompanied by a similar suppression of the flux at the X-ray band." In this regime of high magnetic field. a further increase in the strength of the magnetic field at the jet base does not significantly change the flux at the X-ray band. as it already saturates (the electrons radiate most of their available energy at this band).," In this regime of high magnetic field, a further increase in the strength of the magnetic field at the jet base does not significantly change the flux at the X-ray band, as it already saturates (the electrons radiate most of their available energy at this band)." However. emission at radio frequencies is further suppressed. because the electrons cool to lower energies. resulting in a further decrease in Ἱέρων.," However, emission at radio frequencies is further suppressed, because the electrons cool to lower energies, resulting in a further decrease in $\nu_{peak}$." This result may thus provide a natural explanation to the outliers seen in Fig. I..," This result may thus provide a natural explanation to the outliers seen in Fig. \ref{gallorel}," which show suppression of the radio flux., which show suppression of the radio flux. For power-law distributed electrons. an additional consequence of a strong magnetic field is that the slope of the spectrum in the X-rays increases by 0.5. with respect to the spectrum obtained for weak magnetic field (see PCO9 for details).," For power-law distributed electrons, an additional consequence of a strong magnetic field is that the slope of the spectrum in the X-rays increases by 0.5, with respect to the spectrum obtained for weak magnetic field (see PC09 for details)." In Fig., In Fig. " 2 we plot the spectral energy distribution for three different values of the magnetic field (B.,/30. Bi. 3B4)."," \ref{seds} we plot the spectral energy distribution for three different values of the magnetic field $_{\rm cr}$ /30, $_{\rm cr}$, $_{\rm cr}$ )." The plot refers to the ballistic case (1e. neglecting adiabatic losses). and an electron energy distribution with a high energy power-law tail (with spectral index jj= 2.5). but the result of the radio quenching ts general.," The plot refers to the ballistic case (i.e. neglecting adiabatic losses), and an electron energy distribution with a high energy power-law tail (with spectral index $p=2.5$ ), but the result of the radio quenching is general." As summarized in refregimes.. à source with a jet magnetic field higher than a critical value would have a strongly quenched radio emission. but a substantially unchanged X-ray emission. with respect to sources with lower magnetic field.," As summarized in \\ref{regimes}, a source with a jet magnetic field higher than a critical value would have a strongly quenched radio emission, but a substantially unchanged X-ray emission, with respect to sources with lower magnetic field." However. the slope of the radio/X-ray correlation is mostly set by the radiative efficiency of the aceretion flow. and its dependency on the aceretion rate (seee.g.Fenderetal.2003.foradiscussiononthis issue)..," However, the slope of the radio/X-ray correlation is mostly set by the radiative efficiency of the accretion flow, and its dependency on the accretion rate \citep[see e.g.][for a discussion on this issue]{fenderetal03}." " Therefore. with all the properties of the accretion flow (including its efficiency) remaining a priori unchanged. it is natural to expect for sources with strong magnetic field. a correlation between the radio and the X-ray fluxes with a similar slope to that shown by the radio-loud BHCs. but with a lower normalization,"," Therefore, with all the properties of the accretion flow (including its efficiency) remaining a priori unchanged, it is natural to expect for sources with strong magnetic field, a correlation between the radio and the X-ray fluxes with a similar slope to that shown by the radio-loud BHCs, but with a lower normalization." If indeed the reason for the low radio emission in some BHCs is the stronger magnetic field. one can look for other possible signatures of jetthis.," If indeed the reason for the low radio emission in some BHCs is the stronger jet magnetic field, one can look for other possible signatures of this." An obvious direction to look at is the overall spectral shape of the jet emission., An obvious direction to look at is the overall spectral shape of the jet emission. The rapid cooling of the radiating electrons implies that for magnetic field stronger than a eritical value. the high-energy (thin-synchrotron) part of the spectrum steepens by a factor of 0.5 with respect to the spectrum obtained for weaker magnetic field (see Fig. 2)).," The rapid cooling of the radiating electrons implies that for magnetic field stronger than a critical value, the high-energy (thin-synchrotron) part of the spectrum steepens by a factor of 0.5 with respect to the spectrum obtained for weaker magnetic field (see Fig. \ref{seds}) )." One would thus expect the radio-quiet BHCs to show a softer X-ray spectrum. assuming the X-ray emission arises from the jet.," One would thus expect the radio-quiet BHCs to show a softer X-ray spectrum, assuming the X-ray emission arises from the jet." " However. such a steepening is expected already below the critical value B,.. described in refregimes.."," However, such a steepening is expected already below the critical value $_{\rm cr}$ described in \\ref{regimes}." This means that. a priort. both radio-quiet and radio-loud BHCs might have a high-enough magnetic field to cause the X-ray steepening. thus showing a similar X-ray spectral slopes.," This means that, a priori, both radio-quiet and radio-loud BHCs might have a high-enough magnetic field to cause the X-ray steepening, thus showing a similar X-ray spectral slopes." Moreover. and more importantly. the X-ray spectrum of BHC in their hard state appears to be different from a simple power law. as would be expected in the case of pure synchrotron emission.," Moreover, and more importantly, the X-ray spectrum of BHC in their hard state appears to be different from a simple power law, as would be expected in the case of pure synchrotron emission." Indeed. the model presented in PCO9 ts clearly a simplification of a much more complex reality.," Indeed, the model presented in PC09 is clearly a simplification of a much more complex reality." Important contributions from processes other than synchrotron (mainly Comptonization. from a hot corona or from the jet itself) are expected to substantially modify the spectral energy distribution at high energies (seee.g.Mac-carone2005:Markoffetal. 2005).," Important contributions from processes other than synchrotron (mainly Comptonization, from a hot corona or from the jet itself) are expected to substantially modify the spectral energy distribution at high energies \citep[see e.g.][]{tom05,markoffetal05}." . Precise estimates and predictions of the slope at high energies are thus expected to be more complex than presented in Fig. 2..," Precise estimates and predictions of the slope at high energies are thus expected to be more complex than presented in Fig. \ref{seds}," " but the main result on the role of the magnetic field holds. and is independent on the origin of the X-ray emission,"," but the main result on the role of the magnetic field holds, and is independent on the origin of the X-ray emission." Furthermore. our model considers only a single acceleration episode.," Furthermore, our model considers only a single acceleration episode." It is natural to expect the production/— of internal shock waves (Kaiseretal.2000)... which may further heat the particles inside the jet (seee.g.Jamiletal.2005).," It is natural to expect the production of internal shock waves \citep{kss00}, which may further heat the particles inside the jet \cite[see e.g.][]{jamiletal08}." This would inevitably modify the results presented here. which however would qualitatively hold (albeit with higher values of B).," This would inevitably modify the results presented here, which however would qualitatively hold (albeit with higher values of $_{\rm cr}$ )." While a clear feature of the model discussed here is the peaked synchrotron emission at optical wavelengths for strong B. we expect the overlapping emission from the companion star and the accretion to make difficult to spectrally identify this feature.," While a clear feature of the model discussed here is the peaked synchrotron emission at optical wavelengths for strong B, we expect the overlapping emission from the companion star and the accretion to make difficult to spectrally identify this feature." On the other hand. it may be possible to detect it through polarimetry studies.," On the other hand, it may be possible to detect it through polarimetry studies." Within the framework of our model. with the intensity of the magnetic field in the jet influencing the overall jet spectral emission. it is reasonable to ask how much of the observed spectral evolution during a BHC outburst could be explained in terms of changes in the magnetic field in the jet of a single source.," Within the framework of our model, with the intensity of the magnetic field in the jet influencing the overall jet spectral emission, it is reasonable to ask how much of the observed spectral evolution during a BHC outburst could be explained in terms of changes in the magnetic field in the jet of a single source." In this perspective. the usual conclusion that the jet is switched off when the radio is quenched does not necessarily hold any longer.," In this perspective, the usual conclusion that the jet is switched off when the radio is quenched does not necessarily hold any longer." More generally. according to our model. the radio (or infrared) flux cannot any longer be considered a good tracer of the jet power.," More generally, according to our model, the radio (or infrared) flux cannot any longer be considered a good tracer of the jet power." For example. radio emission from BHCs is known to quench at (or around) the transition out of the hard. state (e.g.thewellstudiedGX339-4:foradiscussiononmoreseeFenderetal. 2009).," For example, radio emission from BHCs is known to quench at (or around) the transition out of the hard state \citep[e.g. the well studied GX 339--4; for a discussion on more sources see][]{fenderetal09}." . Could this radio quenching be due to an increase in the magnetic field of the jet?, Could this radio quenching be due to an increase in the magnetic field of the jet? If the magnetic field were to increase during the hard-state rise of the outburst. the effects on the radio/X-ray correlation would not be distinguishable from those due to the increase of the accretion rate.," If the magnetic field were to increase during the hard-state rise of the outburst, the effects on the radio/X-ray correlation would not be distinguishable from those due to the increase of the accretion rate." In both cases the overall jet spectrum would remain approximately the same. albeit increasing its normalization (under the hypothesis of the X-rays coming from the jet).," In both cases the overall jet spectrum would remain approximately the same, albeit increasing its normalization (under the hypothesis of the X-rays coming from the jet)." However. once the magnetic field reaches a critical value. a qualitative change would occur.," However, once the magnetic field reaches a critical value, a qualitative change would occur." A further increase of the magnetic field would leave almost unchanged the X-ray luminosity. which for a given accretion rate would saturate. although the X-ray spectrum would show a steepening.," A further increase of the magnetic field would leave almost unchanged the X-ray luminosity, which for a given accretion rate would saturate, although the X-ray spectrum would show a steepening." At the same time the radio luminosity would drop., At the same time the radio luminosity would drop. This is qualitatively consistent with what is observed during, This is qualitatively consistent with what is observed during "galaxy samples, obscured star formation may have been missed (e.g.,Miller&Owen2001;Goto2007).","galaxy samples, obscured star formation may have been missed \citep[e.g.,][]{mo01,go07}." ". However, some contamination by a dusty star-forming population will not compromise our results (see Section 4.1)."," However, some contamination by a dusty star-forming population will not compromise our results (see Section 4.1)." " To obtain a homogeneous sample and to avoid modeling degeneracies, our selection intentionally excludes younger or heavily dust-obscured post-starburst galaxies and specifically targets galaxies with short star formation timescales, for which the TP-AGB phase is most prominent."," To obtain a homogeneous sample and to avoid modeling degeneracies, our selection intentionally excludes younger or heavily dust-obscured post-starburst galaxies and specifically targets galaxies with short star formation timescales, for which the TP-AGB phase is most prominent." " Therefore, our sample is likely more restrictive than other spectroscopically selected post-starburst galaxy samples (e.g.,Quinteroet"," Therefore, our sample is likely more restrictive than other spectroscopically selected post-starburst galaxy samples \citep[e.g.,][]{qu04}." " However, for the purpose of this Letter it is not relevant2004).. whether our sample is complete, as long as the selection is not biased toward any particular SPS model."," However, for the purpose of this Letter it is not relevant whether our sample is complete, as long as the selection is not biased toward any particular SPS model." " In order to make a composite spectrum, we deredshift the SEDs of all galaxies to rest frame, without changing the observed fluxes."," In order to make a composite spectrum, we deredshift the SEDs of all galaxies to rest frame, without changing the observed fluxes." " All SEDs are normalized at 5000A,, the longest wavelength for which the variations between the different SPS models are negligible Figure 1))."," All SEDs are normalized at 5000, the longest wavelength for which the variations between the different SPS models are negligible (see Figure \ref{fig:ill}) )." We create a composite SED by averaging (seethe rest-frame fluxes in wavelength bins of 20 data points each., We create a composite SED by averaging the rest-frame fluxes in wavelength bins of 20 data points each. The uncertainties on the composite spectrum are determined by bootstrapping., The uncertainties on the composite spectrum are determined by bootstrapping. Figure 3 shows the composite post-starburst galaxy SED in black., Figure \ref{fig:sed} shows the composite post-starburst galaxy SED in black. The photometric data points of the individual galaxies are represented by the gray dots., The photometric data points of the individual galaxies are represented by the gray dots. " The uniformity of all individual SEDs is remarkable and results in a high-quality, low-resolution spectrum of a post-starburst galaxy."," The uniformity of all individual SEDs is remarkable and results in a high-quality, low-resolution spectrum of a post-starburst galaxy." " Even subtle features, such as the absorption line at 2800 aand the continuum break at 2640A,, are detected."," Even subtle features, such as the absorption line at 2800 and the continuum break at 2640, are detected." The high quality of the composite post-starburst galaxy SED allows the assessment of the different SPS models., The high quality of the composite post-starburst galaxy SED allows the assessment of the different SPS models. " We fit the composite SED by both the Bruzual&Charlot(2003) and Maraston(2005) models, assuming a star formation history (SFH) of the form wv(t)οκ and leaving age (t), the e-folding time (7), exp(—t/r)the amount of dust attenuation (Ay)), and metallicity (Z) as free parameters (see note to Table 1))"," We fit the composite SED by both the \cite{bc03} and \cite{ma05} models, assuming a star formation history (SFH) of the form $\psi(t)\propto{\rm exp}(-t/\tau)$ and leaving age $t$ ), the $e$ -folding time $\tau$ ), the amount of dust attenuation ), and metallicity $Z$ ) as free parameters (see note to Table \ref{tab:mod}) )." " We assume the Calzettietal.(2000) attenuation curve, which we implement as a uniform screen."," We assume the \cite{ca00} attenuation curve, which we implement as a uniform screen." " We adoptthe Salpeter(1955) initial mass function (IMF), as this IMF is available for both SPS models."," We adoptthe \cite{sa55} initial mass function (IMF), as this IMF is available for both SPS models." Compared to a Kroupa(2001) or Chabrier(2003) IMF our choice will primarily affect the mass-to-light ratio and has little impact on other stellar population properties., Compared to a \cite{kr01} or \cite{ch03} IMF our choice will primarily affect the mass-to-light ratio and has little impact on other stellar population properties. " For each bin, we determine the effective filter curve, by adding the deredshifted filter curves of all included data points."," For each bin, we determine the effective filter curve, by adding the deredshifted filter curves of all included data points." " In most cases, this is a variety of broadband and medium-band filters with different observedwavelengths, as our sample spans a large range in redshift."," In most cases, this is a variety of broadband and medium-band filters with different observedwavelengths, as our sample spans a large range in redshift." We start by fitting the full wavelength range., We start by fitting the full wavelength range. " The best fits for Bruzual&Charlot(2003) and Maraston(2005) are represented by the orange and purple fits in Figure 3,, respectively."," The best fits for \cite{bc03} and \cite{ma05} are represented by the orange and purple fits in Figure \ref{fig:sed}, respectively." " The Bruzual&Charlot models yield an acceptable fit to the data, while(2003) the Maraston(2005) models do not fit the full wavelength range simultaneously."," The \cite{bc03} models yield an acceptable fit to the data, while the \cite{ma05} models do not fit the full wavelength range simultaneously." " The best-fit stellar population properties are broadly consistent, with a slightly lower value for stellar mass (M.) and ffor the Maraston(2005) models (Table 1))."," The best-fit stellar population properties are broadly consistent, with a slightly lower value for stellar mass $M_{*}$ ) and for the \cite{ma05} models (Table \ref{tab:mod}) )." " We have explored other SFHs as well, such as a delayed exponential SFH (v(t)~t a truncated SFH preceded by a constant star exp(—t/r)),formation rate (SFR, with T=tstop— tstart), a truncated SFH preceded by an exponentially increasing SFR, and a two-component population, but none provide a significantly better correspondence between the Maraston(2005) models and the composite SED."," We have explored other SFHs as well, such as a delayed exponential SFH $\psi(t)\sim t~{\rm exp}(-t/\tau)$ ), a truncated SFH preceded by a constant star formation rate (SFR, with $\tau=t_{\rm stop}-t_{\rm start}$ ), a truncated SFH preceded by an exponentially increasing SFR, and a two-component population, but none provide a significantly better correspondence between the \cite{ma05} models and the composite SED." " The SFH used to generate the model SEDs in Figure 3 produces a sharply peaked spectrum; adding an older or dusty star-forming population would only broaden the model SED, which would then produce an even larger discrepancy between the Maraston models and the data."," The SFH used to generate the model SEDs in Figure \ref{fig:sed} produces a sharply peaked spectrum; adding an older or dusty star-forming population would only broaden the model SED, which would then produce an even larger discrepancy between the \cite{ma05} models and the data." " To better understand(2005) the discrepancies between the models in the rest-frame near-infrared, we repeat the fitting, but now restricting the wavelength range to 6000 A."," To better understand the discrepancies between the models in the rest-frame near-infrared, we repeat the fitting, but now restricting the wavelength range to $\lambda<6000$ ." ". The Bruzual&Charlot(2003) and Maraston(2005) models, as represented by the red and blue curves, respectively, fit this wavelength range nearly equally well and yield consistent values for M,, t, T, and "," The \cite{bc03} and \cite{ma05} models, as represented by the red and blue curves, respectively, fit this wavelength range nearly equally well and yield consistent values for $M_*$ , $t$ , $\tau$ , and (Table \ref{tab:mod}) )." "However, while Bruzual&Charlot(2003) also fit ((Tablethe 1)).full wavelength coverage, the Maraston(2005) models overpredict the rest-frame near-infrared flux."," However, while \cite{bc03} also fit the full wavelength coverage, the \cite{ma05} models overpredict the rest-frame near-infrared flux." moderately active nuclei (AGNs) of central member galaxies (Binney Tabor 1995; Voit Donahue 2005).,moderately active nuclei (AGNs) of central member galaxies (Binney Tabor 1995; Voit Donahue 2005). But then such internal inputs can produce heating and outflows of the ICP so as to substantially lower Ly or equivalently raise the entropy., But then such internal inputs can produce heating and outflows of the ICP so as to substantially lower $L_X$ or equivalently raise the entropy. To affect the ICP at large. inputs of a few keVs per particle are required. and are easily provided by powerful AGNs energized by accreting supermassive black holes (BHs) in member galaxies (Wu et al.," To affect the ICP at large, inputs of a few keVs per particle are required, and are easily provided by powerful AGNs energized by accreting supermassive black holes (BHs) in member galaxies (Wu et al." 2000: Cavaliere et al., 2000; Cavaliere et al. 2002: Nath Roychowdhury 2002; Lapi et al., 2002; Nath Roychowdhury 2002; Lapi et al. 2005)., 2005). These not only effectively control the central cool cores within 100 kpc. but also can raise K by some 107 keV em? over much larger ICP masses (Lapi et al.," These not only effectively control the central cool cores within $100$ kpc, but also can raise $K$ by some $10^2$ keV $^2$ over much larger ICP masses (Lapi et al." 2005)., 2005). In fact. imprints of such inputs in action are directly observed in the ICP out to rz3«107 kpe. where they excavate extensive cavities or launch far-reaching blastwaves (Birrzan al.," In fact, imprints of such inputs in action are directly observed in the ICP out to $r\approx 3\times 10^2$ kpc, where they excavate extensive cavities or launch far-reaching blastwaves (Bîrrzan al." 2004: Nulsen et al., 2004; Nulsen et al. 2005: Forman et al., 2005; Forman et al. 2005: Cavaliere Lapi 2000)., 2005; Cavaliere Lapi 2006). Taking up from Lapi et al. (, Taking up from Lapi et al. ( 2005). we show next how these AGN inputs provide a unified key to both the steep of the local Ly—T relation and the apparently non-monotonic evolution of itsfefght.,"2005), we show next how these AGN inputs provide a unified key to both the steep of the local $L_X - T$ relation and the apparently non-monotonic evolution of its." . What kind of AGNs are most effective in this context. depends on z and on the BH accretion rates a (Eddington units).," What kind of AGNs are most effective in this context, depends on $z$ and on the BH accretion rates $\dot m$ (Eddington units)." Αη5% and low z=0.5 the dominant component to the outputs is constituted by “kinetic power’. in the form of high speed conical winds and narrow relativistic jets associated with radio emissions (see Churazov et al.," At $\dot{m}\la 5\%$ and low $z\la 0.5$ the dominant component to the outputs is constituted by `kinetic power', in the form of high speed conical winds and narrow relativistic jets associated with radio emissions (see Churazov et al." 2005: Blundell Kuncic 2007; Merloni Heinz 2007; Heinz et al., 2005; Blundell Kuncic 2007; Merloni Heinz 2007; Heinz et al. 2007)., 2007). Such outputs already in kinetic form end up with coupling a substantial energy fraction f;7| to the surrounding medium. interstellar or ICP.," Such outputs already in kinetic form end up with coupling a substantial energy fraction $f_k\approx 1$ to the surrounding medium, interstellar or ICP." At higher #7 the radiative activity is held to be dominant (see Churazov et al., At higher $\dot{m}$ the radiative activity is held to be dominant (see Churazov et al. 2005). and is also well known to evolve strongly with z.," 2005), and is also well known to evolve strongly with $z$." So this 1s expected to take over in affecting the ICP despite the weaker photon-particle energetic coupling. bounded to levels f.zv/2cz:0.05 by momentum conservation setting an outflow speed v.," So this is expected to take over in affecting the ICP despite the weaker photon-particle energetic coupling, bounded to levels $f_r \approx v/2c\approx 0.05$ by momentum conservation setting an outflow speed $v$." We stress that values of that order effectively account in terms of AGN feedback not only for the local shape of the Ly—T correlation in clusters and groups that started up the present investigation. but also for several other observables: the galaxy stellar mass and luminosity functions (Springel et al.," We stress that values of that order effectively account in terms of AGN feedback not only for the local shape of the $L_X-T$ correlation in clusters and groups that started up the present investigation, but also for several other observables: the galaxy stellar mass and luminosity functions (Springel et al." 2005); the luminosity functions of quasars and the mass distribution of relic BHs (Hopkins et al., 2005); the luminosity functions of quasars and the mass distribution of relic BHs (Hopkins et al. 2006; Lapi et al., 2006; Lapi et al. 2006): the correlation between these masses and the velocity dispersions in the host bulges (Vittorini et al., 2006); the correlation between these masses and the velocity dispersions in the host bulges (Vittorini et al. 2005)., 2005). On the other hand. velocities up to v~0.1—0.2c and metals spread out to some 10 kpe are widely observed around radioquiet quasars. indicating the action of efficient radiation-driven outflows or blastwaves (e.g.. Pounds Page 2006. Stockton et al.," On the other hand, velocities up to $v\sim 0.1 - 0.2\, c$ and metals spread out to some $10^2$ kpc are widely observed around radioquiet quasars, indicating the action of efficient radiation-driven outflows or blastwaves (e.g., Pounds Page 2006, Stockton et al." 2006)., 2006). The radiation thrust may involve absorbtion in many atomic lines. or Thomson scattering. of the continuum in the galactic plasma.," The radiation thrust may involve absorbtion in many atomic lines, or Thomson scattering of the continuum in the galactic plasma." Based on the latter. King (2003) has computed in detail outflows starting from the Compton-thick vicinities of the central BH and continuously accelerated to high speeds. that drive powerful blastwaves propagating into the outskirts of the host galaxy and beyond.," Based on the latter, King (2003) has computed in detail outflows starting from the Compton-thick vicinities of the central BH and continuously accelerated to high speeds, that drive powerful blastwaves propagating into the outskirts of the host galaxy and beyond." At that point the Thomson optical depth retains values of several 107. having decreased as 777? or slower in the hot galactic plasma with its flatter distribution relative to DM's.," At that point the Thomson optical depth retains values of several $10^{-2}$, having decreased as $r^{-0.5}$ or slower in the hot galactic plasma with its flatter distribution relative to DM's." The integrated input levels in these two regimes are related to a first approximation by the simple ‘golden rule’ fi~ const. cf.," The integrated input levels in these two regimes are related to a first approximation by the simple `golden rule' $f\, \dot{m} \approx $ const, cf." Churazov et al. (, Churazov et al. ( 2005).,2005). But their z-dependencies differ strongly as stressed by Merloni Heinz (2007) and Heinz et al. (, But their $z$ -dependencies differ strongly as stressed by Merloni Heinz (2007) and Heinz et al. ( 2007). with the kinetic power roughly constant (or slowly decreasing) out to z 0.5. and the radiative power strongly increasing out to z2.5 if limited in its effects by weaker coupling.,"2007), with the kinetic power roughly constant (or slowly decreasing) out to $z \approx 0.5$ , and the radiative power strongly increasing out to $z \approx 2.5$ if limited in its effects by weaker coupling." " These two components involve an activity fraction Ας for radio loud or radio quiet AGNs. and contribute energies W,,. which combine after the reckoning given in Table | to yield the overall input As to W, we adopt the evaluations providedby Merloni"," These two components involve an activity fraction $R_{k,r}$ for radio loud or radio quiet AGNs, and contribute energies $W_{k,r}$ which combine after the reckoning given in Table 1 to yield the overall input As to $W_{k,r}$ we adopt the evaluations providedby Merloni" All objects in Tab.,All objects in Tab. 1 exhibit a hard (ay< 1) spectrum in the N-rayv domain. with JJ0682|057 havingaving ea particularly hard spectrum.," 1 exhibit a hard $\alpha_{X}<$ 1) spectrum in the X-ray domain, with J0632+057 having a particularly hard spectrum." The TeV spectral indices of all objects are consistent with each other and all considerably softer than the corresponding X-ray. spectrum., The TeV spectral indices of all objects are consistent with each other and all considerably softer than the corresponding X-ray spectrum. ALL objects appear to have their peak energv output in the MeV. to GeV range., All objects appear to have their peak energy output in the MeV to GeV range. Note that GeV emission has only been detected using Fermi coincident with 11613303 and. 550390 (?).., Note that GeV emission has only been detected using Fermi coincident with 303 and 5039 \citep{Fermi:cat0}. Upper limits for the other sources have been estimated using detected: sources close to the objects of interest. to determine the local detection threshold., Upper limits for the other sources have been estimated using detected sources close to the objects of interest to determine the local detection threshold. The 5-ray binaries all display variable racio emission with a wide range of spectral. properties including lowenergy. spectral turnovers (scee.g. 2). , The $\gamma$ -ray binaries all display variable radio emission with a wide range of spectral properties including lowenergy spectral turnovers \citep[see e.g.][]{Godambe08}. . (77) ," \citep{Paredes98,Ribo08} " Be stars are rapidly rotating main sequence or eat stars that are characterized by the presence of (variable) a cunission. caused by ligh-deusity cieunstellar gas.,"Be stars are rapidly rotating main sequence or giant stars that are characterized by the presence of (variable) $\alpha$ emission, caused by high-density circumstellar gas." Often the Πα line profile is double-peaked aud its width correlates with the projected rotational velocity sin ii) of the wunderlving star (e.g.7)., Often the $\alpha$ line profile is double-peaked and its width correlates with the projected rotational velocity $\sin$ i) of the underlying star \citep[e.g.][]{1986A&A...159..276D}. At infrared auc radio wavelengths. the coutimmiun euergev distribution of Be stars is dominated by free-free aud bomud-free Ciissio from the high-densityo circumstellar ogas. which also causes the Πα cussion.," At infrared and radio wavelengths, the continuum energy distribution of Be stars is dominated by free-free and bound-free emission from the high-density circumstellar gas, which also causes the $\alpha$ emission." Direct imaging of the cimeuustellar material at radio wavelengths (7) and iu the Πα line. (e.c.7). shows that the eas is in a disc-like ecometry.," Direct imaging of the circumstellar material at radio wavelengths \citep{1992Natur.359..808D} and in the $\alpha$ line, \citep[e.g.][]{1998A&A...332..268S} shows that the gas is in a disc-like geometry." " This fattened geometry is also evident from the optical continui linear polarisation (co.ο,7?7) due to electron scattering.", This flattened geometry is also evident from the optical continuum linear polarisation \citep[e.g.][]{1979AJ.....84..812P} due to electron scattering. The physical mechanisni responsible for the disc-ike eeometry is related to the rapid rotation of the star., The physical mechanism responsible for the disc-like geometry is related to the rapid rotation of the star. Models proposed in the literature iuclude the wind compressed dise model (?).. viscocitv-diveu outflow iu 1ο equatorial regions (?) and non-cradial pulsatious (2)..," Models proposed in the literature include the wind compressed disc model \citep{1993ApJ...409..429B}, viscocity-driven outflow in the equatorial regions \citep{1999iau..conf..okazaki} and non-radial pulsations \citep{1983ApJ...269..250V}." Which of these models is correct. cau be tested by investigating the density aud kinematical structure of ie disc., Which of these models is correct can be tested by investigating the density and kinematical structure of the disc. We use the infrared. spectral region to explore je structure of Be star discs., We use the infrared spectral region to explore the structure of Be star discs. At these waveleneths disc nission donuunates he spectzunu. and a rich hydrogen id helm enuüssou Lue spectrum ds available.," At these wavelengths disc emission dominates the spectrum, and a rich hydrogen and helium emission line spectrum is available." The oeifrarec lines probe the inner regions of the disc. aud their streneth :id width are imiportaut diagnostic tools for the (cusity and kinematical structure of the disc.," The infrared lines probe the inner regions of the disc, and their strength and width are important diagnostic tools for the density and kinematical structure of the disc." Caomad-based infrared spectra of + Cas were previously reported by oe. 2.. ? and ?..," Ground-based infrared spectra of $\gamma$ Cas were previously reported by e.g. \citet{1983A&A...127..279C}, \citet{1985ApJ...290..325L} and \citet{1987ApJ...318..356H}." The Infrared Space Observatory (ISO) (?) with its Short Wavelength Spectrometer (SWS) is vorv well suited to explore the infrared part of the spectrum of Be stars., The Infrared Space Observatory (ISO) \citep{1996A&A...315L..27K} with its Short Wavelength Spectrometer (SWS) \citep{1996A&A...315L..49D} is very well suited to explore the infrared part of the spectrum of Be stars. Tn this study we present a preliminary analysis of the ISO-SWS spectrum of one of the brightest and best studied Be stars iu the sky. + Cas (BO.SIVe).," In this study we present a preliminary analysis of the ISO-SWS spectrum of one of the brightest and best studied Be stars in the sky, $\gamma$ Cas (B0.5IVe)." We will show, We will show of the first flare are similar to other flares found iu Class Ls and Class II|UIs.,of the first flare are similar to other flares found in Class $_c$ s and Class II+IIIs. The second flare shows unusual time profiles iu he flux and enussion measure (EAL)., The second flare shows unusual time profiles in the flux and emission measure (EM). Uowever. the cluperature profile is more typical of the normal dare: at phase 7 it iucreases rapidly. aud ucarly stavs constant or shows eradual decay.," However, the temperature profile is more typical of the normal flare; at phase 7 it increases rapidly, and nearly stays constant or shows gradual decay." These profiles may ο understood by the partial occultation of a flare due o the stellar rotations., These profiles may be understood by the partial occultation of a flare due to the stellar rotations. We hence ft the light curve of he second flare with a model of expoucutial flare) « sinusoidal (rotation modulation) function. aud obtain he rotation period of —231 hours.," We hence fit the light curve of the second flare with a model of exponential (flare) $\times$ sinusoidal (rotation modulation) function, and obtain the rotation period of $\sim$ 34 hours." Figure 9 (right panel) is the spectra curing the aree flare., Figure 9 (right panel) is the spectrum during the large flare. A remarkable finding is an additional cluission liue feature near the 6.7 keV hue of highly ionized⋅⋅ iron., A remarkable finding is an additional emission line feature near the 6.7 keV line of highly ionized iron. ⋅ The↴ best fit ⋅⋅liue energy ⋡⋅⋅⋃⊳⊥is IN keV.- which is attributable to ueutral or low ionized ion.," The best fit line energy is $^{+0.1}_{-0.4}$ keV, which is attributable to neutral or low ionized iron." The inmost plausible origin is fluorescence from cold iron iu the ciremustellar eas., The most plausible origin is fluorescence from cold iron in the circumstellar gas. If the circumstellar gas is spherically distributed around the N-vayv source. the equivalent width of rou is estimated to be 5-10 Zed Ng flor? 2) ον. where Zp. and Nyy ave the abundance of ou aud coluuu deusitv. respectively (Inoue 1985).," If the circumstellar gas is spherically distributed around the X-ray source, the equivalent width of iron is estimated to be $\approx$ 10 $_{\rm Fe}$ $N_{\rm H}$ $^{22}$ $^{-2}$ ) eV, where $_{\rm Fe}$ and $N_{\rm H}$ are the abundance of iron and column density, respectively (Inoue 1985)." " Since the observed colin density of L7< 10°? cm? includes the interstellar gas, that of circtuustellar eas should be less than this value."," Since the observed column density of $\times$ $^{22}$ $^{-3}$ includes the interstellar gas, that of circumstellar gas should be less than this value." Using the iron abundance of 0.3 solar. we predict the anit equivalent width to be 15 eV. which is sienificautly lower than the observed value of z100 eV. ence we require non-spherical ecometry: a larger amount of gas should be preseut out of the lue-ofsieht.," Using the iron abundance of 0.3 solar, we predict the maximum equivalent width to be $\approx$ 15 eV, which is significantly lower than the observed value of $\approx$ 100 eV. Hence we require non-spherical geometry; a larger amount of gas should be present out of the line-of-sight." A possible scenario is that YLW. 16A has a disk with face-on ecometry (Sekimoto et al., A possible scenario is that YLW 16A has a disk with face-on geometry (Sekimoto et al. 1997). and this disk is responsible for the fluorescent 6.1 keV line.," 1997), and this disk is responsible for the fluorescent 6.4 keV line." Since we see no time-lae (reflectiou time scale) between the flare on-set aud the 6.1 keV. iron line appearance witlin - sec. the separation between the star aud the reflecting region should be less than < 20 AU. consistent with the disk origin.," Since we see no time-lag (reflection time scale) between the flare on-set and the 6.4 keV iron line appearance within $\lesssim$ $^4$ sec, the separation between the star and the reflecting region should be less than $\lesssim$ 20 AU, consistent with the disk origin." ROX s21. a Class HI. has the brightest quiesceut flux and exhibits a flare (Figure 10. left panel).," ROX s21, a Class III, has the brightest quiescent flux and exhibits a flare (Figure 10, left panel)." Uulike the other sources. a single temperature plasma fit is completely rejected.," Unlike the other sources, a single temperature plasma fit is completely rejected." Thus we add another thin thermal component. aud find the fit to be acceptable. allowing the abuudauce to be fee.," Thus we add another thin thermal component, and find the fit to be acceptable, allowing the abundance to be free." The best-fit parameters are listed in Table £., The best-fit parameters are listed in Table 4. The temperature aud fux ofthe soft component do not change from quiesceut to fare. while those of the hard component increase during the Hare (Figure 10. right panel).," The temperature and flux of the soft component do not change from quiescent to flare, while those of the hard component increase during the flare (Figure 10, right panel)." In fact. if we subtract he quiescent spectriuui from that of the flare phase. we obtain a residual 5-keV plasima.," In fact, if we subtract the quiescent spectrum from that of the flare phase, we obtain a residual 5-keV plasma." We thus suspect hat RON s21 may have fairly steady component with a temperature of 0.81 keV. aud luminosity of «1027? eres +. and higher temperature plasima arises from ποιοι flares: a larger oue may be recognized as a “flare” (a 5-keV plasiaa iu the present case).," We thus suspect that ROX s21 may have fairly steady component with a temperature of 0.84 keV and luminosity of $\times$ $^{29}$ ergs $^{-1}$, and higher temperature plasma arises from frequent flares; a larger one may be recognized as a “flare” (a 5-keV plasma in the present case)." A 100-ks observation on the p Oph cloud with Chandra revealed the followine: l., A 100-ks observation on the $\rho$ Oph cloud with $Chandra$ revealed the following: 1. " We detect 87 N-rav sources from the cloud with a limiting luminosity of ~ 107 eres 4,", We detect 87 X-ray sources from the cloud with a limiting luminosity of $\sim$ $^{28}$ ergs $^{-1}$. " 2,", 2. We detect N-ravs from 7 Class Is. 11 Class Ls. The XN-rav detection rates are both ~ 70%.," We detect X-rays from 7 Class Is, 11 Class $_c$ s. The X-ray detection rates are both $\sim$ 70." . 3., 3. " No Neravs are found from starless cores with even younger ages than Class I. 1,", No X-rays are found from starless cores with even younger ages than Class I. 4. We detect N-ravs from 1 BD and 1 BD..., We detect X-rays from 1 BD and 1 $_c$. X- properties of these sources are the same as Class II|IIIS of more mnassive stars., X-ray properties of these sources are the same as Class II+IIIs of more massive stars. 5., 5. We fud Li. 12. 9. and 1 fares from 18 Class I|Ls 20 Class ID|HIS. 17 unclassi&ied: sources. auc 29 unidentified sources.," We find 14, 12, 9, and 1 flares from 18 Class $_c$ s, 20 Class II+IIIs, 17 unclassified sources, and 29 unidentified sources." Thus the duty ratio of flares in Class Ls is nearly equal to. or slightly higher than that of the other classes.," Thus the duty ratio of flares in Class $_c$ s is nearly equal to, or slightly higher than that of the other classes." Most of the fares show typical solar-like profiles. a fast rise and slow decay. except for a eiut flare from YLAV 16À. 6.," Most of the flares show typical solar-like profiles, a fast rise and slow decay, except for a giant flare from YLW 16A. 6." Most of the N-rav spectra are well fitted with a suele temperature thin plasma model of 0.3 solar abuudances., Most of the X-ray spectra are well fitted with a single temperature thin plasma model of 0.3 solar abundances. In general. Class [es have a higher temperature and absorption column than Class IT|WI.," In general, Class $_c$ s have a higher temperature and absorption column than Class II+IIIs." T., 7. " Woe find that Class Ls have a systematically sanaller LL, value than Class IT|IIs.", We find that Class $_c$ s have a systematically smaller $L_{X}$ $L_{\rm bol}$ value than Class II+IIIs. S., 8. We derive the eimipirical relation of Nyy = 1.26 Et.J IF) 10220. ? for the cloud members., We derive the empirical relation of $N_{\rm H}$ = 1.26 $J-H$ ) $^{22}$ $^{-2}$ for the cloud members. 9., 9. From the AL EM relation obtained by Shibata Yokoviuna (1999). we infer the magnetic field to be 15500 C. with a hint that Class Us have systematically strouser magnetic fields than Class IT|ΤΠ».," From the $kT$ –EM relation obtained by Shibata Yokoyama (1999), we infer the magnetic field to be 15–500 G, with a hint that Class $_c$ s have systematically stronger magnetic fields than Class II+IIIs." 10., 10. Luiuimosity ratios between flare and. quiesceut phases of Class Ts are systematically larger than those of Class IT|ITs., Luminosity ratios between flare and quiescent phases of Class $_c$ s are systematically larger than those of Class II+IIIs. 11., 11. We find 29 unidentified sources (no IB/optical counterpart). which are generally hard aud heavily absorbed.," We find 29 unidentified sources (no IR/optical counterpart), which are generally hard and heavily absorbed." Most of the unidentified sources are Likely to be hackeround ACNs., Most of the unidentified sources are likely to be background AGNs. 1994. so precede the data in the current paper by (wo pulsation evcles.,"1994, so precede the data in the current paper by two pulsation cycles." Desmurs confirmed the tangential linear. polarization morphology toward TX Cam in observations in April 1996., \citet{desmurs00} confirmed the tangential linear polarization morphology toward TX Cam in observations in April 1996. Taken together with the current data. this suggests that this morphology mav be an inter-cvcle property of the SiO maser emission (toward (his star.," Taken together with the current data, this suggests that this morphology may be an inter-cycle property of the SiO maser emission toward this star." It is not vel clear however. whether this is a generic property of SiO linear polarization in (his transition toward Iate-tvpe evolved stus in general.," It is not yet clear however, whether this is a generic property of SiO linear polarization in this transition toward late-type evolved stars in general." Desnnusetal.(2000) report a similar tangential morphology in the SiO maser emission Coward IRC--10011., \citet{desmurs00} report a similar tangential morphology in the SiO maser emission toward IRC+10011. However. for a sample of Mira variables monitored in e=1.2.J1—0 SiO maser emission in a full-polarization VLBI imaging study. and reported in a series of papers by Cotton.Perrin.&Lopezrelerences (herein).. the results are more mixed.," However, for a sample of Mira variables monitored in $v=1,2,\ J=1-0$ SiO maser emission in a full-polarization VLBI imaging study, and reported in a series of papers by \citet[and references therein]{cotton08}, the results are more mixed." Early images suggested no pervasive linear polarization pattern (Cottonefal.2004): however. later. a bimodal EVPA distribution (in the sense of being either parallel or perpendicular to (he projected shell) was reported for U Ori and ο Cet (Cottonefaf.2006).," Early images suggested no pervasive linear polarization pattern \citep{cotton04}; however, later, a bimodal EVPA distribution (in the sense of being either parallel or perpendicular to the projected shell) was reported for U Ori and o Cet \citep{cotton06}." . ILowever. not all sources for which images are shown bv Cotton.Perrin.&Lopez(2008) show tangential linear polarization structure.," However, not all sources for which images are shown by \citet{cotton08} show tangential linear polarization structure." Further observations of larger samples are needed to resolve (his important question., Further observations of larger samples are needed to resolve this important question. There are several possible theoretical explanations for tangential linear polarization structure in SiO maser eniission. as we see in the cata presented here.," There are several possible theoretical explanations for tangential linear polarization structure in SiO maser emission, as we see in the data presented here." However. these interpretations are conditional on (he Cheoretical assumptions made concerning (he underlving naser emission: we locus here only on the observational implications of these theoretical issues in what follows.," However, these interpretations are conditional on the theoretical assumptions made concerning the underlying maser emission; we focus here only on the observational implications of these theoretical issues in what follows." silicon monoxide is a non-paramagnetic molecule and the rotational transition considered jere is in (he small-splitting Zeeman regime., Silicon monoxide is a non-paramagnetic molecule and the rotational transition considered here is in the small-splitting Zeeman regime. " Following Elitzur(1996).. the ratio wry of the Zeeman splitting to the Doppler linewidth Ar, is (IXemball&Diamond1997): For the case of ry«1. as equation 1 indicates is applicable to SiO. competing models for the transport of polarized maser emission have been presented (Elitzur1996:Watson therein).."," Following \citet{elitzur96}, the ratio $x_B$ of the Zeeman splitting to the Doppler linewidth $\Delta v_D$ is \citep{kemball97}: For the case of $x_B \ll 1$, as equation \ref{eqn-xb} indicates is applicable to SiO, competing models for the transport of polarized maser emission have been presented \citep[and references therein]{elitzur96, watson02}." Both series of papers extend (he parameter space ancl eeneralize the original foundational work of Goldreich.IXeelev.&Kwan(1973)., Both series of papers extend the parameter space and generalize the original foundational work of \citet{goldreich73}. . There also remaius uncertainty in the literature as to whether SiO masers are pumped by collisional (Elitzur or radiative mechanisms (Dujarrabal&Nguyen-Q-Iieu1981).," There also remains uncertainty in the literature as to whether SiO masers are pumped by collisional \citep{elitzur80} or radiative mechanisms \citep{bujarrabal81}." . Finally. an additional consideration is the degree to which m—anisolropic pumping of the magnetic substates dominates.," Finally, an additional consideration is the degree to which $m-$ anisotropic pumping of the magnetic substates dominates." We neglect [ον (he purposes of this discussion the role of magnetic or velocity eradients in (he masing regions. and any considerations that apply specifically to transitions with spins higher (han J=1— 0.," We neglect for the purposes of this discussion the role of magnetic or velocity gradients in the masing regions, and any considerations that apply specifically to transitions with spins higher than $J=1-0$ ." slreanis. (,streams. ( 3) In the case of photoevaporation. gas in (lie region of the disk photoevaporation radius (few AU: Font et 22004: Liffman 2003) is being evaporated away [faster than it can be replenished by viscous accretion.,"3) In the case of photoevaporation, gas in the region of the disk photoevaporation radius (few AU; Font et 2004; Liffman 2003) is being evaporated away faster than it can be replenished by viscous accretion." " As a result. the inner disk is decoupled from the outer disk and accretes onto the star. leaving behind a (rue ""inner hole” in the gas distribution and lvom the region within 24,4. l"," As a result, the inner disk is decoupled from the outer disk and accretes onto the star, leaving behind a true “inner hole” in the gas distribution and from the region within $R_{\rm hole}$." low do the properties of (he gaseous inner disk of TW Iva compare will these predictions?, How do the properties of the gaseous inner disk of TW Hya compare with these predictions? UV [Inorescent LI» and CO fundamental emission. which are both believed to probe Che inner ~| AAU of T Tauri disks (see Najita et 22007b for a review). have been detected from the inner disk of TW Iva (IHercezeg et 22002: Rettig et 22004: Salvk et 22007: Najita et 22007b).," UV fluorescent $\Htwo$ and CO fundamental emission, which are both believed to probe the inner $\sim 1$ AU of T Tauri disks (see Najita et 2007b for a review), have been detected from the inner disk of TW Hya (Herczeg et 2002; Rettig et 2004; Salyk et 2007; Najita et 2007b)." The spectroastrometric study of Pontoppidan et ((2008) further demonstrates that the CO emission arises from a rotating disk close to the star (~0.1 AAU)., The spectroastrometric study of Pontoppidan et (2008) further demonstrates that the CO emission arises from a rotating disk close to the star $\sim 0.1$ AU). Thus. the inner disk is not completely cleared of gas. a result that is consistent with the ongoing stellar accretion in the svstem and inconsistent with the EUV-driven photoevaporation scenario. (," Thus, the inner disk is not completely cleared of gas, a result that is consistent with the ongoing stellar accretion in the system and inconsistent with the EUV-driven photoevaporation scenario. (" The situation is somewhat different if photoevaporation is driven by N-ravs.,The situation is somewhat different if photoevaporation is driven by X-rays. Recent work bv Ercolano and collaborators finds Chat photoevaporation driven by N-ravs rather (han LUV can create a transition-like SED at much higher disk masses and accretion rates than in (he EUV-driven photoevaporation case., Recent work by Ercolano and collaborators finds that photoevaporation driven by X-rays rather than EUV can create a transition-like SED at much higher disk masses and accretion rates than in the EUV-driven photoevaporation case. Under these conditions. the star max continue to accrete αἱ a measurable rate for a longer fraction of the svstem lifetime after disk clearing has begun: Owen et 22010.)," Under these conditions, the star may continue to accrete at a measurable rate for a longer fraction of the system lifetime after disk clearing has begun; Owen et 2010.)" TheSp4zer specirum allows us to probe the gaseous disk at radii bevoud the region probed by UV fInorescent II» and CO fundamental emission. because the features in the SII spectrum probe emission from cooler gas.," The spectrum allows us to probe the gaseous disk at radii beyond the region probed by UV fluorescent $\Htwo$ and CO fundamental emission, because the features in the SH spectrum probe emission from cooler gas." In the spectrum of AA Tau. a typical T Tauri star (hat possesses an optically thick inner disk. the molecular features detected in SII (1150. OIL. ο. HCN. COs). probe gas with temperatures of NIN and disk emitting areas corresponding to a few AU in radius. i.e.. (he inner planet formation region of the disk (Carr Najita 2008).," In the spectrum of AA Tau, a typical T Tauri star that possesses an optically thick inner disk, the molecular features detected in SH $\HtwoO$, OH, $\CtwoHtwo$, HCN, $\COtwo$ ), probe gas with temperatures of K and disk emitting areas corresponding to a few AU in radius, i.e., the inner planet formation region of the disk (Carr Najita 2008)." One of the most striking aspects of theSpilzer spectrum of TW Ilva is the weak molecular emission compared to that seen in classical T Tauri stars such as AA Tan (Carr Najila 2005: Salvk et 22008: Carr Najita. in preparation: Pontoppidan et al..," One of the most striking aspects of the spectrum of TW Hya is the weak molecular emission compared to that seen in classical T Tauri stars such as AA Tau (Carr Najita 2008; Salyk et 2008; Carr Najita, in preparation; Pontoppidan et al.," in preparation)., in preparation). The scenario of a gap carved in the gaseous disk by an orbiting giant. planet would appear to naturally lead to the suppression of the molecular emission from (he inner disk region. like that observed.," The scenario of a gap carved in the gaseous disk by an orbiting giant planet would appear to naturally lead to the suppression of the molecular emission from the inner disk region, like that observed." With the size of the optically (hin region in the TW Ilva svstem (c AAU) suggesting that an orbiting planet would reside at a few AU. we might expect the inner few AU region of the disk to be mostly cleared of gas.," With the size of the optically thin region in the TW Hya system $\sim 4$ AU) suggesting that an orbiting planet would reside at a few AU, we might expect the inner few AU region of the disk to be mostly cleared of gas." diffusion rates.,diffusion rates. A similar result was obtained by Fiorentinietal.(1999) bv using conditions αἱ the base of the convective zone to constrain the diffusion rates., A similar result was obtained by \citet{fiore:1999} by using conditions at the base of the convective zone to constrain the diffusion rates. A detailed study by Turcotte shows that diffusion velocities depend on the dillerent assumptions mace in the caleulation for different elements and. at different regions of the Sun. the variation ranges [rom a few percent to about40%.," A detailed study by \citet{turcotte:1998} shows that diffusion velocities depend on the different assumptions made in the calculation for different elements and, at different regions of the Sun, the variation ranges from a few percent to about." . Here. we adopt an intermediate fiducial value συ=20% as the uncertaintv in the diffusion rates.," Here, we adopt an intermediate fiducial value $\sigma_{\rm Diff}=20\%$ as the uncertainty in the diffusion rates." It should be notedthat (he uncertainty in μι because of uncertainties in the diffusion rate are only one-twelfth that of uncertainties in the dilfusion rate., It should be notedthat the uncertainty in $\yim$ because of uncertainties in the diffusion rate are only one-twelfth that of uncertainties in the diffusion rate. Then. for opi=20%. the contribution of diffusion to the total uncertainty in Yi is only1.," Then, for $\sigma_{\rm Diff}=20\%$, the contribution of diffusion to the total uncertainty in $\yim$ is only." 7... Thus. We now scale the relation to the Sun by adopting the present-day surface helium abundance determined using helioseismology.," Thus, We now scale the relation to the Sun by adopting the present-day surface helium abundance determined using helioseismology." We adopt the value determined by Dasu&Antia (2004).. i.e.. Y?!=0.2485+0.0034. where the uncertainty accounts lor svsteniatics. including those caused by uncertainties in the equation of state (see Basu&Antia2008 [or a recent discussion about the determination of Ytst ).," We adopt the value determined by \citet{ys_basu04}, i.e., $\ysms= 0.2485\pm0.0034$, where the uncertainty accounts for systematics, including those caused by uncertainties in the equation of state (see \citealt{review_basu08} for a recent discussion about the determination of $\ysms$ )." Then. the solar initial helium abundance Y? can be expressed as In the above expression. standard solar models (SSAIs) play a (wo-Iolded role.," Then, the solar initial helium abundance $\yims$ can be expressed as In the above expression, standard solar models (SSMs) play a two-folded role." First. a reference model is used to get the scaling factors Yinig aud Yio.," First, a reference model is used to get the scaling factors $Y_{\rm ini,0}$ and $Y_{\rm surf,0}$." »econd. models are used to determine the exponent that relate YW! andYour.," Second, models are used to determine the exponent that relate $\ysms$ and." However. as we show in the following section. Equation 10. has predictive power independent of the (standard) solar model used as a reference.," However, as we show in the following section, Equation \ref{eq:final} has predictive power independent of the (standard) solar model used as a reference." As a Bust test of Equation 10.. we use values and obtained from S5M caleulations of Serenellietal.(2009).," As a first test of Equation \ref{eq:final}, we use values and obtained from SSM calculations of \citet{ssm09}." . The results are summarized in Table 3. where we have identified (he solar models by the solar composition adopted for each of them., The results are summarized in Table \ref{tab:results} where we have identified the solar models by the solar composition adopted for each of them. The second and (third. columns give the 59M predictions for the iniial and present-day. surface helium mass fraction., The second and third columns give the SSM predictions for the initial and present-day surface helium mass fraction. The fourth column gives the Y values estimated using Equation 10:: the uncertainty in all cases is Gin= z0.006., The fourth column gives the $\yims$ values estimated using Equation \ref{eq:final}; ; the uncertainty in all cases is $\sigma_{\yims}=\pm 0.006$ . " Comparing results for the different standard solar models we find thatthe dispersion in 377"" is about ten times smaller than oyin and", Comparing results for the different standard solar models we find thatthe dispersion in $\yims$ is about ten times smaller than $\sigma_{\yims}$ and the first half of the observation.,the first half of the observation. Sinultaneouslv. there was a multi-wavelength campaign on this source usingASCARATE.LST. and ground base telescopes (e.g.. Turner οἱ al.," Simultaneously, there was a multi-wavelength campaign on this source using, and ground base telescopes (e.g., Turner et al." 2001 and Eclelson et al., 2001 and Edelson et al. 2002)., 2002). We downloaded the screened data from GSFC rev2 archive and created the lighteurve from June 1 to July 7., We downloaded the screened data from GSFC rev2 archive and created the lightcurve from June 1 to July 7. To evaluate the 210 keV flux state during the observation. we compare the count rate ancl variability from iin the observation with those in the whole observation.," To evaluate the 2–10 keV flux state during the observation, we compare the count rate and variability from in the observation with those in the whole observation." We summarized the average count rate and the fractional RAIS variability in Table 1.., We summarized the average count rate and the fractional RMS variability in Table \ref{tab:var}. During the observation. the source was slightly brighter than average by about 20 and variability is πμ compared with the oobservation.," During the observation, the source was slightly brighter than average by about 20 and variability is typical, compared with the observation." An identilving feature of active galaxies is (heir N-rayv variability., An identifying feature of active galaxies is their X-ray variability. Their variability is not periodic but rather a featureless power law on (me scales of weeks to davs (e.g.. Lawrence Papacakis 1993).," Their variability is not periodic but rather a featureless power law on time scales of weeks to days (e.g., Lawrence Papadakis 1993)." This is unfortunate. because no Gime scales (hat might correspond to physical size scales such as the size of the emission region. can be found.," This is unfortunate, because no time scales that might correspond to physical size scales such as the size of the emission region, can be found." As well as fine spectroscopy. an advantage of the oobservatorv is the continuous data sampling. which allows us to compute power spectral density (PSD) directly in the frequency range around 2x10.! Uz.," As well as fine spectroscopy, an advantage of the observatory is the continuous data sampling, which allows us to compute power spectral density (PSD) directly in the frequency range around $2\times10^{-4}$ Hz." In principle. because of (he continuous data sampling and [fairly large effective area. power spectral density. analysis should allow us to observe the power spectrum on short enough time scales to look for breaks that may be indicative of a physical size scale.," In principle, because of the continuous data sampling and fairly large effective area, power spectral density analysis should allow us to observe the power spectrum on short enough time scales to look for breaks that may be indicative of a physical size scale." We created the lighteurve binned at 64 s and caleulated the power spectrum in the frequency range between 2.0xLO? and 7.8xLO* Hz., We created the lightcurve binned at 64 s and calculated the power spectrum in the frequency range between $2.0\times10^{-5}$ and $7.8\times10^{-3}$ Hz. Fig., Fig. 2 shows the PSD of Ark 564 during the oobservation., \ref{fig:pds} shows the PSD of Ark 564 during the observation. In order to obtain reasonable signal to noise. we grouped in sets of 20 data points and averaged their logarithm (Dapadakis&Lawrence1993).," In order to obtain reasonable signal to noise, we grouped in sets of 20 data points and averaged their logarithm \citep {papa93}." . The background due to Poisson noise is not sublracted and we find that it dominates the lrequencies above 10?*(2yoi2.0x1ο 7) Lz., The background due to Poisson noise is not subtracted and we find that it dominates the frequencies above $10^{-2.7}(=2.0\times10^{-3}$ ) Hz. Below this frequency. the fitted power-law index (a where PSD," Below this frequency, the fitted power-law index $\alpha$ where PSD" We now discuss the simulation results for the binary plus circumbinary disk runs.,We now discuss the simulation results for the binary plus circumbinary disk runs. The upper panel of Figure 1 shows a snapshot of the disk surface density after 1.2x10? binary orbits., The upper panel of Figure \ref{rho_459} shows a snapshot of the disk surface density after $1.2\times 10^5$ binary orbits. " Here, the disk surrounds a binary with mass ratio qp=0.1."," Here, the disk surrounds a binary with mass ratio $q_{b}=0.1$." " The binary initially evolves on a circular orbit and the initial separation between the two stars is a,=0.4.", The binary initially evolves on a circular orbit and the initial separation between the two stars is $a_b=0.4$. " The lower panel displays the corresponding azimuthal average of the disk surface density, as well as the initial surface density profile."," The lower panel displays the corresponding azimuthal average of the disk surface density, as well as the initial surface density profile." Torques exerted by the binary truncate the inner edge of the disk., Torques exerted by the binary truncate the inner edge of the disk. " We find that the gap size is ~2.5a, which is consistent with analytical estimates from Artymowicz Lubow (1994)."," We find that the gap size is $\sim 2.5a$, which is consistent with analytical estimates from Artymowicz Lubow (1994)." " Figure 2 shows the evolution of the binary semi-major axis and eccentricity as a function of time, deduced from low-resolution simulations with 128x grid cells."," Figure \ref{orbit_bin} shows the evolution of the binary semi-major axis and eccentricity as a function of time, deduced from low-resolution simulations with $128\times 128$ grid cells." " As a result of angular momentum being transferred to the disk, the binary separation shrinks at a rate da/dt~10:5."," As a result of angular momentum being transferred to the disk, the binary separation shrinks at a rate $da/dt\sim 10^{-8}$." " This value is consistent with the orbital decay that we would expect from analytical estimates (i.e Armitage Natarajan 2005): where Mz, is the disk mass and M» the mass of the secondary.", This value is consistent with the orbital decay that we would expect from analytical estimates (i.e Armitage Natarajan 2005): where $M_d$ is the disk mass and $M_2$ the mass of the secondary. " The orbital decay ofthe binary is slow enough that the 1:3 commensurability at r~2.08ap, which corresponds to the eccentric Lindblad resonance which is expected to be important in determining the evolution of the binary orbit, always resides inside the computational domain."," The orbital decay ofthe binary is slow enough that the 1:3 commensurability at $r\sim 2.08 \;a_{b}$, which corresponds to the eccentric Lindblad resonance which is expected to be important in determining the evolution of the binary orbit, always resides inside the computational domain." " This makes it possible to do long-term evolution runs over ~10? binary orbits, at least at low-resolution."," This makes it possible to do long-term evolution runs over $\sim 10^5$ binary orbits, at least at low-resolution." " We note that the location of the 1:3 resonance is just at the base of the gap in fig. 1,,"," We note that the location of the 1:3 resonance is just at the base of the gap in fig. \ref{rho_459}," showing that the density there is quite low., showing that the density there is quite low. The lower panel in fig., The lower panel in fig. " 2 shows that the binary eccentricity, after some transients lasting for ~5x10°, grows until it saturates at e~0.08."," \ref{orbit_bin} shows that the binary eccentricity, after some transients lasting for $\sim 5\times 10^3$, grows until it saturates at $e \sim 0.08$." The initial eccentricity growth is due to the resonant nature of the interaction between the disk and the binary., The initial eccentricity growth is due to the resonant nature of the interaction between the disk and the binary. " This interaction is expected to occur mainly at the location of the 1:3 outer Lindblad resonance, which promotes eccentricity growth."," This interaction is expected to occur mainly at the location of the 1:3 outer Lindblad resonance, which promotes eccentricity growth." " As time goes by and the eccentricity grows, there is evidence that this resonance saturates due to non linear effects (i.e. the density at the resonance is decreased), and this saturation combined with higher-order resonances coming into play (Artymowicz 1992) causes the eccentricity to reach a steady value."," As time goes by and the eccentricity grows, there is evidence that this resonance saturates due to non linear effects (i.e. the density at the resonance is decreased), and this saturation combined with higher-order resonances coming into play (Artymowicz 1992) causes the eccentricity to reach a steady value." " We also need to consider the secular interaction between disk and binary, as this also plays an important role."," We also need to consider the secular interaction between disk and binary, as this also plays an important role." We plot the evolution of the longitudes of pericentre for the disk (wg) and binary (ων) in the upper panel of fig. 3.., We plot the evolution of the longitudes of pericentre for the disk $\omega_d$ ) and binary $\omega_{b}$ ) in the upper panel of fig. \ref{w_disk+bin}. . The disk eccentricity evolution is plotted in the lower panel., The disk eccentricity evolution is plotted in the lower panel. Arnowit. Deser and Misner complete what we now call the ADM formulation of GR. namely its hamiltonian version iu appropriate variables. which ereatly simplify the hamiltonian formulation and make its ecometrical reading trauspareut [15]..," Arnowit, Deser and Misner complete what we now call the ADM formulation of GR, namely its hamiltonian version in appropriate variables, which greatly simplify the hamiltonian formulation and make its geometrical reading transparent \cite{ADM}." Iu relatiou to the quantization. Arnowit. Deser and Misner present an iuflueutial argunent for the finiteness of the self energy of a point particle in classical CR and use it to argue that nouperturbative quantum eravity should be &uite.," In relation to the quantization, Arnowit, Deser and Misner present an influential argument for the finiteness of the self energy of a point particle in classical GR and use it to argue that nonperturbative quantum gravity should be finite." Fevinnan attacks the task of computing transition amplitudes in quautuu eravitv., Feynman attacks the task of computing transition amplitudes in quantum gravity. He shows that trec-aimplitucdes lead to the pliysics one expects frou the classical theory [19].., He shows that tree-amplitudes lead to the physics one expects from the classical theory \cite{feynman62}. DeWitt starts developing lis background field methods for the computation of perturbative trausition anplitudes [20].., DeWitt starts developing his background field methods for the computation of perturbative transition amplitudes \cite{dewitt62}. Beremaun aud IKonar clarify what oue should expect from a Wilbert space formulation of GR [21].., Bergmann and Komar clarify what one should expect from a Hilbert space formulation of GR \cite{bergmankomar}. Following the ADM methods. Peres writes the Hamilton-Jacobi formulation of GR [22] which will lead to the Wheeler-DeWitt equation.," Following the ADM methods, Peres writes the Hamilton-Jacobi formulation of GR \cite{peres} which will lead to the Wheeler-DeWitt equation." 445 is the ADM 3anetzic and C the Newton constant., $q_{ab}$ is the ADM 3-metric and $G$ the Newton constant. John Wheeler realizesthat the quanti fluctuations of the eravitational field must be short scale fluctuations of the ecometry aud introduces the plivsical idea of spacetime foam [23]., John Wheeler realizes that the quantum fluctuations of the gravitational field must be short scale fluctuations of the geometry and introduces the physical idea of spacetime foam \cite{wheeler63}. . Wheelers Les Touches lecture note are remarkable in many respects. and are the source of mauy of the ideas still current iu the field.," Wheeler's Les Houches lecture note are remarkable in many respects, and are the source of many of the ideas still current in the field." " Just to mention two others: ""Problemi 56° suegeests that eravity iu 211 dimensions may not be so trivial after all. aud iudicates if may be au interesting model to explore. “"," Just to mention two others: “Problem 56"" suggests that gravity in 2+1 dimensions may not be so trivial after all, and indicates it may be an interesting model to explore. “" Problem 57 suggests to study quantum eravity by micas of a Feviuman inteeral over a spacetime lattice.,"Problem 57"" suggests to study quantum gravity by means of a Feynman integral over a spacetime lattice." multidimensional simulations.,multidimensional simulations. E.J.L. is supported by grants from the NASA Astrophysics Theory and Fundamental Physics Program (grant number NNHIIAQ721) and the NSF PetaApps Program (grant number OCI-0749242)., E.J.L. is supported by grants from the NASA Astrophysics Theory and Fundamental Physics Program (grant number NNH11AQ72I) and the NSF PetaApps Program (grant number OCI-0749242). A.M. and W.R.H. are supported by the Department of Energy Office of Nuclear Physies: and A.M. and O.E.B.M. are supported by the Department of Energy Office of Advanced Scientific Computing Research., A.M. and W.R.H. are supported by the Department of Energy Office of Nuclear Physics; and A.M. and O.E.B.M. are supported by the Department of Energy Office of Advanced Scientific Computing Research. M.L. is supported by the Swiss National Science Foundation (grant numbers PPOOP2-124879 and 200020-122287)., M.L. is supported by the Swiss National Science Foundation (grant numbers PP00P2-124879 and 200020-122287). This research was supported in part by the National Science Foundation through TeraGrid resources provided by National Institute for Computational Sciences under grant number TG-MCAO08X010., This research was supported in part by the National Science Foundation through TeraGrid resources provided by National Institute for Computational Sciences under grant number TG-MCA08X010. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory. which 1s supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-ACOS-," This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725." The acquisition of optical identifications for radio sources is not only useful in providing optical information. it also gives the opportunity to make a distinction between Iow-redshift sources and more distant ones.,"The acquisition of optical identifications for radio sources is not only useful in providing optical information, it also gives the opportunity to make a distinction between low-redshift sources and more distant ones." Passive radio galaxies are known to be reliable standard candles (see c.g. Hine Longair. 1979: Rixon. Wall Benn. 1991).," Passive radio galaxies are known to be reliable standard candles (see e.g. Hine Longair, 1979; Rixon, Wall Benn, 1991)." The mean absolute magnitude in the red. band. is Δρ~23 (seo e.g. MLA2000). and there is little scatter about the mean (NLA2000. estimate AALp20.25 at the leo level).," The mean absolute magnitude in the red band is $M_R\simeq -23$ (see e.g. MA2000), and there is little scatter about the mean (MA2000 estimate $\Delta$ $_R \simeq 0.25$ at the $\sigma$ level)." Εις measurementsof the apparent magnitude I for these sources can provide us with an estimate of their redshifts according to the relation where d; the luminosity distance., Thus measurementsof the apparent magnitude $R$ for these sources can provide us with an estimate of their redshifts according to the relation where $d_L$ the luminosity distance. Phe id-sample is complete to #~19.5. and from this formula we expect that objects brighter than &~19.5 should be found in the redshift range 0z2203. As we saw in the previous Section. the optically extended id-sample is mostlv made up of earlv-tvpe galaxies. with star-bursting objects contributing only a small fraction.," The id-sample is complete to $R \sim 19.5$, and from this formula we expect that objects brighter than $R \sim 19.5$ should be found in the redshift range $0\simlt z\simlt 0.3$ As we saw in the previous Section, the optically extended id-sample is mostly made up of early-type galaxies, with star-bursting objects contributing only a small fraction." So we can apply equation (1)) to the whole subsample of racio ealaxies. and deduce that it cntains racio-sources that are mostly closer than z20.3.," So we can apply equation \ref{eq:R}) ) to the whole subsample of radio galaxies, and deduce that it contains radio-sources that are mostly closer than $z\simeq 0.3$." Phe spread in the &2 relation means that the upper redshift limit will be a gradual cutoll: see also MLA2000., The spread in the $R-z$ relation means that the upper redshift limit will be a gradual cutoff; see also MA2000. The other sources that appear in the id-sample are mainly QSO with a very small contamination from nearby stars., The other sources that appear in the id-sample are mainly QSO with a very small contamination from nearby stars. Unfortunately. we have no simple way to distinguish between these two classes of objects. or to estimate the QSO redshift.," Unfortunately, we have no simple way to distinguish between these two classes of objects, or to estimate the QSO redshift." Llowever. apart. from rare exceptions. we expect QSO to be all placed at high redshifts. at least. bevond 2 >03. The optical distinction between point-like ancl extended sources as discussed in the previous Section. allows us to divide the id-sample in a low-z subsample - comprising mostly of early-type galaxies and roughly complete to - and à sample of QSO mostly found at. redshifts well bevond 0.3.," However, apart from rare exceptions, we expect QSO to be all placed at high redshifts, at least beyond z $\simgt 0.3$ The optical distinction between point-like and extended sources as discussed in the previous Section, allows us to divide the id-sample in a low-z subsample - comprising mostly of early-type galaxies and roughly complete to $z\simeq 0.3$ - and a sample of QSO mostly found at redshifts well beyond 0.3." Figure 10 shows the angular clistribution of these sources projected on the sky., Figure \ref{fig:distrib} shows the angular distribution of these sources projected on the sky. The bottom. panel represents the distribution of all the objects in the id-sample with 5;< 21.5. limit for completeness ancl uniformity of the optical catalogue. while the middle one includes radio. sources identified as galaxies and the top one is for point-like sources (both in the case of 6;x 20.5).," The bottom panel represents the distribution of all the objects in the id-sample with $b_J \le 21.5$ , limit for completeness and uniformity of the optical catalogue, while the middle one includes radio sources identified as galaxies and the top one is for point-like sources (both in the case of $b_J \le 20.5$ )." We can quantify the level of clustering in cach sample womeans of the two-point correlation function., We can quantify the level of clustering in each sample by means of the two-point correlation function. beleally one would like to obtain the spatial correlation function (1) but. since we do not have measured. redshifts for any sources in he ic-sample. we have to deal with its angular counterpart ie(8).," Ideally one would like to obtain the spatial correlation function $\xi(r)$ but, since we do not have measured redshifts for any sources in the id-sample, we have to deal with its angular counterpart $w(\theta)$." " We recall here that the angular two-point correlation function measures the excess probability. with respect to a random Poisson distribution. of finding two sources in the solid angles 80, 80» separated by an angle 0."," We recall here that the angular two-point correlation function measures the excess probability, with respect to a random Poisson distribution, of finding two sources in the solid angles $\delta\Omega_1$ $\delta\Omega_2$ separated by an angle $\theta$." I is defined as where n is the mean number density of objects in the catalogue under consideration., It is defined as where $n$ is the mean number density of objects in the catalogue under consideration. We calculated (0) using the estimator. (Hamilton. 1993) where the number of data-data. rancom-random ancl clata-random. pairs separated by an angle 6 are denoted by DD. RR and DI. Random catalogues were gencratecd with a spatial distribution. modulated by both the APAL ancl FIRST coverage maps. so that the instrumental window functions do not allect the measured. clustering.," We calculated $w(\theta)$ using the estimator (Hamilton, 1993) where the number of data-data, random-random and data-random pairs separated by an angle $\theta$ are denoted by DD, RR and DR Random catalogues were generated with a spatial distribution modulated by both the APM and FIRST coverage maps, so that the instrumental window functions do not affect the measured clustering." We estimate. the errors on the dw(0) measurements by assuming the the pair counts follow Poisson statistics., We estimate the errors on the $w(\theta)$ measurements by assuming the the pair counts follow Poisson statistics. This. underestimates the uncertainties. but we do not expect. this bias to be a laree factor.," This underestimates the uncertainties, but we do not expect this bias to be a large factor." However. the errors in (0) at cach point are correlated. so it is easy to overestimate the significance of any features apparent in e.," However, the errors in $w(\theta)$ at each point are correlated, so it is easy to overestimate the significance of any features apparent in $w$." " 1n Figure 11. we show the results for (0) of the whole id-sample with 6, 21.5.", In Figure \ref{fig:wall} we show the results for $w(\theta)$ of the whole id-sample with $b_J \le 21.5$ . As already stated. error-bars are given. by Poisson estimates for the catalogue under consideration.," As already stated, error-bars are given by Poisson estimates for the catalogue under consideration." The clustering signal is significantly. greater than zero at all angular scales: if we assume a power-law form for (6). w(8)=οἱ03 we lind. via à X7 fit to the data. cl~0.018 and 5~1.3. Llowever. as we have already seen. the id-sample is a hvbrid. mixture of low- anc high-z sources. which means that this measurement is not. particularly relevant.," The clustering signal is significantly greater than zero at all angular scales; if we assume a power-law form for $w(\theta)$, $w(\theta)=A\: \theta^{1-\gamma}$, we find, via a $\chi^2$ fit to the data, $A\sim 0.018$ and $\gamma\sim1.3$ However, as we have already seen, the id-sample is a hybrid mixture of low- and high-z sources, which means that this measurement is not particularly relevant." More interesting information can be derived from the analysis of the clustering signal produced by the two different classes of objects. namely stellar and extended sources.," More interesting information can be derived from the analysis of the clustering signal produced by the two different classes of objects, namely stellar and extended sources." We then estimated w(8) for the stellar-IHike sources (535 objects with b;< 20.5). and the resulting 1|w(@) is shown in Figure 12..," We then estimated $w(\theta)$ for the stellar-like sources (535 objects with $b_J \le 20.5$ ), and the resulting $1+w(\theta)$ is shown in Figure \ref{fig:wstars}." Vhe clustering signal is dominated. by large errors due to the small number of objects., The clustering signal is dominated by large errors due to the small number of objects. Nevertheless the signal is positive at almost all angular scales up to 8—5," Nevertheless the signal is positive at almost all angular scales up to $\theta\sim 5^\circ$." The most interesting result. is. represented. by the angular correlation function for the 1494 radio galaxies in the id-sample., The most interesting result is represented by the angular correlation function for the 1494 radio galaxies in the id-sample. As illustrated by figure. 13... in this case the signal is quite strong. showing once again that racio sources are more clustered than normal galaxies (see. also Peacock Nicholson. 1991: Cress et al.," As illustrated by figure \ref{fig:wgals}, in this case the signal is quite strong, showing once again that radio sources are more clustered than normal galaxies (see also Peacock Nicholson, 1991; Cress et al.," 1996: Loan. Wall Lahav. 1997: Alaglioechetti et al.," 1996; Loan, Wall Lahav, 1997; Magliocchetti et al.," 1998: Magliocchetti et al..," 1998: Magliocchetti et al.," 1999)., 1999). In fact. if we parameterize w(8) as a power-law: w(8)=gt. we find - via a X? fit to the data - 2d0.03 and 5 2.1. with a value for the slope close το those obtained. for samples of earlv-tvpe galaxies only. known to be more strongly clustered. thanother galaxy populations (sce e.g. Maddox et al..," In fact, if we parameterize $w(\theta)$ as a power-law: $w(\theta)=A\:\theta^{1-\gamma}$, we find - via a $\chi^2$ fit to the data - $A\sim 0.03$ and $\gamma\sim 2.1$ , with a value for the slope close to those obtained for samples of early-type galaxies only, known to be more strongly clustered thanother galaxy populations (see e.g. Maddox et al.," . 1990€ and. Loveday ct al.," 1990c and Loveday et al.," 1995)., 1995). Note that this result. also agrees with the observational, Note that this result also agrees with the observational correspond to specitic models of rapidly rotating neutron stars.,correspond to specific models of rapidly rotating neutron stars. Since the solution has four nonvanishing multipole moments. but only three free parameters. one can at most match three multipole moments of any given numerical solution.," Since the solution has four nonvanishing multipole moments, but only three free parameters, one can at most match three multipole moments of any given numerical solution." The fourth multipole moment will then be determined by the analytic solution. and its relative difference with the (known) numerical value will be a measure of the accuracy of the analytic solution.," The fourth multipole moment will then be determined by the analytic solution, and its relative difference with the (known) numerical value will be a measure of the accuracy of the analytic solution." The four multipole moments are not equally important for specifying a solution. 53 being the least important. even for the most rapidly rotating models.," The four multipole moments are not equally important for specifying a solution, $S_3$ being the least important, even for the most rapidly rotating models." Therefore we choose to match the analytic exterior solution to known numerical solutions by matching the gravitational mass AM. the specitic angular momentum ¢ and the mass-quadrupole moment Q.," Therefore we choose to match the analytic exterior solution to known numerical solutions by matching the gravitational mass $M$, the specific angular momentum $a$ and the mass-quadrupole moment $Q$." One then hopes that the resulting analytic solution will yield a value for the current-octupole moment ὃν that is close to the corresponding value in the numerical model., One then hopes that the resulting analytic solution will yield a value for the current-octupole moment $S_3$ that is close to the corresponding value in the numerical model. As we will show. there exists a branch of solutions for which this is indeed the case.," As we will show, there exists a branch of solutions for which this is indeed the case." Manko 20002) also used the quadrupole moment to match numerical and analytic solutions. but their examples correspond to the other branch of solutions. for which the analytic value of 53 does not agree well with the numerical value.," Manko (2000a) also used the quadrupole moment to match numerical and analytic solutions, but their examples correspond to the other branch of solutions, for which the analytic value of $S_3$ does not agree well with the numerical value." For a given model of a rapidly rotating neutron star. we first construct a highly accurate numerical solution. as described in section 2..," For a given model of a rapidly rotating neutron star, we first construct a highly accurate numerical solution, as described in section \ref{numgravfield}." In the analytic solution (55)). we set AY and a to be equal to the obtained numerical values.," In the analytic solution \ref{solution}) ), we set $M$ and $a$ to be equal to the obtained numerical values." The remaining parameter bis then determined by solving the equation where Qw is the value of the quadrupole moment obtainec by the numerical code., The remaining parameter $b$ is then determined by solving the equation where $Q_{\rm N}$ is the value of the quadrupole moment obtained by the numerical code. A plot of QΟν as a function of the parameter 5. for the most rapidly rotating model of the sequence for EOS FPS. is shown in Fig. 2..," A plot of $Q-Q_{\rm N}$ as a function of the parameter $b$, for the most rapidly rotating model of the maximum-mass sequence for EOS FPS, is shown in Fig. \ref{analytic_bf}." Two possible rea solutions for 5 exist: a solution that is usually negative. b.. and a solution that is always positive. 5. .," Two possible real solutions for $b$ exist: a solution that is usually negative, $b_-$, and a solution that is always positive, $b_+$ ." Thus. for each set of physica parameters ια and Q. there exists two different branches of solutions. with parameters (A. a. b. 0 and (M. a. b. . respectiveut," Thus, for each set of physical parameters $M, a$ and $Q$, there exists two different branches of solutions, with parameters $M$, $a$, $b_-$ ) and $M$, $a$, $b_+$ ), respectively." In the remainder of the paper. we will refer to these two differen branches as the negative solution (-) and the positive solution (+).," In the remainder of the paper, we will refer to these two different branches as the negative solution (-) and the positive solution (+)." As we will show next. these two branches correspond to very different spacetimes.," As we will show next, these two branches correspond to very different spacetimes." In the previous section. we estimated that the analytic solution should be relevant for rapidly rotating neutron stars only for values of j roughly larger than 0.5.," In the previous section, we estimated that the analytic solution should be relevant for rapidly rotating neutron stars only for values of $j$ roughly larger than 0.5." Fig., Fig. 3. shows a more slowly rotating model than the model shown in Fig. 2..," \ref{analytic_bs} shows a more slowly rotating model than the model shown in Fig. \ref{analytic_bf}," along the same evolutionary sequence., along the same evolutionary sequence. It is obvious that no solution to equation (70)) exists for any real value of the parameter 5., It is obvious that no solution to equation \ref{Qmatch}) ) exists for any real value of the parameter $b$. Along each sequence there is a critical rotation rate above which one can match the numerical interior solution to the analytic exterior solution., Along each sequence there is a critical rotation rate above which one can match the numerical interior solution to the analytic exterior solution. In Tables €1-—5)) we list all computed physieal properties for the selected sequences., In Tables \ref{EOSA}- \ref{EOSAPRb}) ) we list all computed physical properties for the selected sequences. The last column lists the parameter = of the branch of the analytic solution (when it exists)., The last column lists the parameter $b=b_-$ of the branch of the analytic solution (when it exists). This is the relevant branch for rapidly rotating neutron stars. as we will show in section 5..," This is the relevant branch for rapidly rotating neutron stars, as we will show in section \ref{checkSol}." In Tables €(1-—5)) some models appear having b=Q., In Tables \ref{EOSA}- \ref{EOSAPRb}) ) some models appear having $b=b_->0$. These models do belong to the positive branch 6., These models do belong to the positive branch $b_+$. They are instead models which are very close to the critical value of the rotation parameter. j=j44: in these particular cases. both solutions to equation (70)) can happen to be positive.," They are instead models which are very close to the critical value of the rotation parameter, $j=j_{crit}$: in these particular cases, both solutions to equation \ref{Qmatch}) ) can happen to be positive." However. in general (as long as a model is rotating somewhat above the critical rate) the negative branch has 50.," However, in general (as long as a model is rotating somewhat above the critical rate) the negative branch has $b_-<0$." Typical values of ορ above which the analytic solution exists are listed in Table 6 for a subset of the considered EOSs., Typical values of $j_{crit}$ above which the analytic solution exists are listed in Table \ref{jcrit} for a subset of the considered EOSs. " For smaller masses. jjj; 18 usually smaller: therefore. for ""canonical"" neutron stars (having mass 1ΕΜ in the non rotating limit) the analytic solution is valid over a wider range of ;j."," For smaller masses, $j_{crit}$ is usually smaller: therefore, for “canonical” neutron stars (having mass $M\sim 1.4 M_\odot$ in the non rotating limit) the analytic solution is valid over a wider range of $j$." In terms of the angular velocity at the mass-shedding limit for uniformly rotating stars. the critical rotation rates are given in the right column of Table 6..," In terms of the angular velocity at the mass-shedding limit for uniformly rotating stars, the critical rotation rates are given in the right column of Table \ref{jcrit}." The critical rotation rate Ολο/Qkepler ranges from ~0.4 to ~0.7 for the M=I.4M. sequence. with the lower ratio corresponding to the stiffest EOS.," The critical rotation rate $\Omega_{crit}/\Omega_{Kepler}$ ranges from $\sim 0.4$ to $\sim 0.7$ for the $M=1.4M_\odot$ sequence, with the lower ratio corresponding to the stiffest EOS." For the maximum-mass sequence the ratio is 0.9. nearly independent of the EOS.," For the maximum-mass sequence the ratio is $\sim 0.9$, nearly independent of the EOS." In conclusion. the analytic exterior solution can be useful for studying rapidly rotating neutron stars.," In conclusion, the analytic exterior solution can be useful for studying rapidly rotating neutron stars." The exterior gravitational field. of massive neutron stars created in binary neutron star mergers. supported temporarily by differential rotation against collapse. could also be described. to some accuracy. by the analytic solution (the accuracy will depend on how significant the higher multipole moments are in the case of strong differentialrotation).," The exterior gravitational field of massive neutron stars created in binary neutron star mergers, supported temporarily by differential rotation against collapse, could also be described, to some accuracy, by the analytic solution (the accuracy will depend on how significant the higher multipole moments are in the case of strong differentialrotation)." If the EOS is very stiff. such as EOS L. then the analytic solution is also valid for for description of accreting neutron stars in Low-Mass-X-Ray binaries (LMXB). with rotational periods of a few milliseconds.," If the EOS is very stiff, such as EOS L, then the analytic solution is also valid for for description of accreting neutron stars in Low-Mass-X-Ray binaries (LMXB), with rotational periods of a few milliseconds." Predicted radio luminosities at lower frequencies (151 and 74 MHz) for the models that agree with 1130 are included in Table Al..,Predicted radio luminosities at lower frequencies $151$ and $74$ MHz) for the models that agree with 130 are included in Table \ref{tbl2}. . Even at 151 MHz the ghost source may not be observable., Even at $151$ MHz the ghost source may not be observable. " However, the models predict that the source will be observable in the 74 MHz band, with luminosity on the order of 107? erg s~*, or, equivalently, 107° W Hz! sr~*."," However, the models predict that the source will be observable in the $74$ MHz band, with luminosity on the order of $10^{43}$ erg $^{-1}$, or, equivalently, $10^{20}$ W $^{-1}$ $^{-1}$." New observations of 1130 could test this., New low-frequency observations of 130 could test this. " Some models predict the lobe lengths in the lower limit of the error tolerance during the observational congruent window of 1130, while predicting the other features accurately."," Some models predict the lobe lengths in the lower limit of the error tolerance during the observational congruent window of 130, while predicting the other features accurately." " If such is the case, perhaps the surrounding density profile is not as simple as we have assumed it to be and allows for the lobes to grow larger than in our models while staying bright in the X-ray."," If such is the case, perhaps the surrounding density profile is not as simple as we have assumed it to be and allows for the lobes to grow larger than in our models while staying bright in the X-ray." " It is plausible that the source is expanding into a pre-existing lobe from a previous episode of jet activity, which cleared away some of the surrounding material and would mean expansion losses are smaller and the lobes can grow larger and brighter."," It is plausible that the source is expanding into a pre-existing lobe from a previous episode of jet activity, which cleared away some of the surrounding material and would mean expansion losses are smaller and the lobes can grow larger and brighter." " Importantly, the minimum Lorentz factor of injected particles into the lobe for 1130 is found to be on the order of ymin rather than ymin=1."," Importantly, the minimum Lorentz factor of injected particles into the lobe for 130 is found to be on the order of $\gamma_{\rm min}=1000$ rather than $\gamma_{\rm min}=1$." " Even a ymin=30 or Ymin=100 is not preferred by 1130: repeating fitting the observable properties of 1130 with models that have ymin=30 and ymin=100 gives only 4 congruent models observational windows of at most 3 Myr, reported in Table 4.."," Even a $\gamma_{\rm min}=30$ or $\gamma_{\rm min}=100$ is not preferred by 130: repeating fitting the observable properties of 130 with models that have $\gamma_{\rm min}=30$ and $\gamma_{\rm min}=100$ gives only $4$ congruent models observational windows of at most $3$ Myr, reported in Table \ref{tbl1c}." " In the model, a higher ymin (while keeping injected electron energy density constant) will produce brighter sources without affecting the lobe growth, which is determined by the jet power and the surrounding density profile."," In the model, a higher $\gamma_{\rm min}$ (while keeping injected electron energy density constant) will produce brighter sources without affecting the lobe growth, which is determined by the jet power and the surrounding density profile." Increasing the jet power makes the jet grow larger and brighter., Increasing the jet power makes the jet grow larger and brighter. " It is the combination of 1130 lobe size, which is not exceptionally large, and X-ray brightness which forces the model to require ymin~1000 to agree with the observational features."," It is the combination of 130 lobe size, which is not exceptionally large, and X-ray brightness which forces the model to require $\gamma_{\rm min}\sim 1000$ to agree with the observational features." " The minimum injected Lorentz factor for 0090543955 is also found to be most likely on the order of ymin=1000 (or also marginally 1), based on only best matching the total lobe luminosities predicted by the model to the observed luminosities."," The minimum injected Lorentz factor for 0905+3955 is also found to be most likely on the order of $\gamma_{\rm min}=1000$ (or also marginally $1$ ), based on only best matching the total lobe luminosities predicted by the model to the observed luminosities." " Considering only the models where p is steeper than implied by I (these values are bold in Table 3)), we see that only ymin=1000 is preferred."," Considering only the models where $p$ is steeper than implied by $\Gamma$ (these values are bold in Table \ref{tbl1b}) ), we see that only $\gamma_{\rm min}=1000$ is preferred." " In previous observations, no X-ray emission is seen in a hotspot of 0090543955 (other than highly energetic X-ray synchrotron requiring extremely high Lorentz factors ?)) which suggests that there is a low-energy cutoff of the freshly injected particles into the lobe above the ;~10? particles required for X-ray emission from upscattering on the CMB."," In previous observations, no X-ray emission is seen in a hotspot of 0905+3955 (other than highly energetic X-ray synchrotron requiring extremely high Lorentz factors \cite{2008MNRAS.386.1774E}) ) which suggests that there is a low-energy cutoff of the freshly injected particles into the lobe above the $\gamma\sim10^3$ particles required for X-ray emission from upscattering on the CMB." " Likely, the minimum energy cutoff is just above the critical Lorentz factor which would result in X-ray emission from the hotspot."," Likely, the minimum energy cutoff is just above the critical Lorentz factor which would result in X-ray emission from the hotspot." " It is important to note that 00905-3955 may be more complicated than described by our simple model, because 0090543955 is asymmetric, probably due to an asymmetric surrounding environment."," It is important to note that 0905+3955 may be more complicated than described by our simple model, because 0905+3955 is asymmetric, probably due to an asymmetric surrounding environment." " There may also be complex mechanisms happening in the lobes, such as reflected shocks or interruptions of the jet at the hotspot (?),, which are so far unaccounted for by our model."," There may also be complex mechanisms happening in the lobes, such as reflected shocks or interruptions of the jet at the hotspot \citep{1995MNRAS.277..995L}, which are so far unaccounted for by our model." " The chosen value of ymin varies by orders of magnitude in previous papers, as it often has to be estimated."," The chosen value of $\gamma_{\rm min}$ varies by orders of magnitude in previous papers, as it often has to be estimated." " The minimum Lorentz factor is assumed to be typically 1 in previous models of FR II evolution by ?,, ?,, ? and ?.."," The minimum Lorentz factor is assumed to be typically $1$ in previous models of FR II evolution by \cite{1997MNRAS.292..723K}, \cite{1997MNRAS.286..215K}, \cite{1999AJ....117..677B} and \cite{2010MNRAS.407.1998N}." " ? use a value of 10, use a value of 100, and ? use a value of 1000."," \cite{2005ApJ...626..733C} use a value of $10$, \cite{1991ApJ...383..554C} use a value of $100$, and \cite{1998Natur.395..457W} use a value of $1000$." " If 1130 and 0090543955 are typical sources, it may be the case that the minimum energy of particles injected into the lobes is large."," If 130 and 0905+3955 are typical sources, it may be the case that the minimum energy of particles injected into the lobes is large." " The value of ymin may at first appear as an eclectic, unimportant detail, but ? show that the typical value of ymin can significantly affect estimates for the total population of FR II sources from a radio luminosity function asit changes the time sources fall below a given flux limit in their evolution."," The value of $\gamma_{\rm min}$ may at first appear as an eclectic, unimportant detail, but \citet{2011MNRAS.413.1107M} show that the typical value of $\gamma_{\rm min}$ can significantly affect estimates for the total population of FR II sources from a radio luminosity function asit changes the time sources fall below a given flux limit in their evolution." A higher ymin will also increase the detectability of IC ghosts., A higher $\gamma_{\rm min}$ will also increase the detectability of IC ghosts. PM would like to acknowledge the award of a Weissman grant from Harvard University., PM would like to acknowledge the award of a Weissman grant from Harvard University. KMB and ACF thank the Royal Society for support., KMB and ACF thank the Royal Society for support. that are released in the gas phase upon formation due to the exothermicity of the reaction.,that are released in the gas phase upon formation due to the exothermicity of the reaction. " Racc(O) is the accretion rate of oxygen, while n(O), n(O3), and n(OH) are the dust surface densities of O, O5, and OH, respectively, in monolayers, e.g., 1 monolayer = coverage."," $R_{acc}(\rm O)$ is the accretion rate of oxygen, while $n(\rm O)$, $n(\rm O_3)$, and $n(\rm OH)$ are the dust surface densities of O, $_3$, and OH, respectively, in monolayers, e.g., 1 monolayer = coverage." These surface densities are listed in Appendix AppendixA:.., These surface densities are listed in Appendix \ref{deriv_eff}. αμ is the mobility of hydrogen atoms on the grain surface.," $\alpha_{\rm H}$ is the mobility of hydrogen atoms on the grain surface." " The efficiency for the formation of water doesnot contain a term with accretion of OH from the gas phase, since the accretion of O followed by OH formation dominates over OH accretion."," The efficiency for the formation of water does contain a term with accretion of OH from the gas phase, since the accretion of O followed by OH formation dominates over OH accretion." " A very important outcome of the simulation is that the formation of OH on grains is dominated by O+H—OH up to temperatures T~30—40 K depending on the environment, and by O5€H—OH*O» at higher temperatures."," A very important outcome of the simulation is that the formation of OH on grains is dominated by $\rm O + H \rightarrow OH$ up to temperatures $T \sim 30 - 40$ K depending on the environment, and by $\rm O_3 + H \rightarrow OH + O_2$ at higher temperatures." " This implies that apart from expressions for n(O) and n(OH), also those for n(O;) and n(O3) are needed."," This implies that apart from expressions for $n(\rm O)$ and $n(\rm OH)$, also those for $n(\rm O_2)$ and $n(\rm O_3)$ are needed." " For completeness, we also give the one for n(H5O)."," For completeness, we also give the one for $n(\rm H_2O)$." The importance of the O5+H reactions is shown in Fig. 6.., The importance of the $\rm O_3 + H$ reactions is shown in Fig. \ref{O3_importance}. It is obvious from the figure that the OH formation efficiency would be underestimated without the consideration of the reaction with Os., It is obvious from the figure that the OH formation efficiency would be underestimated without the consideration of the reaction with $\rm O_3$. " These results are not inconsistent with those obtained by(2008),, where the formation of H50 is dominated by the reaction sequence: H-O?—HO», H+HO; H50O; followed by H+H2O2 H50 OH."," These results are not inconsistent with those obtained by, where the formation of $_2$ O is dominated by the reaction sequence: $\rm H + O_2 \rightarrow HO_2$, $\rm H + HO_2 \rightarrow H_2O_2$ followed by $\rm H + H_2O_2 \rightarrow H_2O + OH$ ." " We do consider the same reaction rate paths in our work, but in this study, molecules are formed ongrains, while considermantles."," We do consider the same reaction rate paths in our work, but in this study, molecules are formed on, while consider." " In our simulation a very significant part of the molecules are desorbed upon formation, while the cycle of photodissociation of HzO and reformation on the grains significantly enhances the amount of water released in the gas phase."," In our simulation a very significant part of the molecules are desorbed upon formation, while the cycle of photodissociation of $_2$ O and reformation on the grains significantly enhances the amount of water released in the gas phase." H20». There is also another way to form H5O that involves Os., There is also another way to form $_2$ O that involves $_3$. " The reaction O+O2— Os, that releases only a very small part into the gas phase upon formation (only a few percent)."," The reaction $\rm O + O_2 \rightarrow O_3$ , that releases only a very small part into the gas phase upon formation (only a few percent)." " So although the efficiency for the formation of O3 is low, there is a significant amount of O3 on the surface to react to OH."," So although the efficiency for the formation of $\rm O_3$ is low, there is a significant amount of $\rm O_3$ on the surface to react to OH." The work by is also very different from ours., The work by is also very different from ours. " They also treat a surface chemistry network, with H5, OH, O2, and some other different species, such as CH, CH», and CH3."," They also treat a surface chemistry network, with $_2$, OH, $_2$, and some other different species, such as CH, $_2$, and $_3$." " They do not include processes with O3 and H20», intermediate species in the processes leading to water formation."," They do not include processes with $_3$ and $_2$ $_2$, intermediate species in the processes leading to water formation." " However, the biggest difference between our models are the processeses to deliver species back into the gas-phase which are thermal, photo, and cosmic-ray desorption in the paper, as they are considering ices in that work, whereas this is desorption upon formation in our work."," However, the biggest difference between our models are the processeses to deliver species back into the gas-phase which are thermal, photo, and cosmic-ray desorption in the paper, as they are considering ices in that work, whereas this is desorption upon formation in our work." " They consider a PDR environment, and therefore they allow for the formation of strongly bound ice-layers."," They consider a PDR environment, and therefore they allow for the formation of strongly bound ice-layers." We assume that this does not occur because of the turbulent motions stripping the grains and the strong photodissociating radiation fields that are internally created by X-rays., We assume that this does not occur because of the turbulent motions stripping the grains and the strong photodissociating radiation fields that are internally created by X-rays. " The approximate analytical fits to the rate equation results arevery good for environments 1, 2, 4 and 5."," The approximate analytical fits to the rate equation results arevery good for environments 1, 2, 4 and 5." " However,"," However," Essentially all Galactic star formation occurs within dense clouds of molecular gas. known as molecular clouds (AIC's).,"Essentially all Galactic star formation occurs within dense clouds of molecular gas, known as molecular clouds (MCs)." " Furthermore. recent observations have demonstrated that on large scales within local galaxies. there is a surprisingly close correlation between the surface densitv of star formation. Mappe and the surface density of molecular hydrogen. Vu, (seee.g.Wong&Blitz2002:Leroyetal.2008:Bigielοἱ2008. 2011)."," Furthermore, recent observations have demonstrated that on large scales within local galaxies, there is a surprisingly close correlation between the surface density of star formation, $\Sigma_{\rm SFR}$, and the surface density of molecular hydrogen, $\Sigma_{\rm H_{2}}$ \citep[see e.g.][]{wong02,leroy08,bigiel08,bigiel11}." .. An obvious interpretation of these observations is that the formation of stars depends on the presence of molecular gas (Ixrumholz&Melxee2005:Elmeercen2007:Ilxrumholzetal. 2009).," An obvious interpretation of these observations is that the formation of stars depends on the presence of molecular gas \citep{krumholzmckee05,elmegreen07,kmt09}." .. However. it is not imimecliately obvious why this should. be the case.," However, it is not immediately obvious why this should be the case." Although LH» can be an important coolant of interstellar gas (Cinedin& 2011).. it is cHleetive only at temperatures of a few hundred Ixelvin or higher.," Although $_{2}$ can be an important coolant of interstellar gas \citep{gk11}, it is effective only at temperatures of a few hundred Kelvin or higher." At the temperatures typical of gas within molecular clouds (7— 10.20 Ix). the HH» cooling rate is tinv. and hence Le cannot plav à direct role in enabling the gas to cool. undergo gravitational collapse. and form stars.," At the temperatures typical of gas within molecular clouds $T \sim 10$ –20 K), the $_{2}$ cooling rate is tiny, and hence $_{2}$ cannot play a direct role in enabling the gas to cool, undergo gravitational collapse, and form stars." A more promising route by which Le can influence the thermocvnamics of the gas is through the fact that its presence is required for the cllicient formation of carbon monoxide (CO)., A more promising route by which $_{2}$ can influence the thermodynamics of the gas is through the fact that its presence is required for the efficient formation of carbon monoxide (CO). Unlike HI». CO can provide elfective cooling even in very low temperature gas. and it is generally. found to be the dominant gas-phase coolant within prestellar cores (Neufeld.Lepp&Alelnick1995:Goldsmith:2001).," Unlike $_{2}$, CO can provide effective cooling even in very low temperature gas, and it is generally found to be the dominant gas-phase coolant within prestellar cores \citep{nlm95,gold01}." . llowever. even if the Hl» and CO were absent. the gas would still be able to cool to low temperatures through fine structure emission from ionized and neutral atomic carbon.," However, even if the $_{2}$ and CO were absent, the gas would still be able to cool to low temperatures through fine structure emission from ionized and neutral atomic carbon." In previous modelling. we have shown that cooling alone can reduce the gas temperature to 2~20 Ix within gas that is shielded from the effects of photoelectrie heating hy dust extinctions of ely~1 2 or more (Glover&MacLow2007)," In previous modelling, we have shown that $^{+}$ cooling alone can reduce the gas temperature to $T \sim 20$ K within gas that is shielded from the effects of photoelectric heating by dust extinctions of $A_{\rm V} \sim 1$ –2 or more \citep{gm07}." ‘To reduce the temperature further. to the LO Ix typical of most prestellar cores. a molecular coolant such as €'O is still required. but it seems unlikely that the dillerence between the ~10 Ix temperatures reachable with molecular cooling and the ~20 Ix temperatures reachable with atomic fine," To reduce the temperature further, to the 10 K typical of most prestellar cores, a molecular coolant such as CO is still required, but it seems unlikely that the difference between the $\sim 10$ K temperatures reachable with molecular cooling and the $\sim 20$ K temperatures reachable with atomic fine" particles were considered to be genuine substructures.,particles were considered to be genuine substructures. In our work. we rise this limit to at least 32 particles.," In our work, we rise this limit to at least $32$ particles." We have checked that. with this choice. ‘evanescent’ substructures (i.e. objects close to the resolution limit that occasionally appear and then disappear) are avoided.," We have checked that, with this choice, `evanescent' substructures (i.e. objects close to the resolution limit that occasionally appear and then disappear) are avoided." This turns out to be important particularly for our GAS runs., This turns out to be important particularly for our GAS runs. We remind the reader that classities all particle inside a FOF group either as belonging to a bound substructure or as being unbound., We remind the reader that classifies all particle inside a FOF group either as belonging to a bound substructure or as being unbound. The self-bound part of the FOF group itself will also appear in the substructure list and represents what we will refer to as the “main halo’., The self-bound part of the FOF group itself will also appear in the substructure list and represents what we will refer to as the `main halo'. This particular halo typically contains 90 per cent of the mass of the FOF group (?).., This particular halo typically contains 90 per cent of the mass of the FOF group \citep{Springel_etal_2001}. The subhalo catalogues have then been used to construct merging histories of all self-bound structures in our simulations. using the same procedure outlined in 2.. as updated in 2..," The subhalo catalogues have then been used to construct merging histories of all self-bound structures in our simulations, using the same procedure outlined in \citet{Springel_etal_2005}, as updated in \citet{2007MNRAS.375....2D}." This procedure is based on the identification of a unique descendant for euch self-bound structure., This procedure is based on the identification of a unique descendant for each self-bound structure. In order to identify the descendant of a given halo. all subhaloes in the following snapshot that contain its particles are identified.," In order to identify the descendant of a given halo, all subhaloes in the following snapshot that contain its particles are identified." Particles are then counted by giving ligher weight to those that are more tightly bound in the halo under consideration., Particles are then counted by giving higher weight to those that are more tightly bound in the halo under consideration. The halo that contains the largest fraction of he most bound particles is chosen as descendant of the halo under consideration., The halo that contains the largest fraction of the most bound particles is chosen as descendant of the halo under consideration. In our GAS runs. the original weighting seheme used in? leads to a number of premature mergers for small structures.," In our GAS runs, the original weighting scheme used in \citet{Springel_etal_2005} leads to a number of premature mergers for small structures." In order to avoid this problem. we increased by a factor of one hird the weight of the most bound particles with respect to the original choice (seealso?)..," In order to avoid this problem, we increased by a factor of one third the weight of the most bound particles with respect to the original choice \citep[see also][]{2008arXiv0808.3401D}." Our choice results in a better tracing of bound structures in our GAS runs. while leaving the results of he DM runs unaffected.," Our choice results in a better tracing of bound structures in our GAS runs, while leaving the results of the DM runs unaffected." The merger trees constructed as describec above represent the basic input needed for the semi-analytic mode described in Sec. 3.., The merger trees constructed as described above represent the basic input needed for the semi-analytic model described in Sec. \ref{sec:SAM}. Figure |. shows differential (left panel) and cumulative Gigh panel) mass functions of the subhaloes identified at +=0 within roo. averaged over the four simulated clusters.," Figure \ref{fi:MF_haloes} shows differential (left panel) and cumulative (right panel) mass functions of the subhaloes identified at $z = 0$ within $r_{200}$, averaged over the four simulated clusters." We have included in these distributions the four main haloes of the simulations. using the corresponding value of {σου for the mass.," We have included in these distributions the four main haloes of the simulations, using the corresponding value of $M_{200}$ for the mass." These corresponc to the mass bins around ~101A!Alpe in the differential mass function., These correspond to the mass bins around $\sim 10^{15}\hm$ in the differential mass function. For all other subhaloes. the mass used in Figure |. is the sum of the masses of all their bound particles.," For all other subhaloes, the mass used in Figure \ref{fi:MF_haloes} is the sum of the masses of all their bound particles." " We will adopt this ""efinition throughout this paper. as well as within the semi-analytic model. whenever an estimate of the substructure mass is needed."," We will adopt this definition throughout this paper, as well as within the semi-analytic model, whenever an estimate of the substructure mass is needed." The left panel of Figure |. shows that the DM mass function lies PZlightly but systematically above that measured from the GAS runs., The left panel of Figure \ref{fi:MF_haloes} shows that the DM mass function lies slightly but systematically above that measured from the GAS runs. This difference is larger than that corresponding to the shift in mass by the baryon fraction. and it cannot be accounted for by assuming that all gas is stripped from all subhaloes.," This difference is larger than that corresponding to the shift in mass by the baryon fraction, and it cannot be accounted for by assuming that all gas is stripped from all subhaloes." It seems that in the non— runs. subhaloes that are stripped of their gas become both less massive more and weakly bound (2)..," It seems that in the non--radiative runs, subhaloes that are stripped of their gas become both less massive more and weakly bound \citep{2008arXiv0808.3401D}." This is probably also he reason of the systematic difference between ουν in DM and GAS runs shown in Table l.., This is probably also the reason of the systematic difference between $M_{200}$ in DM and GAS runs shown in Table \ref{t:clus}. The g8 cluster is an exception: for his cluster. A/ooy in the GAS run is larger than the corresponding value from the DM run. and the number of subhaloes within rou in he GAS run is much lower than the corresponding number in the DM run.," The g8 cluster is an exception: for this cluster, $M_{200}$ in the GAS run is larger than the corresponding value from the DM run, and the number of subhaloes within $r_{200}$ in the GAS run is much lower than the corresponding number in the DM run." The peculiar behaviour of this cluster can be explained by aking into account its accretion history., The peculiar behaviour of this cluster can be explained by taking into account its accretion history. This is the most massive cluster in our sample. and it did not undergo any major merger event after >—1.," This is the most massive cluster in our sample, and it did not undergo any major merger event after $z\sim 1$." As a consequence. subhaloes in the GAS run spent a ong time in a hot. high-pressure atmosphere that can efficiently remove their gas through ram-pressure stripping.," As a consequence, subhaloes in the GAS run spent a long time in a hot, high–pressure atmosphere that can efficiently remove their gas through ram–pressure stripping." Turning back to Figure |. the drop at masses =10177.1A. is due to our choice of considering only substructures with at least 32 bound particles.," Turning back to Figure \ref{fi:MF_haloes}, the drop at masses $\mincir 10^{10.5} h^{-1} M_\odot$ is due to our choice of considering only substructures with at least 32 bound particles." In the GAS runs. the drop occurs at slightly lower masses because of the reduced value of the gas particle mass with respect to the DM particle mass.," In the GAS runs, the drop occurs at slightly lower masses because of the reduced value of the gas particle mass with respect to the DM particle mass." Although the difference is small. Figure |. shows that our GAS runs contain less substructures than the corresponding DM runs.," Although the difference is small, Figure \ref{fi:MF_haloes} shows that our GAS runs contain less substructures than the corresponding DM runs." In the following sections. we will analyse the impact of these differences on prediction from a semi-analytic model of galaxy formation.," In the following sections, we will analyse the impact of these differences on prediction from a semi-analytic model of galaxy formation." In this work. we use the semi-analvytic. model described in ?..," In this work, we use the semi-analytic model described in \citet{2007MNRAS.375....2D}." We recall that the semi-analytic model we employ builds upon the methodology originally introduced by ?.. 2 and ?..," We recall that the semi-analytic model we employ builds upon the methodology originally introduced by \citet{Kauffmann_etal_1999}, \citet{SP01.1} and \citet*{2004MNRAS.349.1101D}." The modelling of various physical processes has been recently updated as described in?) who also included a model for the suppression of cooling flows by ‘radio-mode’ AGN feedback., The modelling of various physical processes has been recently updated as described in \citet{2006MNRAS.365...11C} who also included a model for the suppression of cooling flows by `radio-mode' AGN feedback. We refer to the original papers for details., We refer to the original papers for details. In this study. we have assumed a Salpeter Initial Mass Function. and a recycled gas fraction equal to 0.3.," In this study, we have assumed a Salpeter Initial Mass Function, and a recycled gas fraction equal to 0.3." The semi-analytic. model adopted in this study includes explicitly dark matter substructures., The semi-analytic model adopted in this study includes explicitly dark matter substructures. This means that the haloes within which galaxies form are still followed even when accreted onto larger systems., This means that the haloes within which galaxies form are still followed even when accreted onto larger systems. As explained in 2. and ?.. the adoption of this particular scheme leads to the detinition of three different ‘types’ of galaxies.," As explained in \citet{SP01.1} and \citet{2004MNRAS.349.1101D}, the adoption of this particular scheme leads to the definition of three different `types' of galaxies." " Each FOF group hosts a ""Type 0° galaxy.", Each FOF group hosts a `Type 0' galaxy. This galaxy is located at the position of the most bound particle of the main halo. and it is the only galaxy fed by radiative cooling from the surrounding hot halo medium.," This galaxy is located at the position of the most bound particle of the main halo, and it is the only galaxy fed by radiative cooling from the surrounding hot halo medium." " All galaxies attached to dark matter substructures are referred to as ""Type |.", All galaxies attached to dark matter substructures are referred to as `Type 1'. These galaxies were previously central galaxy of a halo that merged to form the larger system in which they currently reside., These galaxies were previously central galaxy of a halo that merged to form the larger system in which they currently reside. The positions and velocities of these galaxies are followed by tracing the surviving core of the parent halo., The positions and velocities of these galaxies are followed by tracing the surviving core of the parent halo. The hot reservoir originally associated with the galaxy is assumed to be kinematically stripped at the time of accretion and is added to the hot component of the new main halo., The hot reservoir originally associated with the galaxy is assumed to be kinematically stripped at the time of accretion and is added to the hot component of the new main halo. Tidal truncation and stripping rapidly reduce the mass ofdark matter substructures below the resolution limit of the simulation (??)..," Tidal truncation and stripping rapidly reduce the mass of dark matter substructures below the resolution limit of the simulation \citep{2004MNRAS.348..333D,2004MNRAS.355..819G}." When this happens. we estimate a residual surviving time for the satellite galaxies using the classical dynamical friction formula (see Sec. 4.3)).," When this happens, we estimate a residual surviving time for the satellite galaxies using the classical dynamical friction formula (see Sec. \ref{sec:Merg_time}) )," and we follow the positions and velocities of the galaxies by tracing the most bound particles of the destroyed substructures., and we follow the positions and velocities of the galaxies by tracing the most bound particles of the destroyed substructures. Galaxies no longer associated with distinct dark matter substructures are referred to as “Type 2 galaxies. and their stellar mass is assumed not to be affected by the tidal stripping that reduces the mass of their parent haloes.," Galaxies no longer associated with distinct dark matter substructures are referred to as `Type 2' galaxies, and their stellar mass is assumed not to be affected by the tidal stripping that reduces the mass of their parent haloes." Figure 2. shows the density map of the cluster gS] from the DM run tleft panels) and from the GAS run (right panels)., Figure \ref{fi:Maps} shows the density map of the cluster g51 from the DM run (left panels) and from the GAS run (right panels). The projections are colour-coded by mass density. computed within a," The projections are colour-coded by mass density, computed within a" Diagram ancl fitting to cosmological models.,Diagram and fitting to cosmological models. Ii practice. there must be a simullaneous minimization for the hunmünositw calibrations and the cosmology. so as to avoid the effects of possible correlations between the indicators and distance.," In practice, there must be a simultaneous chi-square minimization for the luminosity calibrations and the cosmology, so as to avoid the effects of possible correlations between the indicators and distance." Ifthe Earth is not along the central axis of the GIRD's jet. Chen various off-axis effects will change the observed. properties.," If the Earth is not along the central axis of the GRB's jet, then various off-axis effects will change the observed properties." " For Πο viewed off-axis bv angle 9 from a jet moving al 9 times (he speed of light. (he transverse Doppler shift. redshift. and beaming will change (he various observed properties by powers of B=(1—ο)—3cos?). The observed value Of E44, wil scaleas D. 7,, will scale as 5LOV will scale asthe inverse of a time and hence as B. while L will have a model dependent variation that scales roughly as B*."," For light viewed off-axis by angle $\theta$ from a jet moving at $\beta$ times the speed of light, the transverse Doppler shift, redshift, and beaming will change the various observed properties by powers of $B=(1- \beta )/(1- \beta cos \theta )$ The observed value of $E_{peak}$ will scaleas $B$, $\tau_{lag}$ will scale as $B^{-1}$, $V$ will scale asthe inverse of a time and hence as $B$, while $L$ will have a model dependent variation that scales roughly as $B^3$." For structured jets (Rossi.Lazzati.&Rees2002:ZhangMeészáros2002).. the Inuiinosity andbulk Lorentz [actor can be parameterized as being proportional to some positive power ol D.," For structured jets \citep{rlr02,zhm02}, the luminosity andbulk Lorentz factor can be parameterized as being proportional to some positive power of $B$." When viewed on-axis. the bursts will presumably. clisplay fairly Gelt lag/Iuminosity and variability/luminosity relations.," When viewed on-axis, the bursts will presumably display fairly tight lag/luminosity and variability/luminosity relations." These relations can be converted to similar relations involving observed off-axis quantities with an extra factor of B to some power., These relations can be converted to similar relations involving observed off-axis quantities with an extra factor of $B$ to some power. " Fortunately. the observed distribution of E, is remarkably narrowlor bursts of a given. brightness (\allozzietal.1995:Drainard1998).. and (he removal of kinematic effects shows that the on-axis [ρω is Virtually constant (Schaeler 2002).."," Fortunately, the observed distribution of $E_{peak}$ is remarkably narrowfor bursts of a given brightness \citep{mal95,bra98}, and the removal of kinematic effects shows that the on-axis $E_{peak}$ is virtually constant \citep{sch02}. ." " Thus. ρω should be proportional onlv (ο some power of D. and this relation can be used to convert the J dependency. of the Iuninosityrelations into a E, dependency."," Thus, $E_{peak}$ should be proportional only to some power of $B$, and this relation can be used to convert the $B$ dependency of the luminosityrelations into a $E_{peak}$ dependency." Essentially. we can use the observed E; value (ο get information about the off-axis angle and correct the observed τν and V. values to those which would be seen on-axis.," Essentially, we can use the observed $E_{peak}$ value to get information about the off-axis angle and correct the observed $\tau_{lag}$ and $V$ values to those which would be seen on-axis." " In practice. (he correction [actor can be taken as some power of E,,,01+z)/400eV. ("," In practice, the correction factor can be taken as some power of $E_{peak}(1+z)/400keV$. (" The division by 400 keV is to minimize correlations between (he normalization constant and the exponent during the fits.),The division by 400 keV is to minimize correlations between the normalization constant and the exponent during the fits.) The exponents of the correction [actors will be free parameters which depend on the scenario and jet structure., The exponents of the correction factors will be free parameters which depend on the scenario and jet structure. With the off-axis correction. the Iuminosities can be derived by filling the relations LXaeToon and∙ LxMESIVer where.uu Tugeor-.-=Tuyο7+z)/400|~) agoand LEutl+ z)/400]*.," With the off-axis correction, the luminosities can be derived by fitting the relations $L \propto \tau_{lag,corr}^{\alpha_{lag}}$ and $L \propto V_{corr}^{\alpha_{V}}$, where $\tau_{lag,corr} = \tau_{lag} \times [E_{peak} (1+z)/400] ^{e_{lag}}$ and $V_{corr} = V \times [E_{peak} (1+z)/400] ^{e_V}$ ." " Plots of Lops versus 754,"" adl Lo versus Vo, lor the nine bursts with known redshilts (see Figure 1) have slopes of à;,, and oy. while the scatter in these plots will be minimized for the best values of e;,, and ey.This gives aig=—1.21 0.20. ay= L570. Plag=0.6LE 0.7. and ey=0.85 40.40."," Plots of $L_{obs}$ versus $\tau_{lag,corr}$ and $L_{obs}$ versus $V_{corr}$ for the nine bursts with known redshifts (see Figure 1) have slopes of $\alpha_{lag}$ and $\alpha_V$, while the scatter in these plots will be minimized for the best values of $e_{lag}$ and $e_V$ .This gives $\alpha_{lag} = -1.27 \pm 0.20$ , $\alpha_V = 1.57 \pm 0.17$ , $e_{lag} = 0.6 \pm 0.7$ , and $e_V = 0.85 \pm 0.40$ ." " Thus: where Lis in ergs. l. Tag is in seconds. V. is dimensionless. and Γεω I in keV. As independent checks. a plot ΟΕ 7,,,,,,. versus Vou, for 93 BATSE bursts will have a slope of"," Thus: where $L$is in $erg ~s^{-1}$ , $\tau_{lag}$ is in seconds, $V$ is dimensionless, and $E_{peak}$ is in keV. As independent checks, a plot of $\tau_{lag,corr}$ versus $V_{corr}$ for 93 BATSE bursts will have a slope of" other applications. such as to studies of the stability of binary stars perturbed by a third body or to investigations of protoplanetary disks perturbed by close passages of stars.,"other applications, such as to studies of the stability of binary stars perturbed by a third body or to investigations of protoplanetary disks perturbed by close passages of stars." We thank Alar Toomre and Avi Loeb for valuable advice., We thank Alar Toomre and Avi Loeb for valuable advice. ED acknowledges support from the Keck Foundation., ED acknowledges support from the Keck Foundation. CAFG ts supported by a fellowship from the Miller Institute for Basic Research in Science. and received further support from the Harvard Merit Fellowship and FQORNT during the course of this work.," CAFG is supported by a fellowship from the Miller Institute for Basic Research in Science, and received further support from the Harvard Merit Fellowship and FQRNT during the course of this work." Our analysis of parabolic tidal encounters results in expressions that involve the generalized Airy functions of (1977).. defined by eq. (58)).," Our analysis of parabolic tidal encounters results in expressions that involve the generalized Airy functions of \citet{PT77}, defined by eq. \ref{Ilmpt77}) )." The first one. Zyy. 1s a modified Bessel function or (conventional) Airy function. Press&Teukolsky(1977) provide the following rational function approximations to πω.ου. and F5). making it possible to straightforwardly estimate the velocity perturbations in a parabolic tidal encounter: These expressions are accurate to around <0.σοι except for very small and very large values of à. where the error rises to a few percent.," The first one, $I_{00}$, is a modified Bessel function or (conventional) Airy function, \citet{PT77} provide the following rational function approximations to $I_{10},~I_{20},$ and $I_{30}$, making it possible to straightforwardly estimate the velocity perturbations in a parabolic tidal encounter: These expressions are accurate to around $\leq 0.1$, except for very small and very large values of $\alpha$, where the error rises to a few percent." To evaluate the limita>x of the parabolic encounter case studied in this work. it is necessary to know the asymptotic behavior of the generalized Airy functions as y5x.," To evaluate the limit $\alpha \to \infty$ of the parabolic encounter case studied in this work, it is necessary to know the asymptotic behavior of the generalized Airy functions as $y \to \infty$." In what follows. we give these asymptoticexpansions and outline the key steps of their derivation.," In what follows, we give these asymptoticexpansions and outline the key steps of their derivation." While the /=0 case corresponds to the usual Airy function. the /=1.2.3 cases have not been extensively studied before. and the numerical fits provided by Press&Teukolsky(1977) are not sufficiently accurate to capture exact cancellations in the results.," While the $l=0$ case corresponds to the usual Airy function, the $l=1,~2,~3$ cases have not been extensively studied before, and the numerical fits provided by \citet{PT77} are not sufficiently accurate to capture exact cancellations in the results." Ostriker(1994) previously calculated these asymptotic expansions to leading order using similar techniques. but some of the limits we take involve exact cancellations at this order. so that it is necessary to compute higher-order terms.," \cite{O94} previously calculated these asymptotic expansions to leading order using similar techniques, but some of the limits we take involve exact cancellations at this order, so that it is necessary to compute higher-order terms." The starting point for the asymptotic expansions ts the integral expression (eq. 58)), The starting point for the asymptotic expansions is the integral expression (eq. \ref{Ilmpt77}) ) The main technical difficulty in determining the asymptotic behavior of [jy)(4/) arises from the fact that the cosine term oscillates extremely rapidly as y»x. and that the value of the integral depends on exactly how the positive and negative parts cancel each other.," The main technical difficulty in determining the asymptotic behavior of $I_{l0}(y)$ arises from the fact that the cosine term oscillates extremely rapidly as $y \to \infty$, and that the value of the integral depends on exactly how the positive and negative parts cancel each other." It is however possible to circumvent this difficulty by expressing equation (AG)) in terms of a contour integral in the complex plane. and by using the method of steepest descent (e.g..Bender&Orszag1978)..," It is however possible to circumvent this difficulty by expressing equation \ref{I l0 integral}) ) in terms of a contour integral in the complex plane, and by using the method of steepest descent \citep[e.g.,][]{1978amms.book.....B}." Specifically. we note that and consider the integration contour shown in Figure A13..," Specifically, we note that and consider the integration contour shown in Figure \ref{contour}." " Making the change of variable s=;&. the integral within the curly brackets is seen to be equal to an equivalent integral along the imaginary axis: Writing the complex integrand as f(s}. the residue theorem implies that ferfsjds=2zià,Reos(f.αν). where the ας are the poles within C=Cy|C2C5 C."," Making the change of variable $s\equiv i \xi$, the integral within the curly brackets is seen to be equal to an equivalent integral along the imaginary axis: Writing the complex integrand as $f(s)$, the residue theorem implies that $\oint_{C} f(s) ds = 2 \pi i \sum_{k=1}^{n} {\rm Res}(f,~a_{k})$, where the $a_{k}$ are the poles within $C=C_{1}+C_{2}+C_{3}+C_{4}$ ." " Since the integrands along C» and C, are exponentially suppressed in modulus. τωc,fisjds> Oas the contour is expanded to infinity. yielding"," Since the integrands along $C_{2}$ and $C_{4}$ are exponentially suppressed in modulus, $\int_{C_{2},C_{4}}f(s)ds\to 0$ as the contour is expanded to infinity, yielding" red-selected sample are affected bv this color bias and consequeutly bv incompleClos in the last bius.,red-selected sample are affected by this color bias and consequently by incompleteness in the last bins. " The fiateniug found by other Authors may be mainly. caused bv the influence of such incompleteness (noise bong equally iuiportaut for faint galaxies. be them at low or hieh redshift) and not to the ""crossing of the Lxiuau break."," The flattening found by other Authors may be mainly caused by the influence of such incompleteness (noise being equally important for faint galaxies, be them at low or high redshift) and not to the “crossing” of the Lyman break." As explained in Section { we selected two samples: the FalW-seclected one should trace the global features of the TIDF-S sample and the F300W-sclected sample evidencing star-forming ealaxics at moderate :., As explained in Section 4 we selected two samples: the F814W-selected one should trace the global features of the HDF-S sample and the F300W-selected sample evidencing star-forming galaxies at moderate $z$. The FalW-sclected catalogue has by far he biggest nuniber of sources. so that the number of galaxies with lower lini sin the other bands is rather high.," The F814W-selected catalogue has by far the biggest number of sources, so that the number of galaxies with lower limits in the other bands is rather high." " We applied a linear fit to the color-magnitude relation by making use of ""survival analysis” (Avnict al.", We applied a linear fit to the color-magnitude relation by making use of “survival analysis” (Avni et al. 1980. Ixobe et al.," 1980, Isobe et al." 1986). in order to avoid uucertanties introduced bv the heavy iuflueuce of censored data.," 1986), in order to avoid uncertainties introduced by the heavy influence of censored data." We applied a linear regressiou based on Isaplan-Meicr residuals., We applied a linear regression based on Kaplan-Meier residuals. This analysis las suggested an almost flat relation for (FISOW yp vs FallWip. FGOGW)yp ws ip ancl FSLIN)4p vs ap for ap>21. while Ντ vs. ap did not reach convergence.," This analysis has suggested an almost flat relation for $-$ $_{AB}$ vs $_{AB}$ , $-$ $_{AB}$ vs $_{AB}$ and $-$ $_{AB}$ vs $_{AB}$ for $_{AB}>24$, while $-$ $_{AB}$ vs $_{AB}$ did not reach convergence." Suiail et al. (, Smail et al. ( 1995) noticed a simular τοσο on theirsample limited at R=27.,1995) noticed a similar tendency on theirsample limited at R=27. After an initial bluiug the median BR. color ects redder. I ects flat. while RT keeps ou following a bluiug trend.," After an initial bluing the median $-$ R color gets redder, $-$ I gets flat, while $-$ I keeps on following a bluing trend." This trend ταν sugeestee the presence of a flat spectrun population. whose colors ποσα to saturate but whose contribution is more and more important at faint naenitudes. as confirmed by the rising fraction of galaxies with — E606NV)45 bluer than a typical nreeular ealaxy.," This trend may suggest the presence of a flat spectrum population, whose colors seem to saturate but whose contribution is more and more important at faint magnitudes, as confirmed by the rising fraction of galaxies with $-$ $_{AB}$ bluer than a typical irregular galaxy." Broadly speaking ealaxy colors are domunated o» blue sources. as noted bv Willams et al. (," Broadly speaking galaxy colors are dominated by blue sources, as noted by Williams et al. (" 1996)in he TIDF-N.that is the median color is always bluer han typical local samples.,"1996)in the HDF-N,that is the median color is always bluer than typical local samples." The F300W-sclected sample shows a very blue E150)45. color. though he relation FISOW)yp vs F300W45. secus alios flat.," The F300W-selected sample shows a very blue $-$ $_{AB}$ color, though the relation $-$ $_{AB}$ vs $_{AB}$ seems almost flat." These two features sueecst a considerable contriution bv flat spectruni sources., These two features suggest a considerable contribution by flat spectrum sources. Comparing the nedian (F300W ΕΟΝyp color with Druzual Charlot (1993) aud CWW predicος colors. the aad contribution may bedue to sources with :> 0.5. while FsliWiip. FsliWw)yp and (E150 F6OGW)yp are compatible with those of local nireenlar galaxies.," Comparing the median (F300W $-$ $_{AB}$ color with Bruzual Charlot (1993) and CWW predicted colors, the main contribution may bedue to sources with $z>0.5$ , while $-$ $_{AB}$ $-$ $_{AB}$ and $-$ $_{AB}$ are compatible with those of local irregular galaxies." the same contamination from the light of the host galaxy.,the same contamination from the light of the host galaxy. " estimated that with the above prescriptions the contamination amounts to about of the host total flux density, which is 0.36, 1.30, 2.89, 4.23, 5.90, 11.83, 13.97, and 10.62 mJy in the U, B, V, R, I, J, H, and K bands, respectively."," estimated that with the above prescriptions the contamination amounts to about of the host total flux density, which is 0.36, 1.30, 2.89, 4.23, 5.90, 11.83, 13.97, and 10.62 mJy in the $U$ , $B$ , $V$ , $R$, $I$, $J$, $H$, and $K$ bands, respectively." " When converting magnitudes into flux densities, we corrected for the Galactic extinction according to the laws, using Ry=3.1, the standard value for the diffuse interstellar medium, andAg1.421998)."," When converting magnitudes into flux densities, we corrected for the Galactic extinction according to the laws, using $R_V=3.1$, the standard value for the diffuse interstellar medium, and$A_B=1.42$." . We adopted the absolute fluxes by(, We adopted the absolute fluxes by. "1998).. Figure 1 shows the best-sampled total R-band light curve from February 2008 to February 2009 built with GASP data, which are not corrected for the host galaxy contribution here."," Figure \ref{erre} shows the best-sampled total $R$ -band light curve from February 2008 to February 2009 built with GASP data, which are not corrected for the host galaxy contribution here." " A noticeable flare was observed at the beginning of the period, in 2008 February-March; afterwards both the average brightness level and the variability amplitude decreased."," A noticeable flare was observed at the beginning of the period, in 2008 February–March; afterwards both the average brightness level and the variability amplitude decreased." " However, the source remained active, its brightness oscillating by several tenths of magnitude on a few-day time scale."," However, the source remained active, its brightness oscillating by several tenths of magnitude on a few-day time scale." This isnot anunusual behaviour for BL Lacertae hours)..,This isnot anunusual behaviour for BL Lacertae . or ?.. which showed an absence of reflection effects in these systems. implving a degenerate companion.,"or \citet{Shimanskii08}, which showed an absence of reflection effects in these systems, implying a degenerate companion." some fraction of the scBopopulation are composite systems. in which [lux excesses at long wavelengths or spectral features indicate the presence of a cool. Ci-Ix-tvpe companion.," Some fraction of the sdB population are composite systems, in which flux excesses at long wavelengths or spectral features indicate the presence of a cool, G-K-type companion." The remaining ‘single’ sdDs may truly be single stars. or they may have unseen white dwarl or fainter. dAl-twpe companions.," The remaining `single' sdBs may truly be single stars, or they may have unseen white dwarf or fainter, dM-type companions." " Using Two Micron All Sky Survey observations. 7. showed the composite and ‘single’ sdB populations can be distinguished by their Jdv. colour. with the single stars having JAN,«|0.05 and the composites having JA,|0.05."," Using Two Micron All Sky Survey observations, \citet{Stark03} showed the composite and `single' sdB populations can be distinguished by their $J-K_s$ colour, with the `single' stars having $J-K_s < +0.05$ and the composites having $J-K_s > +0.05$." In figure 7 of ? a histogram of the Jἰνς colours of all of the πας in the 2ALASS Second Incremental Data Release showed a clear bimocal distribution., In figure 7 of \citet{Stark03} a histogram of the $J-K_s$ colours of all of the sdBs in the 2MASS Second Incremental Data Release showed a clear bimodal distribution. In Figure 4 we reproduce this histogram for the sdBs in our programme., In Figure \ref{fig:histogram} we reproduce this histogram for the sdBs in our programme. We plot separately the scBs which show no radial velocity variations. the sdDs which are strong binary candidates but. without an orbital period determination. and the solved binaries. comprising the 28 svstems [rom this paper ancl those previously published in ? ancl ?..," We plot separately the sdBs which show no radial velocity variations, the sdBs which are strong binary candidates but without an orbital period determination, and the solved binaries, comprising the 28 systems from this paper and those previously published in \citet{Maxted02} and \citet{MoralesRueda03}." We exclude from. this histogram the Witt Peak-Downes (XPD: ?)) survey objects. since they are close to the galactic plane and thus potentially significantly redcdened.," We exclude from this histogram the Kitt Peak-Downes (KPD; \citealt{Downes86}) ) survey objects, since they are close to the galactic plane and thus potentially significantly reddened." " If we examine first the histogram for the sdBs which shown no radial velocity variation. we see the same bimocal distribution around af A, value of |0.05 as was found in ?.."," If we examine first the histogram for the sdBs which shown no radial velocity variation, we see the same bimodal distribution around a $J-K_s$ value of $+0.05$ as was found in \citet{Stark03}." " By comparison. the histogram of the solved. binaries shows only two svstems with JA,c|0.05: P€GH253|284 and PO1558-007."," By comparison, the histogram of the solved binaries shows only two systems with $J-K_s > +0.05$: PG1253+284 and PG1558-007." P€6:1558-007 was identified as a composite system by ?.. but 2. disputed this identification. attributing the JoAVS colour to interstellar recdening.," PG1558-007 was identified as a composite system by \citet{Allard94}, but \citet{Heber02} disputed this identification, attributing the $J-K_s$ colour to interstellar reddening." P€6$1253|284 was identified as a composite system. by 2.. but. for this svstem 2 ckermined PO€1253]|284 (referred to as TON 139 in that paper) to be a triple svstem via iimagine. and concluded that the J9A colour in this svstem is due o the third. distant. component. and not the companion in the close binary.," PG1253+284 was identified as a composite system by \citet{Ulla98}, but for this system \citet{Heber02} determined PG1253+284 (referred to as TON 139 in that paper) to be a triple system via imaging, and concluded that the $J-K_s$ colour in this system is due to the third, distant component, and not the companion in the close binary." The third. histogram (the potential rut unsolved: binaries) indicates the presence of a further ive composite systems., The third histogram (the potential but unsolved binaries) indicates the presence of a further five composite systems. Aside [rom the possibility that hese are close binaries with a Ci-Ix. companion. there are hree explanations for these measurements.," Aside from the possibility that these are close binaries with a G-K companion, there are three explanations for these measurements." Firstly. some of hese composite sdDs may not actually be close binaries: urther observations may show the radial velocity variations detected to date are not significant.," Firstly, some of these composite sdBs may not actually be close binaries: further observations may show the radial velocity variations detected to date are not significant." Secondly. some of the Jody. measurements may be due to a third. component. interstellar reddening or a nearby unresolved. field. star.," Secondly, some of the $J-K_s$ measurements may be due to a third component, interstellar reddening or a nearby unresolved field star." Thirdly. some of these unsolved. binaries mav actually be long period systems. as we noted in Section 4.3..," Thirdly, some of these unsolved binaries may actually be long period systems, as we noted in Section \ref{sec:binfrac}." ‘To investigate this further. we generated mean spectra for all of the objects in our target List. and. classified them with the aid of synthetic spectra from the grid described in Section 4.1..," To investigate this further, we generated mean spectra for all of the objects in our target list, and classified them with the aid of synthetic spectra from the grid described in Section \ref{sec:tefflogg}." 25 objects show contamination in their spectra indicative of à cool companion. which would indicate these are composite svstems.," 25 objects show contamination in their spectra indicative of a cool companion, which would indicate these are composite systems." " We would. classify these sdBs as ""double-lined. spectroscopic binaries’. to distinguish them. from the single-lincel spectroscopic binaries. the nature of which we identify via racial velocity. variations."," We would classify these sdBs as `double-lined spectroscopic binaries', to distinguish them from the single-lined spectroscopic binaries, the nature of which we identify via radial velocity variations." “There is strong overlap between the double-lined spectroscopic binaries and the composite systems we identified through 2MLASS. with all but five of the 2ALASS systems showing a contaminating component in their spectra.," There is strong overlap between the double-lined spectroscopic binaries and the composite systems we identified through 2MASS, with all but five of the 2MASS systems showing a contaminating component in their spectra." We list our candidate composite binaries in. Table 7.., We list our candidate composite binaries in Table \ref{tab:composite}. We exclude PO2059|013 from this table: while the JJdv. colour of this sdD is consistent with it being à composite svstem. but the ? dust maps show it to be significantly reddened.," We exclude PG2059+013 from this table: while the $J-K_s$ colour of this sdB is consistent with it being a composite system, but the \citet{Schlegel98} dust maps show it to be significantly reddened." This table contains five systems in which we believe we detect. significant radial velocity variations. and hence are potentially close binaries.," This table contains five systems in which we believe we detect significant radial velocity variations, and hence are potentially close binaries." 1n summary then. almost all of the svstems which we identify as close binaries do not show the presence of a dwarf Ci-Ix. companion.," In summary then, almost all of the systems which we identify as close binaries do not show the presence of a dwarf G-K companion." The companions in these systems are therefore most. likely white cwarfs or AL cwarls., The companions in these systems are therefore most likely white dwarfs or M dwarfs. The composite svstems are almost entirely found in the group of sdBs in which we detected no racial velocity. variations., The composite systems are almost entirely found in the group of sdBs in which we detected no radial velocity variations. A CG-Ix companion therefore seems to be indicative of a longer period svstem: a wide binary in which the sdB has evolved independently of the companion., A G-K companion therefore seems to be indicative of a longer period system: a wide binary in which the sdB has evolved independently of the companion. There are some potential exceptions to this rule: these sdBs are prime candidates for further observation in order to determine if they are inclecd binaries. as the data collected to date would suggest. and furthermore if they are close binaries.," There are some potential exceptions to this rule: these sdBs are prime candidates for further observation in order to determine if they are indeed binaries, as the data collected to date would suggest, and furthermore if they are close binaries." As we remarked in Section 4.3.. two of these candidates (P1610|519 and D€23171046) show evidence for binaritv. but all of the current aliases sugeest a long orbital period. which would be consistent with our Composite identification.," As we remarked in Section \ref{sec:binfrac}, two of these candidates (PG1610+519 and PG2317+046) show evidence for binarity, but all of the current aliases suggest a long orbital period, which would be consistent with our composite identification." "for heating. 6,=3. suddenly. reduces the size of the voids to values which are even too small: 777) further increasing ὃμ makes the void sizes approaching those of the non preheated run. owing to the progressively smaller. amount. of heated gas which ends up in the forest: £e) the entropy level within galaxy groups. at roy Can be already matched in non preheated simulations. which however fail at accounting for this level at resua: 0) à fairly strong entropy injection. with AycLOO keV cnr. is required to match the entropy.temperature relation of poor syslenms al οσο.","for heating, $\delta_{\rm h}=3$, suddenly reduces the size of the voids to values which are even too small; $iii)$ further increasing $\delta_{\rm h}$ makes the void sizes approaching those of the non pre--heated run, owing to the progressively smaller amount of heated gas which ends up in the forest; $iv)$ the entropy level within galaxy groups at $r_{500}$ can be already matched in non pre–heated simulations, which however fail at accounting for this level at $r_{2500}$ ; $v)$ a fairly strong entropy injection, with $K_{\rm fl}>100$ keV $^2$, is required to match the entropy–temperature relation of poor systems at $r_{2500}$." The need of reproducing the entropy structure of the lowrecshift intra.ogroup medium and the void statistics of the high.redshift forest leads us to conclude that for a mechanism of noneravitational heating to work. it must provide a fairly large amount of extra entropy at relatively high overdensities. comparable to those characteristic of virialized. halos.," The need of reproducing the entropy structure of the low–redshift intra–group medium and the void statistics of the high–redshift forest leads us to conclude that for a mechanism of non--gravitational heating to work, it must provide a fairly large amount of extra entropy at relatively high overdensities, comparable to those characteristic of virialized halos." Our conclusion. in agreement with the argument by ?.. is that the amount of preheating required by lowredshift galaxy clusters and. groups should avoid low density regions for it not to produce too large voids in the forest or should act at lower redshift. 25;1.," Our conclusion, in agreement with the argument by \cite{shang}, is that the amount of pre–heating required by low–redshift galaxy clusters and groups should avoid low density regions for it not to produce too large voids in the forest or should act at lower redshift, $z\mincir 1$." AXclmittecdlv. our scheme of nongravitational heating is an oversimplified one.," Admittedly, our scheme of non–gravitational heating is an oversimplified one." For this reason. our aim is not to look for the best values of Aq and oy. which are able to fit at the same time he observed intragroup entropy ancl void statistics of the forest.," For this reason, our aim is not to look for the best values of $K_{\rm fl}$ and $\delta_{\rm h}$, which are able to fit at the same time the observed intra–group entropy and void statistics of the forest." Rather. the main goal of our analysis is to ον]ο an indication of the general properties that a jausible mechanism. of nongravitational heating. should aave.," Rather, the main goal of our analysis is to provide an indication of the general properties that a plausible mechanism of non–gravitational heating should have." We defer to a forthcoming analysis a detailed: study of the combined constraints of the low and z 1M o»operties using physically motivated: models. of heating roni astrophysical sources. such as supernovae. active ealactic nuclei and DM annihilation.," We defer to a forthcoming analysis a detailed study of the combined constraints of the low and $z$ IGM properties using physically motivated models of heating from astrophysical sources, such as supernovae, active galactic nuclei and DM annihilation." We acknowledge useful discussions with D. Fabjan. M. Sun and M. Vout.," We acknowledge useful discussions with D. Fabjan, M. Sun and M. Voit." We thank CG. Alurante for help. with the halo finder., We thank G. Murante for help with the halo finder. The simulations were performed: with the Darwin Supercomputer at. the Ligh Performance Computing Service of the University of Cambridge (http://www.hpce.cam.ac.uk/)., The simulations were performed with the Darwin Supercomputer at the High Performance Computing Service of the University of Cambridge (http://www.hpc.cam.ac.uk/). This work has been partially supported.by the INEN-PD51 grant and by the ASILAAL Theory Grant., This work has been partially supportedby the INFN-PD51 grant and by the ASI-AAE Theory Grant. Intense UV radiation [rom massive stars is one of (he main mechanisms responsible for the heating of the interestelar medium in (he nuclear region of starburst galaxies.,Intense UV radiation from massive stars is one of the main mechanisms responsible for the heating of the interestelar medium in the nuclear region of starburst galaxies. This mechanism is parlicularly important in the latest stages of starburst (SB) galaxies where the newly formed massive star clusters are responsible for creating large photodissociation regions (PDRs)}., This mechanism is particularly important in the latest stages of starburst (SB) galaxies where the newly formed massive star clusters are responsible for creating large photodissociation regions (PDRs). This is the case lor the prototvpical SB galaxy 832. where (hie large observed. abundanunces of molecular species such as IICO. . CO. and Πο are claàmed to be probes of the high ionization rates in large PDRs formed as a consequence of ils extended evolved nuclear starburst (Garcia-Burilloetal.2002:FuentederTaketal. 2008).," This is the case for the prototypical SB galaxy 82, where the large observed abundances of molecular species such as HCO, $^+$ , $^+$ , and $_3$ $^+$ are claimed to be probes of the high ionization rates in large PDRs formed as a consequence of its extended evolved nuclear starburst \citep{Burillo02,Fuente06,VdTak08}." . Observational evidences point (o a significant enhancement in the abundance of in regions with large ionization fractions., Observational evidences point to a significant enhancement in the abundance of $^+$ in regions with large ionization fractions. The abundance ratio |=270 is found in the prototypical Galactic PDRs of the Orion Dar (Apponietal.1999)., The abundance ratio $^+$ $^+$ $=270$ is found in the prototypical Galactic PDRs of the Orion Bar \citep{Apponi99}. . Similar or even lower abundance ratios are observed in the PDRs 77023 2003).. DB2(OII) and 22024 (360-900.Ziurvs&Apponi1995; 1997).. and the ILorsehead. (75-200Goicoecheaetal.2009).. as well as in diffuse clouds (10-120.Lisztetal.2004).," Similar or even lower abundance ratios are observed in the PDRs 7023 \citep[50-120,][]{Fuente03}, B2(OH) and 2024 \citep[360-900,][]{Ziurys95,Apponi97}, and the Horsehead \citep[75-200][]{Goico09}, as well as in diffuse clouds \citep[70-120,][]{Liszt04}." . This is in contrast with the much larger ratiosof z1000found in dense molecular elouds well shielded [rom the UV radiation., This is in contrast with the much larger ratiosof $\gg 1000$found in dense molecular clouds well shielded from the UV radiation. However. these low," However, these low" Fieure 3. shows the correlation signal resulting [rom comparing the positions of all 1037 1FGL 5-rav sources within the PAO field of view with the directions of energetic cosmic rav evenis.,Figure \ref{fig:all} shows the correlation signal resulting from comparing the positions of all 1037 1FGL $\gamma$ -ray sources within the PAO field of view with the directions of energetic cosmic ray events. The upper panel shows the measured CCTEs. with angular separations ranging from 1* (approximately the lo uncertainty in the arrival directions of PAO cosmic rays) up to 10.," The upper panel shows the measured CCFs, with angular separations ranging from $1^\circ$ (approximately the $1\sigma$ uncertainty in the arrival directions of PAO cosmic rays) up to $10^\circ$." The lower panels display the probability. P., The lower panels display the probability $P$. Both panels of Figure 3. show that the number of observed correlated events follows the pattern of isotropic expectations within (he lo significance until vse4°., Both panels of Figure \ref{fig:all} show that the number of observed correlated events follows the pattern of isotropic expectations within the $1\sigma$ significance until $\psi \approx 4^\circ$. In the range of angular separations 4°Sce<6. there is a systematic paucity of measured correlations with respect to chance expectations with S>lo.," In the range of angular separations $4^\circ \lesssim \psi < 6^\circ$, there is a systematic paucity of measured correlations with respect to chance expectations with $S>1\sigma$." " In particular. the maximal “anti-association” between the IFGL and PAO datasets corresponds to the global minimum of the probability signal P4,=0.6%.which occurs at e25.17."," In particular, the maximal “anti-association” between the 1FGL and PAO datasets corresponds to the global minimum of the probability signal $P_{\rm min}=0.6 \%$,which occurs at $\psi \approx 5.1^\circ$." This minimal probability corresponds to the significance level S=2.70., This minimal probability corresponds to the significance level $S=2.7\sigma$. At ὁ25. 22 PAO events correlate with all LFGL sources while 25.8 are expected [rom an isotropic fIux.," At $\psi \approx 5^\circ$, 22 PAO events correlate with all 1FGL sources while 25.8 are expected from an isotropic flux." " The case corresponding to circles of radius 3.1"" deserves special attention.", The case corresponding to circles of radius $3.1^\circ$ deserves special attention. This is the estimated. angular radius around AGNs in the Vérron-Cettv and Vérron catalog that maximizes their correlation with the arrival directions of UIECRs (Abraham, This is the estimated angular radius around AGNs in the Vérron-Cetty and Vérron catalog that maximizes their correlation with the arrival directions of UHECRs \citep{pa}. etal.2007).. Figure 3 illustrates that at i=3.1° we find a high probability of chance correlation. 2?=0.6 (S= 0.50).," Figure \ref{fig:all} illustrates that at $\psi = 3.1^\circ$ we find a high probability of chance correlation, $P=0.6$ $S=0.5\sigma$ )." This agrees with the analvsis of Mirabal&Ova(2010)., This agrees with the analysis of \citet{mirabal10}. ". The IFGL catalog consists of a ""mixed bag"" of Galactic ancl extragalactic 5-ray sources with quite different properties.", The 1FGL catalog consists of a “mixed bag” of Galactic and extragalactic $\gamma$ -ray sources with quite different properties. In the subsections below. we investigate (he correlation of the individual classes of ο -ταν sources identified by Abdoetal.(2010a) with the positions ol PAO events.," In the subsections below, we investigate the correlation of the individual classes of $\gamma$ -ray sources identified by \citet{1fgl} with the positions of PAO events." Figure 4. shows the correlation signal measured in the subset of 93 1FGL Galactic sources., Figure \ref{fig:gal} shows the correlation signal measured in the subset of 93 1FGL Galactic sources. The number of observed correlated events follows well the pattern of an isotropic expectation within (he lo significance., The number of observed correlated events follows well the pattern of an isotropic expectation within the $1\sigma$ significance. There is a narrow fluctuation in the signal above ο—lc ab v2.4., There is a narrow fluctuation in the signal above $S=1\sigma$ at $\psi \approx 2.4^\circ$ . Nevertheless. there are only 3 correlated events at this angular distance with 1 correlation expected [rom isotropy.," Nevertheless, there are only 3 correlated events at this angular distance with 1 correlation expected from isotropy." One of the primary goals of the Large Haclrou Collider (LHC). a protou-proton collider with a center of mass energy TeV. will be to investigate the sector responsible for the breakiug of the electroweak symmetry.,"One of the primary goals of the Large Hadron Collider (LHC), a proton-proton collider with a center of mass energy TeV, will be to investigate the sector responsible for the breaking of the electroweak symmetry." In the Staucard Model (SM). a single Higgs doublet is respousible for the spontaneous breakdown ofthe gauge group toUCU(1)p4;.," In the Standard Model (SM), a single Higgs doublet is responsible for the spontaneous breakdown of the gauge group to." . The coupling coustauts of the sole physical Higgs scalar to the rest of the SM particles are completely determined by their masses. an consequently there is little guesswork involved in determining the most promising channels [1.2]. it which one might hope to discover such a scalar.," The coupling constants of the sole physical Higgs scalar to the rest of the SM particles are completely determined by their masses, and consequently there is little guesswork involved in determining the most promising channels \cite{Asai:2004ws,Abdullin:2005yn} in which one might hope to discover such a scalar." For a relatively light (114GeVηS125 SN. Higgs boson. those chanuels are gg—f55 and Mh—bb). while for au iuterimecdiate-1nass (125GeVXingS110 GeV) Higgs. the single most promising channel is the weak-bosou [usiot (WBE) [3]. process qq>qq'h(h—77) |I]..," For a relatively light $114\mbox{~GeV}\lesssim m_h\lesssim 125\mbox{~GeV}$ ) SM Higgs boson, those channels are $gg\rightarrow h\rightarrow\gamma\gamma$ and $t\bar{t}h(h\rightarrow b\bar{b})$, while for an intermediate-mass $125\mbox{~GeV}\lesssim m_h\lesssim 140\mbox{~GeV}$ ) Higgs, the single most promising channel is the weak-boson fusion (WBF) \cite{wbf} process $qq'\rightarrow qq'h(h\rightarrow\tau\tau)$ \cite{Rainwater:1998kj}." " For a heavier Higgs. with mr,o>]I0GeV. the most relevant. channels are //2WW"" aud /—ZZ"". with the Higgs produced via either elton fusion or WBE [1. 2].."," For a heavier Higgs, with $ m_h\gtrsim 140\mbox{~GeV}$, the most relevant channels are $h\rightarrow WW^{\ast}$ and $h\rightarrow ZZ^{\ast}$, with the Higgs produced via either gluon fusion or WBF \cite{Asai:2004ws,Abdullin:2005yn}. ." "J—K, for mean field dwarfs.",$J-K_{\rm s}$ for mean field dwarfs. " The mean color of field dwarfs as a function of spectral type was calculated from a fourth order polynomial fit to the field L and T dwarfs plotted in Figure 4:: J—K,(MKO)=10-?spt?+1.69x 10-4spt, where LO corresponds to spt=O and T8 to spt=18."," The mean color of field dwarfs as a function of spectral type was calculated from a fourth order polynomial fit to the field L and T dwarfs plotted in Figure \ref{fig2}: $J-K_{\rm s}({\rm MKO}) = 1.218+4.95\times10^{-2} \times {\rm spt} + 3.21\times10^{-2} {\rm spt}^2 -5.33\times10^{-3} {\rm spt}^3 + 1.69\times10^{-4} {\rm spt}^4$ , where L0 corresponds to ${\rm spt}=0$ and T8 to ${\rm spt}=18$." " The figure shows a clear one-to-one correlation between the J—K, color offsets of the primary and secondary components.", The figure shows a clear one-to-one correlation between the $J-K_{\rm s}$ color offsets of the primary and secondary components. All published L and T binaries fall within +1lo of the scatter (2M1404-3159 does so only marginally)., All published L and T binaries fall within $\pm$ $1$ $\sigma$ of the scatter (2M1404-3159 does so only marginally). " is the only known outlier to this distribution, with J1619+0313A being mmag redder than a typical T2.5 and J16194-0313B being"," is the only known outlier to this distribution, with A being mag redder than a typical T2.5 and B being" abundances given before have been estimated.,abundances given before have been estimated. We adoptec 12+log(O/Hy;=8.830.20Ay and Z«=0.02 (Asplunc 2004)..," We adopted $12 + log(O/H)_{\odot} = 8.83 \pm 0.20= A_{\odot}$ and $Z_{\odot} = 0.02$ \citep{Asp04}. ." Given that Z=KZ. Κωστα=109e07 and Kreger=105ΗΕ we obtain metallicities for the HII regions of the polar disk of Zz0.008 in UGC7576 anc Z=0.002 in UGC9796 which correspond respectively to Z=(0.40040.002)Z.. and Z=(0.100+ 0.001)Zs. in good agreement with the values obtained by Radtkeetal.(2003) (see Tab. 3)).," Given that $Z \approx K Z_{\odot}$, $K_{UGC7576} = 10^{[A_{UGC7576} - A_{\odot}]}$ and $K_{UGC7576} = 10^{[A_{UGC9796} - A_{\odot}]}$, we obtain metallicities for the HII regions of the polar disk of $Z \simeq 0.008$ in UGC7576 and $Z \simeq 0.002$ in UGC9796 which correspond respectively to $Z \simeq (0.400 \pm 0.002) Z_{\odot}$ and $Z \simeq (0.100 \pm 0.001) Z_{\odot}$ , in good agreement with the values obtained by \cite{Rad03} (see Tab. \ref{ox}) )." The mean values for the oxygen abundance along the polar structure of UGC7576 and UGC9796. derived by the empirical method (see sec. ??)).," The mean values for the oxygen abundance along the polar structure of UGC7576 and UGC9796, derived by the empirical method (see sec. \ref{oxy}) )," " are compared with those for a sample of late-type disk galaxies by Kobulnicky&Zaritsky(1999)., as function of the total luminosity."," are compared with those for a sample of late-type disk galaxies by \cite{Kob99}, as function of the total luminosity." To this aim. we converted the absolute blue magnitude for the objects in the sample of Kobulnicky&Zaritsky(1999) by using Ho=75 km/s/Mpe.," To this aim, we converted the absolute blue magnitude for the objects in the sample of \citet{Kob99} by using $H_{0} =75$ km/s/Mpc." Results are shown in Fig. 6.., Results are shown in Fig. \ref{conf}. We found that UGC7576 is located 1n the region where spiral galaxies are found. and. contrary to its high luminosity. it has metallicity lower than spiral galaxy disks of the same total luminosity and it is consistent with that observed for NGC46030A. UGC9796 instead is even more metal-poor than UGC7576 and NGC4650A. in fact it is located in the region where HII and trregular galaxies are also found. characterized by lower lummosities and metallicities with respect to the spiral galaxies.," We found that UGC7576 is located in the region where spiral galaxies are found, and, contrary to its high luminosity, it has metallicity lower than spiral galaxy disks of the same total luminosity and it is consistent with that observed for NGC4650A. UGC9796 instead is even more metal-poor than UGC7576 and NGC4650A, in fact it is located in the region where HII and irregular galaxies are also found, characterized by lower luminosities and metallicities with respect to the spiral galaxies." " We also compare our new results with those obtained by Perez-Monteroetal.(2009) for I[Zw71]. a blue compact dwarf galaxy also catalogued as a probable polar ring: consistently with its low luminosity. the metallicity of the brightest knots in the ring of ILZw71 is lower with respect to that of UGC7576. but it is slightly higher than those of UGC9796,Taking into account the total magnitude. such values are somewhat lower than that expected by the metallicity-luminosity relation."," We also compare our new results with those obtained by \cite{Per09} for IIZw71, a blue compact dwarf galaxy also catalogued as a probable polar ring: consistently with its low luminosity, the metallicity of the brightest knots in the ring of IIZw71 is lower with respect to that of UGC7576, but it is slightly higher than those of UGC9796.Taking into account the total magnitude, such values are somewhat lower than that expected by the metallicity-luminosity relation." " The H, emission is detected in both systems with adequate signal-to-noise. and from the measured integrated flux we can derive the star formation rate in the polar ring structure."," The $H_{\alpha}$ emission is detected in both systems with adequate signal-to-noise, and from the measured integrated flux we can derive the star formation rate in the polar ring structure." " We have derived the SFR for the polar structures of UGC7576 and UGC9796. from the H,, luminosity using the expression given by Kennicutt(1998) SFR=7.9x1077L(H,)."," We have derived the SFR for the polar structures of UGC7576 and UGC9796, from the $H_{\alpha}$ luminosity using the expression given by \cite{Ken98} $SFR = 7.9 \times 10^{-42} \times L(H_{\alpha})$." We find that it is almost constant along the disks of both galaxies. within alarge scatter in the individual values.," We find that it is almost constant along the disks of both galaxies, within alarge scatter in the individual values." " From the average values of LUH,)=2.36x1076 ere/s for UGC7576 and L(H,)= erg/s for UGC9796. we have obtained an average SFR~19x10°M./yr and SFR~42x10°°Ma/yr respectively."," From the average values of $L(H_{\alpha}) \simeq 2.36 \times 10^{36}$ erg/s for UGC7576 and $L(H_{\alpha}) \simeq 5.33 \times 10^{35}$ erg/s for UGC9796, we have obtained an average $SFR \sim 1.9 \times 10^{-5} M_{\odot}/yr$ and $SFR \sim 4.2 \times 10^{-6} M_{\odot}/yr$ respectively." These values are significantly lower than those obtained for NGC46S0A (Spavoneetal.2010)... which is SFR~0.06M../vr and IIZw71 (Perez-Monteroetal..2009).. which is SFR~0.035M.ήν.," These values are significantly lower than those obtained for NGC4650A \citep{Spav10}, which is $SFR \sim 0.06 M_{\odot}/yr$ and IIZw71 \citep{Per09}, which is $SFR \sim 0.035 M_{\odot}/yr$." Taking into account that the polar structure in both PRGs is very young. since the last burst of star formation occurred less than 1 Gyr ago (Reshetnikov&Combes.1994).. we check if the present SFR and even 2and 3 times higher (1.8. SFR=38xIO? Myr. SFR=57xΙΟM.vr and SFR=84xIO M./vr. SFR=126xΙΟ ΜΥ). can give the inferred metallicities ofZ=0.4Z.. (forUGC7576) and Z=0.1Z. (for UGC9796) and how strongly could increase the metallicity with time.," Taking into account that the polar structure in both PRGs is very young, since the last burst of star formation occurred less than 1 Gyr ago \citep{Res94}, we check if the present SFR and even 2and 3 times higher (i.e. $SFR = 3.8 \times 10^{-5} M_{\odot}/yr$ , $SFR = 5.7 \times 10^{-5} M_{\odot}/yr$ and $SFR = 8.4 \times 10^{-6} M_{\odot}/yr$ , $SFR = 1.26 \times 10^{-5} M_{\odot}/yr$ ), can give the inferred metallicities of $Z=0.4 Z_{\odot}$ (forUGC7576) and $Z=0.1 Z_{\odot}$ (for UGC9796) and how strongly could increase the metallicity with time." The Tavlor series of this term up to third order in P is We separate this piece from the iutegral for the telescope 1. where the major difference refDel\lodLps— is that this inteeral does not vanish. because the atmosphere is now hit at two different angles egxUg.,"The Taylor series of this term up to third order in $P$ is We separate this piece from the integral for the telescope 1, where the major difference \\ref{DelModl.ps} is that this integral does not vanish, because the atmosphere is now hit at two different angles $\psi_H^{(1)}\neq \psi_H^{(2)}$." The iutegral would also not vanish. if the factor à would be cropped to deduce thegeometric path difference of the curved beans.," The integral would also not vanish, if the factor $n$ would be dropped to deduce the path difference of the curved beams." The constance of the product. risinc along cach curved trajectory€6L16)).. is inserted into the previous equation. The term in square brackets allows another Tavlor expansion All correction terms of the spherical geometry in ((19)) (21)) have a positive sign.," The constance of the product $rn\sin\psi$ along each curved trajectory, is inserted into the previous equation, The term in square brackets allows another Taylor expansion All correction terms of the spherical geometry in \ref{eq.taylDv}) \ref{eq.TaylIntf}) ) have a positive sign." The contribution of the term of O(P2) amouuts to 2:2 nuu. and of the term of OCP?) to ~G0 im as the zenith angle approaches 60 deg at b=100 ni. A consistency check of ((21)) is that its contribution of the first. linear Taylor order to the integral in ((23)) becomes iu the Vactiuii limit. such that the term Pauci cancels the fist term iun ((19)). and ouly the term Ptan+ depending ou the true topocentric zenith angele remains. equivaleut to 1tDelModl.ps..," The contribution of the term of $O(P^2)$ amounts to $\approx 2$ mm, and of the term of $O(P^3)$ to $\approx 60$ nm as the zenith angle approaches $60$ deg at $b=100$ m. A consistency check of \ref{eq.TaylIntf}) ) is that its contribution of the first, linear Taylor order to the integral in \ref{eq.DIntf}) ) becomes in the vacuum limit, such that the term $P \tan\psi_H^{(2)}$ cancels the first term in \ref{eq.taylDv}) ), and only the term $P\tan z$ depending on the true topocentric zenith angle remains, equivalent to \\ref{DelModl.ps}." The influence of the spherical geometry. oui the atmospheric path leneth difference is demonstrated in rofDds.ps.., The influence of the spherical geometry on the atmospheric path length difference is demonstrated in \\ref{Dds.ps}. Up to here. au accurate computation of the delay D by iutegration over the atmosphere livers is not competitive against measuring the equivalent value on the erouud," Up to here, an accurate computation of the delay $D$ by integration over the atmosphere layers is not competitive against measuring the equivalent value on the ground" We calculated Equation (3)) bv counting the contribution from computational grid zones along stacked boxes up to mock sources as where νέος)E is (he number of grid zones up to sources al ο.,We calculated Equation \ref{eq3}) ) by counting the contribution from computational grid zones along stacked boxes up to mock sources as where $N_s(z_s)$ is the number of grid zones up to sources at $z_s$. The density aud magnetic field strength are in units of em.* and µία. respectively.," The density and magnetic field strength are in units of ${\rm cm^{-3}}$ and $\mu$ G, respectively." For A/(2). we used the proper size of erid zone. which is 0.195h.'(1+2)! Mpe.," For $\Delta l(z)$, we used the proper size of grid zone, which is $0.195~h^{-1}(1+z)^{-1}$ Mpc." With the simulation FOV of 6?=(14.14)? deg. {he maximum tilt of LOSs relative to the coordinates of simulation box is cos(0/2)=0.99. so we ienored the effect on .A/(:).," With the simulation FOV of $\theta^2 = (14.14)^2$ ${\rm deg}^2$, the maximum tilt of LOSs relative to the coordinates of simulation box is $\cos(\theta/2) = 0.99$, so we ignored the effect on $\Delta l(z)$." In the hot gas with 7Z10* IX. X-ray emission is produced mainly by thermal lung.," In the hot gas with $T \ga 10^7$ K, X-ray emission is produced mainly by thermal lung." e We hence considered only the bremsstrahllunge emission from electrons. and neglectedex line emissions [rom ions.," We hence considered only the lung emission from electrons, and neglected line emissions from ions." " The emissivity of thermal bremsstrahlung can be expressed as where 7... and v ave in units of IN. em7. and Hz. respectively. and fr, and hp are the Planck ancl Bolizmannconstants. respectively1979)."," The emissivity of thermal bremsstrahlung can be expressed as where $T$ , $n_e$, and $\nu$ are in units of K, ${\rm cm^{-3}}$, and Hz, respectively, and $h_{\rm p}$ and $k_{\rm B}$ are the Planck and Boltzmannconstants, respectively." ". We adopted the approximate Gaunt [actor g©0.9(hyp/NgT)0.5""7. and used the bolometric emissivity. (hat is. νι—0 and rs=x."," We adopted the approximate Gaunt factor, $\bar{g} \approx 0.9(h_{\rm p}\nu/k_{\rm B}T)^{-0.3}$, and used the bolometric emissivity, that is, $\nu_1 = 0$ and $\nu_2 = \infty$." For the X-ray temperature of clusters and groups. we calculated (he N-rav temperature as over a spherical volume of comoving radius 0.57.1 Mpc.," For the X-ray temperature of clusters and groups, we calculated the X-ray emissivity-weighted temperature as over a spherical volume of comoving radius $0.5 h^{-1}$ Mpc." For (he X-ray surface brightness and surface temperature up to redshift z. we first sought all the grid zones. A. ancl their proper volume. Vi. which enters within the angular beam of GN9)?.," For the X-ray surface brightness and surface temperature up to redshift $z$, we first sought all the grid zones, $k$ and their proper volume, $V_k$, which enters within the angular beam of $(\Delta\theta)^2$." Note that A@=0.414 aremin corresponds to the comoving size of a grid zone 1955.! kpe at z220.6: hence perpendicular to a LOS. less then one zone enters at lower redshilts. but more than one at higherredshifts within (AQ).," Note that $\Delta\theta = 0.414$ arcmin corresponds to the comoving size of a grid zone $195\ h^{-1}$ kpc at $z \simeq 0.6$; hence perpendicular to a LOS, less then one zone enters at lower redshifts, but more than one at higherredshifts within $(\Delta\theta)^2$ ." For each erid at redshift τε.the X-ray luminosity was calculated as," For each grid at redshift $z_k$ ,the X-ray luminosity was calculated as" uaguetic field bas been directly detected: and. its properties ard Consequences have long been «ΠΟΝΝΗ (e.g. 1re Suns large-scale 1iaguetic ield that is responsibe for the 22-vear sunspot cycle). while the active role of magnetic jelds iu «Xher astrophysical pleuoniena has only recently. been 'ecognised (stchi as its role in auguar nioneitum transport iu acc'etiou discs).,"magnetic field has been directly detected and its properties and consequences have long been known (e.g. the Sun's large-scale magnetic field that is responsible for the 22-year sunspot cycle), while the active role of magnetic fields in other astrophysical phenomena has only recently been recognised (such as its role in angular momentum transport in accretion discs)." While in some cases it is possible hat the maguetic fied coid |ye he remnant of a clecaying fossil field. in others it is jelieved tha the field is sustained agalnist he actior oL Olunic ¢issipation via the operation of a iwdromagueic dynamo — a mechat]snu hrotel which the kinetic energy of the plasiua is converted into magnetic euergy.," While in some cases it is possible that the magnetic field could be the remnant of a decaying fossil field, in others it is believed that the field is sustained against the action of Ohmic dissipation via the operation of a hydromagnetic dynamo – a mechanism through which the kinetic energy of the plasma is converted into magnetic energy." Understandiug the evolution of magnetic fields in the uuiverse remalns one of the most important unsolved problems in astrophysics., Understanding the evolution of magnetic fields in the universe remains one of the most important unsolved problems in astrophysics. Due to he enormous scale of astrojohysical objects. in virtually all cases it is believed that the low that leads ο clynamo action is turbulent.," Due to the enormous scale of astrophysical objects, in virtually all cases it is believed that the flow that leads to dynamo action is turbulent." The generated magnetic field then exhibits complex spatial and temporal characteristics ou a wide rauge of scales. a complete uuderstaucdiug of which ‘epreseuts a formidable problem.," The generated magnetic field then exhibits complex spatial and temporal characteristics on a wide range of scales, a complete understanding of which represents a formidable problem." Progress with astropliysical dyuamo theory is therefore typically uade by breaking the problem down into a number of fundamental sub-problems., Progress with astrophysical dynamo theory is therefore typically made by breaking the problem down into a number of fundamental sub-problems. A natural starting j»oiut is to consider the initial stages of evolution of a weak seed field., A natural starting point is to consider the initial stages of evolution of a weak seed field. During this kinematic phase he field is assumed to be so weak as to have no dyuauical ellects on the turbulence., During this kinematic phase the field is assumed to be so weak as to have no dynamical effects on the turbulence. The equations governing the evolution of the flow then decouple Crom the induction equation eoverniug the uagnetie evolution. viz.," The Navier-Stokes equations governing the evolution of the flow then decouple from the induction equation governing the magnetic evolution, viz." where 5 is the magnetic diffusivity., where $\eta$ is the magnetic diffusivity. The problem therefore reduces considerably to solving equations (1)). given a flow u(x./).," The problem therefore reduces considerably to solving equations \ref{eq:induction}) ), given a flow $\mathbf{u}(\mathbf{x},t)$." IE the flow is a kinematic dynamo the magnetic Geld grows exponentially aud the task is to determiue the magnetic erowth rate and the preferred lenetlscale ol the dyuaimo instability., If the flow is a kinematic dynamo the magnetic field grows exponentially and the task is to determine the magnetic growth rate and the preferred lengthscale of the dynamo instability. Iu reality. the exponential growth cannot continue iucelinitely.," In reality, the exponential growth cannot continue indefinitely." Eventually the generated magnetic field will be strong enough to react back ou the flow (via the Loreuz lorce in the momenttun equation) aud the growth will saturate., Eventually the generated magnetic field will be strong enough to react back on the flow (via the Lorentz force in the momentum equation) and the growth will saturate. In this nonlinear phase the aim is to uucerstand the dualics of the saturation process aid to determiue the amplitude of the resulting Ποια., In this nonlinear phase the aim is to understand the dynamics of the saturation process and to determine the amplitude of the resulting field. It is important to uote a further distiuction that is often made: Large scale dyuamios are those in which he magnetic field) has a scale of variation much larger than the characteristic velocity correlation length. while in small scale cdlyuamos the magnetic field varies ou scales comparable with or sinaller than the scale of the driving flow.," It is important to note a further distinction that is often made: Large scale dynamos are those in which the magnetic field has a scale of variation much larger than the characteristic velocity correlation length, while in small scale dynamos the magnetic field varies on scales comparable with or smaller than the scale of the driving flow." Iu this paper we shall be concerned with the kinematic. sinall-scale dyuaimo problem.," In this paper we shall be concerned with the kinematic, small-scale dynamo problem." There are esseutially three different avenues of research that have developed for addressing this scenario., There are essentially three different avenues of research that have developed for addressing this scenario. They diTer in the way in which the flow is specified., They differ in the way in which the flow is specified. In the first. one cousiders the amplification of inagnetic ields ln a laminar flow that has a given analytical form (see the monograph by )).," In the first, one considers the amplification of magnetic fields in a laminar flow that has a given analytical form (see the monograph by \cite{childressg1995}) )." The second method is similar. except that the flow is specified utumerically.," The second method is similar, except that the flow is specified numerically." It is typically eitier a solution of the Navier-Stokes equations or it is syuthesized to have certain properties., It is typically either a solution of the Navier-Stokes equations or it is synthesized to have certain properties. In the third approach. the flow is assumed to be a random process with prescribed statistics.," In the third approach, the flow is assumed to be a random process with prescribed statistics." Iu this case the aim is then to determine the correspoucing statistical properties of the, In this case the aim is then to determine the corresponding statistical properties of the "Figures d. and 2. coufirin that there are no valid solutions to the relevant equations for & iu the range οιNXOX,0.5.",Figures \ref{fig1} and \ref{fig2} confirm that there are no valid solutions to the relevant equations for $\kappa$ in the range $\phi_A<\kappa<\phi_A+0.5$. We now compare this model with BNL aud PTB data., We now compare this model with BNL and PTB data. In our earlier power spectrum analysis (Sturrock.etal. 2010a).. we followed Alburecretal.(1986). αμα considered only the ratio of the 7 Cl and 778i decay rates.," In our earlier power spectrum analysis \citep{stu10a}, we followed \citet{alb86} and considered only the ratio of the $^{36}$ Cl and $^{32}$ Si decay rates." ILlowever. dnce we are now interested primarily in the phases of the decay-rate oscillations (rather than their auplitudes). it is necessary to consider the two datasets separately.," However, since we are now interested primarily in the phases of the decay-rate oscillations (rather than their amplitudes), it is necessary to consider the two datasets separately." We determine the phase of the maxim iu the anual variation of cach dataset bv using a likelihood method xeviouslv. iutroduced for the analysis of solarποπΊππο data (Sturrockctal.2005)., We determine the phase of the maximum in the annual variation of each dataset by using a likelihood method previously introduced for the analysis of solarneutrino data \citep{stu05}. . However. rather thau scau he power 9 as a function of frequency. we now set the yequency at d | and scan the power as a fuuction of xiase o.," However, rather than scan the power $S$ as a function of frequency, we now set the frequency at 1 $^{-1}$ and scan the power as a function of phase $\phi$." " We show the results in Fieures 3.. L. and 5 or BNL Cl. BNL 781, aud PTB Πα, respectively."," We show the results in Figures \ref{fig3}, \ref{fig4}, and \ref{fig5} for BNL $^{36}$ Cl, BNL $^{32}$ Si, and PTB $^{226}$ Ra, respectively." The results are sununarized in Table 1. where we list. or each elemeut of each experiment. the phase op ofthe uaxinmn power. the παπα power Sp. the amplitude of the modulation. aud the phases or.or. for which the power is less than the maximum by 0.5.," The results are summarized in Table \ref{tbl:1} where we list, for each element of each experiment, the phase $\phi_P$ of the maximum power, the maximum power $S_P$, the amplitude of the modulation, and the phases $\phi_L,\phi_U$ , for which the power is less than the maximum by 0.5." " The pliases aud op.or denote the ""ασια. offsets."," The phases and $\phi_L,\phi_U$ denote the “1-sigma” offsets." "Th© Bravmabionartational ""ensmglensi orf distantcustant galaxyeal images⋅ hasfas thwe to be a powerful l",The gravitational lensing of distant galaxy images has the potential to be a powerful cosmological tool. "ensing effect potentialdirectly probes the matter cosmologicaldistribution tool.as a Thefunction of redshift, and thus tells us about the expansion historyand growth of structure in the Universe."," The lensing effect directly probes the matter distribution as a function of redshift, and thus tells us about the expansion history and growth of structure in the Universe." " In this way it allows us to constrain the dark energy equation of state, or whatever is causing the apparent accelerated expansion."," In this way it allows us to constrain the dark energy equation of state, or whatever is causing the apparent accelerated expansion." Weak gravitational lensing poses a number of tough technical challenges if its true potential is to be exploited., Weak gravitational lensing poses a number of tough technical challenges if its true potential is to be exploited. " The typical cosmic shear induced on galaxies of interest is of order1%,, which is significantly smaller than the intrinsic ellipticity of the galaxies themselves."," The typical cosmic shear induced on galaxies of interest is of order, which is significantly smaller than the intrinsic ellipticity of the galaxies themselves." " Of course we, as observers, have no access to the galaxy images so we must treat a population of galaxies statistically to recover the cosmological information contained in the cosmic shear signal."," Of course we, as observers, have no access to the galaxy images so we must treat a population of galaxies statistically to recover the cosmological information contained in the cosmic shear signal." The correlation function of galaxy shapes as a measure of gravitational lensing was first proposed by ? and first observed by ??? and ?..," The correlation function of galaxy shapes as a measure of gravitational lensing was first proposed by \citet{kaiser92} and first observed by \citet{Bacon:2000yp,Kaiser:2000if,Wittman:2000tc} and \citet{van_Waerbeke:2000rm}." " For reviews see ???,, and ?.."," For reviews see \citet{Bartelmann:1999yn,Munshi:2006fn,Refregier:2003ct}, and \citet{hoekstra_jain_2008}." A naive approach to cosmic shear assumes that the intrinsic distribution of galaxy ellipticities is random across the sky., A naive approach to cosmic shear assumes that the intrinsic distribution of galaxy ellipticities is random across the sky. " If this was the case observed ellipticities on a certain patch of sky could be averaged to recover the cosmic shear, because the intrinsic ellipticity would average to zero."," If this was the case observed ellipticities on a certain patch of sky could be averaged to recover the cosmic shear, because the intrinsic ellipticity would average to zero." " However it was soon pointed out that this assumption of random intrinsic ellipticity distribution is unjustified (2222"""," However it was soon pointed out that this assumption of random intrinsic ellipticity distribution is unjustified \citep{HRH,catelankb01,crittendennpt01,croftm00}." In fact galaxies may be expected to align with the large scale gravitational potentials in which they form so we expect physically close galaxies to be preferentially aligned with each other (known as the Intrinsic-Intrinsic (II) correlation)., In fact galaxies may be expected to align with the large scale gravitational potentials in which they form so we expect physically close galaxies to be preferentially aligned with each other (known as the Intrinsic-Intrinsic (II) correlation). ? noted an additional negative correlation between foreground galaxies shaped by α particular gravitational potential and background galaxies which are lensed by the same potential (known as the Gravitational-Intrinsic (GI) correlation) which can be of greater magnitude than the II term., \citet{hiratas04} noted an additional negative correlation between foreground galaxies shaped by a particular gravitational potential and background galaxies which are lensed by the same potential (known as the Gravitational-Intrinsic (GI) correlation) which can be of greater magnitude than the II term. " After the alignment of galaxy ellipticities from linear response to the gravitational potential was proposed as an effect by ? the study was put on firm analytic footing by the introduction of the Linear Alignmenta (LA) model by ?,, hereafter HS04."," After the alignment of galaxy ellipticities from linear response to the gravitational potential was proposed as an effect by \citet{catelankb01} the study was put on a firm analytic footing by the introduction of the Linear Alignment (LA) model by \citet{hiratas04}, hereafter HS04." " This approach, in which the orientation of galaxies responds linearly to the large-scale gravitational potential in which they form, has become the standard"," This approach, in which the orientation of galaxies responds linearly to the large-scale gravitational potential in which they form, has become the standard" treatments are valid.,treatments are valid. We make the comparison at densities typical of red giant cores (p~10? — 105&/cm?).," We make the comparison at densities typical of red giant cores $\rho\!\sim\!10^5$ – $10^6 \,\mathrm{g/cm^3}$ )." The acceptable temperature rauge is then bouuded by two restrictions in the [toletal.(1983) analysis., The acceptable temperature range is then bounded by two restrictions in the \citet{itoh83} analysis. On the upper eud there is the restriction that D>2., On the upper end there is the restriction that $\Gamma > 2$. Ou the lower end is the requiremeut that a high-temperature classical limit apply to the treatiment of the tonic system., On the lower end is the requirement that a high-temperature classical limit apply to the treatment of the ionic system. This is expressed by the coucition y«1 where the parameter y is defined with Ay beingthe Fermi waventiiber of the electrons aul AZ the mass of an ion., This is expressed by the condition $y \ll 1$ where the parameter $y$ is defined with $k_F$ beingthe Fermi wavenumber of the electrons and $M$ the mass of an ion. Mitake. found that the higb-temperaure classical limit is adecuale as long as y«0.01., \citet{mitake} found that the high-temperature classical limit is adequate as long as $y < 0.01$. In the range 0.01«yuw0.1. thowh. their results siow that a quantui1 correction not included in the Itohetal.(1983) anaysis dends to recice the concuctive opacities by up to 255.," In the range $0.01 < y < 0.1$, though, their results show that a quantum correction not included in the \citet{itoh83} analysis tends to reduce the conductive opacities by up to ." ". Iu Figure 1. we have plotted the conciClive opacitles al censiies of 10°"" anc 10?g/cm'"" for temperatures where D72 and y«0.1. all we show the temperatWes Corresponcing to y—0.01."," In Figure \ref{copacfig} we have plotted the conductive opacities at densities of $10^{5.0}$ and $10^{5.5}\, \mathrm{g/cm^3}$ for temperatures where $\Gamma > 2$ and $y < 0.1$, and we show the temperatures corresponding to $y =0.01$." " The agreement between the diflerent. treatuents is beter al hel igher tempera1Ο». where the Classical reatiment of tous by Ποetal. is inost valid aud also wlere the temperatures approacan those typically fouud in red giant cores (T.~10* — 109"" Is)."," The agreement between the different treatments is better at the higher temperatures, where the classical treatment of ions by \citeauthor{itoh83} is most valid and also where the temperatures approach those typically found in red giant cores $T \sim 10^{7.5}$ – $10^{8.0}$ K)." lu the region where y<0.01 t lreatinens agree (o wlthin25%. with the Holetal. values runi18oO 5- below the values.," In the region where $y < 0.01$ the treatments agree to within, with the \citeauthor{itoh83} values running 5 – below the \citet{hubbard} values." Takiig all of this into consideration. we estiuate that curreut values for the conductive opacity in red plant cores are uncertain by about a the l-o level.," Taking all of this into consideration, we estimate that current values for the conductive opacity in red giant cores are uncertain by about at the $\sigma$ level." " We the'efore multiply our staudal values (οXalned as described above (rom Sweigarts fit to the Hubba«d&Lampe tables aud t 'elativisti¢ Canuto treatment) by a [actor draw 1[roi1 the Gaussian clistribiion 1.00—30,corrections."," We therefore multiply our standard values (obtained as described above from Sweigart's fit to the \citeauthor{hubbard} tables and the relativistic Canuto treatment) by a factor drawn from the Gaussian distribution $1.00 \pm .20$." . In order to coiipare our stellar evolulon 1jodels to 0servalLOL. it is necessary to transfori1 the physical quautities tsed in stellar eveη{1ο1 calculations to those quautities measured by ο»ervers.," In order to compare our stellar evolution models to observations, it is necessary to transform the physical quantities used in stellar evolution calculations to those quantities measured by observers." Specifically. we ust trausform he tπ calculated »olometri€ luminosity. effe livetemperature. aid surface gravity to precict (1e observatioial magnitudes or specili€ pass bands.," Specifically, we must transform the theoretically calculated bolometric luminosity, effective temperature, and surface gravity to predict the observational magnitudes for specific pass bands." Gererally. this trausformatiou is nacle using cokyx tabes based ou heoretical realtinens of stellar anosj»heres. possibly caliated by empirical data.," Generally, this transformation is made using color tables based on theoretical treatments of stellar atmospheres, possibly calibrated by empirical data." Purely empirical ‘elatiouships yetweell iagnitude a nde[ective temperature are also available based ou ellective elyperattuves neasured for nearby sars. but these relatiouships are valid ouly for a restricted range o- Anetallicities aud evolutionary sagETen.," Purely empirical relationships between magnitude and effective temperature are also available based on effective temperatures measured for nearby stars, but these relationships are valid only for a restricted range of metallicities and evolutionary stages." The ransfornmatious used in our alalysis are based. ou the color tables constricted for the Revised Y.ale IsochrdLes (Crreen.Demareqιο&Wine1987)., The transformations used in our analysis are based on the color tables constructed for the Revised Yale Isochrones \citep{ryi}. . These transformations are anu empirical recalibration of the ileoretical colors aud bolometric correctious of Vaudeuberg&Be1(1985) aud υπο (1979)..," These transformations are an empirical recalibration of the theoretical colors and bolometric corrections of \citet{van85} and \citet{kurucz}. ." In hus study wewill exatine the V-baud maguitude of the RGB bum). SO we Lust estimate the unceraiuty in the V-baud bolometric corrections.," In this study wewill examine the $V$ -band magnitude of the RGB bump, so we must estimate the uncertainty in the $V$ -band bolometric corrections." Weiss&Salaris(1999) COLnupare," \citet{weiss} compare" which corresponds to 1500 km ο.,which corresponds to 1500 km $^{-1}$. There is a clear excess of galaxies at the redshift of the WAT source. with a distinct peak at the redshift bin 0.22 < κ 1.225.," There is a clear excess of galaxies at the redshift of the WAT source, with a distinct peak at the redshift bin 0.22 $\leq$ z $<$ 0.225." 20 galaxies lie in the peak-recshilt bin. and a urther 22 galaxies lie in the two neighbouring bins resulting in 42 galaxies over three recshift bins. the concentration being significant at τσ.," 20 galaxies lie in the peak-redshift bin, and a further 22 galaxies lie in the two neighbouring bins resulting in 42 galaxies over three redshift bins, the concentration being significant at $\sim$ $\sigma$." Properties of he galaxies in the peak histogram bin and the two adjacent bins. which includes the putative cD galaxy ab a redshift of 0.2204. are listed. in Table 3...," Properties of the galaxies in the peak histogram bin and the two adjacent bins, which includes the putative cD galaxy at a redshift of 0.2204, are listed in Table \ref{peak}." " The otal spread in velocity of the 42 galaxies is 74500 kin ο, and the velocity. dispersion is —870 km s"," The total spread in velocity of the 42 galaxies is $\sim$ 4500 km $^{-1}$ , and the velocity dispersion is $\sim$ 870 km $^{-1}$." This is similar to the spread for typical rich clusters in he local Universe undergoing mergers such as [3667 and AS33876 which both show relic emission and jwe a velocity spread. of ~4200 km (Johnston-al.2010:Owers.Couch&Nulsen 2009).," This is similar to the spread for typical rich clusters in the local Universe undergoing mergers such as A3667 and A3376 which both show relic emission and have a velocity spread of $\sim$ 4200 km $^{-1}$ \citep{mjh08, mjh10, Owers09}." . Phe redshift distribution of the 42 galaxies is shown in greater detail as an inset in Fig. 7.., The redshift distribution of the 42 galaxies is shown in greater detail as an inset in Fig. \ref{z_hist}. Phe distribution is not a smooth Gaussian and shows sub-structure. consistent with dynamic. merging systems.," The distribution is not a smooth Gaussian and shows sub-structure, consistent with dynamic, merging systems." In Fig., In Fig. S we plot the positions of the 42 galaxies listed in Table 3.. with the galaxies in the three reclshilt bins (0.215 < z « 0.22: 0.22 xz « 0.225: 0.225 < z < 0.23) indicated by circles of varving size.," \ref{spatialdist} we plot the positions of the 42 galaxies listed in Table \ref{peak}, , with the galaxies in the three redshift bins (0.215 $\leq$ z $<$ 0.22; 0.22 $\leq$ z $<$ 0.225; 0.225 $\leq$ z $<$ 0.23) indicated by circles of varying size." Despite considerable overlap. there is a suggestion of a velocity eradient with the galaxies in the lowest redshift bin (largest circles) extending towards the south-west and those in the highest. redshift bin (smallest. circles) extending towards the south-east.," Despite considerable overlap, there is a suggestion of a velocity gradient with the galaxies in the lowest redshift bin (largest circles) extending towards the south-west and those in the highest redshift bin (smallest circles) extending towards the south-east." Although galaxy redshifts were measured within a radius of ~12 Alpe from the WAT. —60 per cent of the galaxies listed in ‘Table 3. ave within 6 Mpe of the WAT (30 arcmin).," Although galaxy redshifts were measured within a radius of $\sim$ 12 Mpc from the WAT, $\sim$ 60 per cent of the galaxies listed in Table \ref{peak} are within 6 Mpc of the WAT (30 arcmin)." We also note that the larger number of sources in the southern part of Fig., We also note that the larger number of sources in the southern part of Fig. SN. is due to the uneven coverage of the one-degrec-racdius field surrounding 81189., \ref{spatialdist} is due to the uneven coverage of the one-degree-radius field surrounding S1189. " The bright) galaxy, SWIRIE3_JJ003419.26-430334.0. located southwest of the WAT source. has a redshift of 0.2204. implying a velocity dillerence between the two galaxies of ~320 km !."," The bright galaxy, J003419.26-430334.0, located southwest of the WAT source, has a redshift of 0.2204, implying a velocity difference between the two galaxies of $\sim$ 320 km $^{-1}$." Their projected separation is 2 arcmin. corresponding to 7420 kpe at a redshift of 0.22.," Their projected separation is $\sim$ 2 arcmin, corresponding to $\sim$ 420 kpc at a redshift of 0.22." .003419.26-430334.0 is the brightest galaxy in the cluster anc has a dilfuse. envelope. therefore we classify it as à possible eD galaxy.," J003419.26-430334.0 is the brightest galaxy in the cluster and has a diffuse envelope, therefore we classify it as a possible cD galaxy." There is à marginal detection of associated. radio emission with a flux density of ~140 μὴν at 1.4 Giz whieh corresponds to a radio luminosity of 1.96 107 Ww +., There is a marginal detection of associated radio emission with a flux density of $\sim$ 140 $\mu$ Jy at 1.4 GHz which corresponds to a radio luminosity of 1.96 $\times$ $^{22}$ W $^{-1}$. Centrally dominant cD galaxies are usually giant ellipticals residing in the centres of clusters of ealaxies., Centrally dominant cD galaxies are usually giant ellipticals residing in the centres of clusters of galaxies. These are much larger and brighter than other galaxies in the cluster and are often surrounded by a diffuse envelope (Matthews.Morgan&Schmidt 1964)., These are much larger and brighter than other galaxies in the cluster and are often surrounded by a diffuse envelope \citep{Matthews64}. . Their large size is usually attributed to mergers and galaxy cannibalism (e.g.DeLucia& Blaizot 2007)., Their large size is usually attributed to mergers and galaxy cannibalism \citep[e.g.][]{DeLucia07}. . In addition to double-lobed radio sources. radio haloes. relics and core haloes or mini haloes may alsobe associated with clusters of galaxies.," In addition to double-lobed radio sources, radio haloes, relics and core haloes or mini haloes may alsobe associated with clusters of galaxies." C'ore- are usually less than ~500 kpe in extent and associated with the dominant galaxy in cooling core clusters., Core-haloes are usually less than $\sim$ 500 kpc in extent and associated with the dominant galaxy in cooling core clusters. LHaloes and relics are not associated. with, Haloes and relics are not associated with distributions could introduce unknown svstematics into the comparative success rates.,distributions could introduce unknown systematics into the comparative success rates. The results could also be used incorrectly (ο draw. lor example. the overall contamination of a SN Ia sample by CC-SNe.," The results could also be used incorrectly to draw, for example, the overall contamination of a SN Ia sample by CC-SNe." The contamination Iraction. while very. valuable for many SN searches. depends strongly on (he intrinsic rates of the different tvpes of CC-SNe as a function ol redshift.," The contamination fraction, while very valuable for many SN searches, depends strongly on the intrinsic rates of the different types of CC-SNe as a function of redshift." Such an estimate of contamination must therefore be tailored to a specilic survey. Lalàng into consideration (he range of possible distributions in SN properties.," Such an estimate of contamination must therefore be tailored to a specific survey, taking into consideration the range of possible distributions in SN properties." For comparison of the results based on our simulated SNe to those based on the real SN samples. we minc (he observational properties of the GOODS sample with its three IIST bandpasses. photometric errors and limiting magnitudes.," For comparison of the results based on our simulated SNe to those based on the real SN samples, we mimic the observational properties of the GOODS sample with its three HST bandpasses, photometric errors and limiting magnitudes." The results in (his section are Lor {his specifie configuration. and serve as an illustration of the capabilities of the SN-ABC.," The results in this section are for this specific configuration, and serve as an illustration of the capabilities of the SN-ABC." As in §??.. we caleulate the synthetic magnitudes of the fake SNe using the SEDs from the spectral templates of Nugentetal.(2002) for tvpes la. Ibe. 1Η: SNe.," As in \ref{model}, we calculate the synthetic magnitudes of the fake SNe using the SEDs from the spectral templates of \citet{NUGENT_02} for types Ia, Ibc, II-P SNe." Since the Nugentοἱal.(2002) spectra of type Ln SNe are theoretical blackbody SEDs. for (his tvpe only we use the templates from Poznanskietal.(2002).," Since the \citet{NUGENT_02} spectra of type IIn SNe are theoretical blackbody SEDs, for this type only we use the templates from \citet{POZ_TP1}." . As in 8??.. absolute magnitudes and (heir clispersions are taken from Dahlenetal.(2004).," As in \ref{model}, absolute magnitudes and their dispersions are taken from \citet{DAHLEN_SNR04}." . The scatter in color within each tvpe is applied to the CC-SNe by adding an intrinsic. normally distributed. noise with standard deviation of go=0.2mag. the value used by Sullivanetal.(2006a).," The scatter in color within each type is applied to the CC-SNe by adding an intrinsic, normally distributed, noise with standard deviation of $\sigma=0.2~\mathrm{mag}$, the value used by \citet{SULL_TP}." . The SNe Ia we simulate are given clilferent stretches s. following the method described in Sullivanetal.(2006a).," The SNe Ia we simulate are given different stretches $s$, following the method described in \citet{SULL_TP}." . We simulate a Gaussian distribution of stretches with an average of s=| and a dispersion of στ(0.25. truncated in the range 0.6€s< 1.4.," We simulate a Gaussian distribution of stretches with an average of $s=1$ and a dispersion of $\sigma=0.25$, truncated in the range $0.6 \leq s \leq 1.4$ ." " We model the stretch-luminosity relation using the formalism Mg,=Mgαί5--1) (Perlmutteretal.1999).. where Aj. and Mj arT the corrected and uncorrected 2 band absolute brightnesses respectively. ancl (he correlation [actor is a= 1.40."," We model the stretch-luminosity relation using the formalism $M_{Bc}=M_B-\alpha(s-1)$ \citep{Perlmutter_99}, where $M_{Bc}$ , and $M_{B}$ are the corrected and uncorrected $B$ band absolute brightnesses respectively, and the correlation factor is $\alpha=1.47$ ." We also apply color-stretchi corrections using the method presented iΕν Knopetal.(2003).. bv dividing the template spectra of normal. s=1. SNe Ia bv smooth spline functions. in order to match their restframe UDVRI colors to those of SNe with variouV. stretches.," We also apply color-stretch corrections using the method presented in \citet{KNOP_03}, by dividing the template spectra of normal, $s=1$, SNe Ia by smooth spline functions, in order to match their restframe $UBVRI$ colors to those of SNe with various stretches." We have measured (he mean photometric errors of the GOODS sample in each band as a function of magnitude. and again assuming the noise is normally clistributed. have added it to each object.," We have measured the mean photometric errors of the GOODS sample in each band as a function of magnitude, and again assuming the noise is normally distributed, have added it to each object." " We further assigned to (he SNe a pseudo-photo-z with a,=0»—0.1 (see 8??)).", We further assigned to the SNe a $z$ with $\sigma_1=\sigma_2=0.1$ (see \ref{SNLS-Ia}) ). Figure 3. shows the average success rate of our algorithm. as a function of SN age and vredshift. for three different stve(ch ranges.," Figure \ref{f:MCstr} shows the average success rate of our algorithm, as a function of SN age and redshift, for three different stretch ranges." " Each panel shows in contours the fraction of SNe Ia that are correctly elassilied bv the SN-ABC. ie.. the fractionof SNethatare given Py, values higher than hall."," Each panel shows in contours the fraction of SNe Ia that are correctly classified by the SN-ABC, i.e., the fractionof SNethatare given $P_{Ia}$ values higher than half." The solid curves show the 50% success level. demarcating the," The solid curves show the $50\%$ success level, demarcating the" The Full morphology pipeline described in Paper 1. works in five stages: cutout extraction from survey images. source detection (usingSExtractor:?).. centroid estimation and aperture photometry (using PHOT). lieht profile fitting (usingGALFIT:?).. ancl point sources identifica(ion.,"The full morphology pipeline described in Paper I, works in five stages: cutout extraction from survey images, source detection \citep[using SExtractor;][]{SExtractor}, centroid estimation and aperture photometry (using ), light profile fitting \citep[using GALFIT;][]{GALFIT}, and point sources identification." Our ceutouts were defined as 80x pixel (274x271) regions around each object: this area was deemed large enough area to compensate astrometric errors in the LAE positions. and allow for photometry of components located on (he edge of our selection region.," Our cutouts were defined as $80 \times 80$ pixel $2\farcs4 \times 2\farcs4$ ) regions around each object; this area was deemed large enough area to compensate astrometric errors in the LAE positions, and allow for photometry of components located on the edge of our selection region." 9Extractor was then used on each eutout. to identify all sources consisting of 9 contiguous pixels above al.65o detection threshold.," SExtractor was then used on each cutout, to identify all sources consisting of 9 contiguous pixels above $\sigma$ detection threshold." As described in Paper 1. each source located within 076 of the eround-based Lya position was defined as an LAE component. and the center of the LAE system was defined as the flux-weighted mean position of all detections within this selection radius.," As described in Paper I, each source located within $0 \farcs 6$ of the ground-based $\alpha$ position was defined as an LAE component, and the center of the LAE system was defined as the flux-weighted mean position of all detections within this selection radius." At the same time. we also used SExtractor to fit and subtract a uniform sky from the cutout. in order to not remove any diffuse Lvo emission: in the local universe. such emission can extend several hall-light radii [rom the center of a galaxy (?)..," At the same time, we also used SExtractor to fit and subtract a uniform sky from the cutout, in order to not remove any diffuse $\alpha$ emission; in the local universe, such emission can extend several half-light radii from the center of a galaxy \citep{ostlin09}." To compute the photometric centroid of each LAE. we again used SExtractor. this time idenüfving all objects with 5 contiguous pixels above the 1.650 threshold and computing their flux-weighted mean position.," To compute the photometric centroid of each LAE, we again used SExtractor, this time identifying all objects with 5 contiguous pixels above the $1.65 \sigma$ threshold and computing their flux-weighted mean position." This enabled us to include components too dim or small for morphological measurements., This enabled us to include components too dim or small for morphological measurements. Using this position. we then measured each LAE's total flux and half-light radius. under the assumption that the total LAE flix is contained with our 076 selection radius.," Using this position, we then measured each LAE's total flux and half-light radius, under the assumption that the total LAE flux is contained with our $0\farcs 6$ selection radius." This should be a good assumption.as LAEs are tvpically quite small (<1 kpc) in the rest-frame UV (72???) and many of our objects remain unresolved even al the depth of the current HIST images.," This should be a good assumption,as LAEs are typically quite small $<1$ kpc) in the rest-frame UV \citep{Venemans05,Pirzkal07,Overzier08,taniguchi} and many of our objects remain unresolved even at the depth of the current HST images." " Finally. as described in Paper I. we use GALFIT (2). to simultaneously fit each detection lo à Sérrsic prolile (?) where r. is the hall-light radius. (he parameter » characterizes (he steepness of the lisht profile. aud r represents the radius vector of model isophotes. i.e.. with x, and y. being the models centroid position. and 4 being ils axis ratio (b/«)."," Finally, as described in Paper I, we use GALFIT \citep{GALFIT} to simultaneously fit each detection to a Sérrsic profile \citep{Sersic} where $r_e$ is the half-light radius, the parameter $n$ characterizes the steepness of the light profile, and $r$ represents the radius vector of model isophotes, i.e., with $x_c$ and $y_c$ being the model's centroid position, and $q$ being its axis ratio $b/a$ )." To facilitate the computation. we generally iniüialized the Sérrsic indices {ο η= 4. lie. a," To facilitate the computation, we generally initialized the Sérrsic indices to $n = 4$ i.e., a" "The observations were performed on 2009, August 1, during the Performance Verification phase of the HIFI heterodyne instrument (de Graauw et al. 2010))","The observations were performed on 2009, August 1, during the Performance Verification phase of the HIFI heterodyne instrument (de Graauw et al. \cite{hifi}) )" on board of the Space Observatory (Pilbratt et al. 2010))., on board of the Space Observatory (Pilbratt et al. \cite{herschel}) ). The band called 1b (555.4—636.2 GHz) was covered in double-sideband (DSB) with a total integration time of 140 minutes., The band called 1b (555.4–636.2 GHz) was covered in double-sideband (DSB) with a total integration time of 140 minutes. The Wide Band Spectrometer was used with a frequency resolution of 1 MHz., The Wide Band Spectrometer was used with a frequency resolution of 1 MHz. " The typical HPBW is 39"".", The typical HPBW is $\arcsec$. The data were processed with the ESA-supported package(Herschel Interactive Processing Environment) for baseline subtraction and sideband deconvolution and then analysed with the software., The data were processed with the ESA-supported package Interactive Processing Environment) for baseline subtraction and sideband deconvolution and then analysed with the software. " All the spectra (here in units of antenna Τι) were smoothed to a velocity resolution of 1 km s7!, except those showing the weakest emission, which were smoothed to lower spectral resolutions (up to 4 km |)."," All the spectra (here in units of antenna $T_{\rm a}$ ) were smoothed to a velocity resolution of 1 km $^{-1}$, except those showing the weakest emission, which were smoothed to lower spectral resolutions (up to 4 km $^{-1}$ )." " At a velocity resolution of 1 km 5-1, the rms noise is 6-13 mK (T, scale), depending on the line frequency."," At a velocity resolution of 1 km $^{-1}$ , the rms noise is 6–13 mK $T_{\rm a}$ scale), depending on the line frequency." " The main-beam efficiency (7,,) has not yet been reliably determined.", The main-beam efficiency $\eta_{mb}$ ) has not yet been reliably determined. " When needed, we adopted an average rj; of 0.72."," When needed, we adopted an average $\eta_{mb}$ of 0.72." " A total of 27 emission lines were detected, with a wide range of upper level energies, from a few tens to a few hundreds of Kelvin."," A total of 27 emission lines were detected, with a wide range of upper level energies, from a few tens to a few hundreds of Kelvin." Table 1 lists the spectroscopic and observational parameters of all the transitions., Table 1 lists the spectroscopic and observational parameters of all the transitions. " For the first time, high excitation (up to ~ 200 K) emission lines related to species whose abundance is largely enhanced in shocked regions were detected."," For the first time, high excitation (up to $\simeq$ 200 K) emission lines related to species whose abundance is largely enhanced in shocked regions were detected." The CO(5-4) and H2O(1 10-101) lines are analysed in Lefloch et al. (2010)).," The CO(5–4) and $_2$ $_{\rm 10}$ $_{\rm 01}$ ) lines are analysed in Lefloch et al. \cite{letter2}) )." Figure 2 presents representative examples of line profiles observed towards L1157-B1., Figure \ref{spectra} presents representative examples of line profiles observed towards L1157-B1. " All the spectra contain lines with blue-shifted wings peaking near 0 km s!, which have a terminal velocity equal to ~ —8,-6 km s."," All the spectra contain lines with blue-shifted wings peaking near 0 km $^{-1}$, which have a terminal velocity equal to $\sim$ –8,–6 km $^{-1}$ ." " Previous PdBI observations showed that L1157-B1 is associated with very high velocities (HVs) of as low as ~ km s! (isp = 42.6 km s!, BP97)."," Previous PdBI observations showed that L1157-B1 is associated with very high velocities (HVs) of as low as $\simeq$ --20 km $^{-1}$ $v_{\rm LSR}$ = +2.6 km $^{-1}$ , BP97)." We cannot exclude the lack of detected emission in the HV regime in the present HIFI spectra being caused by their relatively low signal-to-noise (S/N) ratio., We cannot exclude the lack of detected emission in the HV regime in the present HIFI spectra being caused by their relatively low signal-to-noise (S/N) ratio. The PdBI images indicate that the brightness of the emission lines in the HV regime is indeed weaker than the emission at low velocities by a factor of 5-10., The PdBI images indicate that the brightness of the emission lines in the HV regime is indeed weaker than the emission at low velocities by a factor of 5–10. The spectra in Fig., The spectra in Fig. 2 clearly show that this weak emission would lie below the noise., \ref{spectra} clearly show that this weak emission would lie below the noise. " On the other hand, the HV gas is detected in the very bright lines of CO and Η2Ο (Lefloch et al. 2010))."," On the other hand, the HV gas is detected in the very bright lines of CO and $_2$ O (Lefloch et al. \cite{letter2}) )." " We note that the HV emission is mostly confined to within the eastern B1a clump (Fig. 1)),"," We note that the HV emission is mostly confined to within the eastern B1a clump (Fig. \ref{maps}) )," " within an emitting region of size < 10"" (Gueth et al. 1998;;", within an emitting region of size $\le$ $\arcsec$ (Gueth et al. \cite{fred98}; " BVCO7), whereas low velocity lines originate in both the bow-structure and the walls of the outflow cavity (e.g., the BOe and BOd in Fig. 1)),"," BVC07), whereas low velocity lines originate in both the bow-structure and the walls of the outflow cavity (e.g., the B0e and B0d in Fig. \ref{maps}) )," " of typical size 15""— 18"".", of typical size $\arcsec$ $\arcsec$. " Therefore, the forthcoming HIFI-CHESS observations at higher frequencies and higher spatial resolution (see the dashed circle in Fig. 1))"," Therefore, the forthcoming HIFI-CHESS observations at higher frequencies and higher spatial resolution (see the dashed circle in Fig. \ref{maps}) )" should allow us to study the HV wings in species other than CO and H5O. The uniqueness of HIFI lies in its high spectral profile resolution for many high excitation transitions of a large number of molecular species., should allow us to study the HV wings in species other than CO and $_2$ O. The uniqueness of HIFI lies in its high spectral profile resolution for many high excitation transitions of a large number of molecular species. " The analysis of the present HIFI spectra reveals a secondary peak occuring between —3.0 and —4.0 km s! (here defined medium velocity, MV) and well outlined by e.g., HCN(7-6)."," The analysis of the present HIFI spectra reveals a secondary peak occuring between –3.0 and –4.0 km $^{-1}$ (here defined medium velocity, MV) and well outlined by e.g., HCN(7–6)." The MV peak is also visible in NH3(10-09) and in some lines of CH3OH and H2CO (see Fig. 3))," The MV peak is also visible in $_3$ $_0$ $_0$ ) and in some lines of $_3$ OH and $_2$ CO (see Fig. \ref{profiles}) )," but its occurrence does not show any clear trend with the choice of tracer of line excitation., but its occurrence does not show any clear trend with the choice of tracer of line excitation. No single-dish spectra had previously detected this spectral feature (BP97; Bachiller et al. 2001))., No single-dish spectra had previously detected this spectral feature (BP97; Bachiller et al. \cite{bach01}) ). An inspection of the spectra observed at PdBI shows that the MV secondary peak is observed in a couple of lines of the CH3OHQx-1x) series (see Fig., An inspection of the spectra observed at PdBI shows that the MV secondary peak is observed in a couple of lines of the $_3$ $_{\rm K}$ $_{\rm K}$ ) series (see Fig. " 3 of BVCO07) and only towards the western B1b clump (size ~ 5"").", 3 of BVC07) and only towards the western B1b clump (size $\sim$ $\arcsec$ ). " This finding implies that there is a velocity component originating mainly in the western side of B1, while the HV gas is emitted from the eastern one (see above)."," This finding implies that there is a velocity component originating mainly in the western side of B1, while the HV gas is emitted from the eastern one (see above)." " Figure 3 compares the profiles of the NH3(1o—0o) and H2CO(8,;-7,6) lines with the H2O(1 ιο--1οι) profile, where the S/N allows such an analysis (MV and LV ranges)."," Figure \ref{profiles} compares the profiles of the $_3$ $_0$ $_0$ ) and $_2$ $_{\rm 17}$ $_{\rm 16}$ ) lines with the $_2$ $_{\rm 10}$ $_{\rm 01}$ ) profile, where the S/N allows such an analysis (MV and LV ranges)." " By assuming that the emission in the MV range is optically thin (including the H2O line) and originates in the same region, we obtained from the comparison of their profiles a straightforward estimate of the relative abundance ratios of the gas at different velocities."," By assuming that the emission in the MV range is optically thin (including the $_2$ O line) and originates in the same region, we obtained from the comparison of their profiles a straightforward estimate of the relative abundance ratios of the gas at different velocities." " As a notable example, the NH3/H5Ointensity ratio decreases by a factor ~ 5 moving towards higher velocities(Fig. 3)),"," As a notable example, the $_3$ $_2$ Ointensity ratio decreases by a factor $\sim$ 5 moving towards higher velocities(Fig. \ref{profiles}) )," implying that a similar decrease in the abundance ratios occurs., implying that a similar decrease in the abundance ratios occurs. This may reflect different pre-shock ice compositions in the gas emitting the MV emission., This may reflect different pre-shock ice compositions in the gas emitting the MV emission. " Alternatively, this behavior is consistent with NH3 being released by grain mantles, but water both being released by grain mantles and, inaddition,"," Alternatively, this behavior is consistent with $_3$ being released by grain mantles, but water both being released by grain mantles and, inaddition," lime scale for planetesimal formation. (2) the infall time scale of the dust grains compared io their growth time and (3) the destruction of dust grains [rom high velocity collisions.,"time scale for planetesimal formation, (2) the infall time scale of the dust grains compared to their growth time and (3) the destruction of dust grains from high velocity collisions." We [ind that dust erain infall due to heachwinel eas drag; prohibits reaching the gravitational instability phase outside a limiting radius that depends on (he transition between Stokes and Epstein drag (the 7=Q! triple point [rom sec., We find that dust grain infall due to headwind gas drag prohibits reaching the gravitational instability phase outside a limiting radius that depends on the transition between Stokes and Epstein drag (the $\tau=\Omega^{-1}$ triple point from sec. 5.1)., 5.1). " For our disc model this occurs al R=Ry, given by Eq. (36)).", For our disc model this occurs at $R = R_{tp}$ given by Eq. \ref{RTriple}) ). " [lis possible that material piles up al 7?=A, which may enhance planetesimal growth at this radius.", It is possible that material piles up at $R=R_{tp}$ which may enhance planetesimal growth at this radius. This latter effect requires further work., This latter effect requires further work. " For R«H, p we find that [or p>10? anda <10.7 turbulence does not catastrophically V.ow the neededle planetesimal growth. as seen in Fig. (3))."," For $R10^{-2}$ and $\alpha \le 10^{-3}$ turbulence does not catastrophically slow the needed planetesimal growth, as seen in Fig. \ref{TimeLargeSmall}) )," even though the time ancl size scales al which the growth occurs still depend stronely on those parameters., even though the time and size scales at which the growth occurs still depend strongly on those parameters. These results depend on (he unknown physics of grain-grain interactions determining p. but the assumption that grain destruction results from collisions with velocities greater (han 30km/hr strictly requires a<107 [or all dises if growth is to be [ast enough.," These results depend on the unknown physics of grain-grain interactions determining $p$, but the assumption that grain destruction results from collisions with velocities greater than $30$ km/hr strictly requires $\alpha < 10^{-2}$ for all discs if growth is to be fast enough." As determined in Sec., As determined in Sec. 6.1.1. values of àc10.7 for discs with substantial dead zones and a10!Ἱ are acceptable.," 6.1.1, values of $\alpha \simeq 10^{-3}$ for discs with substantial dead zones and $\alpha \simeq 10^{-4}$ are acceptable." The condition that the grain infall time be longer than the grain growth time (as discussed in section 7.2) also leads (ο an o independent minimum acceptable p as seen in Fig. (9))., The condition that the grain infall time be longer than the grain growth time (as discussed in section 7.2) also leads to an $\alpha$ independent minimum acceptable $p$ as seen in Fig. \ref{HWrc}) ). We find that as p Falls below τ the distance from the star at which gravitational instability can be reached and planetesimal formation occurs [alls below 3 AU., We find that as $p$ falls below $\frac{1}{10}$ the distance from the star at which gravitational instability can be reached and planetesimal formation occurs falls below $3$ AU. For p=103 planetesimal formation won't occur outside of roughly 1 AU., For $p=10^{-2}$ planetesimal formation won't occur outside of roughly $1$ AU. Values of e below 10.7 are too low to produce rapid enough planetesimal growth in the absence of additional plivsies., Values of $c$ below $10^{-2}$ are too low to produce rapid enough planetesimal growth in the absence of additional physics. Although more detailed caleulations with grain size spectra. collisional velocity spectra. and a more detailed grain-grain collision model are needed. our most robust conclusion is (hat planetesimal growth in an initially eravilationally stable turbulent disc is not prohibited by turbulence with 10510L7 we do not find"" much opportunityn forB growth. even for discs with a dead zone. and additional physics to promote dust exowth suchas laree scale vorlices. or theconsequences of mass pile up at. 2=fij, need to be considered."," For $\alpha \ge 10^{-2}$ we do not find much opportunity for growth, even for discs with a dead zone, and additional physics to promote dust growth suchas large scale vortices, or theconsequences of mass pile up at $R=R_{tp}$ need to be considered." ]lere we derives the various formulas for Tables 3. and 4.., Here we derives the various formulas for Tables \ref{RegimeSize} and \ref{RegimeTime}. . bv this short exposure.,by this short exposure. The total detected emission from within one core radius. assuming al keV thermal bremsstrahlung spectrum. was 1.5x10** eres band can be accounted [or bv the two detected. sources.," The total detected emission from within one core radius, assuming a 1 keV thermal bremsstrahlung spectrum, was $1.5\times10^{33}$ ergs $^{-1}$, and can be accounted for by the two detected sources." " A deeper ACIS exposure could measure spectra. confirm the possible 43.6 minute period for source D. and identify low-Iuminositv sources such as CVs,"," A deeper ACIS exposure could measure spectra, confirm the possible 43.6 minute period for source B, and identify low-luminosity sources such as CVs." Several potential CVs or hot white dwarls on the WF2 and WEZ chips are indicated in Figure 2., Several potential CVs or hot white dwarfs on the WF2 and WF4 chips are indicated in Figure 2. Additional blue non-variable stars are noted on the PC chip: their lack of variability and blue colors resemble (he non-flickerers noted in NGC 6397 and proposed to be Le white cdwarfs (Edmonds et 11999)., Additional blue non-variable stars are noted on the PC chip; their lack of variability and blue colors resemble the non-flickerers noted in NGC 6397 and proposed to be He white dwarfs (Edmonds et 1999). However. these could be field stars.," However, these could be field stars." Using the figures from latnatunga and Baheall (1985) for Galactic star counts in the direction of NGC! 6652. we estimate thal we should see ~1.2 stars with 2—Vκ0.8 between 19«€myc23 in the PC field. and ~11 stars with 2—V«0.8 between 210. ie. the temperature increases with height while lor 5>1. p/p—(p/p)|.-a must be <0. ie. the temperature decreases with height.," For $\gamma < 1$ , $p/\rho -(p/\rho)|_{z=0}$ must be $> 0$, i.e. the temperature increases with height while for $\gamma > 1$, $p/\rho -(p/\rho)|_{z=0}$ must be $< 0$, i.e. the temperature decreases with height." Note that along fiekl lines the temperature is a linear function of height. whieh must therefore cross zero and become negative at some height.," Note that along field lines the temperature is a linear function of height, which must therefore cross zero and become negative at some height." Such solutions may still be used to model solar prominences since {μον are of finite vertical extent., Such solutions may still be used to model solar prominences since they are of finite vertical extent. In the separable case. the plasma pressure and temperature are given by where A=pyle)/poleig is à constant length scale.," In the separable case, the plasma pressure and temperature are given by where $\lambda =p_0(\psi )/\rho_0 (\psi)g$ is a constant length scale." The Grad-Shalfranov. Equation (6)) is Note that the temperature is independent of e in this separable case. since p and p have common c-dependence. ancl the position of (his zero-point is 2=zi on all field lines.," The Grad-Shafranov Equation \ref{reducedfb}) ) is Note that the temperature is independent of $\psi$ in this separable case, since $p$ and $\rho$ have common $\psi$ -dependence, and the position of this zero-point is $z=z_0$ on all field lines." In order for the plasma pressure and temperature to be well-defined) and positive in the domain of interest. the factor —(5—λεςzo) must be positive tliroughout that domain.," In order for the plasma pressure and temperature to be well-defined and positive in the domain of interest, the factor $-(\gamma-1)(z-z_0)$ must be positive throughout that domain." The gradientof the linear variation of Z with altitude is determined entirely by the polviropic index 5., The gradientof the linear variation of $T$ with altitude is determined entirely by the polytropic index $\gamma$. 7 is an increasing function of height for ><1 and a decreasing function of height for +>1., $T$ is an increasing function of height for $\gamma < 1$ and a decreasing function of height for $\gamma > 1$. Thus. for example. Low Zhang chose their 2) to be negative to keep this critical point oul ol the wav beneath the base of the corona because they were working with values of 5«I.," Thus, for example, Low Zhang chose their $z_0$ to be negative to keep this critical point out of the way beneath the base of the corona because they were working with values of $\gamma <1$." For cases wilh 5«lI. zo must be placed above the domain of interest ancl lor 5>1 τμ must be placed beneath.," For cases with $\gamma <1$, $z_0$ must be placed above the domain of interest and for $\gamma>1$ $z_0$ must be placed beneath." I£ 21 this introduces difficulties for the construction of solutions in which all of space is populated by plasma. such as the one in Figure 5.. but for isolated prominence plasma enhancementsin emplv atmospheres these solutions are appropriate.," If $\gamma >1$ this introduces difficulties for the construction of solutions in which all of space is populated by plasma, such as the one in Figure \ref{noniso}, but for isolated prominence plasma enhancementsin empty atmospheres these solutions are appropriate." For the general case py= puy(o). the solution is not separable and the pressure and lemperalure are given bv," For the general case $\rho_0 =\rho_0 (\psi )$ , the solution is not separable and the pressure and temperature are given by" an L>0.11 galaxy in a small projected diameter pencil beam survey such as this is quite small.,an $L>0.1L^{\star}$ galaxy in a small projected diameter pencil beam survey such as this is quite small. " Assuming the Schechter function parameters of the i band galaxy luminosity distribution from Blantonetal.(2003) of M;= —21.59, ¢*=0.005 Mpc?, and a=—1.00, we have estimated the number of galaxies with L>0.1L* that will be intercepted in a random 100 arcsec” field, shown in Figure 3 as a function of redshift."," Assuming the Schechter function parameters of the $i$ band galaxy luminosity distribution from \citet{Blanton03} of $_{i}^{\star}=-21.59$ , $\phi^{\star}=0.005$ $^{-3}$, and $\alpha=-1.00$, we have estimated the number of galaxies with $L>0.1L^{\star}$ that will be intercepted in a random 100 $^2$ field, shown in Figure \ref{Fig:Schechter} as a function of redshift." " As can be seen, we expect to intercept less than one L>0.11 galaxy in a random 100 arcsec” field for 2<1.5."," As can be seen, we expect to intercept less than one $L>0.1L^{\star}$ galaxy in a random 100 $^{2}$ field for $z<1.5$." " Hence, the likelihood of each of these fields containing bright galaxies not associated with the hosts of the sub-DLAs are very small."," Hence, the likelihood of each of these fields containing bright galaxies not associated with the hosts of the sub-DLAs are very small." Using the luminosity function parameters at z~1 from (2005) results in the same conclusions., Using the luminosity function parameters at $z\sim1$ from \citet{Ilb05} results in the same conclusions. We have compiled the available data from the literature on impact parameters for absorption systems that have known at z<1., We have compiled the available data from the literature on impact parameters for absorption systems that have known at $z\la1$. These data are given in Table 1.., These data are given in Table \ref{Tab:Lit}. " We have taken a sub-sample of these data to include only the systems that have spectroscopically confirmed galaxy redshifts, or secure photometric redshifts."," We have taken a sub-sample of these data to include only the systems that have spectroscopically confirmed galaxy redshifts, or secure photometric redshifts." " A Kendall's T test was used to determine the probability of a correlation between and impact parameter p, resulting in 7=—0.23 and a probability of no correlation of 0.47."," A Kendall's $\tau$ test was used to determine the probability of a correlation between and impact parameter $\rho$, resulting in $\tau=-0.23$ and a probability of no correlation of $0.47$." " If one includes the data points that do not have spectroscopic redshifts of the galaxies, Kendall's 7 then becomes 7——0.48 with a probability of no correlation of 0.05."," If one includes the data points that do not have spectroscopic redshifts of the galaxies, Kendall's $\tau$ then becomes $\tau=-0.48$ with a probability of no correlation of 0.05." " We have preformed a linear regression on these data, using survival analysis to include the mixed censored data in the fit using Schmitt’s Binning method."," We have preformed a linear regression on these data, using survival analysis to include the mixed censored data in the fit using Schmitt's Binning method." " We find the best fit trend line of log =(20.67+0.23)—(0.028+0.014)xp when using only the spectroscopically confirmed galaxies, and log =(20.86+0.14)—(0.030.008)xp when including galaxies without redshift information."," We find the best fit trend line of log $(20.67\pm0.23) - (0.028\pm0.014)\times\rho$ when using only the spectroscopically confirmed galaxies, and log $(20.86\pm0.14) - (0.03\pm0.008)\times\rho$ when including galaxies without redshift information." " Figure 4 shows a plot of impact parameter vs. for the literature data, and the points from the observations in this investigation."," Figure \ref{Fig:Lit} shows a plot of impact parameter vs. for the literature data, and the points from the observations in this investigation." " For Q1228+1018, and Q1436—0051 we give the impact parameter as a lower limit as it is uncertain to which galaxy in these fields the absorption is linked to without spectroscopic observations of the galaxies."," For Q1228+1018, and $-$ 0051 we give the impact parameter as a lower limit as it is uncertain to which galaxy in these fields the absorption is linked to without spectroscopic observations of the galaxies." " For the absorber at z,5,,—00.8426 in Q1009—0026 we give the impact parameter as an upper limit based on a 2” threshold radius inside the PSF.", For the absorber at 0.8426 in $-$ 0026 we give the impact parameter as an upper limit based on a $\arcsec$ threshold radius inside the PSF. " Also shown in Figure 4 are the radial 21 cm profile of Malinl1, a nearby low surface brightness (LSB) galaxy from Pickeringetal.(1994) and the average Sc type 21 cm radial profile from Swatersetal. (2002)."," Also shown in Figure \ref{Fig:Lit} are the radial 21 cm profile of Malin1, a nearby low surface brightness (LSB) galaxy from \citet{Pick94} and the average Sc type 21 cm radial profile from \citet{Swat02}." ". The data in that work are normalized relative to the 21 cm H I radius (ie. R/R#), so we have used the median H I radius for L~L* galaxies from Noordermeeretal.(2005) of 28 kpc to scale the profile."," The data in that work are normalized relative to the 21 cm H I radius (i.e. $_H$ ), so we have used the median H I radius for $\sim$ $^{\star}$ galaxies from \citet{Noor05} of 28 kpc to scale the profile." " The minimal correlation between impact parameter and indicates that the QSO absorber population stems from a range of environments and morphological types, which is also supported in the heterogeneous collection of galaxies that comprise the literature sample."," The minimal correlation between impact parameter and indicates that the QSO absorber population stems from a range of environments and morphological types, which is also supported in the heterogeneous collection of galaxies that comprise the literature sample." The random orientations of galaxy disk inclinations increases the dispersion in the trend between impact parameter andτ., The random orientations of galaxy disk inclinations increases the dispersion in the trend between impact parameter and. . Monte Carlo simulations of p vs reported in (Chenetal.2005) have a scatter of ~0.5 dex in for a given impact parameter., Monte Carlo simulations of $\rho$ vs reported in \citep{Chen05} have a scatter of $\sim$ 0.5 dex in for a given impact parameter. " These simulations were conducted using idealized smooth H I profiles, using more realistic simulations that include the patchy and filamentary features typically seen in the ISM of the Milky Way and nearby galaxies would likely increase the scatter even more."," These simulations were conducted using idealized smooth H I profiles, using more realistic simulations that include the patchy and filamentary features typically seen in the ISM of the Milky Way and nearby galaxies would likely increase the scatter even more." A larger sample of DLAs and sub-DLAs with imaging data at z«1 would allow for a direct comparison of objects in terms of their impact parameters an luminosities., A larger sample of DLAs and sub-DLAs with imaging data at $z<1$ would allow for a direct comparison of objects in terms of their impact parameters an luminosities. "Accreting. milliseconcls pulsars (AMIS? ""Ain the following). are the long sought connection. between low mass X-ray. binaries. (LAINBs)ny ancl millisecond- radio. pulsars.",Accreting millisecond pulsars (AMSP in the following) are the long sought connection between low mass X-ray binaries (LMXBs) and millisecond radio pulsars. In fact.. although ⋠ ⋠ ⋅ ⊔∖∖⋎⋜↧⋡∖↓↕∙∖⇁↓≻∪⇂↓∐⊾⋡∖↓⋡∖⋖⊾∠⇂⋡∖∪∪⊔⋜↧∐⋖⊾↓⋅↥⇂↥⋖⋅↓↓⋅∠∐⋡∖≼∙∪∖⇁⋖⊾↓⋅∙∖⇁↥⇂⋯⇂⇂⋜↧⋡∖↥MN ⋅ spinning⋠⋠ radio. pulsars were crecvcled- by an aceretion. phase in. a LMXDEN system. during. which. the neutron star (NS) DANis spunup (see for⋅ a review. Bhattacharva5 van den lleuvel 1991). evidence has been elusive since SAN J18SOS.4-3658. the first accretion-driven millisecond X-ray pulsar. was discovered (Wijnands van der Klis 1998).," In fact, although it was hypothesised soon after their discovery that fast spinning radio pulsars were “recycled” by an accretion phase in a LMXB system, during which the neutron star (NS) is spun–up (see for a review Bhattacharya van den Heuvel 1991), evidence has been elusive since SAX J1808.4-3658, the first accretion-driven millisecond X-ray pulsar, was discovered (Wijnands van der Klis 1998)." SAN JISOS4-3658. with a spin period of 2.5 ms. exhibiting both X-ray bursts and coherent pulsations. proved. to be the missing link between the two classes of sources.," SAX J1808.4-3658, with a spin period of $2.5$ ms, exhibiting both X-ray bursts and coherent pulsations, proved to be the missing link between the two classes of sources." Since then. six more müllisecond. X-ray. pulsars were discovered. (see. WijnancWu. 2006 for an observational review).," Since then, six more millisecond X-ray pulsars were discovered (see Wijnands 2006 for an observational review)." All of these sources are transients with usually low duty eveles., All of these sources are transients with usually low duty cycles. Except for the case of ΠΙΕΙΣ J1900.1-2455. which remained active for more than a vear after its discovery in June 2005 (Calloway ct al., Except for the case of HETE J1900.1-2455 which remained active for more than a year after its discovery in June 2005 (Galloway et al. 2007). the outbursts of AMISP last for∙ no more than a couple of⋅ months. with. recurrence times usually larger than 2 vr (Galloway 2006).," 2007), the outbursts of AMSP last for no more than a couple of months, with recurrence times usually larger than $2$ yr (Galloway 2006)." Although the sample is still small. monitoring of future outbursts exhibited by the known sources is extremely important. [or our understanding of LAINBs and their evolution.," Although the sample is still small, monitoring of future outbursts exhibited by the known sources is extremely important for our understanding of LMXBs and their evolution." The study of the rotational behaviour of these sources curing outbursts is on the other hand obviously fundamental as à test of theories⊀ of⋅ accretion. physics., The study of the rotational behaviour of these sources during outbursts is on the other hand obviously fundamental as a test of theories of accretion physics. . As à matter of fact.⋅ the measure of⋅ the variationsD. of⋅ the spin.⊀⋅ [requency . . ⋏∙≟↓∖⇁⋖⋅⊳∖↓⊔↓⊔↓⋖⋅∠⊔⋜⋯⊾⊔⊔∠⇂⋖⋅↓⋅⊳∖∣⋜⋯∠⊔⊔⋏∙≟∪⇂↓↕⋖⋅⋯↓⋅⊏↥⋯⊾⊳∖⋖⋅⇀∖↓≻⋖⋅↓⋅⊓⋅⊔≼∙⋖⋅∠⇂: ⋅ ⊀ by the compact object. because of. the accretion. of⋅ matter. ancl further⋅ allows a model dependent dynamical. estimate. of⋅ the instantaneous⊀ mass accretion⊀ rate.," As a matter of fact, the measure of the variations of the spin frequency gives immediate understanding of the torques experienced by the compact object because of the accretion of matter, and further allows a model dependent dynamical estimate of the instantaneous mass accretion rate." ⊀Timing techniques. performed. on the coherently pulsed. emission. (see e.g. Dlancdford Jeukolskv 1976). represent the Καν tool in. order to directly measure the variations of the spin rate of this kind of accretors., Timing techniques performed on the coherently pulsed emission (see e.g. Blandford Teukolsky 1976) represent the key tool in order to directly measure the variations of the spin rate of this kind of accretors. The application of this kind of analyses on the X-ray emission of these sources. as observed by the high temporal resolution satellite Rossi X-Ray Timing Explorer TE) (Bradt et al.," The application of this kind of analyses on the X-ray emission of these sources, as observed by the high temporal resolution satellite Rossi X-Ray Timing Explorer ) (Bradt et al." 1983). allowed the measurement of∙ the spin frequency. derivative in the case of LGR: J00291|5934 (Falanga et al.," 1983), allowed the measurement of the spin frequency derivative in the case of IGR J00291+5934 (Falanga et al." 2005: Burderi et al., 2005; Burderi et al. 2007). NTE J0925-314 (Galloway et al.," 2007), XTE J0929-314 (Galloway et al." 2002). STE JIS14-338 (Papitto ct al.," 2002), XTE J1814-338 (Papitto et al." 2007). NTE JINQT294 (Riggio ct al.," 2007), XTE J1807–294 (Riggio et al." 2007) and of one of the oubursts. shown. by aaSANd J1s05.43658Svan (Burderiρν aqet τε]al., 2007) and of one of the oubursts shown by SAX J1808.4–3658 (Burderi et al. aloo2006)., 2006). ⋅ See Di Salvo et al. (, See Di Salvo et al. ( 2007) and references therein for à review.,2007) and references therein for a review. Even though the shortness of the outbursts generally exhibited: by AAISP strongly. limits the capability of the timing analvsis in cliscriminating between various accretion models. observations have alreacly shown how the behaviour of these sources can be variable. in fact. as a result. of accretion. some of them are observed. to. spin. up. while," Even though the shortness of the outbursts generally exhibited by AMSP strongly limits the capability of the timing analysis in discriminating between various accretion models, observations have already shown how the behaviour of these sources can be variable, in fact, as a result of accretion, some of them are observed to spin up, while" where h is approximately equal to wnily in the middle of the habitable zone. ancl to 2/3.4/3 al ils inner and outer edge. respectively (?2?7)..,"where $h$ is approximately equal to unity in the middle of the habitable zone, and to $2/3, 4/3$ at its inner and outer edge, respectively \citep{Charbonneau2007, Tarter2007, Scalo2007}." There is presently significant uncertainty in (his equation., There is presently significant uncertainty in this equation. The nearby clwarl Gliese 581. with a stellar mass of 0.31M... has three known planets. one of which has an / value of 1.39 ancl is generally considered to be possibly habitable.," The nearby dwarf Gliese 581, with a stellar mass of $0.31\, {\rm M_\odot},$ has three known planets, one of which has an $h$ value of 1.39 and is generally considered to be possibly habitable." Another of its planets has an value of 0.41. and is generally considered not to be habitable (??).. though mitigating effects have been proposed (?)..," Another of its planets has an $h$ value of 0.41, and is generally considered not to be habitable \citep{vonBloh2007, Selsis2007}, , though mitigating effects have been proposed \citep{Chylek2007}." The idea motivating our work is to explore the action as a gravitational lens of a nearby dwarf star that hosts a planet in its zone of habitabilitv., The idea motivating our work is to explore the action as a gravitational lens of a nearby dwarf star that hosts a planet in its zone of habitability. The deflection of light [rom a distant star bv an intervening mass causes (he image of the source to be split. distorted. and maegnilied.," The deflection of light from a distant star by an intervening mass causes the image of the source to be split, distorted, and magnified." When the lens is located in our Galaxy. and has mass comparable to that of a star or planet. the images of the source are separated by (oo small an angle to resolve.," When the lens is located in our Galaxy, and has mass comparable to that of a star or planet, the images of the source are separated by too small an angle to resolve." We can. however. detect the increase in the amount of light received [rom (he source when its position. u. projected onto the lens plane is comparable to the Einstein radius. Hj.," We can, however, detect the increase in the amount of light received from the source when its position, $u,$ projected onto the lens plane is comparable to the Einstein radius, $R_E$." " where D, is the distance to the lens and D is the distance to the source star.", where $D_L$ is the distance to the lens and $D_S$ is the distance to the source star. We have assumed (hat the mass of the planet is a small fraction of the mass of the star., We have assumed that the mass of the planet is a small fraction of the mass of the star. Expressing win units of Ry. the magnification is 3456.66.2%.1% when uw=1.2.3.3.5. respectively.," Expressing $u$ in units of $R_E,$ the magnification is $34\%, 6\%, 2\%, 1\%$ when $u = 1, 2, 3, 3.5,$ respectively." " Comparing equations (1) and (2) reveals (hat the spatial scale that defines (he habitable zone is compatible with (he size of the Einstein ring lor a wide range of stellar masses ancl distances. D,. This is fortuitous. because the chances of detecting a planet around a lens star are erealest when (he orbital distance is comparable in size to the Einstein radius."," Comparing equations (1) and (2) reveals that the spatial scale that defines the habitable zone is compatible with the size of the Einstein ring for a wide range of stellar masses and distances, $D_L.$ This is fortuitous, because the chances of detecting a planet around a lens star are greatest when the orbital distance is comparable in size to the Einstein radius." In this Letter we focus on planetary. svstems located within about a kiloparsec., In this Letter we focus on planetary systems located within about a kiloparsec. These svslenms are near enought that we can hope to conduct follow-up observations to learn more about the planet aud perhaps eventually test for the presence of life., These systems are near enought that we can hope to conduct follow-up observations to learn more about the planet and perhaps eventually test for the presence of life. It is convenient {ο deline (he parameter a to be the ratio between the semimajor axis and (he value of the Einstein radius: «=aRy. Figure 1 shows values of a as a function of distance. for planets in (he zones of habitability around their stars.," It is convenient to define the parameter $\alpha$ to be the ratio between the semimajor axis and the value of the Einstein radius: $a = \alpha\, R_E.$ Figure 1 shows values of $\alpha$ as a function of distance, for planets in the zones of habitability around their stars." Depending on the stellar mass. planets in the habitable zone are detectable through their action as lenses for planetary svstenis as close to us as a parsec (for the lowest-mass dwarf stars). ancl out to distances as far as a kiloparsec or more when the stellar mass is 0.5M. or larger.," Depending on the stellar mass, planets in the habitable zone are detectable through their action as lenses for planetary systems as close to us as a parsec (for the lowest-mass dwarf stars), and out to distances as far as a kiloparsec or more when the stellar mass is $0.5\, {\rm M_\odot}$ or larger." Galactic fountains (GEs) are believed to occur in the Milky Way as well as in the otier disk galaxies.,Galactic fountains (GFs) are believed to occur in the Milky Way as well as in the other disk galaxies. A GE takes place when the Tvpe HL supernovae (SNe HD) belonging to an OB association are sullicienty numerous to create a superbubble and to drive its expansion above the seale height of the gaseous disk (???)..," A GF takes place when the Type II supernovae (SNe II) belonging to an OB association are sufficiently numerous to create a superbubble and to drive its expansion above the scale height of the gaseous disk \citep{shafi76, breg80, kahn81}." As the break out occurs (?7).. the gas heated by the SNe LL fals back to the Galactic plane as cold eas. mostly concentrated in clouds formed through thermal instabilities.," As the break out occurs \citep{mamcno89,kmck92}, the gas heated by the SNe II falls back to the Galactic plane as cold gas, mostly concentrated in clouds formed through thermal instabilities." The GE mechanism is thought to be linked to à number oL issues which have been discussed in some detail in ?.there-alterPayer LL.," The GF mechanism is thought to be linked to a number of issues which have been discussed in some detail in \citet [][thereafter Paper I]{mel08}." Herewe brielly recall them: 7) the formation of the olserved thick H1 laver having a mass of 1/10 of the total LEL and rotating with velocity about 20-50 km s smaller han that of the gas on the plane: 77) the presence of high velocity clouds (HIVCs) and/or intermediate. velocity clouds (VCs).," Herewe briefly recall them: $i$ ) the formation of the observed thick H layer having a mass of 1/10 of the total H, and rotating with velocity about 20-50 km $^{-1}$ smaller than that of the gas on the plane; $ii$ ) the presence of high velocity clouds (HVCs) and/or intermediate velocity clouds (IVCs)." It is important to understand whether these cleuds are formed. by Cbs. or represent external gas accreting on the disk (?): Hi) the presence of giant. holes in the I disk of many galaxies. which can be produced," It is important to understand whether these clouds are formed by GFs, or represent external gas accreting on the disk \citep{safra08}; $iii$ ) the presence of giant holes in the H disk of many galaxies, which can be produced" "1300 is still controversial (Fynboetal.2005);; the simulations of three body interactions are challenging, and yet, become feasible task in near future thanks to the improved computer resources (seee.g.,Kurokawa&Kato2005,andtherefer-ences there)..","C is still controversial \citep{fyn05}; the simulations of three body interactions are challenging, and yet, become feasible task in near future thanks to the improved computer resources \citep[see e.g., ][and the references there]{kur05}." " In the next section, we elaborate the input physics adopted in the stellar evolution program."," In the next section, we elaborate the input physics adopted in the stellar evolution program." " In §3, we present the result of computations of evolution of low mass Z=0 model stars with updated input physics, and discuss the model characteristics and their dependences on the input physics including the resonant and non-resonant reaction rates of 3 o reactions."," In 3, we present the result of computations of evolution of low mass $Z=0$ model stars with updated input physics, and discuss the model characteristics and their dependences on the input physics including the resonant and non-resonant reaction rates of 3 $\alpha$ reactions." " In section 4, comparisons with other works with the different input physics taken into account, and, in 85, we summarize conclusions."," In section 4, comparisons with other works with the different input physics taken into account, and, in 5, we summarize conclusions." " The original program to compute stellar evolution was constructed by Iben(1965) and has been modified periodically (e.g.,seeIben1975;etal. 1992)."," The original program to compute stellar evolution was constructed by \citet{ibe65} and has been modified periodically \citep[e.g., see][]{ibe75,ibe92}." ". The size of each mass shell and the time step are regulated, respectively, by the gradients with respect to space and time of structure and composition variables."," The size of each mass shell and the time step are regulated, respectively, by the gradients with respect to space and time of structure and composition variables." " Typically, 200-300 mesh points are required for main sequence models and 700-800 for core helium-burning models with hydrogen-burning shells."," Typically, 200-300 mesh points are required for main sequence models and 700-800 for core helium-burning models with hydrogen-burning shells." " The number of equilibrium models required to follow evolution from the zero-age main sequence to the end of RGB or AGB phase varies from 5000 and 30000, with the exact number depending on initial mass."," The number of equilibrium models required to follow evolution from the zero-age main sequence to the end of RGB or AGB phase varies from 5000 and 30000, with the exact number depending on initial mass." The stellar structure equations are typically satisfied to better than one part in 10°., The stellar structure equations are typically satisfied to better than one part in $10^{5}$. " In the program, the radiative opacity is obtained by interpolation in OPAL tables (Iglesias&Rogers and in tables by Alexander&Fergu-son(1994,hereinafter,AF94tables) and the conductive opacity is from Itohetal. (1983). "," In the program, the radiative opacity is obtained by interpolation in OPAL tables \citep{igl96} and in tables by \citet[][ hereinafter, AF94 tables]{ale94} and the conductive opacity is from \citet{ito83}. ." "The equation of state involves fits by al.(1992) to work by Abe(1959),, BowersSalpeter (1960),, Slatteryetal. (1980),, etal. (1982),, Iyetomi&Ichimaru (1982),, Hansen (1973),, Hansen&Mazighi (1978),, Cohen&Kef-fer (1955),, and Carr(1961)."," The equation of state involves fits by \cite{ibe92} to work by \cite{abe59}, \cite{bow60}, \cite{sla80}, \cite{sla82}, \cite{iye82}, \cite{han73}, \cite{han78}, \cite{coh55}, and \cite{car61}." ". Neutrino energy-loss rates are from Itohetal.(1996,inthefollowing196) for plasma, photo, pair and bremsstrahlung processes."," Neutrino energy-loss rates are from \citet[][ in the following I96]{ito96} for plasma, photo, pair and bremsstrahlung processes." " In order to compare with other works, we make use of two sets of nuclear reaction rates: those given by Caughlan&Fowler(1988,inthefollowingCF88) and those given in the latest NACRE compilation (Anguloetal.1999).."," In order to compare with other works, we make use of two sets of nuclear reaction rates: those given by \citet[][ in the following CF88]{cau88} and those given in the latest NACRE compilation \citep{ang99}." " Nuclear screening factors for weak and strong screening are also taken into consideration using standard prescriptions (see,e.g.,Bohm-Vitense1958), but only weak screening is dominant in the actual computational range in this work."," Nuclear screening factors for weak and strong screening are also taken into consideration using standard prescriptions \citep[see, e.g.,][]{bohm58}, but only weak screening is dominant in the actual computational range in this work." " Nine nuclear species are considered: HH, ?HHe, HHe, 12300, 4NN, 1600. 1500, ?NNe, and ?MMg."," Nine nuclear species are considered: H, He, He, C, N, O, O, Ne, and Mg." " Abundances of these isotopes are determined by 16 nuclear reactions which include proton, electron, and alpha captures."," Abundances of these isotopes are determined by 16 nuclear reactions which include proton, electron, and alpha captures." " In regions of high temperature and high density which are not covered by OPAL tables, we use the analytical radiative opacities from the fits by Iben(1975) to Cox&Stewart(1970a,b) ones."," In regions of high temperature and high density which are not covered by OPAL tables, we use the analytical radiative opacities from the fits by \cite{ibe75} to \cite{cox70a,cox70b} ones." " At table boundaries, no interpolation is made between table values and analytical values."," At table boundaries, no interpolation is made between table values and analytical values." " Hence, jumps in the radiative opacity occur at table boundaries, but jumps are normally smaller than a factor of 2 and do not seriously affect model convergence, primarily because, in regions not covered by the tables, the overall opacity is dominated by electron conductivity."," Hence, jumps in the radiative opacity occur at table boundaries, but jumps are normally smaller than a factor of 2 and do not seriously affect model convergence, primarily because, in regions not covered by the tables, the overall opacity is dominated by electron conductivity." " At low temperature and low density, interpolation between OPAL and AF94 tables is accomplished by setting κ.=κοραι,(1—0)+kar O, where O=sin?(π/2)(Τ—T1)/(T5Τι) for the temperature T' between Τι=8000 K and Το=10000 K, and kKopay and ΚΑΕ are OPAL and AF94 opacities, respectively."," At low temperature and low density, interpolation between OPAL and AF94 tables is accomplished by setting $\kappa=\kappa_{\rm OPAL}\ (1-\Theta)+\kappa_{\rm AF}\ \Theta$ , where $\Theta=\sin^2{(\pi/2)(T-T_1)/(T_2-T_1)}$ for the temperature $T$ between $T_1=8000$ K and $T_2=10000$ K, and $\kappa_{\rm OPAL}$ and $\kappa_{\rm AF}$ are OPAL and AF94 opacities, respectively." " In surface layers of all modelsdiscussed here, AF94 tables provide opacities for all densities and temperatures encountered."," In surface layers of all modelsdiscussed here, AF94 tables provide opacities for all densities and temperatures encountered." " In regions of overlap, OPAL and AF94 opacities agree rather well, so switching from one table to the other introduces little uncertainty."," In regions of overlap, OPAL and AF94 opacities agree rather well, so switching from one table to the other introduces little uncertainty." " Although the quantum correction to the conductivity at low temperatures has been calculated (Mitakeetal. 1984),, it is now believed that the approximation employed is not appropriate at the temperatures considered."," Although the quantum correction to the conductivity at low temperatures has been calculated \citep{mit84}, it is now believed that the approximation employed is not appropriate at the temperatures considered." " Therefore, we use the analytic fits devised by I83 for the conductive opacity at low temperature; the liquid metal phase for various elemental compositions as well as strong degeneracy are taken into consideration."," Therefore, we use the analytic fits devised by I83 for the conductive opacity at low temperature; the liquid metal phase for various elemental compositions as well as strong degeneracy are taken into consideration." " Strong degeneracy prevails if T« ΤΕ, whereTp(K)= 1), pg is the density in units of 10° g cm-?, and"," Strong degeneracy prevails if $T \ll T_{\rm F}$ , where$T_{\rm F}(K) = 5.930 \times 10^{9}\ ((1+1.018(\rho_{6}/\mu_e)^{2/3} )^{1/2} -1 )$ , $\rho_{6}$ is the density in units of $10^{6}$ g $^{-3}$ , and" with observations.,with observations. We have therefore used a coustaut intermediate value. LO cu? ee|. independent of temperate aud clensity.," We have therefore used a constant intermediate value, 10 $^2$ $^{-1}$, independent of temperature and density." Because the pluue is optically thin. varving the mass of the plume has the same (nearly liucar) effect on the modeled helt curves as varving the opacity.," Because the plume is optically thin, varying the mass of the plume has the same (nearly linear) effect on the modeled light curves as varying the opacity." " Ποσο, the impactor mass aud opacity do not chanee (to first order) the of our modeled πο curves. they merely scale the fluxes."," Hence, the impactor mass and opacity do not change (to first order) the of our modeled light curves, they merely scale the fluxes." To specify à nominal plume mass (Table 1)). we matched the peak of the modeled curve to the ftux of the wellobserved R impact(?).," To specify a nominal plume mass (Table \ref{tabpar}) ), we matched the peak of the modeled curve to the flux of the well-observed R impact." . Although we have relied on the R-immpact to calibrate the mass scaling factor for our models. most of our calculations used au L-fraement mass.," Although we have relied on the R-impact to calibrate the mass scaling factor for our models, most of our calculations used an L-fragment mass." " Our nominal plune contains a shell of mass at the highest velocity. aud the uecessity for this ~vaneuarc’ of mass is discussed in paper 1. Πωπονο, we have also calculated svuthetic helt curves for a plume wherein the vanguard is claninated. and a nou-vauguud light curve is shown in rofsseciuruvle.."," Our nominal plume contains a shell of mass at the highest velocity, and the necessity for this `vanguard' of mass is discussed in paper I. However, we have also calculated synthetic light curves for a plume wherein the vanguard is eliminated, and a `non-vanguard' light curve is shown in \\ref{ssecmrnvlc}." We adopted an observed temperature profile for the jovian atmosphere derived frou Vovager IRIS measurements(?).. supplemented by Galileo probe results at the exeatest heights.," We adopted an observed temperature profile for the jovian atmosphere derived from Voyager IRIS measurements, supplemented by Galileo probe results at the greatest heights." " Since this eimipirical atusosphere is not im gray radiative οκπα, coupling it to ZEUS introduces unaccounted sources aud sis of energy. but these siiall imbalances lave no significant effect on our results."," Since this empirical atmosphere is not in gray radiative equilibrium, coupling it to ZEUS introduces unaccounted sources and sinks of energy, but these small imbalances have no significant effect on our results." Tow should we couple the plume from the expaudiug fireball iuto our splasliback model?, How should we couple the plume from the expanding fireball into our splashback model? As the fireball expands to ereater Leights. if encouuters decreased atmosplierie pressure. and its internal pressure also decreases ereatly.," As the fireball expands to greater heights, it encounters decreased atmospheric pressure, and its internal pressure also decreases greatly." Above some ransition height. its motion becomes controlled. by ballistics rather than lvdrodvuamics.," Above some transition height, its motion becomes controlled by ballistics rather than hydrodynamics." Based ou the results of?.. we infer this to occur at 2~LOO kin above the 1) bar level.," Based on the results of, we infer this to occur at $z\sim400$ km above the $1-$ bar level." Re-cutry of the plume will shock the jovian atmosphere even or ;22LOO kin. but these shocks at very great height will produce negligible IR cussion. and will not deaccelerate he infalling pluie siguificautly.," Re-entry of the plume will shock the jovian atmosphere even for $z>>400$ km, but these shocks at very great height will produce negligible IR emission, and will not deaccelerate the infalling plume significantly." Accordingly. we add the infalling plume mass aud momentum fluxes to our model in the aver LOO kin above the 1. bar level. interpolating these fluxes from the phuue model at cach ZEUS r value aud time step.," Accordingly, we add the infalling plume mass and momentum fluxes to our model in the layer $400$ km above the $1-$ bar level, interpolating these fluxes from the plume model at each ZEUS $r$ value and time step." The intalling plime is believed to be cold (ZM95). so we have adopted an initial plume temperature of 100 I. this being equal to the upper atmospheric boundary temperature in οταν radiative equilibrium. (," The infalling plume is believed to be cold (ZM95), so we have adopted an initial plume temperature of 100 K, this being equal to the upper atmospheric boundary temperature in gray radiative equilibrium. (" Our results are not seusitive to the initial plume temperature.),Our results are not sensitive to the initial plume temperature.) The ZEUS computational boundaries at maximum z aud were configured to be trausuiüttiug., The ZEUS computational boundaries at maximum $z$ and $r$ were configured to be transmitting. The lowest-2 surface at the greatest atinosplierie pressure (5 bars) was specified as reflecting. although splasliback etfects do not penetrate even close to this depth.," The $z$ surface at the greatest atmospheric pressure (5 bars) was specified as reflecting, although splashback effects do not penetrate even close to this depth." We experimented with a variety of erid spacines iu the model. in order to determine a grid coufieuration which resolves the splashiback shocks. while remaining computationally tractable.," We experimented with a variety of grid spacings in the model, in order to determine a grid configuration which resolves the splashback shocks, while remaining computationally tractable." Our adopted eid uses 20 lavers of 10 kin thickness in the region below 200 kin. 100 lavers of 1 kan thickness from 200 to 600 kan (where the splasliback effects ave most promincut). aud an additional LO lavers of 10 kin thickness above 600 Iau.," Our adopted grid uses 20 layers of 10 km thickness in the region below 200 km, 100 layers of 4 km thickness from 200 to 600 km (where the splashback effects are most prominent), and an additional 40 layers of 10 km thickness above 600 km." Our radial eid spacing was 75 kin. extending from +=0 to Ξ12000 kin in 160 zones.," Our radial grid spacing was $75$ km, extending from $r=0$ to $r=12000$ km in 160 zones." We verified that finer grid resolution or ereater extent will not chanee our results significantly., We verified that finer grid resolution or greater extent will not change our results significantly. Because the plume is injected iuto the code at +=LOO kim. the layers overbviug this height participate only minimally by. for example. οποιο matter which rebounds upward.," Because the plume is injected into the code at $z=400$ km, the layers overlying this height participate only minimally by, for example, `catching' matter which rebounds upward." Accordingly. we do uot illustrate these lavers in our Figures.," Accordingly, we do not illustrate these layers in our Figures." Note also that the matter which they contain is counted as plume matter by the advection scheme described iu rofseccp.., Note also that the matter which they contain is counted as plume matter by the advection scheme described in \\ref{seccp}. They initially contain jovian atmosphere. but this accounting error has a negligible effect. since the cohuun density above LOO Iau is verv siiall.," They initially contain jovian atmosphere, but this accounting error has a negligible effect, since the column density above $400$ km is very small." Since our conrputations attempt specifically to isolate phenomena related to the splashback. we ignore plenomena related to the r=0 boundary. aud we couple to ZEUS only pluue material ejected on paths at or above the horizontal.," Since our computations attempt specifically to isolate phenomena related to the splashback, we ignore phenomena related to the $r=0$ boundary, and we couple to ZEUS only plume material ejected on paths at or above the horizontal." We also ignore the channel created by the eutzy of the fragment ito the atmosphere., We also ignore the channel created by the entry of the fragment into the atmosphere. Some possible effects of this chauncl are discussed ii rofssecimrop.., Some possible effects of this channel are discussed in \\ref{ssecmrop}. The structure and evolution of splasliback shocks las been discussed by., The structure and evolution of splashback shocks has been discussed by. Z96.. Our results are ecnerally consistent with Z96'« conclusions. but provide additional insights.," Our results are generally consistent with Z96's conclusions, but provide additional insights." Figure 3. illustrates our calculations of the shock development aud evolution at tines extending up to the peak of the main event at TOO seconds post-inipact., Figure \ref{figtempvpre} illustrates our calculations of the shock development and evolution at times extending up to the peak of the main event at 700 seconds post-impact. Each panel is labeled by time and gives a false-color represeutatiou of the log of temperature. aud also includes overlaid velocity vectors.," Each panel is labeled by time and gives a false-color representation of the log of temperature, and also includes overlaid velocity vectors." At 100 sec. most ofthe iufalling mass has not vet hit the shock aud is still cold. producing the dark region filline the upper left corner.," At 100 sec, most of the infalling mass has not yet hit the shock and is still cold, producing the dark region filling the upper left corner." But the border of this region is bright. denoting a shock.," But the border of this region is bright, denoting a shock." The shock is hottest at the right edee., The shock is hottest at the right edge. At this carly time. the infalhug pliame mass cannot exhibit large + velocities. because huge :-volocitv material requires longer times for re-cutry.," At this early time, the infalling plume mass cannot exhibit large $z$ velocities, because large $z$ -velocity material requires longer times for re-entry." But large r velocities are present. expecially in the vauguard.," But large $r$ velocities are present, especially in the vanguard." Since this shock comes frou the highest velocity material. it is hot. aud is most casily seen in the ascending brauch of light. curves at the shortest wavelenethsων or in strong spectral bands such as inethane(?).. rather than the long thermal waveleugths(??).," Since this shock comes from the highest velocity material, it is hot, and is most easily seen in the ascending branch of light curves at the shortest wavelengths, or in strong spectral bands such as methane, rather than the long thermal wavelengths." . In our svuthetic light curves it produces the ‘third precursors’ noted by? aud other observers., In our synthetic light curves it produces the `third precursors' noted by and other observers. IST imaging of plumes at the lib shows cunission attributed to an upward-propagating shock near this time., HST imaging of plumes at the limb shows emission attributed to an upward-propagating shock near this time. Upward-propagating shocks from the carly plume expansion are deliberately omitted from our model. but the cussion seen by? and the racially-propagating shock modeled in Figure 9. are parts of the same coutiuuous process of plume expausion aud splashback.," Upward-propagating shocks from the early plume expansion are deliberately omitted from our model, but the emission seen by and the radially-propagating shock modeled in Figure \ref{figtempvpre} are parts of the same continuous process of plume expansion and splashback." At 300 seconds οποιο] pluie material has fallen to drive a shock down to 200 kin above the E. bar level (uei &=1500 kan}. and the lateral shock has now expanded to r=LOOO Xin.," At 300 seconds enough plume material has fallen to drive a shock down to 200 km above the $1-$ bar level (near $r=1500$ km), and the lateral shock has now expanded to $r=4000$ km." Additional infalline plume material now encounters previoush-fallen plume. and a second shock begins to propagate back iuto the iufall. as predicted by 2960," Additional infalling plume material now encounters previously-fallen plume, and a second shock begins to propagate back into the infall, as predicted by Z96." ", This is becoming evident as a warm region above the hottest shock iu the kc—L0003000 kin interval.", This is becoming evident as a warm region above the hottest shock in the $r=1000-3000$ km interval. Note also that for r<1000 kin the jovian atinosphere has temporarily rebounded from the pressure of the initial plume iufall., Note also that for $r<1000$ km the jovian atmosphere has temporarily rebounded from the pressure of the initial plume infall. This rebound is the first siew, This rebound is the first sign that the large amount of substructure detected in the external regions of the clusters (r> 1200) is not spurious.,that the large amount of substructure detected in the external regions of the clusters $r>r_{200}$ ) is not spurious. Figure 7 shows the fraction of substructure detected in the MC-simulated clusters without substructure as function of cluster radius., Figure \ref{f6} shows the fraction of substructure detected in the MC-simulated clusters without substructure as function of cluster radius. The substructure was detected by the DS test as in the real clusters using a global value of 6299 or individual values for the different clusters ójoo (see section 4).," The substructure was detected by the DS test as in the real clusters using a global value of $\delta_{g,99}$ or individual values for the different clusters $\delta_{i,99}$ (see section 4)." Figure 7 shows that the fraction of galaxies in substructure detected at all radial distances is between 1 and 2 per cent., Figure \ref{f6} shows that the fraction of galaxies in substructure detected at all radial distances is between 1 and 2 per cent. There is no excess of galaxies detected in substructure in the outer regions of the cluster., There is no excess of galaxies detected in substructure in the outer regions of the cluster. This rules out the possibility that the substructure detected in the outermost regions of the clusters might be dominated by spurious detections., This rules out the possibility that the substructure detected in the outermost regions of the clusters might be dominated by spurious detections. " One of our richest clusters is Abell 85, located at z=0.055 with 273 confirmed members brighter than m,=17.88."," One of our richest clusters is Abell 85, located at z=0.055 with 273 confirmed members brighter than $_{r}$ =17.88." The substructure of Abell 85 has been previously studied in the literature (Ramella et al., The substructure of Abell 85 has been previously studied in the literature (Ramella et al. 2007; Bravo-Alfaro et al., 2007; Bravo-Alfaro et al. " 2009), and there are also available X-ray data for this cluster (Durret et al."," 2009), and there are also available X-ray data for this cluster (Durret et al." " 2003), making this cluster ideal for comparing the substructure obtained by us with other studies."," 2003), making this cluster ideal for comparing the substructure obtained by us with other studies." Bravo-Alfaro et al. (, Bravo-Alfaro et al. ( 2009) used the DS test to detect the substructure in Abell 85 and found five prominent regions of substructure.,2009) used the DS test to detect the substructure in Abell 85 and found five prominent regions of substructure. The first was located near the centre of the cluster and was identified as C2., The first was located near the centre of the cluster and was identified as C2. " Another substructure was found to the south called SB, and two more appear in the south-east region of Abell 85: one along the X-ray filament detected by Durret et al. ("," Another substructure was found to the south called SB, and two more appear in the south-east region of Abell 85: one along the X-ray filament detected by Durret et al. (" "2003) was labelled F, and the other along an extension of the latter called SE.","2003) was labelled F, and the other along an extension of the latter called SE." They also detected a final substructure to the west of the cluster (W)., They also detected a final substructure to the west of the cluster (W). Ramella et al. (, Ramella et al. ( "2007), using a","2007), using a" The XRT on board of detected. during the last vear. numerous X-rav [lares in GRB alterelows (Burrows ct al.,"The XRT on board of detected, during the last year, numerous X-ray flares in GRB afterglows (Burrows et al." 2005: Nousek et al., 2005; Nousek et al. 2006: Goad ct al., 2006; Goad et al. 2006: Romano οἱ al., 2006; Romano et al. 2006: Falcone et al., 2006; Falcone et al. 2006: O'Brien ct al., 2006; O'Brien et al. 2006)., 2006). These observations confirmed. earlier findings of BeppoSAX (Piro et al., These observations confirmed earlier findings of BeppoSAX (Piro et al. 1998. 2005: Galli Piro 2006: in't Zand et al.," 1998, 2005; Galli Piro 2006; in't Zand et al." 2004) ancl ASCAA (Yoshida et abl.," 2004) and ASCA (Yoshida et al.," 1999)., 1999). These Iares have been interpreted. as arising from late time activity of the central engine (Ixing ct al., These flares have been interpreted as arising from late time activity of the central engine (King et al. 2005: Perna et al., 2005; Perna et al. 2006 and Proga Zhang 2006) producing either internal shocks (Fan Wei 2005: Zhang ct al., 2006 and Proga Zhang 2006) producing either internal shocks (Fan Wei 2005; Zhang et al. 2006: Zou. Xu Dai 2006: Wu et al.," 2006; Zou, Xu Dai 2006; Wu et al." 2006) or internal magnetic dissipation (Fan. Zhang Proga 2005a).," 2006) or internal magnetic dissipation (Fan, Zhang Proga 2005a)." The Bare detected. in the afterglow of GRB 050502b peaks in the soft. N-ravs (Falcone ct al., The flare detected in the afterglow of GRB 050502b peaks in the soft X-rays (Falcone et al. 2006)., 2006). Llowever. the peak energy of most [lares is unknown (D. Zhang. 2006. private communication).," However, the peak energy of most flares is unknown (B. Zhang, 2006, private communication)." It is possible. and even likely. that a significant fraction of the energy or even most of it is emitted in the far-ultraviolet (EUN). banc.," It is possible, and even likely, that a significant fraction of the energy or even most of it is emitted in the far-ultraviolet (FUV) band." For example. in. the internal energy dissipation model the typical svnchrotron radiation frequency depends: sensitively on the physical xwameters (Pan Wei 2005: Zhang et al., For example in the internal energy dissipation model the typical synchrotron radiation frequency depends sensitively on the physical parameters (Fan Wei 2005; Zhang et al. 2006: Fan οἱ al., 2006; Fan et al. 2005a) and the svnchrotron self-absorption frequency is ~10Lz (Fan Wei 2005)., 2005a) and the synchrotron self-absorption frequency is $\sim{\rm 10^{15}~Hz}$ (Fan Wei 2005). Lt is possible. therefore. that he observed. X-ray. Hares are the high energy. tails of FUY lares.," It is possible, therefore, that the observed X-ray flares are the high energy tails of FUV flares." IH is also possible that there are FUY fares that have not been detected at all., It is also possible that there are FUV flares that have not been detected at all. Further support for this idea arises rom the possible interpretation of the optical Dare seen in GRB 050904 (Boecr et al., Further support for this idea arises from the possible interpretation of the optical flare seen in GRB 050904 (Böeer et al. 2006) as a late time activity of he inner engine (Wei. Yan Fan 2006).," 2006) as a late time activity of the inner engine (Wei, Yan Fan 2006)." Even i£ FUY [lares exist they won't be observed as the IFUV photons are absorbed by the neutral hydrogen in the CRB host galaxy as well as in our Galaxy., Even if FUV flares exist they won't be observed as the FUV photons are absorbed by the neutral hydrogen in the GRB host galaxy as well as in our Galaxy. We show here that an underlving PUY flare will be upscattered. and. produce (after. inverse. Compton) a sub-CGeV. flare that may. be detected by the upcoming (GLAST: see httpi//elast.gsfe.nasa.gov/) satellite., We show here that an underlying FUV flare will be upscattered and produce (after inverse Compton) a sub-GeV flare that may be detected by the upcoming (GLAST; see http://glast.gsfc.nasa.gov/) satellite. Phough (sub-)CeV. llashes in. GRB afterglows could arise in other scenarios (o.g.. Mésszárros Rees 1994: Plaga 1995: Ciranot Guetta 2003: Dermer Atovan 2004: Beleborodoy 2005: Fan. Zhang Wei 2005b). the high energy. photon Lashes," Though (sub-)GeV flashes in GRB afterglows could arise in other scenarios (e.g., Mésszárros Rees 1994; Plaga 1995; Granot Guetta 2003; Dermer Atoyan 2004; Beleborodov 2005; Fan, Zhang Wei 2005b), the high energy photon flashes" function out to ;20.7.,function out to $z\simeq0.7$. The Sereudipitous Higbh-redshift Archival ROSAT Cluster (SITARC) survey (ΠριAwww.αποσαshare) is a project to ideutify >100 X-ray clusters at redshifts ereater than ο2=0.3., The Serendipitous High-redshift Archival ROSAT Cluster (SHARC) survey (http://www.astro.nwu.edu/sharc) is a project to identify $\gtrsim 100$ X-ray clusters at redshifts greater than $z=0.3$. Althoueh similar in aims aud approach. it is much larger than the citepr95.. citecas97 and citefje96.— survevs: which complete it will cover =200 square degrees.," Although similar in aims and approach, it is much larger than the \\cite{pr95}, \\cite{cas97} and \\cite{fjc96} surveys: when complete it will cover $\gtrsim 200$ square degrees." The SIUARC survey N-rav data pipeline is fully automated auc is based on the reduction package aud a wavelet transform sourcedetection aleoritlain., The SHARC survey X-ray data pipeline is fully automated and is based on the \\cite{sls94} reduction package and a wavelet transform source detection algorithm. The pipeline has beeu thoroughly aud has already been citeakr97 to 530 hieli ealactic latitude PSPC poiutiues., The pipeline has been thoroughly \\cite{rcn97} and has already been \\cite{akr97} to 530 high galactic latitude PSPC pointings. A further ~500 PSPC and &200 TIRT poiutines will be added to the survey in 1997., A further $\simeq500$ PSPC and $\simeq200$ HRI pointings will be added to the survey in 1997. Optical follow-up is nucderway at the ARC 3.512. ESO 3.61 aud AAT 3.512. telescopes.," Optical follow-up is underway at the ARC 3.5m, ESO 3.6m and AAT 3.9m telescopes." The primary research goal of the SUARC survey is the robust quautification of N-rav cluster evolution., The primary research goal of the SHARC survey is the robust quantification of X-ray cluster evolution. Reports of rapid negative evolution iu the X-ray cluster luminosity function (NCLF) seen iu the, Reports of rapid negative evolution in the X-ray cluster luminosity function (XCLF) seen in the The classification of the source is unclear.,The classification of the source is unclear. The source might contain old radio plasma that originated in the AGN to the west., The source might contain old radio plasma that originated in the AGN to the west. " In this case, the source could be classified as a radio phoenix or AGN relic."," In this case, the source could be classified as a radio phoenix or AGN relic." VLSS J1515.1+0424 is located in the cluster (z0.0972;?) to the east of the cluster center., VLSS J1515.1+0424 is located in the cluster \citep[$z=0.0972$; ][]{1999ApJS..125...35S} to the east of the cluster center. The source has a largest extent of 310 kpc (see Fig., The source has a largest extent of 310 kpc (see Fig. " 10 top left panel), and has a complex morphology."," \ref{fig:gmrt325_s25} top left panel), and has a complex morphology." Only the brighter parts of the source are seen in the VLA 1.4 GHz C-array image (Fig., Only the brighter parts of the source are seen in the VLA 1.4 GHz C-array image (Fig. 10 top right panel)., \ref{fig:gmrt325_s25} top right panel). No polarized flux is detected from the source., No polarized flux is detected from the source. " We set an an upper limit on the polarization fraction of for the source, again requiring a SNR of 5 for a detection."," We set an an upper limit on the polarization fraction of for the source, again requiring a SNR of 5 for a detection." " An optical V, R, and I color image of the cluster with 610 MHz contours overlaid does not reveal an obvious optical counterpart for the source."," An optical V, R, and I color image of the cluster with 610 MHz contours overlaid does not reveal an obvious optical counterpart for the source." " The spectral index map between 325, 610, and 1425 MHz, is shown in Fig."," The spectral index map between 325, 610, and 1425 MHz, is shown in Fig." 10 (bottom left panel)., \ref{fig:gmrt325_s25} (bottom left panel). No systematic spectral index gradients are seen across the source., No systematic spectral index gradients are seen across the source. " A region with a flat spectral index (@> —0.5) is located under the southern “arm” of the source at RA 15 15"" 08.65, Dec 404?08""."," A region with a flat spectral index $\alpha > -0.5$ ) is located under the southern “arm” of the source at RA $^\mathrm{h}$ $^\mathrm{m}$ $^\mathrm{s}$, Dec $+$." . This part is associated with the galaxy in front of the cluster from SDSS DR7) (see Fig., This part is associated with the galaxy in front of the cluster from SDSS DR7) (see Fig. 10 bottom right panel)., \ref{fig:gmrt325_s25} bottom right panel). The spectral index of the relic is steep with an average value of about —1.7 between 1425 and 325 MHz., The spectral index of the relic is steep with an average value of about $-1.7$ between 1425 and 325 MHz. The complex morphology of the radio source suggests that the source can be classified as a radio phoenix., The complex morphology of the radio source suggests that the source can be classified as a radio phoenix. The steep curved radio spectrum is consistent with this interpretation., The steep curved radio spectrum is consistent with this interpretation. " If the source is indeed a radio phoenix, the radio plasma should have originated in a galaxy that has gone through phases of AGN activity."," If the source is indeed a radio phoenix, the radio plasma should have originated in a galaxy that has gone through phases of AGN activity." A candidate is the elliptical galaxy (z=0.095032;?)., A candidate is the elliptical galaxy \citep[$z=0.095032$; ][]{1998ApJS..115....1S}. This galaxy is currently active and located close to the eastern end of the southern “arm”., This galaxy is currently active and located close to the eastern end of the southern “arm”. " However, there are several other elliptical galaxies around, although at the moment they are not radio-loud."," However, there are several other elliptical galaxies around, although at the moment they are not radio-loud." " A ROSAT image (see?) of the cluster shows a substructure to the east of the main cluster, which implies that the cluster is presently undergoing a merger."," A ROSAT image \citep[see][]{2009A&A...508...75V} of the cluster shows a substructure to the east of the main cluster, which implies that the cluster is presently undergoing a merger." " The velocity dispersion, c, of the galaxies in the cluster is 857 km s! (?).."," The velocity dispersion, $\sigma$ , of the galaxies in the cluster is 857 km $^{-1}$ \citep{2008MNRAS.389.1074S}." The bolometric X-ray luminosity is 1.914x10* erg s7!., The bolometric X-ray luminosity is $1.914 \times 10^{44}$ erg $^{-1}$. On the basis of the Lx—o relation (X-ray luminosity versus velocity dispersion) from ? we predict a velocity dispersion of 765+40 km s! given the X-ray luminosity., On the basis of the $L_{\rm{X}}-\sigma$ relation (X-ray luminosity versus velocity dispersion) from \citeauthor{2008MNRAS.389.1074S} we predict a velocity dispersion of $765\pm40$ km $^{-1}$ given the X-ray luminosity. " This islower than the observed value, which is not inconsistent with the cluster having undergone a"," This islower than the observed value, which is not inconsistent with the cluster having undergone a" dynamically measured 1115 ancl stellar velocity dispersions.,dynamically measured BHs and stellar velocity dispersions. In acidition. we include galaxies studied by ?2.. who measured the central BLE mass via masers.," In addition, we include galaxies studied by \citet{Greene}, who measured the central BH mass via masers." We refer to the sum of these samples as our dvnamicalls-based. sample., We refer to the sum of these samples as our dynamically-based sample. We consider a second set of galaxies with DlIs estimated via reverberation mapping (?).., We consider a second set of galaxies with BHs estimated via reverberation mapping \citep{Woo}. We select galaxies with classical bulges when possible., We select galaxies with classical bulges when possible. This is clone because ? observe that Alpy does not correlate with the properties of galaxyclisks or pseudobulges. and ? fine) smaller intrinsic scatter. of DII. mass-host galaxy property relations when excluding galaxies with pseudobulges.," This is done because \citet{Kormendy} observe that $\Mbh$ does not correlate with the properties of galaxydisks or pseudobulges, and \citet{Sani} find smaller intrinsic scatter of BH mass-host galaxy property relations when excluding galaxies with pseudobulges." According to bulge classification of the ealaxies included. in ?.. whose classification relies on the galaxy morphology ancl stellar. population property. we select the only galaxy. (NI1194) that has a classical bulge with nuclear luminosity at 10.717Liu. and we also select the galaxy (UGC 3789). which has an unclassified: bulge with nuclear luminosity at 10ULSDLg.," According to bulge classification of the galaxies included in \citet{Greene}, whose classification relies on the galaxy morphology and stellar population property, we select the only galaxy (N1194) that has a classical bulge with nuclear luminosity at $10^{-2.17}~L_{Edd}$, and we also select the galaxy (UGC 3789), which has an unclassified bulge with nuclear luminosity at $ 10^{-0.82}~L_{Edd}$." For the other cdvnamically-based galaxies. we select classical bulge galaxies according to (2).. who classify galaxies with classical bulges by selecting galaxies which have Sérrsie indices higher than two.," For the other dynamically-based galaxies, we select classical bulge galaxies according to \citep{Sani}, who classify galaxies with classical bulges by selecting galaxies which have Sérrsic indices higher than two." We include all the reverberation-based. galaxies as it is dillieult to classify the morphology of galaxies with AG, We include all the reverberation-based galaxies as it is difficult to classify the morphology of galaxies with AGN. Next. we estimate the bolometric nuclear luminosity.," Next, we estimate the bolometric nuclear luminosity." First we consider the sample of ?.. who estimate the nuclear bolometric Luminosity for their sample using OHI]. which is strong ancl ubiquitous in obseurecl megamaser systems (??)..," First we consider the sample of \citet{Greene}, who estimate the nuclear bolometric luminosity for their sample using O[III], which is strong and ubiquitous in obscured megamaser systems \citep{Kauffmann03, Zakamska03}. ." In this approach. OLI] luminosity is converted. to Abosug. where Mozoo is the magnitude atA. and then to bolometric Luminosity following the Also LOLLY (?). and AMosoo bolometric correction (7). for unobsceured: quasars.," In this approach, O[III] luminosity is converted to $M_{2500}$, where $M_{2500}$ is the magnitude at, and then to bolometric luminosity following the $M_{2500}-L$ [OIII] \citep{Reyes08} and $M_{2500}$ bolometric correction \citep{Richards06} for unobscured quasars." The total uncertainty. introduced. is 0.5 dex. (?).., The total uncertainty introduced is $\sim 0.5$ dex \citep{Liu09}. This is smaller than our smallest bin size (one dex) when we compare the scatter in the Adpy—0 relation with respect to nuclei luminosity., This is smaller than our smallest bin size (one dex) when we compare the scatter in the $\Mbh-\sigma$ relation with respect to nuclei luminosity. 1n order to obtain the nuclear luminosity for the ? and 2? samples. we select. galaxies with nuclear luminosity measured in the soft X-Ray band by the X-rav observatory (??777?)..," In order to obtain the nuclear luminosity for the \citet{Gultekin} and \citet{Graham} samples, we select galaxies with nuclear luminosity measured in the soft X-Ray band by the X-ray observatory \citep{Pellegrini10, Pellegrini05, Zhang, Gonz}." At the lowest luminosity in our sample (2«107xergs Ly the central X-ray source has luminosity comparable to the N-rav. binary population(~107Iores 13 (2).," At the lowest luminosity in our sample $\sim2\times10^{38}{\rm~erg~s^{-1}}$ ), the central X-ray source has luminosity comparable to the X-ray binary $\sim10^{38-40}{\rm~erg~s^{-1}}$ ) \citep{King01}." " ""Phe use of data is therefore essential because it has sullicient angular resolution to isolate galactic nuclear from bright X-ray binaries.", The use of data is therefore essential because it has sufficient angular resolution to isolate galactic nuclear from bright X-ray binaries. For the reverberation-based. sample. we select those with known X-rav luminosity in the NAASA/IPAC Extraglactic Database," For the reverberation-based sample, we select those with known X-ray luminosity in the NASA/IPAC Extraglactic Database." Jocause these galaxies have nuclear luminosityονergs. 1) much higher than the X-ray binaries. the X-ray luminosity of the galaxy. is dominated by the AGN.," Because these galaxies have nuclear $\sim2\times10^{43}{\rm~erg~s^{-1}}$ ) much higher than the X-ray binaries, the X-ray luminosity of the galaxy is dominated by the AGN." ‘Thus. we associate the N-rav. luminosity of the galaxy. with that of the AGN.," Thus, we associate the X-ray luminosity of the galaxy with that of the AGN." Most. of the N-rav. data are. obtained from NAIAI-Newton (?22?).. except for Mrk202 and LC 120. which are obtained. [rom ASCA (7). and. BeppoSAX (7?) separately (detailed. properties and references see Table 2).," Most of the X-ray data are obtained from XMM-Newton \citep{Bianchi09, Markowitz09, Nandra07}, except for Mrk202 and IC 120, which are obtained from ASCA \citep{Ueda05} and BeppoSAX \citep{Verrecchia} separately (detailed properties and references see Table 2)." " 1n order to obtain the X-ray. luminosity from N-rav Huxes. we estimate distances assuming 44)=73kms!Mpe. +. Q,,=027. O4=0.73 for z0.01 galaxies. with redshift measurements obtained from NED. which compiled multiple consistent redshilt measurements for each. galaxy."," In order to obtain the X-ray luminosity from X-ray fluxes, we estimate distances assuming $H_0 = 73\rm~km~s^{-1}Mpc^{-1}$ , $\Omega_m = 0.27$, $\Omega_\Lambda = 0.73$ for $z>0.01$ galaxies, with redshift measurements obtained from NED, which compiled multiple consistent redshift measurements for each galaxy." For galaxies. we obtain distances from the Extragalactic Distance Database. which gives updated best distances for galaxies within 3000kms+ (?)..," For galaxies, we obtain distances from the Extragalactic Distance Database, which gives updated best distances for galaxies within $3000 \rm~km~s^{-1}$ \citep{Tully09}." Yo convert the X-ray [uminositv to bolometric luminosity. we first convert the X-ray luminosity of cilferent bands in the literature to luminosity in the band 210keV assuming an energv index of lef. =constant) with an uncertainty factor of ~2 (Martin. Elvis. private communication).," To convert the X-ray luminosity to bolometric luminosity, we first convert the X-ray luminosity of different bands in the literature to luminosity in the band $2-10\,\rm{keV}$ assuming an energy index of $-1$ $\nu f_{\nu} = constant$ ) with an uncertainty factor of $\sim2$ (Martin Elvis, private communication)." Then. we convert the N-rav. luminosity to bolometric Luminosity by the bolometric correction for AGNs: Liufbx=15.8. with an uncertainty of ~0.3 dex (?)..," Then, we convert the X-ray luminosity to bolometric luminosity by the bolometric correction for AGNs: $L_{bol}/L_X = 15.8$, with an uncertainty of $\sim0.3$ dex \citep{Ho09}. ." " Therefore. the nuclear bolometric Luminosity is calculated where £5 and ££, represent the upper and lower bound of the observed. X-ray. banc."," Therefore, the nuclear bolometric luminosity is calculated where $E_2$ and $E_1$ represent the upper and lower bound of the observed X-ray band." We include the properties of the BLE and host spheroids for our cdvnamicallv-based. ancl reverberation-basecl sample in Table 1 and Table 2 separately., We include the properties of the BH and host spheroids for our dynamically-based and reverberation-based sample in Table 1 and Table 2 separately. In reality. the correction. factor. Loa4/Lx. depends on the nuclear luminositv: low luminosity XCGNs. tend to be. oX-rav-loucdl” (72)..," In reality the correction factor, $L_{bol}/L_X$, depends on the nuclear luminosity: low luminosity AGNs tend to be “X-ray-loud"" \citep{Ho99, Ho09}." . In. other words. the. lower X-ray nuclear luminosity corresponds to an even lower bolometric nuclear luminosity anc vice versa.," In other words, the lower X-ray nuclear luminosity corresponds to an even lower bolometric nuclear luminosity and vice versa." Note that this additional. complexity. does not. mix the order. of galaxies with respect to their nuclei luminosity., Note that this additional complexity does not mix the order of galaxies with respect to their nuclei luminosity. As we compare galactic properties of lower nuclear. Luminosity ealaxy to those of higher nuclear luminosity galaxies. without computing the exact. bolometric Luminosity. our conclusion is not allected by assuming a constant bolometric correction factor.," As we compare galactic properties of lower nuclear luminosity galaxy to those of higher nuclear luminosity galaxies, without computing the exact bolometric luminosity, our conclusion is not affected by assuming a constant bolometric correction factor." Because the bolometric correction factor only introduces an uncertainty of ~0.3 dex (2). the total uncertainty of the bolometric luminosity is less than the smallest bin width. one dex.," Because the bolometric correction factor only introduces an uncertainty of $\sim0.3$ dex \citep{Ho09}, the total uncertainty of the bolometric luminosity is less than the smallest bin width, one dex." Therefore. we expect our results o be largely. unallected by the uncertainties in. nuclear xometric Luminosity.," Therefore, we expect our results to be largely unaffected by the uncertainties in nuclear bolometric luminosity." In total. we have 38 galaxies with dvnamically measured DII mass and 17 galaxies with reverberation-mapping DII nis measurements in our sample.," In total, we have 38 galaxies with dynamically measured BH mass and 17 galaxies with reverberation-mapping BH mass measurements in our sample." For the cbvnamically-xsed sample. the range of the nuclear Luminosity is limited cause the nuclear. luminositw is. dillicult to measure or low nuclear luminosity galaxies and the BIL mass is cillicult to estimate dynamically for high nuclear luminosity galaxies.," For the dynamically-based sample, the range of the nuclear luminosity is limited because the nuclear luminosity is difficult to measure for low nuclear luminosity galaxies and the BH mass is difficult to estimate dynamically for high nuclear luminosity galaxies." The reverberation mapping measurements are normalized by setting a constant virial coefficient. so that the reverberation mapping-basecd ancl civnamicallv-based Alou0 relations agree., The reverberation mapping measurements are normalized by setting a constant virial coefficient so that the reverberation mapping-based and dynamically-based $\Mbh-\sigma$ relations agree. The assumption of a constant virial coefficient could potentially introduce a larger scatter for the reverberation-based. sample., The assumption of a constant virial coefficient could potentially introduce a larger scatter for the reverberation-based sample. In addition. the virial cocllicient may. depend. on the nuclear luminosity.," In addition, the virial coefficient may depend on the nuclear luminosity." H£ so. choosing a constant virial coefficient may introduce a DIL mass uncertainty that depends on the nuclearIuminositv.," If so, choosing a constant virial coefficient may introduce a BH mass uncertainty that depends on the nuclearluminosity." This could. affect our result., This could affect our result. In order to mitigate this potential bias. we do not rely heavily oncomparing galaxies across our two samples.," In order to mitigate this potential bias, we do not rely heavily oncomparing galaxies across our two samples." With AZpg. σ and nuclear luminosity in hand. we are now in a position to consider thescatter in the Alpy0 relation with respect to nuclear luminosity.," With $\Mbh$ , $\sigma$ and nuclear luminosity in hand, we are now in a position to consider thescatter in the $\Mbh-\sigma$ relation with respect to nuclear luminosity." In. order to, In order to appearing at ~GOkkmss +.,appearing at $\sim$ $^{-1}$. The feature at kkmss| is a sidelobe of 18.460-0.004., The feature at $^{-1}$ is a sidelobe of 18.460-0.004. " ""Vhese are a closely spaced. pair of sources. previously listed as one known site. but now distinguished as two sites."," These are a closely spaced pair of sources, previously listed as one known site, but now distinguished as two sites." 18.661|0.034 extends to the higher velocities., 18.661+0.034 extends to the higher velocities. 18.667|0.025 is mainly the features al 77kkmssο anc | and is associated with an Extended Green Object (7).., 18.667+0.025 is mainly the features at $^{-1}$ and $^{-1}$ and is associated with an Extended Green Object \citep{cyganowski09}. “These sources are a closely spaced pair of new detections., These sources are a closely spaced pair of new detections. The bright. peak feature at belongs to 18.735-0.227. but the 3 other peaks are 18.733-0.224.," The bright peak feature at $^{-1}$ belongs to 18.735-0.227, but the 3 other peaks are 18.733-0.224." 'Phis. new source was also recently detected by 2 associated with an Extended Green Object., This new source was also recently detected by \citet{cyganowski09} associated with an Extended Green Object. Επ new source was also recently detected by 2.. listed as L8.99-0.04.," This new source was also recently detected by \citet{ellingsen07}, listed as 18.99-0.04." Lt was seen ollset fron a GLIAIPSE source by 1.5 aremin and is unlikely to be physically associated., It was seen offset from a GLIMPSE source by 1.5 arcmin and is unlikely to be physically associated. his source does not include the feature seen at 25kkniss| which is a sidelobe of 19.365-0.030., This source does not include the feature seen at $^{-1}$ which is a sidelobe of 19.365-0.030. " Pwo sources separated by less than 4 aresec. are distinguished bv an ""n identifving the source with the more northerly declination (previously the southern. site was. instead identified with an ‘sw’ e.g. ον, but we adopt an n in accord with the Galactic centre region results of 7))."," Two sources separated by less than 4 arcsec, are distinguished by an `n' identifying the source with the more northerly declination (previously the southern site was instead identified with an `sw' e.g. \citealt{caswell09a}, but we adopt an `n' in accord with the Galactic centre region results of \citealt{caswell10mmb1}) )." The northern site contains the features at 18.5. 22 and 23kkniss+ the southern site. the features between 13 and ss," The northern site contains the features at 18.5, 22 and $^{-1}$ the southern site, the features between 13 and $^{-1}$." 19.486|0.151 comprises the other features at + and bevond to higher velocities.," 19.486+0.151 comprises the other features at $^{-1}$ , $^{-1}$ and beyond to higher velocities." " ""Vhis source consists of two main features. one at kkinss+ and one at +."," This source consists of two main features, one at $^{-1}$ and one at $^{-1}$." Phe ss feature hack been the strongest. feature. at 0.4 Jv. in the 1992 discovery spectrum (2)...," The $^{-1}$ feature had been the strongest feature, at 0.4 Jy, in the 1992 discovery spectrum \citep{caswell95d}." However this feature was a marginal detection in the survey cube data (2007 August)., However this feature was a marginal detection in the survey cube data (2007 August). Fortunately the weak feature. of 0.25 Jv at. 40kkmss in 1992 Uared to 1 Jw in the survey cube. allowing an ATCA position measurement in 2007 July (0.4 Jv. peak).," Fortunately the weak feature of 0.25 Jy at $^{-1}$ in 1992 flared to 1 Jy in the survey cube, allowing an ATCA position measurement in 2007 July (0.4 Jy peak)." The + feature rose to 0.5 Jv in an MX in March 2008. but was undetectable in an MX in March. 2000.," The $^{-1}$ feature rose to 0.5 Jy in an MX in March 2008, but was undetectable in an MX in March 2009." The 7 feature had a peak Lux density of 0.65 Jv in the AIX measurement of 2009 March (and is shown in Figure 1))., The $^{-1}$ feature had a peak flux density of 0.65 Jy in the MX measurement of 2009 March (and is shown in Figure \ref{spectra}) ). 777 ascribe this source to a far kinematic distance based on an absence of LEE self-absorption. whilst ? ascribe it to a near kinematic distance based on an absence of formaldehyde absorption.," \citet{kolpak03, anderson09a, roman09} ascribe this source to a far kinematic distance based on an absence of HI self-absorption, whilst \citet{downes80b} ascribe it to a near kinematic distance based on an absence of formaldehyde absorption." As identified by 2.. in addition to the main source 19.612-0.120 which has several [features between 49 and |. there is a narrow olfset source peaking at ss.7.," As identified by \citet{walsh98}, , in addition to the main source 19.612-0.120 which has several features between 49 and $^{-1}$, there is a narrow offset source peaking at $^{-1}$." " Both ? and 7. ascribe the associated region to a far kinematic distance based on IHE absorption and LIE self-absorption. in contrast to ὃν, who ascribe it to a near kinematic distance based on the absence of formaldehyde absorption."," Both \citet{kolpak03} and \citet{anderson09a} ascribe the associated region to a far kinematic distance based on HI absorption and HI self-absorption, in contrast to \citet{downes80b}, who ascribe it to a near kinematic distance based on the absence of formaldehyde absorption." This source peakecl in emission at “in the survey cube observation. but. pealed at ‘in the MX observation. with the ss feature doubling in strength from the MX observation from Ll Jv to 2.2 Jv.," This source peaked in emission at $^{-1}$ in the survey cube observation, but peaked at $^{-1}$ in the MX observation, with the $^{-1}$ feature doubling in strength from the MX observation from 1.1 Jy to 2.2 Jy." The features either side of the ss feature have also increased considerably in ux density. (whilst the original feature has. remained approximately the same)., The features either side of the $^{-1}$ feature have also increased considerably in flux density (whilst the original $^{-1}$ feature has remained approximately the same). " ""Vhis source has been identified as a far-side object from the presence of formaldehyde absorption (at a level of τσ) by 7..", This source has been identified as a far-side object from the presence of formaldehyde absorption (at a level of $\sigma$ ) by \citet{sewilo04}. In contrast ο identify it as a near-side object based on the *on-olf LIE self absorption technique. as do ? based on a line-width to distance relation.," In contrast \citet{roman09} identify it as a near-side object based on the `on-off' HI self absorption technique, as do \citet{solomon87} based on a line-width to distance relation." Discussion of the global. properties of the methanol maser population will be deferred. until the full MIAIB catalogue is published., Discussion of the global properties of the methanol maser population will be deferred until the full MMB catalogue is published. Llere we discuss the properties of the sources within the 6 to 20° longitude region with reference to those in the Galactic centre region (?).., Here we discuss the properties of the sources within the $^{\circ}$ to $^{\circ}$ longitude region with reference to those in the Galactic centre region \citep{caswell10mmb1}. The maser population in the 6 to 20 longitude region is confined to a narrow range of latitude (Eig. 2)):, The maser population in the $^\circ$ to $^\circ$ longitude region is confined to a narrow range of latitude (Fig. \ref{latdist}) ); of the sources (115 out of 119 sources) are at a latitucle within 1* of the Galactic planc., of the sources (115 out of 119 sources) are at a latitude within $^\circ$ of the Galactic plane. EPhis narrow distribution is very similar to that seen in the 345 to 6 Longitude region (?).., ÊThis narrow distribution is very similar to that seen in the $^\circ$ to $^\circ$ longitude region \citep{caswell10mmb1}. EL four sources with latitudes outside 17 of the plane were previously known (11407-1485. 16.864-2.159. 17.021-2.403. 15.341|1.765).," ÊAll four sources with latitudes outside $^\circ$ of the plane were previously known (11.497-1.485, 16.864-2.159, 17.021-2.403, 18.341+1.768)." The brightest 6668-MLlIZz methanol maser detected to date. | 0.196. is within the current region and. was found to have a survey. cube peak Dux density of 75200 Jv.," The brightest 6668-MHz methanol maser detected to date, $+$ 0.196, is within the current region and was found to have a survey cube peak flux density of $\sim$ 5200 Jy." The brightest new source detected in the survey is 6.189-0.358 with a survey cube peak Εν density of 2220 Jy (and an MX flux density of ~230 Jv)., The brightest new source detected in the survey is 6.189-0.358 with a survey cube peak flux density of $\sim$ 220 Jy (and an MX flux density of $\sim$ 230 Jy). The weakest known source in this region is 6.539-0.108 with a survey cube peak IHux density of 0.5 Jv (and an MX flux clensity of 0.6 Jv)., The weakest known source in this region is 6.539-0.108 with a survey cube peak flux density of 0.5 Jy (and an MX flux density of 0.6 Jy). The weakest new detection in the region is 16.983|0.000 with a survey cube peak flux density of 0.7 Jv (0.64 Jv in the follow-up AIX observation)., The weakest new detection in the region is 16.983+0.000 with a survey cube peak flux density of 0.7 Jy (0.64 Jy in the follow-up MX observation). Comparable to the 345° to 6 region we had only three new sources with peak Ilux densities above 20 Jv: 6.189-0.358. 8.832-0.028 ancl S.872-0.493. with survey cube Lux densities of 222 Jv. 127 Jy and 27 Jy respectively.," Comparable to the $^{\circ}$ to $^{\circ}$ region we had only three new sources with peak flux densities above 20 Jy: 6.189-0.358, 8.832-0.028 and 8.872-0.493, with survey cube flux densities of 222 Jy, 127 Jy and 27 Jy respectively." There were four sources at or below the survey cube 4 sigma sensitivity limit of0.7 Jy. two new (16.403-0.181 and 16.076- and two known (6.539-0.108 ancl 12.202-0.120).," There were four sources at or below the survey cube 4 sigma sensitivity limit of0.7 Jy, two new (16.403-0.181 and 16.976-0.005) and two known (6.539-0.108 and 12.202-0.120)." . AL four sources were confirmed with the higher sensitivity MX observations and TCX positioning observations., All four sources were confirmed with the higher sensitivity MX observations and ATCA positioning observations. The ratio of peak flux density between the survey cube andthe MX observations has a median value of 1.01., The ratio of peak flux density between the survey cube andthe MX observations has a median value of 1.01. Only, Only shorter than 160 d. This limiting period corresponds to a Roche radius of 70 wwhen masses of 1.3 ffor the giant and 0.6 ffor the companion are adopted.,shorter than 160 d. This limiting period corresponds to a Roche radius of 70 when masses of 1.3 for the giant and 0.6 for the companion are adopted. In fact. no M giant binary lies to the left of the solid line in Fig. 6..," In fact, no M giant binary lies to the left of the solid line in Fig. \ref{Fig:elogP-SB9}," representing the locus of à constant periastron distance ULο=157 wwhich corresponds to a Roche radius of 70 for a system with such masses (see Paper ILD., representing the locus of a constant periastron distance $A(1-e) = 157$ which corresponds to a Roche radius of 70 for a system with such masses (see Paper III). In contrast. K giants. which are more compact. may be found at much shorter periods.," In contrast, K giants, which are more compact, may be found at much shorter periods." However. many M giants have radii that are much smaller than the 70 tthreshold obtained above: Fig.," However, many M giants have radii that are much smaller than the 70 threshold obtained above: Fig." 3 shows M giants with radit as small as 30.... in agreement with the spread observed by for the radit of M giants.," \ref{Fig:R_Sb} shows M giants with radii as small as 30, in agreement with the spread observed by for the radii of M giants." Stars with such small radii could in principle be found to the left of the 70 RRLOF limit in the ο — logP diagram. but they are not.," Stars with such small radii could in principle be found to the left of the 70 RLOF limit in the $e$ – $\log P$ diagram, but they are not." Part of the explanation could be that the observed envelopes in the «-logP diagram are defined by tidal interactions more than by RLOF -- and tidal interactions operate well before stars fill their Roche lobe., Part of the explanation could be that the observed envelopes in the $e$ $\log P$ diagram are defined by tidal interactions more than by RLOF – and tidal interactions operate well before stars fill their Roche lobe. This is especially indicated by the K giants. as they contain a prominent circularised population around and below the minimal period of their «—log7? envelope (Figs. 6.. 7).," This is especially indicated by the K giants, as they contain a prominent circularised population around and below the minimal period of their $e$ $\log P$ envelope (Figs. \ref{Fig:elogP-SB9}, \ref{Fig:elogP_cluster_mass}) )." Among the M giant binaries. the short-period circular. subpopulation is less pronounced.," Among the M giant binaries, the short-period circular subpopulation is less pronounced." Still. they stay within the 70 eenvelope. not extending down to Roche radii of ~30..," Still, they stay within the 70 envelope, not extending down to Roche radii of $\sim 30$." .. If the «—logP envelope were due to the tidal interactions. should it not differ in shape from the periastron RLOF type envelope?," If the $e$ $\log P$ envelope were due to the tidal interactions, should it not differ in shape from the periastron RLOF type envelope?" For comparison. Fig.," For comparison, Fig." 6 also displays short- and long-dashed lines. corresponding to the evolution of systems during circularisation. which leaves the angular momentum per unit reduced mass |.=(1 ο] constant(??).," \ref{Fig:elogP-SB9} also displays short- and long-dashed lines, corresponding to the evolution of systems during circularisation, which leaves the angular momentum per unit reduced mass $h = A (1-e^2)$ ] constant." . Using Kepler's third law. this condition becomes P?(1ο) = constant in the eccentricity — period diagram.," Using Kepler's third law, this condition becomes $P^{2/3} (1-e^2)$ = constant in the eccentricity – period diagram." The two dashed lines in Fig., The two dashed lines in Fig. 6 were plotted adopting the same component masses of 1.3 παπά 0.6Af... and with the usual expression for the Roche radius (2).. the Roche radit corresponding to the circular orbits at the base of the two lines in Fig.," \ref{Fig:elogP-SB9} were plotted adopting the same component masses of 1.3 and 0.6, and with the usual expression for the Roche radius , the Roche radii corresponding to the circular orbits at the base of the two lines in Fig." 6 are 70 and 200FH., \ref{Fig:elogP-SB9} are 70 and 200. .. However. lines of this shape do not follow the observed ε-- logP envelopes as closely as the lines of constant pertastron distance do (especially in the upper panel of Fig. 7)).," However, lines of this shape do not follow the observed $e$ $\log P$ envelopes as closely as the lines of constant periastron distance do (especially in the upper panel of Fig. \ref{Fig:elogP_cluster_mass}) )." Either the shorter period objects are left outside the circularisation line or a large empty area is included under this supposed envelope., Either the shorter period objects are left outside the circularisation line or a large empty area is included under this supposed envelope. This may be explained as follows., This may be explained as follows. Circularisation becomes fast when the giant comes close to filling its Roche lobe at periastron., Circularisation becomes fast when the giant comes close to filling its Roche lobe at periastron. But since the circularisation path in the ο — logP? diagram is steeper thar the periastron line (see Fig. 6)).," But since the circularisation path in the $e$ – $\log P$ diagram is steeper than the periastron line (see Fig. \ref{Fig:elogP-SB9}) )," the system evolves somewhat away from the periastron line and thus away from the strong circularisation regime., the system evolves somewhat away from the periastron line and thus away from the strong circularisation regime. [t does not “slide” all the way dow! along the circularisation path. because it loses the driver.," It does not “slide” all the way down along the circularisation path, because it loses the driver." Only when other effects bring the star and its Roche lobe closer again does circularisation also accelerate again., Only when other effects bring the star and its Roche lobe closer again does circularisation also accelerate again. It should only be fast close to the the periastron envelope., It should only be fast close to the the periastron envelope. Of these two lines. it is thus the periastron envelope that would regulate the evolution of the e — logP? diagram of an ensemble of systems.," Of these two lines, it is thus the periastron envelope that would regulate the evolution of the $e$ – $\log P$ diagram of an ensemble of systems." In any ease. the minimal Roche lobe radii inferred from the M giant e — logP. diagram are apparently much too large for the measured radi for A giants.," In any case, the minimal Roche lobe radii inferred from the M giant $e$ – $\log P$ diagram are apparently much too large for the measured radii for M giants." They correspond to Roche lobe-filling factors ΠΠ. which are much too small for eircularisation to operate efficiently (i.e.. on a time scale comparable to the RGB evolutionary time scale).," They correspond to Roche lobe-filling factors $R/R_R$, which are much too small for circularisation to operate efficiently (i.e., on a time scale comparable to the RGB evolutionary time scale)." Interestingly enough. a similar difficulty has been pointed out by and in the context of symbiotic stars.," Interestingly enough, a similar difficulty has been pointed out by and in the context of symbiotic stars." The former authors have noticed that. surprisingly. the 4 componentsin. symbiotic," The former authors have noticed that, surprisingly, the M componentsin symbiotic" "The central SZ. decrement asstuuine selfsiuülar evolution aud solar abundances of hydrogen aud helm (ji,= LAL). from equation 2.. is The total flux density. assuming au observing frequency of 30 GIIz. can be calculated from equation 3: where AQ4n—A178.","The central SZ decrement assuming self-similar evolution and solar abundances of hydrogen and helium $\mu_e=1.14$ ), from equation \ref{eqn:dec}, is The total flux density, assuming an observing frequency of 30 GHz, can be calculated from equation \ref{eqn:flux}: where $\Delta_{178}\equiv \Delta/178$." " In a universe with ©,,=1 the spherical collapse iuodel predicts A=178. with smaller values for low-density universes."," In a universe with $\Omega_m=1$ the spherical collapse model predicts $\Delta=178$, with smaller values for low-density universes." For a given temperature. the central density is fixed bv the central entropy. and we can use equation 6 to solve for the appropriate value of the core-to-virial ratio R.," For a given temperature, the central density is fixed by the central entropy, and we can use equation \ref{eqn:nss} to solve for the appropriate value of the core-to-virial ratio $\mathcal{R}$." For the selfsimuilar case the central eutropy simply scales with T sud Ro=constant., For the self-similar case the central entropy simply scales with $T$ and $\mathcal{R}=constant$. À non-zero eutropv floor breaks the sel£siniluitwv and Ro becomes a fiction of temperature., A non-zero entropy floor breaks the self-similarity and $\mathcal{R}$ becomes a function of temperature. We assmne that the cutropy from eravitational heating is equal to that expected in the selfsinular case and add entropy from non-gravitational heating., We assume that the entropy from gravitational heating is equal to that expected in the self-similar case and add entropy from non-gravitational heating. We can still use equations 7 auc &.. but we must now solve for R as a function of mass.," We can still use equations \ref{eqn:mod_dec} and \ref{eqn:mod_flux}, , but we must now solve for $\mathcal{R}$ as a function of mass." For low- clusters. this leads to significantly different evolution and appearance. as well as a depressed cluster gas mass fraction.," For low-mass clusters, this leads to significantly different evolution and appearance, as well as a depressed cluster gas mass fraction." " As an example. for O,,=1. the seclfsimilar case would predict that the ceutral decrement would scale as ALL|i. whereas the eutropy floor would predict a scaling as APPPApSL"," As an example, for $\Omega_m=1$, the self-similar case would predict that the central decrement would scale as $M(1+z)^3$, whereas the entropy floor would predict a scaling as $M^{3/2}(1+z)^{9/4}$." This relation is different in both its mass scaling and its redshift depeucdence., This relation is different in both its mass scaling and its redshift dependence. Iu this scenario. low-mass high-redshift clusters will be sienificautly less compact than in a selfsimnülar picture.," In this scenario, low-mass high-redshift clusters will be significantly less compact than in a self-similar picture." This would have observable consequences. both in the properties of ligh-redshift clusters and in their signature in CAIB experiments (see &1).," This would have observable consequences, both in the properties of high-redshift clusters and in their signature in CMB experiments (see 4)." For clusters well below ~Lott)TAL. the core radius can become significantly larger than the virial radius for ligh values of the eutropy floor., For clusters well below $\sim 10^{14}h^{-1} M_\odot$ the core radius can become significantly larger than the virial radius for high values of the entropy floor. In such cases. the gas distribution is still trumeated at the virial radius in our models.," In such cases, the gas distribution is still truncated at the virial radius in our models." This is simply indicating that the entropy of the central gas is sufficicutly hieh that the ceutral density is not sienificautly hieher than the eas density near the virial radius., This is simply indicating that the entropy of the central gas is sufficiently high that the central density is not significantly higher than the gas density near the virial radius. In this regime. the accreion process could be seriously affected by the eutropyv foor aud it is nof clear that our simple model is applicable.," In this regime, the accretion process could be seriously affected by the entropy floor and it is not clear that our simple model is applicable." Iu this work. we asstune a relatively high value for the entropy floor of δρ.=200keV.cu? as an extreme case.," In this work, we assume a relatively high value for the entropy floor of $s_{floor}= 200~{\rm keV~cm^2}$ as an extreme case." Ciuvent estimates of the eutropy floor (Pomman.Cannon.andNavarro1999) are ronehly κε=100keVcu’., Current estimates of the entropy floor \citep{ponman99} are roughly $s_{floor}=100~{\rm keV~cm^{2}}$. We amodeled the cosmological evolution of cluster abuudances with the Press-Schechter prescription (PressandSehechterΤΙBoundefaf 1901)... which vives the comoving ununber deusity as a function of both mass and redshift.," We modeled the cosmological evolution of cluster abundances with the Press-Schechter prescription \citep{press74,bond91}, which gives the comoving number density as a function of both mass and redshift." We followed the procedure outlined in Holder et al. (, We followed the procedure outlined in Holder et al. ( 2000). with two nünor modifications.,"2000), with two minor modifications." " The power spectrum was computed using the fitting fuuctious of LiseusteimaudThi(1999)... aud the redshift evolution of the power spectrum was evaluated uunerically frou linear theory (ο,ο,, Peebles 1980)."," The power spectrum was computed using the fitting functions of \cite{eisenstein99a}, and the redshift evolution of the power spectrum was evaluated numerically from linear theory (e.g., Peebles 1980)." Given the comoving uuniber density. it ds straightforward to obtain the number of clusters per steradian above some iass threshold Αν ax a simple integral over the comoving number density.," Given the comoving number density, it is straightforward to obtain the number of clusters per steradian above some mass threshold $M_{lim}$ as a simple integral over the comoving number density." To estimate the angular power spectrum of the thermal SZ. we follow Cole and IWaiser (1988). and assume that only Poisson coutributious to the aneular power spectrum are nuportaut.," To estimate the angular power spectrum of the thermal SZ, we follow Cole and Kaiser \nocite{cole88}, and assume that only Poisson contributions to the angular power spectrum are important." " For this work. we assune that O,/=0.3.O4LF.og=Land fh=0.65."," For this work, we assume that $\Omega_m=0.3,\ \Omega_\Lambda=0.7, \ \sigma_8=1$ and $h=0.65$." The expected counts are very sensitive to cosmological parameters. as may authors have found.," The expected counts are very sensitive to cosmological parameters, as many authors have found." The effects of preheating ou cluster structure cau be seen in Figure 1.., The effects of preheating on cluster structure can be seen in Figure \ref{fig:dt_rc}. The largest effects of preheating are seen at low iasses and high redshift., The largest effects of preheating are seen at low masses and high redshift. These models have been designed to agree with observed properties of N-rav cutting clusters aud groups at low redshift. so the true test of these models will be how they fare at lüeh redshift.," These models have been designed to agree with observed properties of X-ray emitting clusters and groups at low redshift, so the true test of these models will be how they fare at high redshift." In particular. important iuformation cau be learned about cluster-to-cluster variations iu the aout of non-gravitational heating and also in the redshift evolution of the amount of preheating in clusters.," In particular, important information can be learned about cluster-to-cluster variations in the amount of non-gravitational heating and also in the redshift evolution of the amount of preheating in clusters." 0.liuper Iu Figure 1. we have marked the limiting survey nass at cach redshift which is required to obtain a surface density per redshift biu of either 1 or 0.01 clusters per square degree per unit redshift.," 0.1in In Figure 1, we have marked the limiting survey mass at each redshift which is required to obtain a surface density per redshift bin of either 1 or 0.01 clusters per square degree per unit redshift." Ti order to ect a ]uge sample of clusters at high redshift. the survey mass limit must be relatively low.," In order to get a large sample of clusters at high redshift, the survey mass limit must be relatively low." Typical expected mass limits for SZ surveys are shown in Figure 2.., Typical expected mass limits for SZ surveys are shown in Figure \ref{fig:mlims}. PLANCK is expected to be able to survey most of the sky. at a resolution of ~5' down to a level of ~Ἰθ0μ]ν.," PLANCK is expected to be able to survey most of the sky, at a resolution of $\sim 5'$ down to a level of $\sim 10\mu K$." Deep ground-based surveys should be able to reach a comparable temperature uncertainty on a few tens of square deerees at a resolution of ~1’., Deep ground-based surveys should be able to reach a comparable temperature uncertainty on a few tens of square degrees at a resolution of $\sim 1'$. The SZ is well suited for surveving. with the nice feature that the survev mass huit should be larecly decoupled from issues of preheating. as illustrated in Figure 2. by the sinall difference in the mass liits between the selfmodel and the fairly extreme preheated model.," The SZ is well suited for surveying, with the nice feature that the survey mass limit should be largely decoupled from issues of preheating, as illustrated in Figure \ref{fig:mlims} by the small difference in the mass limits between the self-similarmodel and the fairly extreme preheated model." We are very erateful to the Horizon. project Clevssieretal.2009) for allowing us to use their. simulation data to calculate our errors. clue to. cosmic variance.,We are very grateful to the Horizon project \citep{Teyssier:2009zd} for allowing us to use their simulation data to calculate our errors due to cosmic variance. " We thank Fakashi LHliramatsu for confirming the Oy, and ax dependence of οἱ. a, and o» using perturbation theory,"," We thank Takashi Hiramatsu for confirming the $\Omega_{\rm m}$ and $\sigma_8$ dependence of $A$, $\alpha_1$ and $\alpha_2$ using perturbation theory." We would also like to thank Shaun Thomas. Alan Lleavens. Sarah. Bridle. Dhuvnesh Jain anc Ben Hovle for their comments.," We would also like to thank Shaun Thomas, Alan Heavens, Sarah Bridle, Bhuvnesh Jain and Ben Hoyle for their comments." DB is supported by an SPEC Advance Fellowship and an RCUlIx. Academic Fellowship., DB is supported by an STFC Advanced Fellowship and an RCUK Academic Fellowship. KK is supported by ERC. SPEC and ROU.," KK is supported by ERC, STFC and RCUK." EB is funded by an SPEC PhD studentship., EB is funded by an STFC PhD studentship. split into two locales.,split into two locales. Optically selected AGN without 24 ym detection are relatively blue in [5.8]—[8.0] color while more than of those with 24 jim detection congregate in the aromatic locus., Optically selected AGN without 24 $\micron$ detection are relatively blue in $-$ [8.0] color while more than of those with 24 $\micron$ detection congregate in the aromatic locus. The bluer MIR locus of optically selected AGN without 24 wm detection is consistent with the Rayleigh-Jeans tail of an old stellar population's photospheric emission that peaks at 1.6 wm., The bluer MIR locus of optically selected AGN without 24 $\micron$ detection is consistent with the Rayleigh-Jeans tail of an old stellar population's photospheric emission that peaks at 1.6 $\micron$. " This suggests the source of 24 emission in an optically selected AGN is likely to be star-forminguim activity, not the AGN."," This suggests the source of 24 $\micron$ emission in an optically selected AGN is likely to be star-forming activity, not the AGN." We have also;z FAGNsearched xrayfor AGN detected in the 5 ks X-ray survey of the ffield (XBoóttes;2005).," We have also searched for AGN detected in the 5 ks X-ray survey of the field \citep[XBo\""{o}t." We define anAGN as any source with two or more X-ray counts and a >25% probability based on the Bayesian matching method described by Brandetal.(2006)., We define an as any source with two or more X-ray counts and a $> 25$ probability based on the Bayesian matching method described by \citet{Brand06}. ". Since XBoóttes is designed to have a large contiguous area and a shallow flux limit, X-ray identification based on the survey will only identify the strongest AGN."," Since XBoöttes is designed to have a large contiguous area and a shallow flux limit, X-ray identification based on the survey will only identify the strongest AGN." The X-ray luminosities of these sources are typically brighter than 107? ergs~ (Hickoxetal. and hence they are unlikely to be dominated by 2009)star-forming activity.," The X-ray luminosities of these sources are typically brighter than $10^{42}$ ${\rm erg}s^{-1}$ \citep{Hickox09} and hence they are unlikely to be dominated by star-forming activity." " Although it is not possible to infer directly the AGN contribution to the 24 wm flux from the strength of the X- emission, strong AGN are known to emit significantly in the MIR (e.g.,Barmbyetal.2006)."," Although it is not possible to infer directly the AGN contribution to the 24 $\micron$ flux from the strength of the X-ray emission, strong AGN are known to emit significantly in the MIR \citep[e.g.,][]{Barmby06}." ". We found 498 X-ray selected AGN at 0.0€zx0.65 and 175 of them are at the redshift range where we construct the LF (0.05 —0.5, would lie blueward in both color indices locus on the diagram) because, as mentioned earlier, (lower-lefttheir SEDs in"," The locus of early type galaxies, which also exhibit power-law SEDs but with $\alpha > -0.5$ , would lie blueward in both color indices (lower-left locus on the diagram) because, as mentioned earlier, their SEDs in" As discussed in paper 2. à mathematical inconsistency arises when one attempts to consider (he low-frequency limit of (4.2)) wath (4.2)).,"As discussed in paper 2, a mathematical inconsistency arises when one attempts to consider the low-frequency limit of \ref{growth1}) ) with \ref{emissivity}) )." One wav of avoiding this difficulty is to consider the average of (4.2)) over solid angle. denoted by an overline: where the choice of the sign cos@=d Elis implicit.," One way of avoiding this difficulty is to consider the average of \ref{growth1}) ) over solid angle, denoted by an overline:, where the choice of the sign $\cos\theta'=\pm1$ is implicit." The average of the eniissivily is evaluated in paper 2. ancl al low frequencies for a triangular wave form il reduces to SAPO) wilh Ai(0)=L/3227D(2/3)0.355.," The average of the emissivity is evaluated in paper 2, and at low frequencies for a triangular wave form it reduces to ^2(0) with ${\rm Ai}(0)=1/3^{2/3}\Gamma(2/3)=0.355$." We use (29)) rather than (4.2)) in the discussion below., We use \ref{growth2}) ) rather than \ref{growth1}) ) in the discussion below. The emissivity (4.2)) is in (he primecl frame. and it is straightlorward to (transform il io the pulsar frame. in which the LAEW is an outward propagating wave.," The emissivity \ref{emissivity}) ) is in the primed frame, and it is straightforward to transform it to the pulsar frame, in which the LAEW is an outward propagating wave." The Lorentz transformation (2.2)) implies ο.," The Lorentz transformation \ref{LT2}) ) implies )," The Lorentz transformation (2.2)) implies ο..," The Lorentz transformation \ref{LT2}) ) implies )," The Lorentz transformation (2.2)) implies ο...," The Lorentz transformation \ref{LT2}) ) implies )," in such timing (which arises almost entirely in fitting the observed light curve to the standard: outhurst templates: see Paper £D) is £0.05 d. We have omitted most of the slow increase of Povo before T= 0. which is given in Paper ] and is tvpical of the dP?pxo/d seen in dwarf novae in general.,"in such timing (which arises almost entirely in fitting the observed light curve to the standard outburst templates: see Paper I) is $\pm$ 0.05 d. We have omitted most of the slow increase of $P_{DNO}$ before $T$ = 0, which is given in Paper I and is typical of the $P_{DNO}$ $t$ seen in dwarf novae in general." The horizontal dashed line at Ppxo = 14.41 s shows the minimum value reached at maximum of outburst., The horizontal dashed line at $P_{DNO}$ = 14.1 s shows the minimum value reached at maximum of outburst. Discussing first the results from the EP analyses. which are biased. towards the stronger signals but show the gross trends. we see that from 7 = 0 to 1) = 0.20 d there is a monotonic single-valued increase in Lov [rom 25 s to 33 s. às already. seen in Paper E but now with additional data.," Discussing first the results from the FT analyses, which are biased towards the stronger signals but show the gross trends, we see that from $T$ = 0 to $T$ = 0.20 d there is a monotonic single-valued increase in $P_{DNO}$ from 25 s to 33 s, as already seen in Paper I but now with additional data." At 7 — 0.20 d the first runs appear in which a Ist harmonic is sometimes present. but only at 2 = 0.25 d does the Ist harmonic dominate over the fundamental.," At $T$ = 0.20 d the first runs appear in which a 1st harmonic is sometimes present, but only at $T$ = 0.25 d does the 1st harmonic dominate over the fundamental." Phe apparent turn-up in the trend of the Bandamoental in its last few points may be due to the unrecognised presence of svnodie rather than direct. DNOs. but we see no evidence for any double DNO in the observations at this stage (in the rare cases when we observed a double DNO at other times we have plotted only the direct period in Fig. 1)).," The apparent turn-up in the trend of the fundamental in its last few points may be due to the unrecognised presence of synodic rather than direct DNOs, but we see no evidence for any double DNO in the observations at this stage (in the rare cases when we observed a double DNO at other times we have plotted only the direct period in Fig. \ref{dno4fig1}) )." From T = 0.25 to 0.50 the Ist harmonic increases in period with little scatter. but from 7 = 0.36 it is occasionally accompanied by a 2nd harmonic. which to our knowledge is the first such observation of frequency. tripling in a CY.," From $T$ = 0.25 to 0.50 the 1st harmonic increases in period with little scatter, but from $T$ = 0.36 it is occasionally accompanied by a 2nd harmonic, which to our knowledge is the first such observation of frequency tripling in a CV." From T = 0.5 to 1.0 d the evolution of the DNOs is characterised by increasing domination of the 2nd harmonic over the Ist. until at. Z7 — 1.0 only the 2nd harmonic. is present and appears to stabilize at à period 30 s. though with considerable scatter.," From $T$ = 0.5 to 1.0 d the evolution of the DNOs is characterised by increasing domination of the 2nd harmonic over the 1st, until at $T$ = 1.0 only the 2nd harmonic is present and appears to stabilize at a period $\sim$ 30 s, though with considerable scatter." For a cay or so after J — LA d. by which time VW Ivi is fully at quiescence. our light curves show no DNOs at all.," For a day or so after $T$ = 1.4 d, by which time VW Hyi is fully at quiescence, our light curves show no DNOs at all." On rare occasions through the 1 —025 1.l d range there are guest appearances of the 'uncdamental., On rare occasions through the $T$ = 0.25 – 1.1 d range there are guest appearances of the fundamental. In most of the runs after. 2 = 0.3 d either the Ist or the 2nd. harmonic is present. and there is alternation tween them within the run. but in runs 86138 and 87342 here are parts where fundamental and both harmonics are simultaneously. present in the Ps: these are shown in the inset in Fie. Ll.," In most of the runs after $T$ = 0.3 d either the 1st or the 2nd harmonic is present, and there is alternation between them within the run, but in runs S6138 and S7342 there are parts where fundamental and both harmonics are simultaneously present in the FTs; these are shown in the inset in Fig. \ref{dno4fig1}." Our Fs show that the 1:2:3 ratios. of »eriods are satisfied within errors of measurement when the components are present together., Our FTs show that the 1:2:3 ratios of periods are satisfied within errors of measurement when the components are present together. In Fig., In Fig. " 20 we illustrate I""Fs that contain combinations of the Fundamental. 2nd and 3rd harmonics present simultaneously (because one or other component usually dominates. the presence of the weaker components is usually only made convincing by inspecting EVs of the immediately preceding or subsequent sections of the runs. where they in turn may dominate)"," \ref{dno4fig2} we illustrate FTs that contain combinations of the fundamental, 2nd and 3rd harmonics present simultaneously (because one or other component usually dominates, the presence of the weaker components is usually only made convincing by inspecting FTs of the immediately preceding or subsequent sections of the runs, where they in turn may dominate)." If the background radio source is extended. and has sub-components with different spectral indices. (hen these sub-components may each be magnilied bv a different [actor Porcas1999).,"If the background radio source is extended and has sub-components with different spectral indices, then these sub-components may each be magnified by a different factor \citep[see, e.g.,][]{pp99}." . In that case. the sum of flux densities of the sub-components in a lensed image would not necessarily have the same spectral index as the corresponding sum in a different image.," In that case, the sum of flux densities of the sub-components in a lensed image would not necessarily have the same spectral index as the corresponding sum in a different image." llowever. in (he case of J16320033. the source is verv compact.," However, in the case of J1632–0033, the source is very compact." From Fig., From Fig. 3. we can limit the separation of sub-components in image A to <5 mas. corresponding to a change in magnification of only AyIL0.01 in an isothermal model.," \ref{fig:vlba-3.5cm} we can limit the separation of sub-components in image A to $<$ 5 mas, corresponding to a change in magnification of only $\Delta\mu\lsim 0.01$ in an isothermal model." Furthermore. the agreement of a. and oj argues against the presence of a significant effect. [rom. Irequency-dependent. radio substructure.," Furthermore, the agreement of $\alpha_{\rm A}$ and $\alpha_{\rm B}$ argues against the presence of a significant effect from frequency-dependent radio substructure." la radio source has structure on large angular scales. wilh Fourier components corresponding (o smaller spatial frequencies (han (those measured by an interferometer. (hen that portion of the radio source is invisible to the interferometer.," If a radio source has structure on large angular scales, with Fourier components corresponding to smaller spatial frequencies than those measured by an interferometer, then that portion of the radio source is invisible to the interferometer." " The invisible radio structure is said {ο be ""resolved out.”", The invisible radio structure is said to be “resolved out.” We must consider the possibility that the spectral indices of A and C are different only because the components are being resolved oul by. different amounts at each frequency., We must consider the possibility that the spectral indices of A and C are different only because the components are being resolved out by different amounts at each frequency. We reject this hypothesis based on three facts., We reject this hypothesis based on three facts. First. there cannot be much structure in components A and D. During a monitoring program. we measured (heir flix densities al 8.4 Gllz with the VLA on 2002 March. 14. simultaneous with the VLBA measurement described in 2..," First, there cannot be much resolved-out structure in components A and B. During a monitoring program, we measured their flux densities at 8.4 GHz with the VLA on 2002 March 14, simultaneous with the VLBA measurement described in \ref{sec:observations}." The VLBA flux densities were 834τά. of the VLA flux densities. despite being measured on angular scales ~200 (times smaller.," The VLBA flux densities were $83\pm 7\%$ of the VLA flux densities, despite being measured on angular scales $\sim$ 200 times smaller." Second. if C is a third quasar image. it is demagnilied by a [actor of &107 and would have an even smaller fraction of resolved-out structure than A or D. Third. even if there is resolved-out structure in A. it would be expected to have a steep radio spectrum. becatse the extended jets of quasars eenerallv have steeper spectra than (he compact cores.," Second, if C is a third quasar image, it is demagnified by a factor of $\sim$ $^2$ and would have an even smaller fraction of resolved-out structure than A or B. Third, even if there is resolved-out structure in A, it would be expected to have a steep radio spectrum, because the extended jets of quasars generally have steeper spectra than the compact cores." This would only worsen the discrepancy between the spectral indices of A and C. by causing the true spectral index of A to be steeper than observed.," This would only worsen the discrepancy between the spectral indices of A and C, by causing the true spectral index of A to be steeper than observed." or the observed. statistical properties of the population of oulsars with interpulses.,for the observed statistical properties of the population of pulsars with interpulses. We have embarked on a long-term timing campaign at the Parkes telescope in Australia to monitor a large sample of voung pulsars with high spin-down energy loss rates ο., We have embarked on a long-term timing campaign at the Parkes telescope in Australia to monitor a large sample of young pulsars with high spin-down energy loss rates $\dot{E}$. This sample of pulsars is compared. with archival Parkes data. which is published in various papers. in order to determine the dilferences between pulsars with high. ancl low values for £ (2).," This sample of pulsars is compared with archival Parkes data, which is published in various papers, in order to determine the differences between pulsars with high and low values for $\dot{E}$ \citep{wj08b}." We refer to that paper lor the details of the observations ancl data reduction., We refer to that paper for the details of the observations and data reduction. The dataset is used. to. determine. the correlation between the pulse width AG and P., The dataset is used to determine the correlation between the pulse width $\Delta\phi$ and $P$. Fig., Fig. 2 suggests that the slope in the AoP plane is less steep than 1/2., \ref{Fig_pulsewidths_p} suggests that the slope in the $\Delta\phi-P$ plane is less steep than $-1/2$. Ehe slope measured by minimizing— the v in log-log space (assuming equal weights) is —0.31+0.05., The slope measured by minimizing the $\chi^2$ in log-log space (assuming equal weights) is $-0.31\pm0.05$. " As pointed out. in the introduction. p is expected. and found. to be proportional to P U7, "," As pointed out in the introduction, $\rho$ is expected, and found, to be proportional to $P^{-1/2}$ ." An identical correlation can. be expected in. the AoP plane. provided that à is independent of P.," An identical correlation can be expected in the $\Delta\phi-P$ plane, provided that $\alpha$ is independent of $P$." Τις measurement is therefore of interest to us because it can be interpreted as evidence for a P? dependence of a., This measurement is therefore of interest to us because it can be interpreted as evidence for a $P$ dependence of $\alpha$. One could argue that the scatter of the points around the correlation in Fig., One could argue that the scatter of the points around the correlation in Fig. 2. is so large that a power law with a slope of 1/2 would fit the data equally well., \ref{Fig_pulsewidths_p} is so large that a power law with a slope of $-1/2$ would fit the data equally well. We therefore also measured the slope using the measured widths at 1400 Mllz by 7.. excluding the milli-seconcl pulsars. as a consistency check.," We therefore also measured the slope using the measured widths at 1400 MHz by \cite{gl98}, excluding the milli-second pulsars, as a consistency check." Although there is some overlap in our samples. that of ? contain many northern pulsars which are not present in our sample.," Although there is some overlap in our samples, that of \cite{gl98} contain many northern pulsars which are not present in our sample." The slope measured in the ? data is also latter then expected (0.23 20.06). which makes us more confident that the observed. trend is real.," The slope measured in the \cite{gl98} data is also flatter then expected $-0.23\pm0.06$ ), which makes us more confident that the observed trend is real." We attempt to explain three observational conclusions by creating a model which is as simple as possible., We attempt to explain three observational conclusions by creating a model which is as simple as possible. If. one understands the geometry one should first of all be able to construct. a model which can predict the observed. fraction of pulsars with an interpulse Or lower. see section 2).," If one understands the geometry one should first of all be able to construct a model which can predict the observed fraction of pulsars with an interpulse or lower, see section 2)." Secondly. the model should. be able to reproduce the observed: period. distribution of pulsars with interpulses.," Secondly, the model should be able to reproduce the observed period distribution of pulsars with interpulses." 'Fhirdly. the model should explain why the observed AGP? correlation. is latter than the expected P?F7. correlation.," Thirdly, the model should explain why the observed $\Delta\phi-P$ correlation is flatter than the expected $P^{-1/2}$ correlation." The etfects of à possible alignment timescale of the magnetic axis and non-circular beams will be explored., The effects of a possible alignment timescale of the magnetic axis and non-circular beams will be explored. The basic approach of this model is to synthesize a population of pulsars in which the 2P distribution is identical to the observed distribution., The basic approach of this model is to synthesize a population of pulsars in which the $P-\dot{P}$ distribution is identical to the observed distribution. We then assign a random geometry to cach pulsar and 16 subpopulation of pulsars with interpulses is identified. using cillerent mocel assumptions., We then assign a random geometry to each pulsar and the subpopulation of pulsars with interpulses is identified using different model assumptions. The statistical properties of the synthesized population of pulsars with interpulses is then compared with the observed. population in order to determine which mocel is able to reproduce the data best., The statistical properties of the synthesized population of pulsars with interpulses is then compared with the observed population in order to determine which model is able to reproduce the data best. The model should. first of all reproduce the observed. P?p distribution for the total observed population of pulsars (those with and without interpulses). which is achieved by simplv using the observed P?P combinations.," The model should first of all reproduce the observed $P-\dot{P}$ distribution for the total observed population of pulsars (those with and without interpulses), which is achieved by simply using the observed $P-\dot{P}$ combinations." Not only does this ensure that the resulting distributions are realistic. it also avoids the necessity to make an full evolutionary model which would require additional assumptions about pulsar birth properties ancl their evolution.," Not only does this ensure that the resulting distributions are realistic, it also avoids the necessity to make an full evolutionary model which would require additional assumptions about pulsar birth properties and their evolution." Note that we are therefore not making any assumptions about the parent distribution that gives rise to the observed. distribution of PP combinations., Note that we are therefore not making any assumptions about the parent distribution that gives rise to the observed distribution of $P-\dot{P}$ combinations. ln the next subsection we will describe geometrical factors which couldmake the period distribution ofthe pulsars with interpulses dillerent to the total population of observed. pulsars., In the next subsection we will describe geometrical factors which couldmake the period distribution of the pulsars with interpulses different to the total population of observed pulsars. "the variations of cach velocity. such as those observed in pulsating cool stars (οιο, Mathias et al.","the variations of each velocity, such as those observed in pulsating cool stars (e.g. Mathias et al." 1997)., 1997). The velocity-velocity cdagrams are shown in Fig., The velocity-velocity diagrams are shown in Fig. δ for our objects with a good time coverage., \ref{lissajous} for our objects with a good time coverage. No evclic behaviour is observed. probably mecaning that the atinosphiere of RSG is not vertically stratified m a simple fashion. aud shock. waves are not spherically sviiectric.," No cyclic behaviour is observed, probably meaning that the atmosphere of RSG is not vertically stratified in a simple fashion, and shock waves are not spherically symmetric." Exaiuples of time variations i both depth aud velocity for each component is shown iu Fie. 9.., Examples of time variations in both depth and velocity for each component is shown in Fig. \ref{depth}. Tere agam. uo evclic or regula behaviour is found. coufirmine the nreenlar nature of the variations. probably associated with (or due to) the asvaiunietric atimospheric structure.," Here again, no cyclic or regular behaviour is found, confirming the irregular nature of the variations, probably associated with (or due to) the asymmetric atmospheric structure." To establish the origiuOo of the atinospherie dyviiuules. we ∱∎⊔⋅↴∖↴↑∐⋜↕↖⇁↸∖↑∪≼∐∖↥⋅↕↖⇁↸∖↑↕∐∖↕⋟∏∐≼↧⋜↕⋯↸∖∐↑⋜↧↕↻⋜∐⋅⋜↧⋯↸∖↑↸∖↥⋅," To establish the origin of the atmospheric dynamics, we first have to derive the fundamental parameters of our stars." ↴∖↴∪↕⋟≺∏∐⋅ ↴∖↴↑⋜∐⋅↴∖↴∙↖↖⊽↕↑∐↑∐↕↴∖↴⋜↧↕⋯∙↖↖⇁↸∖∏↴∖↴↸∖≼↧↑∐↸∖↻∐∪↑∪∐∐∖⊓⋅⋅↖⇁⋜⋯≼↧↑∐↸∖ bolometric fluxes eiven dun paper I aux the distances aud extinction (4i) from Levesque et al.," With this aim, we used the photometry and the bolometric fluxes given in paper I and the distances and extinction $A_V$ ) from Levesque et al." (2005)7.. Following Schlegel ct al. (, Following Schlegel et al. ( 1998). we adopt Ay=Q.112Ay-.,"1998), we adopt $A_K \, = \, 0.112 A_V$." For a Ori. we adopt a distance of 110 pc roni its Tipparcos parallax.," For $\alpha$ Ori, we adopt a distance of 140 pc from its Hipparcos parallax." The teiiperatures are based ou the (V-I) colour aud Bessell et al. (, The temperatures are based on the (V-K) colour and Bessell et al. ( "1998). polynomial fit Oo T,.,y for giauts",1998) polynomial fit to $_{eff}$ for giants In this paper. we build on our earlier merger rate studies by investigating the mass growth of haloes. and its environmental dependence. via two sources: growth from. mergers with other haloes (a quantity closely related to the results of FAIOO). and. growth from aceretion of non-halo material. which we will refer to as “dilfuse” accretion.,"In this paper, we build on our earlier merger rate studies by investigating the mass growth of haloes, and its environmental dependence, via two sources: growth from mergers with other haloes (a quantity closely related to the results of FM09), and growth from accretion of non-halo material, which we will refer to as ""diffuse"" accretion." Due to the finite resolution of the simulations. we expect a portion of this cdilfuse component to. be comprised. of unresolved haloes. which. in a higher-resolution simulation. should larecly follow the merger physics and. scaling laws of their higher mass counterparts in our earlier studies.," Due to the finite resolution of the simulations, we expect a portion of this diffuse component to be comprised of unresolved haloes, which, in a higher-resolution simulation, should largely follow the merger physics and scaling laws of their higher mass counterparts in our earlier studies." The diffuse non-halo component. however. can in principal also contain truly diffuse dark matter particles that either were tically stripped. from. existing haloes or were never eravitationally bound to any haloes.," The diffuse non-halo component, however, can in principal also contain truly diffuse dark matter particles that either were tidally stripped from existing haloes or were never gravitationally bound to any haloes." As reported below. we find that diffuse accretion plays an important role in contributing to halo mass growth in the Millennium. simulation.," As reported below, we find that diffuse accretion plays an important role in contributing to halo mass growth in the Millennium simulation." Moreover. we will show hat this growth component correlates with the local halo environment in an opposite wav from the component. due o mergers. with dilfuse accretion. plaving an increasingly important role in halo growth in the voids. and mergers rlaving a more important role in the densest regions.," Moreover, we will show that this growth component correlates with the local halo environment in an opposite way from the component due to mergers, with diffuse accretion playing an increasingly important role in halo growth in the voids, and mergers playing a more important role in the densest regions." This dillerence suggests that the diffuse component is not simply an extension of the resolved. haloes down to lower masses. out rather that there is an intrinsic dillerence between the wo components that results in the opposite environmental rends.," This difference suggests that the diffuse component is not simply an extension of the resolved haloes down to lower masses, but rather that there is an intrinsic difference between the two components that results in the opposite environmental trends." An implication of this result. is that Alilky-\Way size galaxies in voids and those that reside near massive clusters may have statistically cistinguishable formation jstoryv. where the galaxies in voids acquire their barvons more quiescentiy via dilfuse accretion. while those in dense regions assemble their barvons mainly via mergers.," An implication of this result is that Milky-Way size galaxies in voids and those that reside near massive clusters may have statistically distinguishable formation history, where the galaxies in voids acquire their baryons more quiescently via diffuse accretion, while those in dense regions assemble their baryons mainly via mergers." Such environmental elfect can show up in galaxy properties such as the star formation rates. colors. and morphologies.," Such environmental effect can show up in galaxy properties such as the star formation rates, colors, and morphologies." The environmental dependence of halo growths reported in this paper also has far-reaching implications or the much-used analytic theories for halo growth. such as the Extended: Press-Schechter (EPS) and excursion set models (?7??7)..," The environmental dependence of halo growths reported in this paper also has far-reaching implications for the much-used analytic theories for halo growth such as the Extended Press-Schechter (EPS) and excursion set models \citep{PS74, BondEPS,LC93}." Phese models assume that all dark matter rarticles reside in haloes. and halo growths depend only on mass and not environment.," These models assume that all dark matter particles reside in haloes, and halo growths depend only on mass and not environment." As we will elaborate on below. »»th assumptions are too simplistic and must. be mocifie o account for the results from numerical simulations.," As we will elaborate on below, both assumptions are too simplistic and must be modified to account for the results from numerical simulations." This paper is organised as follows., This paper is organised as follows. retfMillenniumSim sumnmiarises the various definitions. of ialo mass and environment used in our analysis. as wel as the means by which we extract. halo merger trees [rom he public data in the Millennium simulation.," \\ref{MillenniumSim} summarises the various definitions of halo mass and environment used in our analysis, as well as the means by which we extract halo merger trees from the public data in the Millennium simulation." In Sec., In Sec. 3 we discuss how the two mass growth rates due to mergers anc clilfuse accretion. Mas and Ma. are defined and computed.," 3 we discuss how the two mass growth rates due to mergers and diffuse accretion, $\B$ and $\C$, are defined and computed." The distributions of the rates for the ~500.000. haloes ab 2=0 and their redshift evolution are presented.," The distributions of the rates for the $\sim 500,000$ haloes at $z=0$ and their redshift evolution are presented." The environmental dependence of halo growths is analysed. in sec., The environmental dependence of halo growths is analysed in Sec. 4., 4. The correlations of four halo properties with the local parameter are investigated: the mass growth rates Adie: density.and Alay 4.1). the fraction of a halo's final nmiass gained via mergers vs. dilluse accretion 4.2). the formation redshift z; 4.3). and the composition of the surrounding mass reservoir outside of the virial radii of the haloes 4.4).," The correlations of four halo properties with the local density parameter are investigated: the mass growth rates $\B$ and $\C$ 4.1), the fraction of a halo's final mass gained via mergers vs. diffuse accretion 4.2), the formation redshift $z_f$ 4.3), and the composition of the surrounding mass reservoir outside of the virial radii of the haloes 4.4)." re[fSojourners— discusses a test that we have performed o verify that the majority of haloes reside in a similar environmental region (e.g. overdense or uncderdense) hroughout their lifetimes., \\ref{Sojourners} discusses a test that we have performed to verify that the majority of haloes reside in a similar environmental region (e.g. overdense or underdense) throughout their lifetimes. In Sec., In Sec. 5 we investigate further he nature of the 7dilfuse component by varying the mass hreshold used to define Miss VS Mu, 5 we investigate further the nature of the “diffuse” component by varying the mass threshold used to define $\B$ vs $\C$. We then discuss the implications of our results for the analytic EPS model of ido growth. which is entirely. independent. of environment in its basic form and therefore must be modified to account or the various environmental trends reported in 4.," We then discuss the implications of our results for the analytic EPS model of halo growth, which is entirely independent of environment in its basic form and therefore must be modified to account for the various environmental trends reported in 4." " The Millennium simulation (7) assumes a ACDAL moclel with ©,=0.25. O,=0.045. O4=0.73. fh=0.73 ancl a spectral index of à?=1 for the primordial density perturbations with normalisation ax=0.9 (7).."," The Millennium simulation \citep{Springel05} assumes a $\Lambda$ CDM model with $\Omega_m=0.25$, $\Omega_b=0.045$, $\Omega_\Lambda=0.73$, $h=0.73$ and a spectral index of $n=1$ for the primordial density perturbations with normalisation $\sigma_8=0.9$ \citep{Springel05}." " Phe clark matter N-bocly simulation followed the trajectories o£ 21607 particles of mass 1.210""AZ. in a (685 Mpc)* box from redshift z=127 to z—0.", The dark matter N-body simulation followed the trajectories of $2160^3$ particles of mass $1.2\times10^9 M_\odot$ in a (685 $^3$ box from redshift $z=127$ to $z=0$. A friends-ol-friends group finder with a linking length. of 6=0.2 is used to identifv ~2.10° dark matter haloes in the simulation down to a mass resolution of 40 particles (~4.71027A£. 3., A friends-of-friends group finder with a linking length of $b=0.2$ is used to identify $\sim 2\times 10^7$ dark matter haloes in the simulation down to a mass resolution of 40 particles $\sim 4.7\times 10^{10} M_\odot$ ). Each FOF halo thus identified is further broken into constituent subhalocs. each with at least 20 particles. by the SUDEIND algorithm that identifies eravitationally bound substructures within the host FOF halo (?)," Each FOF halo thus identified is further broken into constituent subhaloes, each with at least 20 particles, by the SUBFIND algorithm that identifies gravitationally bound substructures within the host FOF halo \citep{Springel01SUBFIND}." Even though the Millennium publie database provides a catalogue of FOL haloes at cach output. it does. not eive the merger trees for these haloes.," Even though the Millennium public database provides a catalogue of FOF haloes at each output, it does not give the merger trees for these haloes." Instead. it. provides merger trees for thesubhalocs. which are constructed. by connecting the subhaloes across the 64 available redshift outputs.," Instead, it provides merger trees for the, which are constructed by connecting the subhaloes across the 64 available redshift outputs." During this construction. a decision must be mace about the ancestral relations of the subhaloes since the particles in à given subhalo may go into more than a subhalo in the subsequent output.," During this construction, a decision must be made about the ancestral relations of the subhaloes since the particles in a given subhalo may go into more than a subhalo in the subsequent output." In this case. à subhalo is chosen to be the descendent of a progenitor subhalo at an earlier output if it hosts the largest number of bound particles in the progenitor. subhalo.," In this case, a subhalo is chosen to be the descendent of a progenitor subhalo at an earlier output if it hosts the largest number of bound particles in the progenitor subhalo." The resulting merger tree of subhaloes can then be processed further to construct the merger tree of the FOR haloes., The resulting merger tree of subhaloes can then be processed further to construct the merger tree of the FOF haloes. This construction is non-trivial due to the fragmentation of FOR haloes: this is cliscussecl at length in FAIOS ancl FALOO., This construction is non-trivial due to the fragmentation of FOF haloes; this is discussed at length in FM08 and FM09. In FALOS and. EMO. we proposed a variety. of. post-processing algorithms to handle FOL fragmentation.," In FM08 and FM09, we proposed a variety of post-processing algorithms to handle FOF fragmentation." Three methods were compared in EMOS:ΕΕ andx.," Three methods were compared in FM08:, and." The snipping method. severs the ancestral relationship between halo fragments and their progenitors., The snipping method severs the ancestral relationship between halo fragments and their progenitors. This is the method. commonly used in the literature ancl sullers from. inflated merger. rates due. to the aberrant remerger. of snipped fragments., This is the method commonly used in the literature and suffers from inflated merger rates due to the aberrant remerger of snipped fragments. " The two stitching algorithms prevent halo fragmentation by ""stitching"" halo fragments together such that cach FOE halo in the simulation has exactly one descendant."," The two stitching algorithms prevent halo fragmentation by ""stitching"" halo fragments together such that each FOF halo in the simulation has exactly one descendant." Stitch-: performs this procedure whenever fragmentation occurs. whereas stitch-3 only reincorporates halo fragments that are destined to remerge within 3 outputs of the fragmentation event.," $\infty$ performs this procedure whenever fragmentation occurs, whereas $3$ only reincorporates halo fragments that are destined to remerge within 3 outputs of the fragmentation event." Both stitching algorithms lower the minor merger rate as they prevent spurious remergers, Both stitching algorithms lower the minor merger rate as they prevent spurious remergers avoided.,avoided. We also considered snapshots spaced uniformly in expansion factor., We also considered snapshots spaced uniformly in expansion factor. We find that no substantial difference in the number of timesteps required to reach a given degree of convergence using this distribution of snapshots., We find that no substantial difference in the number of timesteps required to reach a given degree of convergence using this distribution of snapshots. This convergence is obtained for mean quantities averaged over large samples of galaxies—the full model in particular shows significant variance for individual galaxies even when using very large numbers of snapshots., This convergence is obtained for mean quantities averaged over large samples of galaxies—the full model in particular shows significant variance for individual galaxies even when using very large numbers of snapshots. Our results should provide guidance as to how many snapshots should ideally be stored from future N-body simulations to ensure that the resulting temporally sparse merger trees do not overly limit the accuracy of subsequent galaxy formation calculations., Our results should provide guidance as to how many snapshots should ideally be stored from future N-body simulations to ensure that the resulting temporally sparse merger trees do not overly limit the accuracy of subsequent galaxy formation calculations. " Our results are for a specific set of cosmological parameters and tree mass resolution, in addition to being for a specific implementation of baryonic physics."," Our results are for a specific set of cosmological parameters and tree mass resolution, in addition to being for a specific implementation of baryonic physics." " The rate of convergence plausibly depends on all of these factors, and will likely differ for galaxy properties other than those considered here."," The rate of convergence plausibly depends on all of these factors, and will likely differ for galaxy properties other than those considered here." " Since iis freely available as an open sourceproject, it is relatively easy for anyone to repeat the analysis performed here for a specific set of simulation parameters and galaxy properties."," Since is freely available as an open source, it is relatively easy for anyone to repeat the analysis performed here for a specific set of simulation parameters and galaxy properties." Our results were obtained with v0.9.0.r491 of aand we have made the input parameters available, Our results were obtained with v0.9.0.r491 of and we have made the input parameters available. Increasing mass resolution in simulations impliesonling™}. that merger trees contain more information., Increasing mass resolution in simulations implies that merger trees contain more information. " However, for this information to be folded into semi-analytic model predictions, trees must be built with finer time-stepping."," However, for this information to be folded into semi-analytic model predictions, trees must be built with finer time-stepping." " Thus, increasing mass resolution would imply increasing both the size of each snapshot and the number of such snapshots, thereby causing a “data tsunami""."," Thus, increasing mass resolution would imply increasing both the size of each snapshot and the number of such snapshots, thereby causing a “data tsunami”." " It would then be recommendable for large high resolution simulations to be post-processed on-the-fly, writing at finely spaced times only (sub)halo catalogues instead of the entire snapshot."," It would then be recommendable for large high resolution simulations to be post-processed on-the-fly, writing at finely spaced times only (sub)halo catalogues instead of the entire snapshot." Recent interest in exploring and constraining the parameter space of semi-analytic galaxy formation models (???) makes it crucial to understand and control numerical inaccuracies in such codes.," Recent interest in exploring and constraining the parameter space of semi-analytic galaxy formation models \citep{henriques_monte_2009,bower_parameter_2010,lu_bayesian_2010} makes it crucial to understand and control numerical inaccuracies in such codes." " Otherwise, quantitative constraints on model parameters will be subject to unknown systematic biases."," Otherwise, quantitative constraints on model parameters will be subject to unknown systematic biases." While many uncertainties, While many uncertainties SN 2001 was discovered spectroscopically by P. Doerliud at the F. L. Whipple Observatory on Feb. 19. 2001 (Jhaotal.. 20011).,"SN 2001V was discovered spectroscopically by P. Berlind at the F. L. Whipple Observatory on Feb. 19, 2001 \cite{iauc7585}) )." The SUpcrlova Was lnunediately classified as of Type Ia based ou the absorption rough at 6150A., The supernova was immediately classified as of Type Ia based on the absorption trough at 6150. ". The blue coutiuuuu suggestedOO that ji SN was discovered. before πα Πο,", The blue continuum suggested that this SN was discovered before maximum light. This was so strenethened by the high expansion velocity (L1 000 c) derived from the ceuter of the liue., This was also strengthened by the high expansion velocity (14 000 $^{-1}$ ) derived from the center of the line. Because ie light curves of Type Ia SNe are now frequently used o infer dist:ices to the host galaxies. such SNe that are identified before maxima are verv important. because 1) the lieht curve can be sampled more effectively. ii) he inferre istances are better coustrained by the light variation around uaxinumni than at later phases.," Because the light curves of Type Ia SNe are now frequently used to infer distances to the host galaxies, such SNe that are identified before maximum are very important, because i) the light curve can be sampled more effectively, ii) the inferred distances are better constrained by the light variation around maximum than at later phases." The lios ealaxy. NGC. 3987 belongs to the sinal erOUp centered on NGC LOO5 (Nilson.LOT3.. Gregory&Thompson. 1978)].," The host galaxy, NGC 3987 belongs to the small group centered on NGC 4005 \cite{nilson}, \cite{greg}) )." This eroup Is located within the medium-sized cluster Zw 127-10 (Zwicky.ctal.. 1961)3., This group is located within the medium-sized cluster Zw 127-10 \cite{zw}) ). NGC 3987 is au edec-on. Shc-type ealaxv with remarkable central dust lane.," NGC 3987 is an edge-on, Sbc-type galaxy with remarkable central dust lane." The IRAS poiut source 115172528 is ocated close to the optical ceuter of this galaxw. which was also detected iu radio (Condon&Broderick. 1986)).," The IRAS point source 11547+2528 is located close to the optical center of this galaxy, which was also detected in radio \cite{condon}) )." SN 2001V is the first supernova discovered iu this ealaxv., SN 2001V is the first supernova discovered in this galaxy. The SN occured in the outskirts. almost at the visible edge of the host (Fig.l).," The SN occured in the outskirts, almost at the visible edge of the host (Fig.1)." The position of the SN as well as its blue colour at naxiuuni niv sugeestOO that the effect of interstellar extinction is probably not very hieh for SN 2001V. Indeed. the galactic component of the reddening in this direction is only £(BV)20402 mag. according to Schlegeletal.," The position of the SN as well as its blue colour at maximum may suggest that the effect of interstellar extinction is probably not very high for SN 2001V. Indeed, the galactic component of the reddening in this direction is only $E(B-V)=0.02$ mag, according to \cite{sfd}." .1998.. There are two recent cistaunce estimates for NGC 3987: Mouldetal.1993 lists pg=33.82 lag (58.1 AMpc) based ou near-IR Tully-Fisher relation. while vanDriclοal..2001 gives e=[361 + as a group-averaged radial velocity corrected for Vireo-intall that results iu d=67.1 Mpe (adopting Z/j265 tMpe 1).," There are two recent distance estimates for NGC 3987: \cite{mould} lists $\mu_0 = 33.82$ mag (58.1 Mpc) based on near-IR Tully-Fisher relation, while \cite{vandriel} gives $v = 4361$ $^{-1}$ as a group-averaged radial velocity corrected for Virgo-infall that results in $d = 67.1$ Mpc (adopting $H_0 = 65$ $^{-1}$ $^{-1}$ )." Based ou he average of these distance estimates. the expected maximi brishtuess of a Type Ia SN is about LLG imag.," Based on the average of these distance estimates, the expected maximum brightness of a Type Ia SN is about 14.6 mag." According to the NASA/TIPAC Extragalactic Database. the redshift of NGC 3987 is 2=0.015.," According to the NASA/IPAC Extragalactic Database, the redshift of NGC 3987 is $z = 0.015$." Thus. SN 2001V is a relatively nearby. low-redshift SN.," Thus, SN 2001V is a relatively nearby, low-redshift SN." Iu the followings. details of the observations aud data reductions are given. then the results of the photometric analysis are presented aud discussed.," In the followings, details of the observations and data reductions are given, then the results of the photometric analysis are presented and discussed." uodel (Claret&IIauschildt2003).,model \citep{claret03}. . This feature also cinerecs from the recent results of Fieldsetal.(2003) on the microleusimg surface scanning of the ο eiaut star related to the EROS BLCG2000-5 event., This feature also emerges from the recent results of \citet{fields03} on the microlensing surface scanning of the K3 giant star related to the EROS BLG2000-5 event. Surface briglituess micasurements for this star are in fact inconsistent with the NextGen best-fit predictions at higher than 106. aud indicate that the derived T(r} vertical structure of the theoretical atinosphiere sensibly overestimates linab-darkening effects.," Surface brightness measurements for this star are in fact inconsistent with the NextGen best-fit predictions at higher than $\sigma$, and indicate that the derived $T(\tau)$ vertical structure of the theoretical atmosphere sensibly overestimates limb-darkening effects." Iu this work we carried out a combined comparison of the two theoretical codes ATLAS 19050) aud NextGen for stellar atinosphere svuthesis., In this work we carried out a combined comparison of the two theoretical codes ATLAS \citep{kurucz92b} and NextGen for stellar atmosphere synthesis. Our tests relied ou the fit of a set 331 target stars of noarlv solar metallicity. spanning the whole sequence of spectral types aud. ποπτν class; observed in the optical rauge by Comm&Stryker(19855). and Jacobyetal.(1981).," Our tests relied on the fit of a set 334 target stars of nearly solar metallicity, spanning the whole sequence of spectral types and luminosity class, observed in the optical range by \citet{gs83} and \citet{jhc84}." For about of this sample we obtained an, For about of this sample we obtained an boundaries depend on the subsample and are given in Sect.,boundaries depend on the subsample and are given in Sect. for z and T., \ref{subsec:data} for $z$ and $T$ . " The integration over x has to be done over the whole valid range of p,.", The integration over $x$ has to be done over the whole valid range of $p_x$. " Finally, the expected differential number density of the i-th cluster is simply given by the convolution To jointly fit both the low and the high-redshift cluster samples of ?,, we have to add the two contributions, finding For the sample by ?,, we proceed analogously, but the situation is much easier since we only deal with one single sample that covers only a small redshift interval."," Finally, the expected differential number density of the $i$ -th cluster is simply given by the convolution To jointly fit both the low and the high-redshift cluster samples of \citet{Vikhlinin2009a}, we have to add the two contributions, finding For the sample by \citet{Ikebe2002}, we proceed analogously, but the situation is much easier since we only deal with one single sample that covers only a small redshift interval." " The latter implies that we do not introduce a significant error if we ignore the redshift evolution of the mass or temperature function, respectively, in the analysis."," The latter implies that we do not introduce a significant error if we ignore the redshift evolution of the mass or temperature function, respectively, in the analysis." " Instead, we compute the theoretical functions at the sample’s median redshift of z=0.046 in the same way as ? did so that we only have to integrate over the temperature when calculating the total expected number of objects from the sample."," Instead, we compute the theoretical functions at the sample's median redshift of $z=0.046$ in the same way as \citet{Ikebe2002} did so that we only have to integrate over the temperature when calculating the total expected number of objects from the sample." " Hence, the C Statistic is given by The conditional probability p,(T|x) is again given by Eqs."," Hence, the $C$ statistic is given by The conditional probability $p_x(T|x)$ is again given by Eqs." " or (45),, respectively, thus assuming the same errors on the relations as for the ? data."," or , respectively, thus assuming the same errors on the relations as for the \citet{Vikhlinin2009a} data." " To better compare with the results by ?,, we shall also use the classical Press-Schechter mass function instead of the one by ? and relate mass and temperature via Eq."," To better compare with the results by \citet{Ikebe2002}, , we shall also use the classical Press-Schechter mass function instead of the one by \citet{Tinker2008} and relate mass and temperature via Eq." with αι=a?a3R/Ry., with $a_1=a_2=a_3\equiv R/R_\mathrm{pk}$ . " We search for minima of the C statistic as a function of the two cosmological parameters Oo and og, which enter both via n(x) and the volume factors dV/dz and Vinax."," We search for minima of the $C$ statistic as a function of the two cosmological parameters $\Omega_\mathrm{m0}$ and $\sigma_8$, which enter both via $n(x)$ and the volume factors $\dd V/\dd z$ and $V_\mathrm{max}$." " Only because the latter is very insensitive to changes in these two parameters, its dependence on O9 and os can be neglected."," Only because the latter is very insensitive to changes in these two parameters, its dependence on $\Omega_\mathrm{m0}$ and $\sigma_8$ can be neglected." ? showed that one can create confidence intervals for the C statistic in the same way as it can be done for a y? fit using properties of the X? distribution., \citet{Cash1979} showed that one can create confidence intervals for the $C$ statistic in the same way as it can be done for a $\chi^2$ fit using properties of the $\chi^2$ distribution. " Following ?,, intervals with confidence y are implicitly given solving for t, where f is the density of the Xp distribution with p degrees of freedom determined by the number of parameters."," Following \citet{Lampton1976}, , intervals with confidence $y$ are implicitly given solving for $t$ , where $f$ is the density of the $\chi^2_p$ distribution with $p$ degrees of freedom determined by the number of parameters." " For confidence and p=2, it follows that t=5.991."," For confidence and $p=2$, it follows that $t=5.991$ ." " Using the minimum of the C statistic, Cmin, we can simply calculate the confidence contours by searching for points in the parameter space for which C=Cin+5.991."," Using the minimum of the $C$ statistic, $C_\mathrm{min}$, we can simply calculate the confidence contours by searching for points in the parameter space for which $C=C_\mathrm{min}+5.991$." " In Fig. 6,,"," In Fig. \ref{fig:confidence}," we present the confidence contours for both the ? and the ? samples., we present the confidence contours for both the \citet{Ikebe2002} and the \citet{Vikhlinin2009a} samples. " Comparing the upper and the lower panels, one can see that the results from both data sets are compatible with each other, although pronounced differences exist."," Comparing the upper and the lower panels, one can see that the results from both data sets are compatible with each other, although pronounced differences exist." " However, for the latter, the confidence contours are smaller due to the additional information on the redshift evolution of the temperature function."," However, for the latter, the confidence contours are smaller due to the additional information on the redshift evolution of the temperature function." " The mass-based temperature functions (red contours)and the potential-based temperature functions using spherical collapse withouttemperature conversion (blue contours) give similar and compatible results, tthe confidence contours are inagreement with eachother and have approximately the samesize."," The mass-based temperature functions (red contours)and the potential-based temperature functions using spherical collapse withouttemperature conversion (blue contours) give similar and compatible results, the confidence contours are inagreement with eachother and have approximately the samesize." Whenredshift evolution informationis added (lower, Whenredshift evolution informationis added (lower Lithium abundances of the stars observed al low resolution were estimated from the strength of the 6707.7 ddoublet relative to that of the line at 6717.6A.,Lithium abundances of the stars observed at low resolution were estimated from the strength of the 6707.7 doublet relative to that of the line at 6717.6. . An empirical relation between the line-depth ratio of Li ancl Ca lines and the Li abundance was derived [rom known Li-rich K giants with Li abundances from high-resolution spectra., An empirical relation between the line-depth ratio of Li and Ca lines and the Li abundance was derived from known Li-rich K giants with Li abundances from high-resolution spectra. Fifteen IX giants in our survey were estimated to be Li-vich on the basis of the low resolution spectra., Fifteen K giants in our survey were estimated to be Li-rich on the basis of the low resolution spectra. Accurate abundances for these stars were then obtained [from high resolution spectroscopic analvsis (Table 1)., Accurate abundances for these stars were then obtained from high resolution spectroscopic analysis (Table 1). Previously known Li-vich giants of which several were reobservecl and reanalvsed are listed in Table 2., Previously known Li-rich giants of which several were reobserved and reanalysed are listed in Table 2. Our survey confirms the earlier survey (Brownetal.1989). that the Li-vich I," Our survey confirms the earlier survey \citep{brown1989} that the Li-rich K" Our survey confirms the earlier survey (Brownetal.1989). that the Li-vich Ix," Our survey confirms the earlier survey \citep{brown1989} that the Li-rich K" Low-mass stars are thought to form from the lrec-lall collapse of a protostellar molecular cloud. core to a protostar with a disc on a timescale of a few 10vr (Shu.Lizano LOST).,"Low-mass stars are thought to form from the free-fall collapse of a protostellar molecular cloud core to a protostar with a disc on a timescale of a few $10^5\,\rm yr$ \citep{shu87}." . Angular momentum. transport in accretion clises is driven by turbulence. thus allowing material to acerete on to the voung star., Angular momentum transport in accretion discs is driven by turbulence thus allowing material to accrete on to the young star. “Phe magneto-rotational instability (ATRL) can drive turbulence if the gas is well coupled. to the magnetic field. (Balbus&Lawley 1991)., The magneto-rotational instability (MRI) can drive turbulence if the gas is well coupled to the magnetic field \citep{balbus91}. . Llowever. with a low ionisation fraction the MIU is suppressed. (Ganunic1996:Cammie&Alenou1998).," However, with a low ionisation fraction the MRI is suppressed \citep{gammie96,gammie98}." The inner parts of a disc around a voung stellar object are hot enough to be thermally ionised., The inner parts of a disc around a young stellar object are hot enough to be thermally ionised. Llowever. further out. the disc becomes lavered with an MIELE turbulent (active) laver at cach surface and a dead zone at the midplane that i5 shiclded from the ionizing radiation of cosmic ravs ancl ravs [rom the star (e.g.Sanoetal.2000:Matsumura&Pu-dritz 2003).," However, further out, the disc becomes layered with an MRI turbulent (active) layer at each surface and a dead zone at the midplane that is shielded from the ionizing radiation of cosmic rays and X-rays from the star \citep[e.g.][]{sano00,matsumura03}." . In this work we concentrate on circumstellar discs. but note that dead zone formation is also favourable in circumplanetary disces (Martin&Lubow2011a.b).," In this work we concentrate on circumstellar discs, but note that dead zone formation is also favourable in circumplanetary discs \citep{martin11a,martin11b}." . A frequenthy used. assumption in calculations of disces with dead zones is that the surface density of the MIL active surface laver is constant with radius (e.g.Armitage.Livio&2008:Matsumura.Pudritz&Thommes 2009).," A frequently used assumption in calculations of discs with dead zones is that the surface density of the MRI active surface layer is constant with radius \citep[e.g.][]{armitage01,zhu09a,terquem08,matsumura09}." . Phe cosmic ravs enter the disc surface and are attenuated exponentially with a stopping depth of surface density around 100gem.” (Umoebasyashi&Nakano1981).," The cosmic rays enter the disc surface and are attenuated exponentially with a stopping depth of surface density around $100\,\rm g\,cm^{-2}$ \citep{umebayashi81}." . However. this does not allow for recombination effects that may play a significant role in determining the ionisation of the disc.," However, this does not allow for recombination effects that may play a significant role in determining the ionisation of the disc." A more realistic wav to determine the cleacd zone is using a magnetic ltevnolds number., A more realistic way to determine the dead zone is using a magnetic Reynolds number. MIID. simulations show that magnetic turbulence cannot be sustained. if the magnetic Itevnolds number is lower than some critical value Hes25A in this work shows ~Ll% at z=l aud ~LOO% at +=6. which is somewhat higher than the LAE fraction in LBC sample (Starkctal.2010.2011:Peu-tericcietal.2011:Scheukeret2012:Ono 2012).," Moreover, the LAEs fraction having $EW > 25~\A$ in this work shows $\sim 44\; \%$ at z=4 and $\sim 100\; \%$ at $z = 6$, which is somewhat higher than the LAE fraction in LBG sample \citep{Stark10, Stark11, Pentericci11, Schenker12, Ono12}." . Towever. in observation. the LAE fraction increases with decreasing UV brightuess.," However, in observation, the LAE fraction increases with decreasing UV brightness." Most of our model galaxies at DE are fainter than the detection threshold in the LBG observation., Most of our model galaxies at $z \gtrsim 3$ are fainter than the detection threshold in the LBG observation. Since the number of galaxies brighter than the threshold of LBG observation is quite stuall (less tla teu). we need a larger sauuple covering a wide lass range to verify the model of LAEs.," Since the number of galaxies brighter than the threshold of LBG observation is quite small (less than ten), we need a larger sample covering a wide mass range to verify the model of LAEs." In addition. although some LAEs have been observed with UV coutimuun. aud hence categorized as LBCs. it is inadequate to study LAEs from LBC-only sample. because a large fraction of LAEs may have UV continuum under the detection limit of current observations.," In addition, although some LAEs have been observed with UV continuum, and hence categorized as LBGs, it is inadequate to study LAEs from LBG-only sample, because a large fraction of LAEs may have UV continuum under the detection limit of current observations." We will address the general properties sucl, We will address the general properties such We will address the general properties sucli, We will address the general properties such "to parametrize the field taueling for computing the dynamically Óaportant modes. and introduce an casily solvable ""square box” model suitable for exploring the parameter range.","to parametrize the field tangling for computing the dynamically important modes, and introduce an easily solvable “square box” model suitable for exploring the parameter range." Finally. in section 6. we use the suite of models built in the previous sections to explore their connection to the OPO phenomenology.," Finally, in section 6, we use the suite of models built in the previous sections to explore their connection to the QPO phenomenology." We find (a) within the standard magnetar model. it is possible to produce strong lone-lived or transient QPOs with frequencies in the rage of around 20 150IIz. but only if the neutrous are decoupled from the Alfveu-like motion of fie core: this implies that at least one of the barvouic colmpoucuts of the core is a quanti jj Our models could uot produce the lieh-fequency 625IIz QPO within the standard paradigm of a maguctar core conmpositiou.," We find (a) within the standard magnetar model, it is possible to produce strong long-lived or transient QPOs with frequencies in the range of around $20$ $150$ Hz, but only if the neutrons are decoupled from the Alfven-like motion of the core; this implies that at least one of the baryonic components of the core is a quantum (b) Our models could not produce the high-frequency $625$ Hz QPO within the standard paradigm of a magnetar core composition." lu this section. we study the motion of a harmonic oscillator (which we hereafter call the aree oscillator) which is coupled to a coutimmiun ofmodoes.," In this section, we study the motion of a harmonic oscillator (which we hereafter call the large oscillator) which is coupled to a continuum of." 7.. This mocl was introduced in LO? aud it provides a qualitative insight into the behaviow of crustal modes (represcuted by the laree oscillator) coupled to a coutimmun of Alfven modes in the core of a maenetar., This model was introduced in L07 and it provides a qualitative insight into the behaviour of crustal modes (represented by the large oscillator) coupled to a continuum of Alfven modes in the core of a magnetar. LO? found tiat if the large oscillators xoper frequency was withi1 the range of the continuii frequencies. then the late-time ydliaviour ofthe system was dominated by oscillatory nioion near the edges of the coutinuum interval.," L07 found that if the large oscillator's proper frequency was within the range of the continuum frequencies, then the late-time behaviour of the system was dominated by oscillatory motion near the edges of the continuum interval." Here. we give au explanation of this phenomenon in terms of themodes.," Here, we give an explanation of this phenomenon in terms of the." Our analysis allows us to use initial data and predict the displacemout züuplitudes aud frequencies of the svstei af late times., Our analysis allows us to use initial data and predict the displacement amplitudes and frequencies of the system at late times. The uodel consists of the large mechanical oscillator with mass A and proper frequency wu. rYopreselnlus a crustal clastic shear mode.," The model consists of the large mechanical oscillator with mass $M$ and proper frequency $\omega_0$, representing a crustal elastic shear mode." " Attached to he large oscillator is a set of NO siualler oscillators of mass 55, aud proper frequency w,, constituting a quasi-continmun of frequencies Vu (where n=1.2... CN)"," Attached to the large oscillator is a set of $N$ smaller oscillators of mass $m_n$ and proper frequency $\omega_n$ constituting a quasi-continuum of frequencies $\omega_n$ (where $n = 1, 2, ..., N$ )." " The coutimmiun is achieved when V>x while the total smal-oscillator mass “in, remains finite.", The continuum is achieved when $N\rightarrow\infty$ while the total small-oscillator mass $\Sigma m_n$ remains finite. The convenicut pictorial represcutation is through suspended peudulae. as shown in Fie.," The convenient pictorial representation is through suspended pendulae, as shown in Fig." 1. (sec also Fie., \ref{Fig1} (see also Fig. 2 of LU?)., 2 of L07). The equations of motion are obtained as follows., The equations of motion are obtained as follows. " Each sanall oscillator is driven by the the motion of the large oscillator: where e, is the displacenent of the n,th snall oscillator in the frame of reference of the large oscillator. wry ds the displacement of the large oscillator im the inertial fraane of reference. and the right-hand side represeuts the nondnertial force acting on the small oscillator due to the acceleration of the large one."," Each small oscillator is driven by the the motion of the large oscillator: where $x_n$ is the displacement of the $n'th$ small oscillator in the frame of reference of the large oscillator, $x_0$ is the displacement of the large oscillator in the inertial frame of reference, and the right-hand side represents the non-inertial force acting on the small oscillator due to the acceleration of the large one." The large oscillator experiences the combined ill of the sinall Tere ay is the frequeney of the big pendulum corrected for the nus loading bv the small peudulae. ie. 11.," The large oscillator experiences the combined pull of the small Here $\tilde{\omega}_0$ is the frequency of the big pendulum corrected for the mass loading by the small pendulae, i.e. $\tilde{\omega}_0^2 = \omega_0^2 \left( M + \sum_i m_i \right)/M $ ." effective temperature.,effective temperature. They find that this stratification will change the disk’s reflection properties substantially., They find that this stratification will change the disk's reflection properties substantially. Although ? study a similar situation in galactic black holes. and find no similar stratification. they focus on cases m which the disk dominates the Juminosity.," Although \cite{2007MNRAS.381.1697R} study a similar situation in galactic black holes, and find no similar stratification, they focus on cases in which the disk dominates the luminosity." For lower disk temperatures stratification could presumably still occur., For lower disk temperatures stratification could presumably still occur. However. ? studied the case where a disk was overlaid with a surface corona. and included the effect of its weight on the gas pressure.," However, \cite{2001ApJ...546..406N} studied the case where a disk was overlaid with a surface corona, and included the effect of its weight on the gas pressure." They found that this was sufficient to prevent stratification., They found that this was sufficient to prevent stratification. An additional caveat in using the constant density models of ? is that they consider AGN disks. which are much cooler and less dense than those in GBHCs.," An additional caveat in using the constant density models of \cite{2005MNRAS.358..211R} is that they consider AGN disks, which are much cooler and less dense than those in GBHCs." As a result. the reflection spectra do not consider the flux in the disk itself (which can change the ionization state significantly). and the effects from things like three-body recombination. which will become important as the disk densities become higher.," As a result, the reflection spectra do not consider the flux in the disk itself (which can change the ionization state significantly), and the effects from things like three-body recombination, which will become important as the disk densities become higher." " Recent work by ? has examined reflection spectra in GBHCs. although they focus on systems in which the disk dominates the spectrum and is hotter (&7,,=0.35 keV) than the disks considered in this work."," Recent work by \cite{2007MNRAS.381.1697R} has examined reflection spectra in GBHCs, although they focus on systems in which the disk dominates the spectrum and is hotter $kT_e = 0.35$ keV) than the disks considered in this work." To calculate the spectrum from inverse Compton scattering through the hot layers of the disk we use a one-dimensional Monte Carlo simulation., To calculate the spectrum from inverse Compton scattering through the hot layers of the disk we use a one-dimensional Monte Carlo simulation. The radial variation of quantities in the disk and hot layer is replaced by representative values. for which we use energy-weighted means.," The radial variation of quantities in the disk and hot layer is replaced by representative values, for which we use energy-weighted means." The simulation assumes a slab geometry. with the cool optically thick disk below a much hotter surface layer with moderate optical depth.," The simulation assumes a slab geometry, with the cool optically thick disk below a much hotter surface layer with moderate optical depth." For the seed photons. we use the disk+reflection spectrum found in the previous two sections.," For the seed photons, we use the disk+reflection spectrum found in the previous two sections." To capture the emission lines in this spectrum. we set the resolution of the simulation to AE/E=0.046.," To capture the emission lines in this spectrum, we set the resolution of the simulation to $\Delta E/E = 0.046$." The number of seed photons followed through the hot layer is of the order 107. sufficient to represent the result to a noise level comparable with typical observations.," The number of seed photons followed through the hot layer is of the order $10^7$, sufficient to represent the result to a noise level comparable with typical observations." The output spectrum is angle dependent (because of the increasing optical depth with inclination). so a value has to be assumed for the inclination angle 8 to the line of sight (measured from the normal of the disk).," The output spectrum is angle dependent (because of the increasing optical depth with inclination), so a value has to be assumed for the inclination angle $\theta$ to the line of sight (measured from the normal of the disk)." For our reference model we use @=0.5 as a representative value., For our reference model we use $\mu=\cos\theta = 0.5$ as a representative value. The input parameters of the Comptonization caleulation are the input spectrum. the optical depth and the temperature of the hot layer.," The input parameters of the Comptonization calculation are the input spectrum, the optical depth and the temperature of the hot layer." The resulting total energy flux i Comptonized photons (integrated over the spectrum and summed over both sides of the hot layer) has to match the energy input into the hot layer: the sum of ion heating and viscous dissipation., The resulting total energy flux in Comptonized photons (integrated over the spectrum and summed over both sides of the hot layer) has to match the energy input into the hot layer: the sum of ion heating and viscous dissipation. " We can estimate the optical depth for the hot layer from the surface density of the hot layer. where (7)=&,Gp)."," We can estimate the optical depth for the hot layer from the surface density of the hot layer, where $\langle\tau\rangle = \kappa_{es}\langle\Sigma_{\rm{Hot}}\rangle$." The temperature of the hot layer is adjusted iteratively in the calculations to meet this condition to an accuracy of10%., The temperature of the hot layer is adjusted iteratively in the calculations to meet this condition to an accuracy of. ". For the reference model. we find AT,= 70keV. and r=0.87."," For the reference model, we find $kT_e = 70$ keV, and $\tau = 0.87$." The resulting emergent spectrum of the hot layer is shown in the blue dotted line in fig. 4..," The resulting emergent spectrum of the hot layer is shown in the blue dotted line in fig. \ref{fig:TESTspec}," for an inclination angle of µ=0.5., for an inclination angle of $\mu = 0.5$. The photon index of this spectrum in the range 2-10 keV is about Γ=1.96., The photon index of this spectrum in the range 2-10 keV is about $\Gamma = 1.96$. In the hot ri£ (where the hot layer has spilled over inside inner edge of the cool disk) there is no underlying cool disk any more and it receives its soft photons only by scattering from larger cistances: it is “photon starved’ compared with the hot layer itself., In the hot ring (where the hot layer has spilled over inside inner edge of the cool disk) there is no underlying cool disk any more and it receives its soft photons only by scattering from larger distances: it is `photon starved' compared with the hot layer itself. Since the energy input by ton heating and viscous dissipation are still similar. the temperature is higher and Comptorization correspondingly stronger.," Since the energy input by ion heating and viscous dissipation are still similar, the temperature is higher and Comptonization correspondingly stronger." The hot ring therefore makes its contribution mostly at the high energy end of the spectrun. and is less important for the ‘soft component of the spectrum that is the focus of our study.," The hot ring therefore makes its contribution mostly at the high energy end of the spectrum, and is less important for the `soft component' of the spectrum that is the focus of our study." We include it. however. since we also want to achieve a reasonable fit to the overall spectral energy distribution in the observations discussed in the next sections.," We include it, however, since we also want to achieve a reasonable fit to the overall spectral energy distribution in the observations discussed in the next sections." The calculation of DSOS relied on the earlier. one-dimensional work of ? in order to set the temperature anc energetic contribution from the hot inner ring. which predicts a very small contribution from the hot ring.," The calculation of DS05 relied on the earlier one-dimensional work of \cite{2002A&A...387..907D} in order to set the temperature and energetic contribution from the hot inner ring, which predicts a very small contribution from the hot ring." With a sufficiently detailed geometrical model for the hot ring. the soft photor πριί by scattering. could in. principle be modelled more accurately. but the level of detail needed is probably beyond the limits of the present model.," With a sufficiently detailed geometrical model for the hot ring, the soft photon input by scattering could in principle be modelled more accurately, but the level of detail needed is probably beyond the limits of the present model." We therefore treat the soft input flux in this component of the model as an adjustable unknowr when fitting to spectra., We therefore treat the soft input flux in this component of the model as an adjustable unknown when fitting to spectra. For this. we introduce a parameter z. which represents the fraction of seed photons from the cool disk that cool the hot layer. so that 1Z goes to cool the hot ring.," For this, we introduce a parameter $\zeta$, which represents the fraction of seed photons from the cool disk that cool the hot layer, so that $1-\zeta$ goes to cool the hot ring." For the reference model. Z 1s set by the contribution predicted from the DS05 model for the hot inner ring.," For the reference model, $\zeta$ is set by the contribution predicted from the DS05 model for the hot inner ring." Also treated as adjustable is the temperature reached by equilibrium between heating and Comptonization., Also treated as adjustable is the temperature reached by equilibrium between heating and Comptonization. We assume that cooling in this region is still moderately efficient. choosing temperatures in the range KT.=180—200 keV. For simplicity (since the angular distribution of seed photons is also uncertain) we model the hot ring with a plane-parallel Monte Carlo simulation with the same resolution as in the hot layer.," We assume that cooling in this region is still moderately efficient, choosing temperatures in the range $kT_{\rm{e}}= 180-200$ keV. For simplicity (since the angular distribution of seed photons is also uncertain) we model the hot ring with a plane-parallel Monte Carlo simulation with the same resolution as in the hot layer." We discuss the limitations of this approach in sect. ??.., We discuss the limitations of this approach in sect. \ref{sec:discussion}. As in the hot layer. the X-ray energy flux produced by Comptonizatio1 has to match the energy input by viscous dissipation. anc ion heating.," As in the hot layer, the X-ray energy flux produced by Comptonization has to match the energy input by viscous dissipation and ion heating." " Together with the now assumed value for the temperature. this determines Z. and the optical depth of the rir5,"," Together with the now assumed value for the temperature, this determines $\zeta$, and the optical depth of the ring." For the reference parameters of this section. we find Z=0.99 and an optical depth of ~0.7.," For the reference parameters of this section, we find $\zeta=0.99$ and an optical depth of $\sim 0.7$." " Ata temperature of 200 keV we find that the ring contributes only of the overall hard flux (Fx=2—200 keV) for the reference values a=02 of the viscosity and Rj,=20Rs.", At a temperature of 200 keV we find that the ring contributes only of the overall hard flux $_{\rm X}= 2-200$ keV) for the reference values $\alpha=0.2$ of the viscosity and $R_{in}=20R_S$. This is because the radial width of the hot ring has a rather limited extent. since the evaporation process Is very efficient.," This is because the radial width of the hot ring has a rather limited extent, since the evaporation process is very efficient." The hot layer evaporates very quickly after it has flowed over inner edge of the cool disk., The hot layer evaporates very quickly after it has flowed over inner edge of the cool disk. The hot Comptonized component from the hot ring is shown in the orange dash-dotted line in fig. 4., The hot Comptonized component from the hot ring is shown in the orange dash-dotted line in fig. \ref{fig:TESTspec}. . The latter conditional probability depends on the process that produced the observed photon map.,The latter conditional probability depends on the process that produced the observed photon map. Calculating for all photons 2; the corresponding iudices oj. we ect the relative frequency distribution of scaling indices. or scaling index spectrin. Depending on the random processes in the considered field. Nypeg(a) has a well-defined euvelope aud shows gaps. where the probability of equation (1)) is zero.," Calculating for all photons $x_i$ the corresponding indices $\alpha_i$, we get the relative frequency distribution of scaling indices, or scaling index spectrum, Depending on the random processes in the considered field, $N_{freq}(\alpha)$ has a well-defined envelope and shows gaps, where the probability of equation \ref{condprob}) ) is zero." The search for sources or density variations in au otherwise homogeneous aud isotropic background is SVILOLVILOUS o the measurement of deviations frou the expected frequency distribution., The search for sources or density variations in an otherwise homogeneous and isotropic background is synonymous to the measurement of deviations from the expected frequency distribution. Any iuliomiogencity or anisotropy will result either in inore power of the frequency distribution at low oe-values or iu filhug up the discrete gaps., Any inhomogeneity or anisotropy will result either in more power of the frequency distribution at low $\alpha$ -values or in filling up the discrete gaps. Since we have. in general. no precise kuowledge:i:bout the process procuciis the ]νοπι and. as far as we know. uo closed. analytical description foy Nyy.yO) exists. another procedure is necessary to separate backerouncd photons from. soiree plotous.," Since we have, in general, no precise knowledge about the process producing the background and, as far as we know, no closed analytical description for $N_{freq}(\alpha)$ exists, another procedure is necessary to separate background photons from source photons." For different scaling ranges [rj.1ο) the scaling iudices are binned with da=LO ©. the computer precision in this case.," For different scaling ranges $\lbrack r_1, r_2\rbrack$ the scaling indices are binned with $\delta\alpha=10^{-6}$ , the computer precision in this case." " The rm are chosen to be about the size of the expected sources, While ro %1054: in our examples we typically used four different scaling ranges."," The $r_1$ are chosen to be about the size of the expected sources, while $r_2$ $\approx 10 r_1$; in our examples we typically used four different scaling ranges." In a first step. the a-values with ερα)X2 are singled out for cach scaling range.," In a first step, the $\alpha$ -values with $N_{freq}(\alpha)\leq 2$ are singled out for each scaling range." Tn a second step. only those o-values that have NepeglO)X 2in at least two scaling ranges are considered as belonging to source photons.," In a second step, only those $\alpha$ -values that have $N_{freq}(\alpha)\leq 2$ in at least two scaling ranges are considered as belonging to source photons." Simulations showed that theummber of photous singled out with this procedure in, Simulations showed that thenumber of photons singled out with this procedure in only a few percentage points of successfully detected galaxies of each type).,only a few percentage points of successfully detected galaxies of each type). This is consistent with the results from the previous section where it was found that the PCA eigenspectra generally carry the same physical information as each other - despite being “statistically” independent., This is consistent with the results from the previous section where it was found that the PCA eigenspectra generally carry the same physical information as each other - despite being `statistically' independent. The results from each ANN are summarised in Table. 2..," The results from each ANN are summarised in Table. \ref{ann}," and once again the (pey.pes) components are shown for the galaxies which have been classified by the ANN (in this case the 9:9:2 configuration) in Fig. 10.., and once again the $pc_1$ $pc_2$ ) components are shown for the galaxies which have been classified by the ANN (in this case the 9:9:2 configuration) in Fig. \ref{fig:net}. Again it can be seen that the classification can be quite accurately expressed using only these first two projections., Again it can be seen that the classification can be quite accurately expressed using only these first two projections. The correspondence with the 2HFGRS η) classification is also shown., The correspondence with the 2dFGRS $\eta$ classification is also shown. One problem that arose when attempting to separate the Early type galaxies in our sample was that we obtained a significant contamination from Late type galaxies (~ 50663)., One problem that arose when attempting to separate the Early type galaxies in our sample was that we obtained a significant contamination from Late type galaxies $\sim50$ ). It was found that this fractional contamination could be reduced somewhat by increasing the complexity of the ANN. however this resulted in a lower percentage of the actual Early type galaxies being correctly classified.," It was found that this fractional contamination could be reduced somewhat by increasing the complexity of the ANN, however this resulted in a lower percentage of the actual Early type galaxies being correctly classified." The actual degree of this contamination will vary according to the galaxy population under consideration., The actual degree of this contamination will vary according to the galaxy population under consideration. In the case of the 2dFGRS we are presented with a 5j-selected sample of galaxies and as such there is a significantly higher proportion of Late type (star-forming) galaxies than Early types., In the case of the 2dFGRS we are presented with a $\bj$ -selected sample of galaxies and as such there is a significantly higher proportion of Late type (star-forming) galaxies than Early types. On the other hand. in the case of a 2MASS (Jarrett 22000) near-infrared selected galaxy sample. the proportion of types is reversed (Madgwick Lahav 2001) and so à more pure sample of Early types ean be determined.," On the other hand, in the case of a 2MASS (Jarrett 2000) near-infrared selected galaxy sample, the proportion of types is reversed (Madgwick Lahav 2001) and so a more pure sample of Early types can be determined." Because our sample of morphologically classified galaxies is drawn from only the most nearby Cand hence the most extended on the sky) galaxies. we must consider the possibility that the observed spectra are not representative of the galaxies as a whole.," Because our sample of morphologically classified galaxies is drawn from only the most nearby (and hence the most extended on the sky) galaxies, we must consider the possibility that the observed spectra are not representative of the galaxies as a whole." " For example. the 2dF fibre (diameter 2-216"") may only sample the light from the bulge of a nearby spiral galaxy - the spectrum from which tends to be more similar to that of an Early type galaxy."," For example, the 2dF fibre (diameter $''$ ) may only sample the light from the bulge of a nearby spiral galaxy - the spectrum from which tends to be more similar to that of an Early type galaxy." In order to test the importance of redshift upon the success of our morphological classitier we return to our ANN (configuration 9:9:2). trained previously.," In order to test the importance of redshift upon the success of our morphological classifier we return to our ANN (configuration 9:9:2), trained previously." If aperture effects are important then we would expect to see that the ANN will recover the galaxy morphology of relatively distant galaxies more accurately than for nearby galaxies. particularly in the case of Late type galaxies.," If aperture effects are important then we would expect to see that the ANN will recover the galaxy morphology of relatively distant galaxies more accurately than for nearby galaxies, particularly in the case of Late type galaxies." For this reason the results from the previous section were re-determined after dividing the testing sample into two redshift bins. +<0.05 (1533 galaxies) and -0.05 (761 galaxies).," For this reason the results from the previous section were re-determined after dividing the testing sample into two redshift bins, $z<0.05$ (1533 galaxies) and $z>0.05$ (761 galaxies)." The results are summarised in Table. 3.., The results are summarised in Table. \ref{aper}. Contrary to our expectations the success of the classification is relatively immune to the redshift being sampled., Contrary to our expectations the success of the classification is relatively immune to the redshift being sampled. Clearly the situation must be more complex than a simple analysis such as this can resolve., Clearly the situation must be more complex than a simple analysis such as this can resolve. One important aspect of the spectra being used in this analysis which may explain this situation is the substantial seeing present at the Anglo-Australian Telescope site., One important aspect of the spectra being used in this analysis which may explain this situation is the substantial seeing present at the Anglo-Australian Telescope site. This seeing acts to “smooth out” any spectral gradients which may be present in a given galaxy., This seeing acts to `smooth out' any spectral gradients which may be present in a given galaxy. " In general the seeing is of the order of |.8-2.5"" and so can effectively double the area being sampled by the 2dF fibre aperture.", In general the seeing is of the order of $''$ and so can effectively double the area being sampled by the 2dF fibre aperture. Another major consideration in an analysis such as this is the stability of the morphological classification with redshift - as more distant galaxies will tend to be fainter and less extended on the sky., Another major consideration in an analysis such as this is the stability of the morphological classification with redshift - as more distant galaxies will tend to be fainter and less extended on the sky. In general the robustness of a morphological classification is difficult to assess because of its subjectivity., In general the robustness of a morphological classification is difficult to assess because of its subjectivity. It has been found in previous work (Naim 11995) that this subjective element results in an uncertainty of the order of 2? T-Types., It has been found in previous work (Naim 1995) that this subjective element results in an uncertainty of the order of 2 T-Types. However. this figure does not incorporate the uncertainties introduced to the classification through inclination. obscuration and other systematic uncertainties.," However, this figure does not incorporate the uncertainties introduced to the classification through inclination, obscuration and other systematic uncertainties." All of these uncertainties add to the importance of being able to estimate morphologies in a more robust manner such as by correlating with galaxy spectra. or indeed for neglecting morphology altogether and simply using a spectral-based classification (see e.g Madgwick Lahav 2001).," All of these uncertainties add to the importance of being able to estimate morphologies in a more robust manner such as by correlating with galaxy spectra, or indeed for neglecting morphology altogether and simply using a spectral-based classification (see e.g. Madgwick Lahav 2001)." Because the galaxy sample considered here has been restrictec to apparent magnitudes greater than 6)=16.5. misclassification is not considered to be as significant an issue in this analysis as 1 might otherwise be.," Because the galaxy sample considered here has been restricted to apparent magnitudes greater than $\bj=16.5$, misclassification is not considered to be as significant an issue in this analysis as it might otherwise be." However when repeating the above analysis using galaxies fainter than this magnitude limit a very substantia systematic misclassitication of spirals was observed., However when repeating the above analysis using galaxies fainter than this magnitude limit a very substantial systematic misclassification of spirals was observed. This was to be expected since the spiral arms of such galaxies will become more difficult to resolve at higher redshift (where most of the faintes galaxies will reside). particularly for galaxies inclined to the line-of-sight.," This was to be expected since the spiral arms of such galaxies will become more difficult to resolve at higher redshift (where most of the faintest galaxies will reside), particularly for galaxies inclined to the line-of-sight." Perhaps one of the most interesting aspects of this work on recovering galaxy morphologies from their spectra. is how closely related the results from advanced statistical methods appear to be to the original 2dFGRS spectral classification. 77.," Perhaps one of the most interesting aspects of this work on recovering galaxy morphologies from their spectra, is how closely related the results from advanced statistical methods appear to be to the original 2dFGRS spectral classification, $\eta$." In some regards this was to be expected. since one is always inclined to relate one's classification to galaxy morphology during its derivation.," In some regards this was to be expected, since one is always inclined to relate one's classification to galaxy morphology during its derivation." For example Folkes ((1999) used a training set of 26 galaxies drawn from the Kennicutt Atlas (Kennicutt. 1992) as a training set to derive the original 2dFGRS spectral classification., For example Folkes (1999) used a training set of 26 galaxies drawn from the Kennicutt Atlas (Kennicutt 1992) as a training set to derive the original 2dFGRS spectral classification. " These 26 galaxies were ""projected onto the (pc,.pcs? plane detined by the 2HFGRS spectra and lines were drawn by-hand to roughly separate the galaxies according to their assumed morphologies.", These 26 galaxies were `projected' onto the $pc_1$ $pc_2$ ) plane defined by the 2dFGRS spectra and lines were drawn by-hand to roughly separate the galaxies according to their assumed morphologies. However. in the case of +) this method was not used. rather the galaxies were classitied solely on the basis of finding the most statistically significant projection in the PCA which was robust to the Known instrumental uncertainties in the 2dF instrument (see Madgwick 22002 for more details).," However, in the case of $\eta$ this method was not used, rather the galaxies were classified solely on the basis of finding the most statistically significant projection in the PCA which was robust to the known instrumental uncertainties in the 2dF instrument (see Madgwick 2002 for more details)." The overall success of correlating galaxy morphologies and spectra. using the methods considered in this paper. is summarised," The overall success of correlating galaxy morphologies and spectra, using the methods considered in this paper, is summarised" Combining. ground- and spaceborne observations we have obtained the spectral energy distribution for the IR/OH star 3004 in the wavelength range 1.25x:Afqgm 60.,"Combining ground- and spaceborne observations we have obtained the spectral energy distribution for the IR/OH star $\,$ $-$ 3004 in the wavelength range $1.25 \le \lambda / \mu$ $ \le 60$ ." The near-IR spectrum has JHK colours corresponding to an M4 star reddened by dust with li;~ I4+mag.," The near-IR spectrum has JHK colours corresponding to an M4 star reddened by dust with $A_{\rm vis}\,\sim\,$ $\,$ mag." The MIR spectrum shows prominent silicate peaks at. 10.4. and 17.5 jm as. well as an SiO absorption around jim. and SiO bandheads in the 4.0 - 4.3/1 range.," The MIR spectrum shows prominent silicate peaks at 10.4 and $\,\mu$ m as well as an SiO absorption around $\,\mu$ m and SiO bandheads in the 4.0 - $\mu$ range." Taken together. the solid-state and molecular features confirm the picture already suggested from the SiO. OH and H»;O masing activity that IRAS 3004 is a luminous oxygen-rich star with a high mass-loss dusty wind.," Taken together, the solid-state and molecular features confirm the picture already suggested from the SiO, OH and $_2$ O masing activity that IRAS $-$ 3004 is a luminous oxygen-rich star with a high mass-loss dusty wind." Neglecting line of sight extinction. the broad band spectral energy distribution of the dust emission and the extinction in the near-IR can be fitted by a spherically symmetrical outflow of a silicate and graphite grain mixture illuminated by an MAI supergiant situated at a distance of < kpe with luminosity 1.3«10°L... dust production rate Μινι| and wind velocity ~ ο.," Neglecting line of sight extinction, the broad band spectral energy distribution of the dust emission and the extinction in the near-IR can be fitted by a spherically symmetrical outflow of a silicate and graphite grain mixture illuminated by an M4I supergiant situated at a distance of $\le$ $\,$ kpc with luminosity $\sim 1.3\times10^5\,{\rm L_\odot}$, dust production rate $\,$ $^{-7}$ $_{\odot}\,{\rm yr}^{-1}$ and wind velocity $\sim\,$ $^{-1}$." " For a distance of kpe. the shell’s inner boundary diameter corresponds to an angular size of ~0.022"", which will make it accessible in future to quantitative observations with the VLA (maser emission) and VLTI (MIR dust emission) respectively."," For a distance of $\,$ kpc, the shell's inner boundary diameter corresponds to an angular size of $\sim 0.022''$, which will make it accessible in future to quantitative observations with the VLA (maser emission) and VLTI (MIR dust emission) respectively." We gratefully acknowledge the support provided by the ISO data centres at MPIA in Heidelberg and MPE in Garching., We gratefully acknowledge the support provided by the ISO data centres at MPIA in Heidelberg and MPE in Garching. We benefited much from discussions with EElitzur. GGail. HHenning. KKáuufl. KKunze. LLutz. K.M.MMenten. WWaters and ZZijlstra.," We benefited much from discussions with Elitzur, Gail, Henning, Käuufl, Kunze, Lutz, Menten, Waters and Zijlstra." Our special thanks go to the referee Volk for his comments. from which the paper profited much.," Our special thanks go to the referee Volk for his comments, from which the paper profited much." In section 4. we interpret the observations in (the context of current. understanding of the llelix's 3-D structure and discuss the number density. mass. evolution and excitation of the knots as revealed by our IH» images.,"In section 4, we interpret the observations in the context of current understanding of the Helix's 3-D structure and discuss the number density, mass, evolution and excitation of the knots as revealed by our $_2$ images." We summarize our conclusions in section 5., We summarize our conclusions in section 5. The Hubble Helix project (GO program 9700: PI: M. Meixner) imaged the 11ος nebula during the 2002 Leonids meteor shower (hat presented a risk to the HST., The Hubble Helix project (GO program 9700; PI: M. Meixner) imaged the Helix nebula during the 2002 Leonids meteor shower that presented a risk to the HST. The imagine involved a 9-panel mosaic of the Helix using the ACS WFC instrument in the F658N filter (iransmittiing equally well both the 66563 aand [N IH] 6584 lines) and the F502N filter (dominated by the [O HI] 5007 lline)., The imaging involved a 9-panel mosaic of the Helix using the ACS WFC instrument in the F658N filter (transmitting equally well both the 6563 and [N II] 6584 lines) and the F502N filter (dominated by the [O III] 5007 line). In parallel with the ACS imaging. we used NICMOS (Thompsonetal.1993). to image 1 of the possible 9 field positions. 5 of which landed on the nebula (positions 1. 2. 3. 4 and 5) and 2 of which were olf (he nebula (positions 7 and 9) aud used Lor background measurements for the 5 fields on the nebula.," In parallel with the ACS imaging, we used NICMOS \citep{thompson98} to image 7 of the possible 9 field positions, 5 of which landed on the nebula (positions 1, 2, 3, 4 and 5) and 2 of which were off the nebula (positions 7 and 9) and used for background measurements for the 5 fields on the nebula." Figure 1. shows the location of these fields on the Helix and ihe RA and Dee of the field centers for field positions 1. 2. 3. 4. and 5 are listed in Table 1..," Figure \ref{helixmap} shows the location of these fields on the Helix and the RA and Dec of the field centers for field positions 1, 2, 3, 4, and 5 are listed in Table \ref{loctab}." These parallel NICAIOS field positions had insignilicant overlap with the the ACS images., These parallel NICMOS field positions had insignificant overlap with the the ACS images. Because we wanted maximum field of view and our target was a diffuse nebula. we used the NIC3 camera. 072 !. with the F212N filter to image the II» 2.12 line emission in the nebula.," Because we wanted maximum field of view and our target was a diffuse nebula, we used the NIC3 camera, $0\farcs2$ $^{-1}$, with the F212N filter to image the $_2$ 2.12 line emission in the nebula." For field positions 1 and 2. half the time was spent in the Paa filler F1STN that is sufficiently low signal-to-noise as to be useless and is not discussed further.," For field positions 1 and 2, half the time was spent in the $\alpha$ filter F187N that is sufficiently low signal-to-noise as to be useless and is not discussed further." For each field position. the (wo dither positions for ACS resulted in two slightly overlapping NIC\IOS/NIC3 images.," For each field position, the two dither positions for ACS resulted in two slightly overlapping NICMOS/NIC3 images." The NICS MULTIACCUM. FAST readout mode was used.," The NIC3 MULTIACCUM, FAST readout mode was used." The Ilabble Helix project aud its results (MeCullough&IIubbleHelixTeam2002) immediatelv went into the public domain., The Hubble Helix project and its results \citep{mccullough02} immediately went into the public domain. The ACS images were analvzed in combination with ground based CTIO images in similar fillers and have been published by (2004)., The ACS images were analyzed in combination with ground based CTIO images in similar filters and have been published by \cite{odell04}. . In this work we analyze and discuss the NICMOS II» 2.12 eenission and its relation to the ionized gas at high spatial resolution., In this work we analyze and discuss the NICMOS $_2$ 2.12 emission and its relation to the ionized gas at high spatial resolution. The NICMOS/NICS3 images were reduced. and calibrated using the standard set. οἱ NICMOS calibration programs provided in the latest version (Version 3.1) ofDAS?., The NICMOS/NIC3 images were reduced and calibrated using the standard set of NICMOS calibration programs provided in the latest version (Version 3.1) of. . The CALNICA calibration routines in STSDAS perform zero-read signal correction. bias subtraction. dark subtraction. detector non-linearity correction. [lat-Hield correction. and," The CALNICA calibration routines in STSDAS perform zero-read signal correction, bias subtraction, dark subtraction, detector non-linearity correction, flat-field correction, and" The Universe at iis now known to be an important epoch in galaxy formation. during which the cosmic star formation rate density peaks as galaxies undergo rapid growth 2).,"The Universe at is now known to be an important epoch in galaxy formation, during which the cosmic star formation rate density peaks as galaxies undergo rapid growth ." Much of this activity occurs in massive. rapidly star-forming galaxies —107101M... SFR ~10200iz ?» identified via their rest-frame optical and near-infrared colors.," Much of this activity occurs in massive, rapidly star-forming galaxies $\sim10^{10}-10^{11}$, SFR $\sim10-200$; ) identified via their rest-frame optical and near-infrared colors." Comparisons of the observed properties of this population (clustering. dynamical masses. SFRs) with dark matter halo properties in cosmological simulations imply that these galaxies will evolve into local bulge-dominated spiral. lenticular. and low-mass elliptical galaxies. increasing in halo mass by a factor of three between aandcitepCon408.," Comparisons of the observed properties of this population (clustering, dynamical masses, SFRs) with dark matter halo properties in cosmological simulations imply that these galaxies will evolve into local bulge-dominated spiral, lenticular, and low-mass elliptical galaxies, increasing in halo mass by a factor of three between and." "Genel-08.. For the majority of the population. this evolution will occur in a ""smooth"" fashion. via accretion and minor mergers. with an average of1 major mergers during this interval(2)."," For the majority of the population, this evolution will occur in a “smooth"" fashion, via accretion and minor mergers, with an average of $0-1$ major mergers during this interval." This smooth yet rapid mass growth. coupled with the lack of disruption by major mergers. renders these galaxies a natural population in which important structures in local galaxies may be assembled and thus a eritical population to study.," This smooth yet rapid mass growth, coupled with the lack of disruption by major mergers, renders these galaxies a natural population in which important structures in local galaxies may be assembled and thus a critical population to study." Detailed dynamical and morphological observations of this galaxy population have revealed that a substantial fraction is characterized by large (~510 kpe). regularly rotating. thick disks (he~1 Κρο e/o~2.6: 22???)," Detailed dynamical and morphological observations of this galaxy population have revealed that a substantial fraction is characterized by large $\sim5-10$ kpc), regularly rotating, thick disks $h_z\sim1$ kpc, $v/\sigma\sim2-6$; )." These galaxies are each populated by 5LO super star-forming (super-SF) clumps (R~d) 3kpe). which collectively account for 30% oof the total baryonic mass in each galaxy(22222).," These galaxies are each populated by $5-10$ super star-forming (super-SF) clumps $R\sim1-3$ kpc), which collectively account for $\sim30$ of the total baryonic mass in each galaxy." " The masses of individual super-SF clumps are limited at the upper end by the ""[oomre"" mass. the characteristic scale of these marginally stable (€~ D rotating galaxies. Alp~2.5.10°M... and are believed o have typical masses M~10""citepGen+08.Elm+09.DekSarCev09.."," The masses of individual super-SF clumps are limited at the upper end by the “Toomre"" mass, the characteristic scale of these marginally stable $Q\sim1$ ) rotating galaxies, ${\rm M}_T\sim2.5\times10^9$, and are believed to have typical masses ${\rm M}\sim10^9$." Simulations suggest. that hese clumps form naturally in gas-rich turbulent disks and that dynamical friction will cause them to spiral in to the center of the dost galaxy on timescales 1 Gyr and form a nascent bulge(222). eaving a fraction of their mass behind in a thin star-forming disk and a quiescent thick disk(2).," Simulations suggest that these clumps form naturally in gas-rich turbulent disks and that dynamical friction will cause them to spiral in to the center of the host galaxy on timescales $\lesssim1$ Gyr and form a nascent bulge, leaving a fraction of their mass behind in a thin star-forming disk and a quiescent thick disk." ". Similar conclusions are reached Tom observations of galaxies in this ophase""(22)... which we will refer to here as sstar-forming galaxies (Ες)."," Similar conclusions are reached from observations of galaxies in this phase"", which we will refer to here as star-forming galaxies (z2SFGs)." Could this phase of galaxy evolution also be associated with the formation of globular clusters (GCs)?, Could this phase of galaxy evolution also be associated with the formation of globular clusters (GCs)? " The high masses o0!10"" M.» and densities (θεα~8o10° ο) of GCs require exceptionally massive and/or dense giant molecular clouds (GMCs): the super- clumps found in z2SFGs are thus good candidates for this", The high masses $\sim10^4-10^6$ ) and densities $\rho_{central}\sim8\times10^3$ $^{-3}$ ) of GCs require exceptionally massive and/or dense giant molecular clouds (GMCs); the super-SF clumps found in z2SFGs are thus good candidates for this the error circles in the NIR with a large aperture telescope.,the error circles in the NIR with a large aperture telescope. We note that the faintness of the optical afterglows may also explain the non-detections in the radio., We note that the faintness of the optical afterglows may also explain the non-detections in the radio. Several conclusions can already be drawn from this early work., Several conclusions can already be drawn from this early work. First. nearly every XRT localization has resulted in the identification of an optical or NIR afterglow: the single exception 0050117a) 1s likely due to large Galactic extinction.," First, nearly every XRT localization has resulted in the identification of an optical or NIR afterglow; the single exception 050117a) is likely due to large Galactic extinction." The optical/NIR afterglow recovery rate for XRT (3/4) and the HETE-2 SXC (12/13) is =>90%., The optical/NIR afterglow recovery rate for XRT (3/4) and the HETE-2 SXC (12/13) is $\gtrsim 90\%$. The brightness of the XRT+SXC sample normalized to ¢=12 hr compared to all other optical afterglows is shown in Figure 6.., The brightness of the XRT+SXC sample normalized to $t=12$ hr compared to all other optical afterglows is shown in Figure \ref{fig:sxcxrt}. The afterglows of the XRT bursts appear to be fainter than about 75% of all afterglows detected prior to ift.. suggesting that past non-detections were mainly the restIt of large error regions and/or shallow searches.," The afterglows of the XRT bursts appear to be fainter than about $75\%$ of all afterglows detected prior to , suggesting that past non-detections were mainly the result of large error regions and/or shallow searches." " This indicates that the fraction of ""dark"" (dust-obscured) GRBs is low. although we note that two of the XRT bursts were localizec in the NIR and may still be dust-obscured."," This indicates that the fraction of “dark” (dust-obscured) GRBs is low, although we note that two of the XRT bursts were localized in the NIR and may still be dust-obscured." If this trend persists then this bodes well for identification of high redshift afterglows using the Lyman break technique. since the main contaminant is dust-obscured bursts.," If this trend persists then this bodes well for identification of high redshift afterglows using the Lyman break technique, since the main contaminant is dust-obscured bursts." Second. in the three cases in which an optical/NIR afterglow was detected. the offset relative to the nominal XRT position has been <<2 aresec. much less than the size of the error circles.," Second, in the three cases in which an optical/NIR afterglow was detected, the offset relative to the nominal XRT position has been $\lesssim 2$ arcsec, much less than the size of the error circles." This suggests that in the near future the XRT will be capable of providing ~2 aresec positions., This suggests that in the near future the XRT will be capable of providing $\sim 2$ arcsec positions. This will significantly reduce the delay from localization to identification of the optical/NIR afterglow in cases when a UVOT sub-arcsecond position is not available., This will significantly reduce the delay from localization to identification of the optical/NIR afterglow in cases when a UVOT sub-arcsecond position is not available. We end by noting that the faintness of the optical/NIR afterglows studied in this paper (R~18 mag at Ar=I hr; Figures 5. and 6)) may make it difficult for small robotic telescopes to provide long-term follow-up of bbursts., We end by noting that the faintness of the optical/NIR afterglows studied in this paper $R\approx 18$ mag at $\Delta t=1$ hr; Figures \ref{fig:moal} and \ref{fig:sxcxrt}) ) may make it difficult for small robotic telescopes to provide long-term follow-up of bursts. However. larger telescopes. while somewhat slower to respond. will allow both long-term follow-up and detection of the faintest afterglows. particularly in the NIR.," However, larger telescopes, while somewhat slower to respond, will allow both long-term follow-up and detection of the faintest afterglows, particularly in the NIR." We thank the staff at the Las Campanas Observatory. the Palomar Observatory. the Keek Observatory. and the Very Large Array.," We thank the staff at the Las Campanas Observatory, the Palomar Observatory, the Keck Observatory, and the Very Large Array." We also thank Mario Hamuy for generous use of his observing time and Dan Kelson for help with his sky background subtraction software., We also thank Mario Hamuy for generous use of his observing time and Dan Kelson for help with his sky background subtraction software. E.B. is supported by NASA through Hubble Fellowship grant HST-01171.01 awarded by the Space Telescope Science Institute. which is operated by AURA. Inc.. for NASA under contract NAS 5-26555.," E.B. is supported by NASA through Hubble Fellowship grant HST-01171.01 awarded by the Space Telescope Science Institute, which is operated by AURA, Inc., for NASA under contract NAS 5-26555." Additional support was provided by NSF and NASA grants., Additional support was provided by NSF and NASA grants. A.G. acknowledges support by NASA through Hubble Fellowship grant HST-HF-01158.01-A awarded by STScl. which is operated by AURA. Inc.. for NASA. undercontract NAS 5-26555.," A.G. acknowledges support by NASA through Hubble Fellowship grant HST-HF-01158.01-A awarded by STScI, which is operated by AURA, Inc., for NASA, undercontract NAS 5-26555." The efficiency of the augular momentum loss via disk depends on the radius at which the viscous coupling ccascs he transport the angular moment to the outflowing uaterial.,The efficiency of the angular momentum loss via disk depends on the radius at which the viscous coupling ceases the transport the angular momentum to the outflowing material. " When the radiative force is negligible. we argue hat this ikelv happens cose to the disk somic (critical) )oiut setig the most efficieut angular ολοται OSS,"," When the radiative force is negligible, we argue that this likely happens close to the disk sonic (critical) point setting the most efficient angular momentum loss." Tn t1e ByosIte case. when the radiative force is 1onneelieilje. there is not a single point bevoud which he viscous coupling disapyears.," In the opposite case, when the radiative force is nonnegligible, there is not a single point beyond which the viscous coupling disappears." The disk is coutiuuouslv ablated low the sonic point. aud the ablated material ceases to be viscously coupled. decreasing the efficiency. of aueular momoentun loss.," The disk is continuously ablated below the sonic point, and the ablated material ceases to be viscously coupled, decreasing the efficiency of angular momentum loss." We describe he method to iuclude these processes iuto evolutionary calculations., We describe the method to include these processes into evolutionary calculations. The procedure provided enables to calculate the mass-loss rate necessary for a required angular monentun loss just from the stellar aud line force paraiucters., The procedure provided enables to calculate the mass-loss rate necessary for a required angular momentum loss just from the stellar and line force parameters. " We can distinguish three different plysical circuustauces: Finally, we uote that. in absence of strong magnetic field. maux of the features discussed here may also be applicable to the case of star-formation accretion disks."," We can distinguish three different physical circumstances: Finally, we note that, in absence of strong magnetic field, many of the features discussed here may also be applicable to the case of star-formation accretion disks." extinction along the line of sight is ον=1.28 (Iloltzmanetal.1993).. and that the dust has a scale height of 120 pe.,"extinction along the line of sight is $A_V=1.28$ \citep{holtzman}, and that the dust has a scale height of 120 pc." We incorporate disk as well as bulge stars in predicting the Holtzmanetal.(L998) star counts.," We incorporate disk as well as bulge stars in predicting the \cite{holtzman} star counts." Since (he disk stellar profile is regarded as well measured (by Zhengοἱal.2002)). we do not adjust (he normalization of the disk profile as we do the bulge prolile. but rather leave it fixed in the form given in 2.1..," Since the disk stellar profile is regarded as well measured (by \citealt{zheng}) ), we do not adjust the normalization of the disk profile as we do the bulge profile, but rather leave it fixed in the form given in \ref{sec:disk}." However. we use the same mass function and mass-My relation for the disk as the bulge.," However, we use the same mass function and $M_V$ relation for the disk as the bulge." In. principle. one should make an independent estimate of these functions.," In principle, one should make an independent estimate of these functions." However. since the disk stars contribute only ~155€ of the counts (see Fig. 1)).," However, since the disk stars contribute only $\sim 15\%$ of the counts (see Fig. \ref{fig:lf}) )," the net corrections [rom more accurate functions would be only a few percent. which is small compared to other uncertainties in the problem.," the net corrections from more accurate functions would be only a few percent, which is small compared to other uncertainties in the problem." Hence. we ignore this distinction in (he interest of simplicity.," Hence, we ignore this distinction in the interest of simplicity." We lix the normalization by demanding agreement between the model predictions aud ihe (mass-weighted) ILoltzmanetal.(1998) star counts over the range 22.5«V.26.5., We fix the normalization by demanding agreement between the model predictions and the (mass-weighted) \citet{holtzman} star counts over the range $22.5>1 onscales, up to the temperature/pressure scale-height of the plasma."," Suppressing the MTI requires having $t_{\mr{buoy}} / t_{\mr{dist}} \gg 1$ on, up to the temperature/pressure scale-height of the plasma." " Because the MTI itself generates nearly sonic velocities, this suppression would require close to supersonic turbulence."," Because the MTI itself generates nearly sonic velocities, this suppression would require close to supersonic turbulence." " In practice, it is therefore unlikely that additional sources of turbulence can fully suppress the MTI in most astrophysical environments where it is likely to occur (e.g., accretion disks and galaxy clusters)."," In practice, it is therefore unlikely that additional sources of turbulence can fully suppress the MTI in most astrophysical environments where it is likely to occur (e.g., accretion disks and galaxy clusters)." " The motion of electrons along, but not across, magnetic field lines in dilute, magnetized plasmas produces efficient, anisotropic transport of heat."," The motion of electrons along, but not across, magnetic field lines in dilute, magnetized plasmas produces efficient, anisotropic transport of heat." " Such plasmas are therefore non-adiabatic, and the standard analysis of buoyancy (or convective) instabilities does not necessarily apply."," Such plasmas are therefore non-adiabatic, and the standard analysis of buoyancy (or convective) instabilities does not necessarily apply." " Quantitatively, conduction plays an essential role on scales less than 7(AH)""/?, where A is the electron mean free path and H is the plasma scale height."," Quantitatively, conduction plays an essential role on scales less than $7 \, (\lambda H)^{1/2}$, where $\lambda$ is the electron mean free path and $H$ is the plasma scale height." " In this “rapid conduction limit,” the temperature gradient, rather than the entropy gradient, dictates the stability of the plasma, and the plasma is unstable for either sign of the temperature gradient (??).."," In this “rapid conduction limit,” the temperature gradient, rather than the entropy gradient, dictates the stability of the plasma, and the plasma is unstable for either sign of the temperature gradient \citep{Balbus2000, Quataert2008}." The convective instability in this limit is known as the HBI (MTI) when the temperature increases (decreases) with height., The convective instability in this limit is known as the HBI (MTI) when the temperature increases (decreases) with height. ?? and ? extended the original linear analysis of the MTI and HBI into the nonlinear regime using numerical simulations.," \citet{Parrish2005, Parrish2007} and \citet{Parrish2008hbi} extended the original linear analysis of the MTI and HBI into the nonlinear regime using numerical simulations." " In this paper, we have reconsidered the nonlinear saturation of the HBI and MTI."," In this paper, we have reconsidered the nonlinear saturation of the HBI and MTI." Our work adds to previous investigations because we have identified a key difference between the two instabilities and are able to understand the nonlinear behavior of the MTI more completely., Our work adds to previous investigations because we have identified a key difference between the two instabilities and are able to understand the nonlinear behavior of the MTI more completely. This paper therefore represents a significant change in our understanding of the possible astrophysical implications of the MTI (but not the HBI)., This paper therefore represents a significant change in our understanding of the possible astrophysical implications of the MTI (but not the HBI). We have also studied the effect of an external source of turbulence on both the MTI and HBI., We have also studied the effect of an external source of turbulence on both the MTI and HBI. " We conclude that other sources of turbulence in a plasma can change the saturation of the HBI, but that it is much harder to disrupt the MTI."," We conclude that other sources of turbulence in a plasma can change the saturation of the HBI, but that it is much harder to disrupt the MTI." " Below we summarize our results and discuss their astrophysical implications, focusing on the intracluster medium (ICM) of galaxy clusters."," Below we summarize our results and discuss their astrophysical implications, focusing on the intracluster medium (ICM) of galaxy clusters." Table , The time variation of the mean star formation rate iu ealaxies is by now well established (Alacdauetal.1996:com 2006).,"The time variation of the mean star formation rate in galaxies is by now well established \citep{Madau, Steidel, Hippelein, HB2006}." ". The star formation rate is either flat or slowly rising with time. reaching a maxim near 2~ 1 2, id then declines precipitously down to the current epoch."," The star formation rate is either flat or slowly rising with time, reaching a maximum near $z \sim$ 1 – 2, and then declines precipitously down to the current epoch." This change in the star formation rate must be closely couplec to both the inventory of eas available for star formation. and the wav in which this eas is chauncled iuto galaxies.," This change in the star formation rate must be closely coupled to both the inventory of gas available for star formation, and the way in which this gas is channeled into galaxies." Stars condeuse only from noleculu eas at the curent epoch and at all epochs im the past., Stars condense only from molecular gas at the current epoch and at all epochs in the past. This statement clevives frou both observational aud theoretical considerations., This statement derives from both observational and theoretical considerations. Observatiionally. the youngest stars are always found to be associaος with their nascent molecular material both in the local Universe aud at high 2 (eg. Blaaw1961:Herbig&KameswaraRao1972: 2002)).," Observationally, the youngest stars are always found to be associated with their nascent molecular material both in the local Universe and at high $z$ (e.g. \citealt{blaauw1964, hr1972, swe1973, omont1996, carilli2002}) )." The iuterstellar gas iu star forming regions is almost completely uolecular. represenlug a stabe phase of the ISM with ittle atomic coient. (Burtonetal. 1975).," The interstellar gas in star forming regions is almost completely molecular, representing a stable phase of the ISM with little atomic content \citep{burton1978}." . Theoreticalv. there is general conseusus lia the -initiation of star fMination requires the nascen HHOris to )comie Jeans unstable. probably mediated by maeretic fields (Shuetal.|987).," Theoretically, there is general consensus that the initiation of star formation requires the nascent gas to become Jeans unstable, probably mediated by magnetic fields \citep{sal1987}." ". Iu star forming regioIs, Tis vpicallv 10 - 20 Kk. but in any event camo he less lan 2.T lk. Iu order to eet a solar mass star at 1 VI. re Joaus mstabiliv criterion would require a ¢Clsi vof pa>UTungGy/36M3)~θαὉ ifa iolecular core forius a star at efficiency."," In star forming regions, $T$ is typically 10 - 20 K, but in any event cannot be less than 2.7 K. In order to get a solar mass star at 10 K, the Jeans instabiliy criterion would require a density of $\rho_J > (kT/{\mu}{m_H}G)^3 (\pi^5/36 M_J^2) \sim 10^6 {\rm cm}^{-3}$ if a molecular core forms a star at efficiency." The deusity iuust be higher if the efficiency. is lower as many observations now sugeest (e.g. Motteetal.1998:Alves2007:Ablvers 20083).," The density must be higher if the efficiency is lower as many observations now suggest (e.g. \citealt{man1998, all2007, myers2008}) )." In order to reach these temperatures aud densities. the eas must be fully molecular iu order to achieve the necessary cooling.," In order to reach these temperatures and densities, the gas must be fully molecular in order to achieve the necessary cooling." We would therefore expect that. ina broad seuse. the gas consumption rate is closcly tied to he star formation rate.," We would therefore expect that, in a broad sense, the gas consumption rate is closely tied to the star formation rate." Untorunatelv. there are few constraints on the gas from oservations because little is known about the listjbiion of neutral eas at high :.," Unfortunately, there are few constraints on the gas from observations because little is known about the distribution of neutral gas at high $z$." There are very few detectiois of atomic eas in οσο at 7Z 0. aud what little we know about the atomic gas comes from Lyuiui-alphla lines seen in absorption toward quasars aud radio-loud ACN (c.g. Prochaska&Wolfe2009:etal.2005:Zwaan&Prochaska 2006)).," There are very few detections of atomic gas in emission at $z \ga$ 0.1, and what little we know about the atomic gas comes from Lyman-alpha lines seen in absorption toward quasars and radio-loud AGN (e.g. \citealt{PW2009,wolfe2005,zp2006}) )." Moleculax line observations at high-: have been largely limited to the brightest objects. though some recent observations at 2o2 have beenn to probe lower huuinositv svstenis (ForsterSchreiberetal.2009:DaddiTacconietal. 2010).," Molecular line observations at $z$ have been largely limited to the brightest objects, though some recent observations at $z\sim 2$ have begun to probe lower luminosity systems \citep{fs2009,Daddi2009,t2010}." ". Gas consuniptiou by star formation 1i galaxies lias been investigated previously via observations of the gas depletion time. Te,=Mgj;4/SPR."," Gas consumption by star formation in galaxies has been investigated previously via observations of the gas depletion time, $\tau_{dep} = M_{gas} / SFR$." This represents the αλλο! of time it will take the ealaxy to completely exhaust its eas supply at the current star ornuation rate., This represents the amount of time it will take the galaxy to completely exhaust its gas supply at the current star formation rate. Studies of individual local disk galaxies fiud «epletiou times on the order of a few Cr. much shorer than the IIubble time (e.g. Larsonctal.1980:Ίναιueuttal. 1991)).," Studies of individual local disk galaxies find depletion times on the order of a few Gyr, much shorter than the Hubble time (e.g. \citealt{Larson1980,k94}) )." This is the eas depletion problem: without sonie form of gas replenislineut. star forimnatioi1 dn disk ealaxies should be coming to an abrupt exl.," This is the gas depletion problem: without some form of gas replenishment, star formation in disk galaxies should be coming to an abrupt end." One proposed solution is stellar recycling. which," One proposed solution is stellar recycling, which" cluster environment. rather than the group environment.," cluster environment, rather than the group environment." find that most of the ealaxies im a galaxv cluster are accreted directly from the feld. rather than from infalling galaxy eroups.," find that most of the galaxies in a galaxy cluster are accreted directly from the field, rather than from infalling galaxy groups." Iu this case. mechanisius such as ealaxy harassincut anc run pressure stripping that are most efficient in massive clusters nist drive this transformation.," In this case, mechanisms such as galaxy harassment and ram pressure stripping that are most efficient in massive clusters must drive this transformation." Simulations have shown that rani pressure stripping can remove some or all of the interstellar medi (ISMD) from late-tvpe galaxies as they euter the cluster potential 2008)., Simulations have shown that ram pressure stripping can remove some or all of the interstellar medium (ISM) from late-type galaxies as they enter the cluster potential . Studies of galaxies iu clusters with observed UT deficieucies or truncated disks support the idea that rai pressure stripping can transform a gasrich spiral galaxy iuto an auenic spiral ealaxv 2008).. which iav eventually evolve iuto a leuticular 02.," Studies of galaxies in clusters with observed HI deficiencies or truncated disks support the idea that ram pressure stripping can transform a gas-rich spiral galaxy into an anemic spiral galaxy , which may eventually evolve into a lenticular ." Ram pressure has also been shown to trigger bursts of star formation in cluster galaxies 2003).. and recent simulations predict cnhanced star formation rates in galaxies undergoing a rani pressure event.," Ram pressure has also been shown to trigger bursts of star formation in cluster galaxies , and recent simulations predict enhanced star formation rates in galaxies undergoing a ram pressure event." While previous studies have examined the impact of rim pressure on individual galaxies falling iuto the ster potential ιο Bullet Cluster provides a unique opportuuitv to exanune the effect of rani pressure induced bv cluster morecrs., While previous studies have examined the impact of ram pressure on individual galaxies falling into the cluster potential the Bullet Cluster provides a unique opportunity to examine the effect of ram pressure induced by cluster mergers. Although galaxies in anv cluster cuvirouluent undergo run pressure as they travel through the ICAL ealaxics in a major merecr event such as those we observe in the Bullet Cluster will expericuce a dramatic cuhancement in the pressure since PXV2.," Although galaxies in any cluster environment undergo ram pressure as they travel through the ICM, galaxies in a major merger event such as those we observe in the Bullet Cluster will experience a dramatic enhancement in the pressure since $P\propto V^2$." It is thus possible that this brief transient phase may have a sienificant impact ou the properties of the cluster ealaxy population., It is thus possible that this brief transient phase may have a significant impact on the properties of the cluster galaxy population. The Bullet Cluster is an ideal site iu which to quantify the iniportauce of such mereer-induced raum pressure., The Bullet Cluster is an ideal site in which to quantify the importance of such merger-induced ram pressure. Tn this paper we couduct an initial exploration of the impact of the shock frout upon polvevclie aromatic, In this paper we conduct an initial exploration of the impact of the shock front upon polycyclic aromatic "e We find a substantial discrepaneyv between our 250) ΠΠ, suele dish and 230 Cz interferometer ueasuremeuts of the thermal dust emission.",$\bullet$ We find a substantial discrepancy between our 250 GHz single dish and 230 GHz interferometer measurements of the thermal dust emission. This strongly sugeests that the dust cussion is distributed at spatial scales larger than the 179«175 svuthesized interferometer jua., This strongly suggests that the dust emission is distributed at spatial scales larger than the $1\farcs9 \times 1\farcs5$ synthesized interferometer beam. The combined uv-plaue data can be fit by a circular Gaussian profile with a size between 0755 aud, The combined uv-plane data can be fit by a circular Gaussian profile with a size between 5 and. 5”. e The optical/near-IR spectroscopy sugecsts that he AGN is located at the brightest AUband source (object à)., $\bullet$ The optical/near-IR spectroscopy suggests that the AGN is located at the brightest $K-$ band source (object ). This is supported by the CO aud dust emission. which both peak at the same position.," This is supported by the CO and dust emission, which both peak at the same position." However. the radio norpholoey suggests that the AGN is located at the central radio component. ssouth of object«.," However, the radio morphology suggests that the AGN is located at the central radio component, south of object." If the ACN is located at objecta the radio source is extremely asymmetric.," If the AGN is located at object, the radio source is extremely asymmetric." Alternatively. the AGN may be locatec at the central radio component. aud could be either heavily obscured in the optical/ucar-IR. or could be located off-centre from the host galaxy.," Alternatively, the AGN may be located at the central radio component, and could be either heavily obscured in the optical/near-IR, or could be located off-centre from the host galaxy." However. this alternative appears unlikely eiven the position ofthe dust/CO peak.," However, this alternative appears unlikely given the position of the dust/CO peak." e We obtain a τς1.3% Iit ou the 22] cmn absorption against the radio source., $\bullet$ We obtain a $\tau < 1.3$ limit on the 21 cm absorption against the radio source. This represents the seventh uou-cetection out of 5 radio ealaxies where 22] cur absorption has been searched., This represents the seventh non-detection out of 8 radio galaxies where 21 cm absorption has been searched. e We estimate the mass of the different. compoucuts iu B3 J2330|3927. which indicates that the CO emission traces the largest fraction of the total mass in the syste.," $\bullet$ We estimate the mass of the different components in B3 J2330+3927, which indicates that the CO emission traces the largest fraction of the total mass in the system." Tn sununuuy. our inultiwaveleusth observations Sugeest the presence of a large gas and dust reservolr surouudius the host ealaxy of D3 J2330|3927.," In summary, our multi-wavelength observations suggest the presence of a large gas and dust reservoir surrounding the host galaxy of B3 J2330+3927." For the fist time. we have found strong medications that these different observations may trace the same material. both in cinission and in absorption.," For the first time, we have found strong indications that these different observations may trace the same material, both in emission and in absorption." The detection of CO cluission therefore müiplies that a substantial part of this reservoir is not primordial. but ust have heen previously enriched. possibly by a starburst-driven superwind.," The detection of CO emission therefore implies that a substantial part of this reservoir is not primordial, but must have been previously enriched, possibly by a starburst-driven superwind." "light curve, but each time the residuals are shifted by a random offset to give Γρ.","light curve, but each time the residuals are shifted by a random offset to give $\vec r_p$." Any residuals that fall off the ‘edge’ are looped back to the beginning., Any residuals that fall off the `edge' are looped back to the beginning. " The new light curve jp is then reconstructed by adding the shifted residuals to the best-fit model, followed by a pointwise multiplication of the best-fit baseline function; The decorrelation and light curve fitting is done as before, to determine p."," The new light curve $\vec y_p$ is then reconstructed by adding the shifted residuals to the best-fit model, followed by a pointwise multiplication of the best-fit baseline function; The decorrelation and light curve fitting is done as before, to determine $\rho$." " The procedure is repeated 1000 times with random perturbations to the shift in residuals, each time varying the starting value for p to ensure the starting parameters do not affect the results."," The procedure is repeated 1000 times with random perturbations to the shift in residuals, each time varying the starting value for $\rho$ to ensure the starting parameters do not affect the results." The resulting distribution of p is then used to estimate its uncertainty in each wavelength channel., The resulting distribution of $\rho$ is then used to estimate its uncertainty in each wavelength channel. The resulting NICMOS transmission spectrum for HD 189733 is shown in Fig. 9.., The resulting NICMOS transmission spectrum for HD 189733 is shown in Fig. \ref{fig:HD189733_trans_spec_all}. " The data from S08 are also plotted for comparison, after converting from transit depth to p."," The data from S08 are also plotted for comparison, after converting from transit depth to $\rho$." " For the most part, the spectra show the same basic shape."," For the most part, the spectra show the same basic shape." " It is not clear exactly where the discrepancies in a few of the wavelength channels arise, but they are likely explained by one or a combination of the following; different pixel columns and widths used for the wavelength channels, different methods used to determine the background, the fact that we fit for the light curve rather than just taking an average of the in-transit orbit, that the decorrelation parameters are extracted slightly differently, and finally the corrections applied by S08 for limb darkening and star spots."," It is not clear exactly where the discrepancies in a few of the wavelength channels arise, but they are likely explained by one or a combination of the following; different pixel columns and widths used for the wavelength channels, different methods used to determine the background, the fact that we fit for the light curve rather than just taking an average of the in-transit orbit, that the decorrelation parameters are extracted slightly differently, and finally the corrections applied by S08 for limb darkening and star spots." We were unable to reproduce exactly the same results as S08 using a global background correction., We were unable to reproduce exactly the same results as S08 using a global background correction. " Another obvious difference between the two spectra is that the uncertainties we calculate using the residual permutation method are significantly larger than those given in S08, particularly at the edge of the spectrum."," Another obvious difference between the two spectra is that the uncertainties we calculate using the residual permutation method are significantly larger than those given in S08, particularly at the edge of the spectrum." " However, we do not believe the residual permutation method fully accounts for the uncertainties in p."," However, we do not believe the residual permutation method fully accounts for the uncertainties in $\rho$." Fig., Fig. 10 shows a plot of the in-transit residuals for three wavelength channels., \ref{fig:HD189733_zoomed_residuals} shows a plot of the in-transit residuals for three wavelength channels. " The residuals are of decorrelated light curves, after subtracting a model generated from the planet-to-star radius ratio measured from the white light curve, and using limb darkening parameters specific to each wavelength channel."," The residuals are of decorrelated light curves, after subtracting a model generated from the planet-to-star radius ratio measured from the white light curve, and using limb darkening parameters specific to each wavelength channel." " 'The difference between models generated for the best-fit planet-to-star radius ratio for each channel (i.e. the value in the transmission spectrum), and the planet-to-star radius ratio from the white light curve (ie. a constant radius model) are also shown."," The difference between models generated for the best-fit planet-to-star radius ratio for each channel (i.e. the value in the transmission spectrum), and the planet-to-star radius ratio from the white light curve (i.e. a constant radius model) are also shown." " As is clear for all three channels, systematic noise is present at a level comparable to or larger than the difference between the two models."," As is clear for all three channels, systematic noise is present at a level comparable to or larger than the difference between the two models." The deviations from a constant transmission spectrum may therefore arise from systematics not removed from the in-transit orbit., The deviations from a constant transmission spectrum may therefore arise from systematics not removed from the in-transit orbit. A similar level of systematics is visible in the residuals for all wavelength channels., A similar level of systematics is visible in the residuals for all wavelength channels. " We are yet to address one final correction on each wavelength channel carried out by S08, the ‘channel-to-channel’ corrections."," We are yet to address one final correction on each wavelength channel carried out by S08, the `channel-to-channel' corrections." " This involves taking the weighted average of the light curve residuals for all the wavelength channels, and subtracting them from individual channels after decorrelating the light curves."," This involves taking the weighted average of the light curve residuals for all the wavelength channels, and subtracting them from individual channels after decorrelating the light curves." This should remove any common time-correlated systematics from the light curves., This should remove any common time-correlated systematics from the light curves. " To check that this did not affect our results significantly,"," To check that this did not affect our results significantly," ". where n,,;; marks the transition [rom NLTE o LTE level populations.","$^{-3}$, where $n_{crit}$ marks the transition from NLTE to LTE level populations." By comparing the clistribution of Aly vs. ng in Figure 2 (Lower-right panel) to the equivalent ligure 3 (panel (0)) in Bromm et al. (, By comparing the distribution of $M_{J}$ vs. $n_{\rmn H}$ in Figure 2 (lower-right panel) to the equivalent Figure 3 (panel (c)) in Bromm et al. ( "1999). it can be seen hat there is no characteristic mass scale in the Z=10""E. case.","1999), it can be seen that there is no characteristic mass scale in the $Z=10^{-3}Z_{\odot}$ case." Such a characteristic scale would correspond to a pile-up of SPIEL particles in the diagram due to long evolutionary inmescales., Such a characteristic scale would correspond to a pile-up of SPH particles in the diagram due to long evolutionary timescales. In the pure 11ο case. on the other hand. there is a preferred mass scale of Al—107AZ..," In the pure H/He case, on the other hand, there is a preferred mass scale of $M \sim 10^{3}M_{\odot}$." The overall range of clump masses. 107Meis 10A2.. is similar in the pure IHl/lle and Z=10Z. simulations. although the relative number of low-mass clumps is significantly higher for the pre-cnrichecl case.," The overall range of clump masses, $10^{2}45^\circ$ (Fig. 1c). in the case of Ayfhe=1. they are unstable for the @>607 (Fig.," 1c), in the case of $k_{R}/k_z=1$, they are unstable for the $\theta>60^\circ$ (Fig." ld)., 1d). In addition. in Figure le and 1d maxiumum growth rates are larger than the ideal ATRL growth rates for the ereat values of piteh angle.," In addition, in Figure 1c and 1d maxiumum growth rates are larger than the ideal MRI growth rates for the great values of pitch angle." Desides. when we consider finite kg wavevector. an unstable mode emerges for 6=90 The normalized wavenumber of the fastest growing mode is given as heey/Q=(15/16)? (Balbus Llawlev 1992).," Besides, when we consider finite $k_{R}$ wavevector, an unstable mode emerges for $\theta=90^\circ$ The normalized wavenumber of the fastest growing mode is given as $k_{z}v_{A}/\Omega=(15/16)^{1/2}$ (Balbus Hawley 1992)." We adopt the same value in the present investigation., We adopt the same value in the present investigation. We plotted. dimensionless growth rates versus pitch angle and fyfh. in Figure 2., We plotted dimensionless growth rates versus pitch angle and $k_{R}/k_{z}$ in Figure 2. " For the 1,5,=|. growth rates are given in Figure 2a and for the VW.=l they are given in Figure 2b."," For the $\tilde{V}_{gyro}^{n}=1$, growth rates are given in Figure 2a and for the $\tilde{V}_{gyro}^{n}=-1$ they are given in Figure 2b." In the case of QTT.B. growth rates have niiximunm. values for the small pitch angles ancl Ay values (Fig 2a)., In the case of $\mathbf{\Omega}\uparrow\uparrow\mathbf{B}_{z}$ growth rates have maximum values for the small pitch angles and $k_{R}$ values (Fig 2a). While there is no unstable wavenumber for the ϱ>60 (Fig 2a) for the case of QtLB. these pitch angles have maximum growth rates (Fig 2b)., While there is no unstable wavenumber for the $\theta>60^\circ$ (Fig 2a) for the case of $\mathbf{\Omega}\uparrow\downarrow\mathbf{B}_{z}$ these pitch angles have maximum growth rates (Fig 2b). To see the effect of the evroviscosity parameter on the erowth rates we assumed the pitch angle as @=45., To see the effect of the gyroviscosity parameter on the growth rates we assumed the pitch angle as $\theta=45^\circ$. Then. we plotted. dimensionless growth rates versus gvroviscosity xwameter and wavenumboers for the ApfA.=O. Apfhe=1 and ferὉ=(15/16)— respectively in the Figure 3a. 3h and 3c.," Then, we plotted dimensionless growth rates versus gyroviscosity parameter and wavenumbers for the $k_{R}/k_z=0$, $k_{R}/k_z=1$ and $k_{z}v_{A}/\Omega=(15/16)^{1/2}$ respectively in the Figure 3a, 3b and 3c." We clearly see that all wavenumbers are unstable for he positive values of the eroviscosity parameter. ic. in the case of QTT. B..," We clearly see that all wavenumbers are unstable for the positive values of the groviscosity parameter, i.e. in the case of $\mathbf{\Omega}\uparrow\uparrow\mathbf{B}_{z}$ ." The positive values of the gvroviscosity xwameter have maximum. growth rates case in the large wavenumbers. but again the growth rates are greater than 150.," The positive values of the gyroviscosity parameter have maximum growth rates case in the large wavenumbers, but again the growth rates are greater than $0.75 \Omega$ ." In Ligure 4. we assumed the pitch angle as 6= 60.," In Figure 4, we assumed the pitch angle as $\theta=60^\circ$ ." Again. we plotted. climensionless growth: rates versus evroviscosity parameter and wavenumboers for the Ayfk.= 0. αμ.= land Κι/Q=(15/16)7 respectively in the Figure da. th and 4c.," Again, we plotted dimensionless growth rates versus gyroviscosity parameter and wavenumbers for the $k_{R}/k_z=0$ , $k_{R}/k_z=1$ and $k_{z}v_{A}/\Omega=(15/16)^{1/2}$ respectively in the Figure 4a, 4b and 4c." We clearly see that all wavenumbers are unstable for the negative values of the groviscosity parameter. i.e. in the case of £2TLD..," We clearly see that all wavenumbers are unstable for the negative values of the groviscosity parameter, i.e. in the case of $\mathbf{\Omega}\uparrow\downarrow\mathbf{B}_{z}$." Maximum growth rates emerge in the small wavenumbers and and the negative values of the gvroviscosity parameter contrary lo previous case (Figure 3)., Maximum growth rates emerge in the small wavenumbers and and the negative values of the gyroviscosity parameter contrary to previous case (Figure 3). In this paper we have investigated a linear axisvmimetric analysis of the MIU with ELIt ellect and paralel viscosity in the hot. dilute and cillerentiallv rotating weakly magnetized plasma.," In this paper we have investigated a linear axisymmetric analysis of the MRI with FLR effect and paralel viscosity in the hot, dilute and differentially rotating weakly magnetized plasma." In a dilute plasma. ion evelotron frequeney. much exceeds the ion-ion collision frequency.," In a dilute plasma, ion cyclotron frequency much exceeds the ion-ion collision frequency." In this regime. the viscous stress tensor is given as the total of the parallel and the evroviscous components (Draginskii 1065).," In this regime, the viscous stress tensor is given as the total of the parallel and the gyroviscous components (Braginskii 1965)." Ες work is not only extension of the Islam Balbus’s (2005) study which is taken into account only parallel viscosity but also is the extension of the Ferraro’s (2007) study which is included: parallel viscosity ancl evroviscosity only with B=62 magnetic Ποιά geometry (also parallel viscosity is negligible in this geometry)., This work is not only extension of the Islam Balbus's (2005) study which is taken into account only parallel viscosity but also is the extension of the Ferraro's (2007) study which is included parallel viscosity and gyroviscosity only with $\mathbf{B}=B\mathbf{\hat z}$ magnetic field geometry (also parallel viscosity is negligible in this geometry). We investigated the nature of evroviscous instability with the more general magnetic Ποια configuration. Le.. à helical field for which the parallel viscosity is important.," We investigated the nature of gyroviscous instability with the more general magnetic field configuration, i.e., a helical field for which the parallel viscosity is important." We obtained the dispersion relation of this instability and also derived the instability criterion., We obtained the dispersion relation of this instability and also derived the instability criterion. The gvroviscous instability shows a complicated dependence on the geometry of the magnetic field through the pitch angle 8., The gyroviscous instability shows a complicated dependence on the geometry of the magnetic field through the pitch angle $\theta$. Quataert. Dorlancl and Llammett (2002) also draw attention to the dependence of the growth rates on the orientation of the magnetic field and the wavevector of the mode.," Quataert, Dorland and Hammett (2002) also draw attention to the dependence of the growth rates on the orientation of the magnetic field and the wavevector of the mode." More important. than that. is the complex coupling between the dynamical cllects and the geometry of the magnetic field that makes it almost impossible to single out the net effect of any one agent contributing to stability or instability., More important than that is the complex coupling between the dynamical effects and the geometry of the magnetic field that makes it almost impossible to single out the net effect of any one agent contributing to stability or instability. But one thing is certain that in its more general case the magnetized. hot and differentially rotating plasmas are always unstable.," But one thing is certain that in its more general case the magnetized, hot and differentially rotating plasmas are always unstable." Our results show that when only evroviscosity act on the hot dilute ancl cifferentially rotating plasma it brings about instability and erowth rates of the instability are higher than MIRI (see Fie 1 and 2)., Our results show that when only gyroviscosity act on the hot dilute and differentially rotating plasma it brings about instability and growth rates of the instability are higher than MRI (see Fig 1 and 2). In this situation. the finite Ay is destabilized all the wavenumber interval for 30° in the case of €TTD. (Fig.," In this situation, the finite $k_{R}$ is destabilized all the wavenumber interval for $30^{\circ}$ in the case of $\mathbf{\Omega}\uparrow\uparrow\mathbf{B}_{z}$ (Fig." 1b and 2a) and for pitch angles greater than 607 in the case of ΩTLD. (Fig 1d and 2b)., 1b and 2a) and for pitch angles greater than $60^{\circ}$ in the case of $\mathbf{\Omega}\uparrow\downarrow\mathbf{B}_{z}$ (Fig 1d and 2b). Although parallel viscosity is greater than gexroviscositv. we see that parallel viscosity slightly supresses the unstable mocdes for the cases of QTTB. and QT].B. according to the situation which parallel viscosity is neglected.," Although parallel viscosity is greater than gyroviscosity, we see that parallel viscosity slightly supresses the unstable modes for the cases of $\mathbf{\Omega}\uparrow\uparrow\mathbf{B}_{z}$ and $\mathbf{\Omega}\uparrow\downarrow\mathbf{B}_{z}$ according to the situation which parallel viscosity is neglected." Also there is an interesting situation: When the angular velocity vector and the D; component of the magneticfield are parallel (€TT Be). pitch angles smaller than 607 have maximum erowth rates in the great. wavenumbers: whenthe angularvelocity vector and the 2. component of the magnetic field are anti parallel (Qt] D.). pitch angles greater than 60 ," Also there is an interesting situation: When the angular velocity vector and the $B_{z}$ component of the magneticfield are parallel $\mathbf{\Omega}\uparrow\uparrow\mathbf{B}_{z}$ ), pitch angles smaller than $60^{\circ}$ have maximum growth rates in the great wavenumbers; whenthe angularvelocity vector and the $B_{z}$ component of the magnetic field are anti parallel $\mathbf{\Omega}\uparrow\downarrow\mathbf{B}_{z}$ ), pitch angles greater than $60^{\circ}$ " Gamma-ray Bursts (GRBs) are the most extreme explosion discovered so far in the universe.,Gamma-ray Bursts (GRBs) are the most extreme explosion discovered so far in the universe. With the discovery of the afterglows and then the measurement of the redshifts in 1997 (seevanParadijsetal.2000.fora review).. the cosmological origin of GRBs has been firmly established.," With the discovery of the afterglows and then the measurement of the redshifts in 1997 \citep[see][for a review]{wijers00}, the cosmological origin of GRBs has been firmly established." The modeling of the late (o107 s) afterglow data favors the external forward shock model (seePiran1999:Mészáros.2002:Zhang&Mészüáros2004.for reviews.," The modeling of the late $t>10^{4}$ s) afterglow data favors the external forward shock model \citep[see][for reviews]{piran99, mesz02, zm04}." The radiation mechanisms employed in the modeling are synchrotron radiation and synchrotron self-Compton (SSC) scattering., The radiation mechanisms employed in the modeling are synchrotron radiation and synchrotron self-Compton (SSC) scattering. In the early time the prolonged activity of the central engine plays an important role in producing afterglow emission too. particularly in X-ray band (e.g..Katzetal.1998:Fan&Wei2005:Nouseketal.2006:Zhang 2006).," In the early time the prolonged activity of the central engine plays an important role in producing afterglow emission too, particularly in X-ray band \citep[e.g.,][]{Katz98,FW05,Nousek06,Zhang06}." . The radiation mechanisms. remaining unclear. are assumed to be the same as those of the prompt soft zamma-ray emission.," The radiation mechanisms, remaining unclear, are assumed to be the same as those of the prompt soft gamma-ray emission." It is expected that in the Fermi era the origin of the prompt emission can be better understood., It is expected that in the Fermi era the origin of the prompt emission can be better understood. This is because the Large Area Telescope (LAT) and the Gamma-ray Burst Monitor (GBM) onboard Fermi. satellite (httpz//fermi.gsfe.nasa.gov/) can measure the spectrum in a very wide energy band (from 8 keV to more than 300 GeV). with which some models may be well distinguished.," This is because the Large Area Telescope (LAT) and the Gamma-ray Burst Monitor (GBM) onboard Fermi satellite (http://fermi.gsfc.nasa.gov/) can measure the spectrum in a very wide energy band (from 8 keV to more than 300 GeV), with which some models may be well distinguished." For example. in he standard internal shock model the SSC radiation can give rise oa distinct GeV excess while in the magnetized outflow model no GeV excess is expected.," For example, in the standard internal shock model the SSC radiation can give rise to a distinct GeV excess while in the magnetized outflow model no GeV excess is expected." Totivated by the detection of some -100 MeV photons rom quite a few GRBs by the Compton Gamma Ray Observatory satellite in 2000 (e.g.Hurleyetal.1994:Fishman&Mee-gan[995:Gonzálezetal. 2003).. the prompt high energy emission ws been extensively investigated and most calculations are within he framework of the standard internal shocks (e.g..Pilla&Loeb2009.ef.Giannios 2007).," Motivated by the detection of some $>100$ MeV photons from quite a few GRBs by the Compton Gamma Ray Observatory satellite in $-$ 2000 \citep[e.g.,][]{Hurley94,fm95,Gonz03}, the prompt high energy emission has been extensively investigated and most calculations are within the framework of the standard internal shocks \citep[e.g.,][cf. Giannios 2007]{Pilla98,pw04,gz07,Bosnjak09}." . The detection prospect for LAT seems very promising (seeFan&Piran2008.forarecentreview)., The detection prospect for LAT seems very promising \citep[see][for a recent review]{fp08}. Since the launch of Fermi satellite on 11 June 2008. signiticant detections of prompt high energy emission from GRBs have been only reported in GRB 0505056 (Bouvieretal.2008).. GRB 080916C (Abdoetal.2009).. GRB 081024B (Omodei2005). GRB 090323 (Ohnoetal...2009b).. GRB 090328 (Cutinietal. 2009).. possibly and GRB 090217 (Ohnoetal.20092). until now (5 May 2009).," Since the launch of Fermi satellite on 11 June 2008, significant detections of prompt high energy emission from GRBs have been only reported in GRB 080825C \citep{Bouvier08}, GRB 080916C \citep{Abdo09}, GRB 081024B \citep{Omodei08}, GRB 090323 \citep{Ohno09b}, GRB 090328 \citep{Cutini09}, possibly and GRB 090217 \citep{Ohno09} until now (5 May 2009)." Though the detection of 3 prompt photons above 10 GeV from GRB 080916C at redshift 2—4.5 (Abdoetal. is amazing and may imply a very high," Though the detection of 3 prompt photons above $10$ GeV from GRB 080916C at redshift $z\sim 4.5$ \citep{Abdo09,Greiner09} is amazing and may imply a very high" At a relativistic shock. a particle remains in the upstream medium until it has been deflected. on average. through an augle of 1/> in the upstream rest frame.,"At a relativistic shock, a particle remains in the upstream medium until it has been deflected, on average, through an angle of $1/\gammabar$ in the upstream rest frame." A turbulent fluctuation of streneth parameter e. deflects a particle of Lorentz factor 5 through an anele «/5.," A turbulent fluctuation of strength parameter $a$, deflects a particle of Lorentz factor $\gamma$ through an angle $a/\gamma$." Provided this angle is small. the diffusion coefficient is simply Dy=a?/57. where vy is the mean scattering frequency.," Provided this angle is small, the diffusion coefficient is simply $\mathcal{D}_\theta=a^2\nu_{\rm sc}/\gamma^2$, where $\nu_{\rm sc}$ is the mean scattering frequency." The average munuber of scatterings in the upstream medium between shock encounters is therefore right))? At cach scattering. the power radiated in pliotous by the energetic particle can be estimated from Larmor's formula:h," The average number of scatterings in the upstream medium between shock encounters is therefore )^2 At each scattering, the power radiated in photons by the energetic particle can be estimated from Larmor's formula:." us] assuniue inverse Compton losses cau be neglected., assuming inverse Compton losses can be neglected. For kinematic reasons. the average energy gain per cycle is roughly a factor of two (Achterbereetal.2001).. so that the acceleration process will saturate when the energy lost in the wpstream iuediuu is roughly 5/062.," For kinematic reasons, the average energy gain per cycle is roughly a factor of two \citep{achterbergetal01}, so that the acceleration process will saturate when the energy lost in the upstream medium is roughly $\gamma mc^2$." This implies INcueArI<1. or Applving the sane aremment. cucrey loss by scattering in the dowustream immedi. where particles must be scattered through au anele of roughly 7/2. iniposes the condition which. since Aq~Ay. IX more restrictive.," This implies $N_{\rm scatt,u}\left.\Delta\gamma/\gamma\right|_{\rm loss,u}<1$, or Applying the same argument, energy loss by scattering in the downstream medium, where particles must be scattered through an angle of roughly $\pi/2$, imposes the condition which, since $\lambda_{\rm d}\sim\lambda_{\rm u}$, is more restrictive." The ballistic τοσο requies αμα<<>. which. according to (3)). is fulfilled for unmaguetized pair shocks for all particles with 5>+. provided ἐνS10. aud σα< 1l.," The ballistic regime requires $a_{\rm u,d}<\gamma$, which, according to \ref{weibelstrength}) ), is fulfilled for unmagnetized pair shocks for all particles with $\gamma>\gammabar$, provided $\ell_{\rm w}\lesssim10$, and $\sigma_{\rm u,d}<1$ ." For electrou-iou shocks. this coudition is unlikely to be satisfied for electrons with 5~5. but is easily satisfied for clectrous that achieve energies comparable to those of thermal ious or higher. provided σα1.," For electron-ion shocks, this condition is unlikely to be satisfied for electrons with $\gamma\sim\bar{\gamma}$, but is easily satisfied for electrons that achieve energies comparable to those of thermal ions or higher, provided $\sigma_{\rm u,d}\ll 1$." Iu the helical transport reguue. energv losses are iuportant at all points along a trajectory. aud. if Bolum diffusion operates. the fiue taken to return to the shock frout is approximately the evro period.," In the helical transport regime, energy losses are important at all points along a trajectory, and, if Bohm diffusion operates, the time taken to return to the shock front is approximately the gyro period." " Under these conditions. the ανα Loreutz factor has becu calculated by Achterbereetal.(2001): At maguetized. relativistic shocks. particle acceleration bv the first-order Fermi uiechanisiua is less plausible. since. at least for προμπατα. shocks. it relics on strong cross-ficld diffusion (οἱ),Baring&ΟΠΟΥ2009)."," Under these conditions, the maximum Lorentz factor has been calculated by \citet{achterbergetal01}: At magnetized, relativistic shocks, particle acceleration by the first-order Fermi mechanism is less plausible, since, at least for superluminal shocks, it relies on strong cross-field diffusion \citep[e.g.,][]{baringsummerlin09}." . However. if the process does operate. particles cau move out of the helical regime iuto the ballistic regime. as their Lorentz factor increases.," However, if the process does operate, particles can move out of the helical regime into the ballistic regime, as their Lorentz factor increases." " Because of this. it is convenieut o define a critical strength: parameter dois such that when @=des, the παπα Loreutz factor caa xxüitted by radiation losses is achieved just at the poiut at which the transport changes character from helical to vallistic."," Because of this, it is convenient to define a critical strength parameter $a_{\rm crit}$ such that when $a=a_{\rm crit}$ the maximum Lorentz factor $\gamma_{\rm max}$ permitted by radiation losses is achieved just at the point at which the transport changes character from helical to ballistic." I£ e2euge all particles remain in the the helical reeine.," If $a>a_{\rm crit}$, all particles remain in the the helical regime." On the other hand. ife <με. particles of the uaxiuun Lorentz factor undergo ballistic transport. but ower enerev particles may be iu the helical regime.," On the other hand, if $a2 svstonis which is closer to the EDCCIIsxice deusities preseuted imn this paper.," They now find $\sim 18\times 10^{-6}\,h^{-3}\,{\rm Mpc^{-3}}$ for RC=1 systems and $\sim 7\times 10^{-6}\,h^{-3}\,{\rm Mpc^{-3}}$ for ${\rm RC}\ge2$ systems which is closer to the EDCCII space densities presented in this paper." " Iu παν, we fxd &ood aereecmeut betwoeenu all three of these surveys (PDCS. olde ret al."," In summary, we find good agreement between all three of these surveys (PDCS, Holden et al." and the EDCCTI) which combined spa1 à redshift range of 0.05<2<0.0., and the EDCCII) which combined span a redshift range of $0.05\le z\le 0.6$. At worst. the differeace between the three surveys isR |!101 (Table 3).," At worst, the difference between the three surveys is $4^{+10}_{-4}$ (Table 3)." This there‘fore justifies our origiial desire to runi he matched filter aeorithin ou the low redshift EDSCC data since we are low comparing clusers selected iu a sximailar wav over this cutive redshift range., This therefore justifies our original desire to run the matched filter algorithm on the low redshift EDSGC data since we are now comparing clusters selected in a similar way over this entire redshift range. We have hus removes oue of the main uncertaiities associated with the PDC'S as we do not see a significat. cifference vetween the low anc lüeh redshift cluster populations (as originally highlehted by Postinan et al., We have thus removed one of the main uncertainties associated with the PDCS as we do not see a significant difference between the low and high redshift cluster populations (as originally highlighted by Postman et al. 1996)., 1996). Moreover. his agreeniewt Προς that there is litle evolution 1ce he space desity. of optical clusters out to.20.5. d agreement wili results from Nrav surveys of clusters (sec Nichol et al.," Moreover, this agreement implies that there is little evolution in the space density of optical clusters out to $z\simeq0.5$, in agreement with results from X–ray surveys of clusters (see Nichol et al." 1997. |999: Burke et al.," 1997, 1999; Burke et al." 1997: Rosati ct al., 1997; Rosati et al. 1998: Vikhliuin et al., 1998; Vikhlinin et al. 1998: Elbcling e al., 1998; Ebeling et al. 1997. 1999).," 1997, 1999)." ILowever. we should rot overstate this claim. since the error1 bars on all iieasureneuts are large.," However, we should not overstate this claim, since the error bars on all measurements are large." In the future. we wi1 need large samples of clusters that spa ra large range i1 redshift: this shouk be possible with the next eeueration of cluster catalogues constructed from srvevs like DPOSS (Gal et al.," In the future, we will need large samples of clusters that span a large range in redshift; this should be possible with the next generation of cluster catalogues constructed from surveys like DPOSS (Gal et al." 1999) aid the SDSS (Cain et al., 1999) and the SDSS (Gunn et al. 1998)., 1998). We also urge the comnunity to adopt one clusterfinding algoritlian so if can be applied to cdiffereut catalogues (at lüeh aud low redshit) cousisteutly., We also urge the community to adopt one cluster–finding algorithm so it can be applied to different catalogues (at high and low redshift) consistently. Iu Table 5.. we present the space deusiv of Abell clusters taken from Postiuau et al. (," In Table \ref{space}, we present the space density of Abell clusters taken from Postman et al. (" 1996 aud references therein).,1996 and references therein). The EDCCII space density measurements apvcar to be svstematically higher than the Abell cataloguewe find ~7 times as many RC~O clusters as Abel., The EDCCII space density measurements appear to be systematically higher than the Abell cataloguewe find $\sim7$ times as many $\sim$ 0 clusters as Abell. However. for RC20. this discrepancy is much less while the errors ou these imieasureiments are large.," However, for ${\rm RC>0}$, this discrepancy is much less while the errors on these measurements are large." Therefore. we must be wary about overinterpretatiug any claimed «lscrepauicv with Abell and simply note that overaL the EDC'CTI has loessenuec the discrepancy previously claimed to )e between the high and low redshift cluster populations.," Therefore, we must be wary about over–interpretating any claimed discrepancy with Abell and simply note that overall, the EDCCII has lessened the discrepancy previously claimed to be between the high and low redshift cluster populations." Our potential disagreciment with the Abel catalogue could beIC due to two factors., Our potential disagreement with the Abell catalogue could be due to two factors. First. like the EDCCII catalogue. the effective area of tle Abe] catalogue could be sinaller than expected (sec Section 3).," First, like the EDCCII catalogue, the effective area of the Abell catalogue could be smaller than expected (see Section 3)." Secoudlv. the EDCCII could be fiudiug more clusters than the Abell cataloge at a eiven richuess.," Secondly, the EDCCII could be finding more clusters than the Abell catalogue at a given richness." The first o‘these two factors is hare o quantity eiven t10 subjective nature of the Abell cataloge. however. the secoud factor can be addressed by crosscorrelating iudividual clusters iu ith the EDCCTI aud Abell catalogues.," The first of these two factors is hard to quantify given the subjective nature of the Abell catalogue, however, the second factor can be addressed by cross–correlating individual clusters in both the EDCCII and Abell catalogues." We discuss the Iater below., We discuss the latter below. Tn total we detec tolS2 of the 321 Abell clusters iu the EDCCIL area. «Du of them (ising a matching radius of 7.5 arciuuins).," In total, we detect 182 of the 324 Abell clusters in the EDCCII area, or of them (using a matching radius of $7.5$ arcmins)." This is in good aegrecient with Luiisden ct al. (, This is in good agreement with Lumsden et al. ( 1992) who fud ~T0 matchup between their orginal EDCC chsters and the Abell catalogue.,1992) who find $\sim70\%$ match–up between their original EDCC clusters and the Abell catalogue. Iu both cases. the perccutage of matchτιos ds independent of richness neither he EDCC or EDCCII appear to have missed Abell οusters of a partictlar richness class (sce Figure 8 of Ταν vet al).," In both cases, the percentage of match–ups is independent of richness neither the EDCC or EDCCII appear to have missed Abell clusters of a particular richness class (see Figure 8 of Lumsden et al.)." " Iu addilon to compare richnesses, we have also compared the disace estimates of O rimatched. aud uunatched. Abell clusers and find little correlaion."," In addition to comparing richnesses, we have also compared the distance estimates of our matched, and unmatched, Abell clusters and find little correlation." Therefore. t10 luissine ~405€ of Abell clusters in the EDCCTI catakgue appear to he sead evenly over all Richuess auc Disance Classes;," Therefore, the missing $\sim40\%$ of Abell clusters in the EDCCII catalogue appear to be spread evenly over all Richness and Distance Classes." " Finalv. for clusters iu COwmon between the EDCCTII and Abell catalogues. we fud no correlation vetween the two difference ricloss estimasie. R,, and Abell vrichuess or RC."," Finally, for clusters in common between the EDCCII and Abell catalogues, we find no correlation between the two difference richness estimates $R_m$ and Abell richness or RC." This agrees wih Luusdeu et al. (, This agrees with Lumsden et al. ( 1992) and Postman et al. (,1992) and Postman et al. ( 190906) ho ho whom detect a large scatter between their ricMess OSiniaes and the Abell richness estimates.,1996) both of whom detect a large scatter between their richness estimates and the Abell richness estimates. lu οςmutrast. there are a total of 2109 EDCCTI ch«ΤΟΥΣ cleected iu the area eiven in Section 2: a factor of ~ὃ nore fran detected in the Abell catalogue over the Sale area (we have excluded the supplementary Abell cataogue here aud iu the above analysis).," In contrast, there are a total of 2109 EDCCII clusters detected in the area given in Section \ref{EDSGC}; a factor of $\sim8$ more than detected in the Abell catalogue over the same area (we have excluded the supplementary Abell catalogue here and in the above analysis)." " This discrepaucy is Iessened when we cousider only &,,2LOO systems where we find 227 EDCCII clusters (however. we note that the LDCCII ouly probes fo iu€ 0.13. while the Abell catalogue contains rich svstems out to 2~ 010)."," This discrepancy is lessened when we consider only $R_m\ge100$ systems where we find 227 EDCCII clusters (however, we note that the EDCCII only probes to $z_{est}\le0.15$ , while the Abell catalogue contains rich systems out to $z\sim0.4$ )." These, These (section 3.3)).,(section \ref{sec:linesig}) ). " To fit the το peak as the red Doppler horn of a disk-line requires an enütting radius 21337, (where ry∶↻⋀∐∐∐↙⋅−≼∐∖∐∪↑↸∖↴∖↴∶↴∙⊾↥⋅⋜↧↖⇁↕↑⋜↧↑↕∪∐⋜↧↕7) ⋅⋅ radii) eAin a low inclination. svstem with. -27E with v62=yy428/95B d.o.f.:"," To fit the keV peak as the red Doppler horn of a disk-line requires an emitting radius $\pm 3 r_g$ (where $r_g = GM_{BH}/c^2$ denotes gravitational radii) in a low inclination system with ${27^{+1}_{-3}}^\circ$ with $\chi^2=128/95\, d.o.f$ .;" the correspoudiug- blue horu is then predicted to lie at kkeV. and the data are consistent with that model., the corresponding blue horn is then predicted to lie at keV and the data are consistent with that model. While there is evidence for line emission iu the kkeV regine. such lines are commonly observed as emission fron ionized species of Fe. aud thus the identification of cussion blue-wurd of κο) ds currentlv aüubieuous.," While there is evidence for line emission in the keV regime, such lines are commonly observed as emission from ionized species of Fe, and thus the identification of emission blue-ward of keV is currently ambiguous." Fits to the mean spectra from each observatiou have shown consistent line fluxes for Fe he and the line at keV aud these show an equivaleut width that appears to have changed as the source flux varied., Fits to the mean spectra from each observation have shown consistent line fluxes for Fe $\alpha$ and the line at keV and these show an equivalent width that appears to have changed as the source flux varied. Figure 7 shows the ratio of data in the Fe Ne regime to a couunon local coutimmna fit: the fact that the source spectruni ds steeper at high fiux is reflected in the systematics of the residuals., Figure \ref{fig:hiloratio} shows the ratio of data in the Fe $\alpha$ regime to a common local continuum fit; the fact that the source spectrum is steeper at high flux is reflected in the systematics of the residuals. To confirm the significance of the chanec in equivalent width we fit the 2008 data with a model that fixed the line equivalent width for the feature at likkeV to hat found durug 2005: afterrefitting tlis resulted in a worse fit with A\?=142., To confirm the significance of the change in equivalent width we fit the 2008 data with a model that fixed the line equivalent width for the feature at keV to that found during 2005; afterrefitting this resulted in a worse fit with $\Delta \chi^2=142$. Alternatively. fixiug he flux of the new lines at the 2005 values aud refitting. we found AQ?=0. iudicating tha the line fluxes may be consistent with lines of coustaut flux across the data.," Alternatively, fixing the flux of the new lines at the 2005 values and refitting, we found $\Delta \chi^2=0$, indicating that the line fluxes may be consistent with lines of constant flux across the data." As the limits on line flux provide the potential to distinguish )tween iuodels. we tested all available ligh-quality data in a seltconsisteut manner.," As the limits on line flux provide the potential to distinguish between models, we tested all available high-quality data in a self-consistent manner." Taking the model frou section 3.3. we fixed the line energy aud width to specifically test the coustancy of the keV. line., Taking the model from section \ref{sec:linesig} we fixed the line energy and width to specifically test the constancy of the keV line. In addition to testing the mean spectrum from each observation. we sub-divided the 2005 and 2008 exposures to sample the line more finely iu fux.," In addition to testing the mean spectrum from each observation, we sub-divided the 2005 and 2008 exposures to sample the line more finely in flux." For 2005 au iuteusitv selection was made on the 0.5-10 keV count rate at (.17 ct 8+ por NIS as before., For 2005 an intensity selection was made on the 0.5-10 keV count rate at 0.47 ct $^{-1}$ per XIS as before. For 2008 intensity selectious weremace δη ct s ΝΙΛ. 2.0 - 3.0 ct 3/NIS G2) and 340 6t L/NIS G3).," For 2008 intensity selections weremade $ < 2.0 $ ct $^{-1}$ /XIS ), 2.0 - 3.0 ct $^{-1}$ /XIS ) and $ > 3.0$ ct $^{-1}$ /XIS )." The results are shown πι Table 3 where both the mean fits for each observation are tabulated. as well as the results.," The results are shown in Table 3 where both the mean fits for each observation are tabulated, as well as the results." As noted previously. the line is required a a ligh level of confidence in the 2008 Nov 6 data (which is more sensitive to 16 features than the Nov 23 data. owing to the loug exposure and lieh flux state of the source).," As noted previously, the line is required at a high level of confidence in the 2008 Nov 6 data (which is more sensitive to the features than the Nov 23 data, owing to the long exposure and high flux state of the source)." Table 3 shows liue flux along with imiproveimieuts in the fit-statistic aud equivalent width for each fit., Table 3 shows line flux along with improvements in the fit-statistic and equivalent width for each fit. Note that the mean observation fits in Table 3 show slightly tighter constraiuts iu line flux for 2005 compared to the values noted im section 3.3 because the initial fits to 2005 data had the line οποιον left free., Note that the mean observation fits in Table 3 show slightly tighter constraints in line flux for 2005 compared to the values noted in section \ref{sec:linesig} because the initial fits to 2005 data had the line energy left free. The data are consisteut with the keV line existing at the same flux level throughout theσα] observations considered in Table 3 and the high significance of the line detection across several time slices of data provides compelling evidence for the reality of the line: conclusively ruling ou the possibility of the line etection being a statistical fluctuation in the spectral data., The data are consistent with the keV line existing at the same flux level throughout the observations considered in Table 3 and the high significance of the line detection across several time slices of data provides compelling evidence for the reality of the line; conclusively ruling out the possibility of the line detection being a statistical fluctuation in the spectral data. Consideriug the three independent detections of the line. as shown in Table 3 observations 1.2 aud 3 vield iuprovenieuts to the fit Ay?=32.19.19 respectively and a probability of all three detections being false is podslot.," Considering the three independent detections of the line, as shown in Table 3 observations 1,2 and 3 yield improvements to the fit $\Delta \chi^2=32,19,19$ respectively and a probability of all three detections being false is $p < 3 \times 10^{-11}$." We repeated the fits with the line cucrey allowed to be free and found. the fitted energy to be cousistent with kkeV. aud that the line flux had not been siguificautlv affected by freezing the energy., We repeated the fits with the line energy allowed to be free and found the fitted energy to be consistent with keV and that the line flux had not been significantly affected by freezing the energy. To extend the test for line fiux variations we reduced and fit the spectra obtained during 2001 and 2002., To extend the test for line flux variations we reduced and fit the spectra obtained during 2001 and 2002. We followed the standard reduction mothod for the pu data. as detailed by ?2). aud found the data to be cousisteut with the presence of a line at the same flux as found usingSuzaku.," We followed the standard reduction method for the pn data, as detailed by \citet{ponti06a} and found the data to be consistent with the presence of a line at the same flux as found using." Au independent analvsis of theNALA data by ?) reported the presence of éj excess of counts in the 5.16.2 keV band. for NGC 1051. compared to their parameterization of the local contiuuun.," An independent analysis of the data by \citet{demarco09a} reported the presence of an excess of counts in the 5.4-6.2 keV band for NGC 4051, compared to their parameterization of the local continuum." Examination of theVALAL data shows an excess of cussion at ~6 keV in theVALZAL spectra aud so tentatively supports the possibility of that additional euergv-hüfted Ime iu this source., Examination of the data shows an excess of emission at $\sim 6$ keV in the spectra and so tentatively supports the possibility of that additional energy-shifted line in this source. DeppoSurc also observed. NOC 1051. finding the source to be iu a verv low flux state durius 1998 as reported by ?73..," also observed NGC 4051, finding the source to be in a very low flux state during 1998 as reported by \citet{guainazzi98b}. ." We extracted aud fit the archived PeppoSa.c Medii Eucrgy. Conceutrator spectruni frou units 2 and 3 (combined) aud, We extracted and fit the archived Medium Energy Concentrator spectrum from units 2 and 3 (combined) and "' MPE. Postfach 1312. 85741 Garching. Germany. ? INAF - Osservatorio Astronomico di Roma. via di Frascati 33. 00040 Monte Porzio Catone. Italy * Department of Physics. Durham University. South Road. Durham. DH]! 3LE. UK + European Space Astronomy Centre. Villafranca del Castillo. Spain ? European Southern Observatory. Karl-Schwarzschild-Strabe 2, 85748 Garching. Germany INAF - Osservatorio Astronomico di Trieste. via Tiepolo I1. 34143 Trieste. Italy IRFU/Service d'Astrophysique. Bàtt.709. CEA-Saclay. 9119] Gif-sur-Yvette Cedex. France","$^1$ MPE, Postfach 1312, 85741 Garching, Germany, $^2$ INAF - Osservatorio Astronomico di Roma, via di Frascati 33, 00040 Monte Porzio Catone, Italy $^3$ Department of Physics, Durham University, South Road, Durham, DH1 3LE, UK $^4$ European Space Astronomy Centre, Villafranca del Castillo, Spain $^5$ European Southern Observatory, e 2, 85748 Garching, Germany $^6$ INAF - Osservatorio Astronomico di Trieste, via Tiepolo 11, 34143 Trieste, Italy $^7$ IRFU/Service d'Astrophysique, Bâtt.709, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France" Equatorial plane mass density contours for our disk simulation. in a format similar to DOT.," Equatorial plane mass density contours for our disk simulation, in a format similar to B07." The contours span approximately 7 orders of magnitude in mass density. using factor of two spacing.," The contours span approximately 7 orders of magnitude in mass density, using factor of two spacing." The box that encloses each image spans 40 AU on each side. accommodating the initial disk radius of 20 AU.," The box that encloses each image spans 40 AU on each side, accommodating the initial disk radius of 20 AU." Shown are density images near the time of the highest amplitude nonaxisvinmetry (top. 0.25 ORD). the time at the end of the equivalent runs in DOT (middle. 3.7 ORP). and the final image (bottom. 5.0Hr ORD).," Shown are density images near the time of the highest amplitude nonaxisymmetry (top, 0.25 ORP), the time at the end of the equivalent runs in B07 (middle, 3.7 ORP), and the final image (bottom, 5.0 ORP)." As in D07. we indicate the highest densities (> ," As in B07, we indicate the highest densities $>$ " Gravitational leusiug provides us with the most direct aud cleanest of methods for probing the distribution of matter in the universe (Mellier 1999. Bartclmann Sclueider 2001).," Gravitational lensing provides us with the most direct and cleanest of methods for probing the distribution of matter in the universe (Mellier 1999, Bartelmann Schneider 2001)." The Ieusiug effect arises due to the scattering of light by perturbations in the metric. stretching and coutracting buudles of light ravs. causing the distortion of backeround galaxy dmaees.," The lensing effect arises due to the scattering of light by perturbations in the metric, stretching and contracting bundles of light rays, causing the distortion of background galaxy images." Ποσο eravitational lensing doces not depend on ay assuniptious about the state of the intervening matter., Hence gravitational lensing does not depend on any assumptions about the state of the intervening matter. These distortions manifest themselves as a shear distortion of the source galaxy image (see c.g. Tyson et al 1990: IKaiser Squires 1993). or a change iu the surface number deusity of source galaxies due to maguification (sce e.g. Broadhurst. Tavlor Peacock 1995: Fort. Mellier Dautel-Fort 1997: Taxlor et al 1998) and can be used to map the two dimensional projected matter distribution of cosmological structure.," These distortions manifest themselves as a shear distortion of the source galaxy image (see e.g. Tyson et al 1990; Kaiser Squires 1993), or a change in the surface number density of source galaxies due to magnification (see e.g. Broadhurst, Taylor Peacock 1995; Fort, Mellier Dantel-Fort 1997; Taylor et al 1998) and can be used to map the two dimensional projected matter distribution of cosmological structure." As the matter content of tle universe is dominated by uon-harvonic and non-Iuuinous matter. gravitational lensing is the most accurate method for probing the distribution of this dark matter.," As the matter content of the universe is dominated by non-baryonic and non-luminous matter, gravitational lensing is the most accurate method for probing the distribution of this dark matter." Weak lensing studies have beeu carried out for a wide range of galaxy clusters. allowing precision ucasureimeuts of cluster masses aud mass distributions (see e.g. Tyson et al 1990. Kaiser Squires 1993. Dounet et al 1991. Squires et al 1996. Ioekstra et al 1998. Luppino I&aiser 1997. Gray et al 2002).," Weak lensing studies have been carried out for a wide range of galaxy clusters, allowing precision measurements of cluster masses and mass distributions (see e.g. Tyson et al 1990, Kaiser Squires 1993, Bonnet et al 1994, Squires et al 1996, Hoekstra et al 1998, Luppino Kaiser 1997, Gray et al 2002)." On arecr scales. the shear due to large-scale structure has been accurately measured by several eroups. (306 e.g. van Waerboke et al 2001. IToekstra et al 2002. Bacon et al 2002. Jarvis et al 2003. Brown ct al 2003).," On larger scales, the shear due to large-scale structure has been accurately measured by several groups (see e.g. van Waerbeke et al 2001, Hoekstra et al 2002, Bacon et al 2002, Jarvis et al 2003, Brown et al 2003)." Depth information. from galaxy redshifts. has already been used in weak lIeusime studies to determine he median redshifts ofthe leus aud backeround populations.," Depth information, from galaxy redshifts, has already been used in weak lensing studies to determine the median redshifts of the lens and background populations." This cau be a linütiug factor iu the analysis. caving uncertaintwv in the overall mass normalisation.," This can be a limiting factor in the analysis, leaving uncertainty in the overall mass normalisation." Iu this review I describe iu application using accurate shear aud redshift information from the COMDOLITT dataset (Wolf et al. 2003) to estimate the first maxima likelihood shear power spectra analysis (Section 2). includiug all of the uncertaiuties associated with source distances (see Brown et al 2003).," In this review I describe an application using accurate shear and redshift information from the COMBO17 dataset (Wolf et al, 2003) to estimate the first maximum likelihood shear power spectrum analysis (Section 2), including all of the uncertainties associated with source distances (see Brown et al 2003)." While the shear power coutains nich important information on the statistics of the dark matter distribution and cosmological parameters. v lot of information is projected out.," While the shear power contains much important information on the statistics of the dark matter distribution and cosmological parameters, a lot of information is projected out." However this is not a uecessury step., However this is not a necessary step. In Section 3 I outline how the full SD dark matter distribution can be recovered from shear aud redshift formation. aud make the first application to the COMDOL? data (see Taylor 2001. Bacon Taylor 2003. Tavlor et al 2003).," In Section 3 I outline how the full 3-D dark matter distribution can be recovered from shear and redshift information, and make the first application to the COMBO17 data (see Taylor 2001, Bacon Taylor 2003, Taylor et al 2003)." Finally. in Section 1. I describe a new method for using shear aud redshifts in a purely ecometrical test to accurately measure the equation of state of the dark energv in the universe and its evolution (See Jain Tavlor 2003).," Finally, in Section 4, I describe a new method for using shear and redshifts in a purely geometrical test to accurately measure the equation of state of the dark energy in the universe and its evolution (See Jain Taylor 2003)." It is clear that the combination of shear aud redshift information provides a powerful tool for cosmolosv. allowing us to not only nage the dark matter directly. but also see its evolution over cosnic time.," It is clear that the combination of shear and redshift information provides a powerful tool for cosmology, allowing us to not only image the dark matter directly, but also see its evolution over cosmic time." Hence future lensing surveys should consider being coupled to photometric redshift surveys. opening up new dimensions in gravitational lensing studies.," Hence future lensing surveys should consider being coupled to photometric redshift surveys, opening up new dimensions in gravitational lensing studies." ⋜↕⊳∖∐∐↥↽≻↥≺↵∑≟↕⋅∐⇂−⊳∖≺↵⋜⋃⋅∢∙∐∖−∐∐∐↓∐∐∠⋜↕⋃∩∐↕⋅∩⋯⋯↩,a simple grid-search $\chi^2$ minimization routine. ⋅∌↥∑∸⋯⋅≺↵∪⊳∖∐∩∖∖↽⊳∖↕∐≺↵↕⋅≺↵⊳∖⋃∐⊳∖⋅⊂∩⋯↥↽≻⋜⋃⋅⋯∑≟↕∐, Figure \ref{fig:ngc450color} shows the results. ≺↵⊳∖↕≺↵∐⋜⋃⋅⋅ ⋅ ⋅↽≻ ⋅⋅⋅ ⋅ EM 1⋅ ↥↽≻∩↥↽≻⇂∐⋜↕⋃∩∐⋜↕∑∸↩⋯⋜↕↥↽≻⊳∖∖∖↽∐∐↥⋟⊂⊲⇀−∖−⊳∖⋯∩∩∐∏∐∑∸↕∩⋃∐⊳∖⋯∩∩↕∐≺↵≺⇂∐↕⋜↕↥↽≻⊳∖⊳∖∐∩∖∖↽⊳∖↕∐⋜↕↕↕∐≺↵↓⋅≺↵↥⊳∖∢∙∩∐⊳∖↥≺⇂≺↵↕⋅⋜↕∣≻↥⊽∖⇁ ∐↕∩↕⋅, Comparing the stellar population age maps with PCA-smoothing to unsmoothed maps shows that there is considerably more scatter in the un-smoothed maps. ≺↵⊳∖∢∙⋜↕⊓≺↵↓⋅↥∐↕∐≺↵⋃∐−⊳∖∐↕∩∩↕∐≺↵≺⇂ naps. Figure 9 also shows that the PCA-smoothine preserves the structural into1nat]on. where HII regions are still prominent in the PCA-simoothed image.," Figure \ref{fig:ngc450color} also shows that the PCA-smoothing preserves the structural information, where HII regions are still prominent in the PCA-smoothed image." The contrast between |xight HII regions alid a faint older disk is preserved during PCA-smoothine., The contrast between bright HII regions and a faint older disk is preserved during PCA-smoothing. Figure 10 qiantilies tlie leve ol scatter iu the best-fit ages., Figure \ref{fig:ngc450age2} quantifies the level of scatter in the best-fit ages. Figure 10. shows the analysis lor a region with lower SNR pixels wlich are located ou the disk region., Figure \ref{fig:ngc450age2} shows the analysis for a region with lower SNR pixels which are located on the disk region. The scatter towards younger ages [or un-sumootrect ¢ata is clea*, The scatter towards younger ages for un-smoothed data is clear. For unsmoothecd data the best-lit ages rauge from 0.1 Gyr to 10 Cyr. where the PCA-sinoothec analysis bas best-fit ages clustered around a few Cyr to 9 Gyr.," For unsmoothed data the best-fit ages range from 0.1 Gyr to 10 Gyr, where the PCA-smoothed analysis has best-fit ages clustered around a few Gyr to 9 Gyr." Since this is real ¢ala. he true age distribution is uot kuown and is uot shown.," Since this is real data, the true age distribution is not known and is not shown." Next PCA-smoothing is run on SDSS J235106.25+01032L1. which ias well clefinecl blue spiral arms nearby a red bulge.," Next PCA-smoothing is run on SDSS J235106.25+010324.1, which has well defined blue spiral arms nearby a red bulge." Figure 11. shows the SDSS color image. the PCA map. PCAÀ-imoothed g-baud image. best-fit model age of the uu-smoothed data. aud best-fit uodel age of the smootlec| data.," Figure \ref{fig:sdss} shows the SDSS color image, the PCA map, PCA-smoothed $g$ -band image, best-fit model age of the un-smoothed data, and best-fit model age of the smoothed data." The top middle pauel of Figure 11. clearly shows that this method separates tle bulge aud spiral arms into dillerent areas in PCA space. as can be seen by the buee pixels being bright zu| the spiral arms being dark.," The top middle panel of Figure \ref{fig:sdss} clearly shows that this method separates the bulge and spiral arms into different areas in PCA space, as can be seen by the bulge pixels being bright and the spiral arms being dark." The separation of spiral arms. versus tle bilge aud inter-disk regious means that they will not be mixed in the PCA-smoothing routines., The separation of spiral arms versus the bulge and inter-disk regions means that they will not be mixed in the PCA-smoothing routines. This paper presents a inet10d for smoothing SDSS data using a variation of Principal Component Analysis., This paper presents a method for smoothing SDSS data using a variation of Principal Component Analysis. Tie inethod is perlmed by running PCA simultaneously on uulti-waveleneth images of galaxies. aud hen smootli1 over pixels that have similar locations in PCA space aud spatial location witun the galaxy.," The method is performed by running PCA simultaneously on multi-wavelength images of galaxies, and then smoothing over pixels that have similar locations in PCA space and spatial location within the galaxy." TIe advantages of the method are 1) no mixiug of colors. 2) the method is geared owards stellar popuation analysis. 3) the parameters are tuiable. and [) the resu are not ext'emely. sensitive ο the input parameters.," The advantages of the method are 1) no mixing of colors, 2) the method is geared towards stellar population analysis, 3) the parameters are tunable, and 4) the results are not extremely sensitive to the input parameters." " The disadvantages of the iuethod. are 1) requiring iitial analysis t0 icentilv the galaxy. 2) running PCA which may take computation"" time. and 3) requires well uierstood aud unifo1u noise characteristic across different wavelengtlis."," The disadvantages of the method are 1) requiring initial analysis to identify the galaxy, 2) running PCA which may take computational time, and 3) requires well understood and uniform noise characteristic across different wavelengths." The snootl[unlug parameters ca1 be tuned to adjust the tradeolT between more smoothing aid more color mixine) versis less soothineOm and more color purity., The smoothing parameters can be tuned to adjust the tradeoff between more smoothing and more color mixing versus less smoothing and more color purity. IuncreasiugOm the SNRenhanced coustant. results iu al increasecl signal-to-nolse of the si1o0tlied. pixel. at the cost of mixing over cifferent colors.," Increasing the $SNRenhanced$ constant, results in an increased signal-to-noise of the smoothed pixel, at the cost of mixing over different colors." Lowejug 1ie SNBenlianced constant. results in a more pure coor with less smoothing over differen colWs. at the cost of a lower sinoothed signal-to-noise.," Lowering the $SNRenhanced$ constant, results in a more pure color with less smoothing over different colors, at the cost of a lower smoothed signal-to-noise." The iuehod was tested aixc demonstrated using a mock galaxy wit Lugric-baud images having SNRs siuila to that seen iu typical SDSS data., The method was tested and demonstrated using a mock galaxy with $ugriz$ -band images having SNRs similar to that seen in typical SDSS data. Figures { aud 5 show hat the FOAL lor the, Figures \ref{fig:IMSTATall} and \ref{fig:ANALYZEHII} show that the $FOM$ for the "Finding Low-redshift galaxies close to high-redshift, QSOs on the plane of the sky is important for probing the interstellar medium (18M) of the disks and halos of present epoch galaxies. since the light of the background. QSO may be absorbed by gas along the line of sight.","Finding low-redshift galaxies close to high-redshift QSOs on the plane of the sky is important for probing the interstellar medium (ISM) of the disks and halos of present epoch galaxies, since the light of the background QSO may be absorbed by gas along the line of sight." Both optical ancl ultraviolet (UV) absorption lines which arise in nearby galaxies have been studied. previously see Bowen. Blades Pettini (1995: hereafter BBP) and refs therein]: in xwticular. the detection of UV lines is important not only or understanding the physies of galaxy ISMs other than hat of the Milky Way. but because these are the same lines observed out to redshifts of ~4 in QSO spectra obtained rom erouncd-basecd observatories.," Both optical and ultraviolet (UV) absorption lines which arise in nearby galaxies have been studied previously [see Bowen, Blades Pettini (1995; hereafter BBP) and refs therein]; in particular, the detection of UV lines is important not only for understanding the physics of galaxy ISMs other than that of the Milky Way, but because these are the same lines observed out to redshifts of $\sim 4$ in QSO spectra obtained from ground-based observatories." The intention is to find ow redshift analogs to the high redshift. systems. which will enable us o understand the origin and evolution of absorbing gas from the earliest epochs.," The intention is to find low redshift analogs to the high redshift systems, which will enable us to understand the origin and evolution of absorbing gas from the earliest epochs." Previous compilations of QSO-galaxy pairs. (Monk et al., Previous compilations of QSO-galaxy pairs (Monk et al. 1986: DBurbidge ct al., 1986; Burbidge et al. 1990) have collated well known cases of QSO-galaxy pairs ancl added: additional. data where available., 1990) have collated well known cases of QSO-galaxy pairs and added additional data where available. Often though. not listed in these catalogs are other (fainter) galaxies closer to the QSO sightline which can also be probed once their redshifts have been determined.," Often though, not listed in these catalogs are other (fainter) galaxies closer to the QSO sightline which can also be probed once their redshifts have been determined." More. seriously. searching lor UV. absorption lines from nearby galaxies requires the use of the. (LEST).," More seriously, searching for UV absorption lines from nearby galaxies requires the use of the )." Unfortunately. the most severe constraint in studving galaxies in this way is the small number of QSOs which are bright enough (particularly in the [ar UV where the satcllite’s speetrographs are less sensitive)and close enough to a galaxy to be of interest.," Unfortunately, the most severe constraint in studying galaxies in this way is the small number of QSOs which are bright enough (particularly in the far UV where the satellite's spectrographs are less sensitive) close enough to a galaxy to be of interest." Hence finding galaxies near to UV bright QSOs is extremely important., Hence finding galaxies near to UV bright QSOs is extremely important. In this paper we present the redshifts of 26 objects which lie within L1 arcmins of nine QSO lines of sight., In this paper we present the redshifts of 26 objects which lie within 11 arcmins of nine QSO lines of sight. Three QSOs were originally observed with aas part of BBP’s Ale LH survev: the field around these QSOs clearly showed galaxies other than those which were being probed. but which had no known redshifts.," Three QSOs were originally observed with as part of BBP's Mg II survey; the field around these QSOs clearly showed galaxies other than those which were being probed, but which had no known redshifts." The lines of sight to two QSOs were also discussed by Bowen. Blades. Pettini (1996) ina AArchival programme designed to search for Lya absorption rom low-redshift ealaxies.," The lines of sight to two QSOs were also discussed by Bowen, Blades, Pettini (1996) in a Archival programme designed to search for $\alpha$ absorption from low-redshift galaxies." The remaining QSOs were observed: as part of the£57 Faint Object. Spectrograph Quasar Absorption. System Snapshot Survey. (“AbSnap’) xograumme (Bowen et al., The remaining QSOs were observed as part of the Faint Object Spectrograph Quasar Absorption System Snapshot Survey (`AbSnap') programme (Bowen et al. 1994: ‘Pytler et al., 1994; Tytler et al. 1900)., 1996). A subsample of the AbSnap target. fields showed: numerous aint galaxies close to the QSO lines of sight in the digitised images collated. by Bowen οἱ al. (, A subsample of the AbSnap target fields showed numerous faint galaxies close to the QSO lines of sight in the digitised images collated by Bowen et al. ( 1004).,1994). ‘These galaxics are interesting because although the exposure times for he AbSnap QSOs were short. the QSOs are some of the xightest available.," These galaxies are interesting because although the exposure times for the AbSnap QSOs were short, the QSOs are some of the brightest available." of signals can be well-approximated by a sparse expansion in terms of a suitable basis. or dictionary of funcüons.,"of signals can be well-approximated by a sparse expansion in terms of a suitable basis, or dictionary of functions." The main idea of compressive sensing is (hat if the signal is sparse. then a small number of measurements contain sufficient information for ils approximate or exact recovery.," The main idea of compressive sensing is that if the signal is sparse, then a small number of measurements contain sufficient information for its approximate or exact recovery." In our case. the problem is to reconstruct a sparseF(6) [rom a relatively small number of POP) measurements.," In our case, the problem is to reconstruct a sparse$F(\phi)$ from a relatively small number of $\tilde{P}(\lambda^{2})$ measurements." Therefore. we assume that the model of F(o) is sparse in an over-coniplete dictionary of functions.," Therefore, we assume that the model of $F(\phi)$ is sparse in an over-complete dictionary of functions." By over-complete we understand (hat the number of functions in the dictionary is larger than the munber of independent observation channels., By over-complete we understand that the number of functions in the dictionary is larger than the number of independent observation channels. Thus. the dictionary [functions may be redundant. (linearly. dependent). and (therefore orthogonal.," Thus, the dictionary functions may be redundant (linearly dependent), and therefore non-orthogonal." In order to give a proper formulation of this approach we need (o introduce a discrete representation of the © space., In order to give a proper formulation of this approach we need to introduce a discrete representation of the $\phi$ space. It is known (Brentjens&deBruyn2005) that. for a discrete sampled Earadaxy dispersion function. the full width at half maximum of the main peak of the RAISF is given by: where AA? is the width of the observation interval.," It is known \citep{Brentjens2005} that, for a discrete sampled Faraday dispersion function, the full width at half maximum of the main peak of the RMSF is given by: where $\Delta\lambda^{2}$ is the width of the observation interval." " Also. using a uniform grid in A7 space one can estimate the maximum observable Faraday depth bv: where 9A?=,NA?/N is the width of an observing channel (Brentjens&deBravn2005).."," Also, using a uniform grid in $\lambda^{2}$ space one can estimate the maximum observable Faraday depth by: where $\delta\lambda^{2}=\Delta\lambda^{2}/N$ is the width of an observing channel \citep{Brentjens2005}." " This estimation of ó,,; is Only an approximation. since in reality only (he frequency v is sampled linearly."," This estimation of $\phi_{max}$ is only an approximation, since in reality only the frequency $\nu$ is sampled linearly." " Therefore. in our discrete representation we consider a nonlinear grid in the 5 52,5/ ↜⇁⋅ ∣∣∶∪⋅⊥⋅↼∖⊽−⊥⋅≀↧↴∐≼⇂∣↽⇀↥⊳∖⊽⊔∐↲⊳∖⇁↕↽≻≼↲≼↲≼⇂∪↓⋟∐≸≟↥∐⋅↼≚↥⋟∖⊽∪⋅∖∖⇁≼↲≺∢∪∐⋟∖⊽↕≺⇂≼↲↕⋅"," Therefore, in our discrete representation we consider a nonlinear grid in the $\lambda^{2}$ space: $\lambda_{n}^{2}=c^{2}/\nu_{n}^{2}$, where $\nu_{n}=(\nu_{max}-\nu_{min})/N$ is the centered frequency of thechannel $n=0,1,...,N-1$, and $c$ is the speed of light." ≀↧↴∐∐≼↲≀↧↴↕⋅≸≟↕⋅↥≼⇂↕∐⊔∐↲∩⋟∖⇁↕↽≻≀↧↴≺∢≼↲⋅ ∖∖⇁↥∐↲↕⋅≼↲⊔∐↲≺∢∪∐↓↕↽≻⋯≀↧↴∐∪∐≀↧↴↥∖∖⇁↕∐≺⇂⋯∖⇁∩⊓⇁∣⋅∣∣⋅⊔∐↲⋟∖⊽≀↕↴∐↓↕↽≻∐∐≸≟↕⋅≼↲⋟∖⊽∪↥∏∐∪∐∩∫≖⋟⋅≀↧↴∐≼⇂⊔∐↲∐∏∐↓∣↽≻≼↲↕⋅∪↓⋟↕↽≻∪↕∐↥⋟∖⊽ AM are sel to: where |.r| is the integer part of ο”.," Also, we consider a linear grid in the $\phi$ space, where the computational window $\phi_{win}$, the sampling resolution $\phi_{R}$, and the number of points $M$ are set to: where $\left\lfloor x\right\rfloor $ is the integer part of $x$." " The model of F(o) is therefore characterized by a uniform grid. ©),=—o6,54+móg. m—0.1......ML1. and a vector 2=συνcy...tay1]€(C. which is assumed sparse. i.e. il has a small number of non-zero components. corresponding to the complex amplitudes of the sources located on the @,, eril."," The model of $F(\phi)$ is therefore characterized by a uniform grid, $\phi_{m}=-\phi_{win}+m\phi_{R}$, $m=0,1,...,M-1$, and a vector $z=[z_{0},z_{1},...,z_{M-1}]\in\mathbb{\mathbb{C}}^{M}$, which is assumed sparse, i.e. it has a small number of non-zero components, corresponding to the complex amplitudes of the sources located on the $\phi_{m}$ grid." " For example. a thin source with the amplitude z,,. located al 6,, . will be approximated by the product of z,, with a Dirac function d(@— 6,,). while a thick source will be characterized by a contiguous set of non-zero aunplitudes in (he vector z."," For example, a thin source with the amplitude $z_{m}$, located at $\phi_{m}$ , will be approximated by the product of $z_{m}$ with a Dirac function $\delta(\phi-\phi_{m})$ , while a thick source will be characterized by a contiguous set of non-zero amplitudes in the vector $z$ ," Tomé 2006). which means the GW amplitude is proportional to a. same as (hose given in Dondarescu et al. (,"Tomé 2006), which means the GW amplitude is proportional to $\alpha$, same as those given in Bondarescu et al. (" 2009).,2009). In the following calculations we should keep in mincl Chat the parameter A used in Chis paper is equivalent to the saturation amplitude a of NS ranocde instabilitv., In the following calculations we should keep in mind that the parameter $K$ used in this paper is equivalent to the saturation amplitude $\alpha$ of NS r-mode instability. From the above equations we can obtain the dimensionless energy. density: Thus. bv setting a value lor A one can caleulate Qe; numerically through Eq.(11)) combined with corresponding equations for CSER. comoving volume element ancl IAIF.," From the above equations we can obtain the dimensionless energy density: Thus, by setting a value for $K$ one can calculate $\Omega_{GW}$ numerically through \ref{Omgw}) ) combined with corresponding equations for CSFR, comoving volume element and IMF." " Here we sei mg,=SAL. and μας=25.M.. while ti, and µας can be determined in such a wav: since eat ol emitted GWs in the source [rame range from μι=77—80 Hz to Vinayc20dthe=1191 Ilz. where the minimum frequency corresponds to the final angular velocity of star - 0.06504, [or A=—5/4 and 0.0674 if WS1. we have iy /(L+2). which means sources with dillerent redshifts (hat produce a signal at the same lrequency v4, should meet the condition: μι)οκ1<2<μεμι1."," Here we set $m_{\rm{min}}=8 M_{\odot}$ and $m_{\rm{max}}=25 M_{\odot}$, while $z_{\rm{min}}$ and $z_{\rm{max}}$ can be determined in such a way: since frequencies of emitted GWs in the source frame range from $\nu_{\rm{min}}=77-80$ Hz to $\nu_{\rm{max}}=2\Omega_{\rm{K}}/3\pi=1191$ Hz, where the minimum frequency corresponds to the final angular velocity of the star - $0.065 \Omega_{\rm{K}}$ for $K =-5/4$ and $0.067 \Omega_{\rm{K}}$ if $K \gg 1$, we have $\nu_{\rm{min}}/(1+z)\leq \nu_{\rm{obs}}\leq \nu_{\rm{max}}/(1+z)$ , which means sources with different redshifts that produce a signal at the same frequency $\nu_{\rm{obs}}$ should meet the condition: $\nu_{\rm{min}}/\nu_{\rm{obs}}-1\leq z \leq \nu_{\rm{max}}/\nu_{\rm{obs}}-1$." " Besicles. we consider signals emitted al early epochs up to the present (2> 0) and take into account {he maximal redshift (2,) of CSFR model."," Besides, we consider signals emitted at early epochs up to the present $z\geq 0$ ) and take into account the maximal redshift $z_{\ast}$ ) of CSFR model." " Then we obtain z,;,=max(Q.μι)ma—1). tax=WZ.Maxfobs—1). which is similar (o (hat of Owen οἱ al. ("," Then we obtain $z_{\rm{min}}= \rm{max}(0,\nu_{\rm{min}}/\nu_{\rm{obs}}-1)$, $z_{\rm{max}}= \rm{min}(z_{\ast},\nu_{\rm{max}}/\nu_{\rm{obs}}-1)$, which is similar to that of Owen et al. (" "1998) where z,c4 is considered to be the maximum redshift where (here was significant star formation.","1998) where $z_{\ast}\simeq 4$ is considered to be the maximum redshift where there was significant star formation." In Fig., In Fig. 3 we plot the dimensionless enerev density Oc calculated Lor the five CSFR models presented in Section 2 by selling A at its minimal value: A.=—5/4 corresponding to the smallest amount of differential rotation at the time when the r-mode instability becomes aclive., 3 we plot the dimensionless energy density $\Omega_{\rm{GW}}$ calculated for the five CSFR models presented in Section 2 by setting $K$ at its minimal value: $K=-5/4$ corresponding to the smallest amount of differential rotation at the time when the r-mode instability becomes active. However. as emphasized bx Sá Tomé (2005). il A is small. namely. Aee0. it is necessary (o consider other nonlinear effects like mode-mode couplings in the calculation of o. which will again limit the maximum r-mode amplitude to values much smaller Chan unity (Arrasetal.2003).," However, as emphasized by Sá Tomé (2005), if $K$ is small, namely, $K\approx 0$, it is necessary to consider other nonlinear effects like mode-mode couplings in the calculation of $\alpha$, which will again limit the maximum r-mode amplitude to values much smaller than unity \cite{Arras2003}." . In this respect. our choice of a minimum A results in an unrealistically hieh upper limit for r-mode background.," In this respect, our choice of a minimum $K$ results in an unrealistically high upper limit for r-mode background." It is worth noting from Fig., It is worth noting from Fig. 3 that no obvious dillerences are recorded. for the three curves of SERI. SER2 and SFR3. and observation-based CSFR models give rise to stochastic backerounds about (wo (mes stronger (han that of 511023. over a broad frequency. band. alihough $1103 leads to a much higher NS formation rate.," 3 that no obvious differences are recorded for the three curves of SFR1, SFR2 and SFR3, and observation-based CSFR models give rise to stochastic backgrounds about two times stronger than that of SH03 over a broad frequency band, although SH03 leads to a much higher NS formation rate." The sharp contrast between Fig., The sharp contrast between Fig. 3 and Fig., 3 and Fig. 2 indicates that the main contribution to the GW background comes from sources because those events happened al higher redshifts have minor influences due {ο (he inverse squared. luminosity distance dependence of the single event energy. [lux., 2 indicates that the main contribution to the GW background comes from low-redshift sources because those events happened at higher redshifts have minor influences due to the inverse squared luminosity distance dependence of the single event energy flux. For, For We detect. 4 candidate sources with SNIt&356 and 7 candidate sources with SNRs in the range 3.50.,"We detect 4 candidate sources with $\mathrm{SNR}\geq3.5\,\sigma$ and 7 candidate sources with SNRs in the range $3.5\,\sigma$." A submillimetre image of the GSS is shown in Fig. l..," A submillimetre image of the GSS is shown in Fig. \ref{fig:850map}," where we number each of these 11 cancliclates. while in Table 1. we present information on the 5 sources for which we performed. follow-up photometry (see & ??).," where we number each of these 11 candidates, while in Table \ref{tab:sources} we present information on the 5 sources for which we performed follow-up photometry (see $\S~\ref{phot}$ )." The signal and noise maps mav be downloaded. fromhttp://cmbr., The signal and noise maps may be downloaded from. physics.ubc.ca/groth. In December 2003 and January 2004. SCUBA photometry observations were performed in the 2-bolometer chopping mode to check some of our candidate map detections.," In December 2003 and January 2004, SCUBA photometry observations were performed in the 2-bolometer chopping mode to check some of our candidate map detections." We selected 2 candidates. GSSS50.7 and GSss50.11. near the noisier edge regions of the map anc a control. CiSS850.2. in a lower-noise region away from the edges.," We selected 2 candidates, GSS850.7 and GSS850.11, near the noisier edge regions of the map and a `control', GSS850.2, in a lower-noise region away from the edges." Also. during one of the observing runs in January 2000. four sources were identified in the map data “by eve’ and selected as targets for follow-up photometry.," Also, during one of the observing runs in January 2000, four sources were identified in the map data `by eye' and selected as targets for follow-up photometry." Only. two of these pointings correspond to candidate detections in the inal map (CISS850.1 and GSSS850.6): this is à warning that our eves often. pick out bright outliers in noisy regions of a map., Only two of these pointings correspond to candidate detections in the final map (GSS850.1 and GSS850.6); this is a warning that our eyes often pick out bright outliers in noisy regions of a map. ALL of the photometry observations were reduced in he standard wav using SURE., All of the photometry observations were reduced in the standard way using SURF. In order to increase the SNR of sources observed in the 2-bolometer mode by a factor of approximately ν3/2. we folded in the signal from the »xosition bolometers to the central bolometer (see Chapmanetal.20002).," In order to increase the SNR of sources observed in the 2-bolometer mode by a factor of approximately $\sqrt{3/2}$, we folded in the signal from the off-position bolometers to the central bolometer (see \citealt{Chapman2000}) )." Ehe results are listed in Table 1. for comparison with the estimated map fluxes., The results are listed in Table \ref{tab:sources} for comparison with the estimated map fluxes. In all cases. the photometry »ointings were within 3 aresec of the positions found by the source-detection algorithm in the map.," In all cases, the photometry pointings were within 3 arcsec of the positions found by the source-detection algorithm in the map." lt appears that we have detected some sources in the map., It appears that we have detected some sources in the map. However none of the candidate sources have very igh SNRs. and so we need to be careful in interpreting hese results.," However none of the candidate sources have very high SNRs, and so we need to be careful in interpreting these results." Confusion can either increase or decrease the input [lux of a source. but a noisy Hlux-limited. map will welerentially contain sources whose true [uxes have been increased. (usually called: Malmeuist. bias) and this elfect is exacerbated. for steep source counts.," Confusion can either increase or decrease the input flux of a source, but a noisy flux-limited map will preferentially contain sources whose true fluxes have been increased (usually called Malmquist bias) and this effect is exacerbated for steep source counts." Our source extraction »ocedure therefore biases lluxes in the map upwards. which we now attempt to quantity.," Our source extraction procedure therefore biases fluxes in the map upwards, which we now attempt to quantify." We performed a set of. simulations to assess. the expected distribution of pixel brightnesses from triple-beam (i.e. double dillerence) observations of a noiseless blank-skv., We performed a set of simulations to assess the expected distribution of pixel brightnesses from triple-beam (i.e. double difference) observations of a noiseless blank-sky. We used a smooth curve fit to (and mildly. extrapolated rom) the number counts of Borysetal.(2003) as an a priori distribution of lluxes in the range 40mv.," We used a smooth curve fit to (and mildly extrapolated from) the number counts of \citet{Borys2003} as an a priori distribution of fluxes in the range $40\,\mathrm{mJy}$." We then populated 3. dilferent patches of noiseless sky ollowing a Poisson cistribution. and sampled each area with a SCUDA Gaussian beam. taking a double dillerence cach ime.," We then populated 3 different patches of noiseless sky following a Poisson distribution, and sampled each area with a SCUBA Gaussian beam, taking a double difference each time." " This was done 1 million times and the anticipated xior distribution of double difference Dux: measurements. AN(S,). 15 plotted in the first panel of Eig. 4.."," This was done 1 million times and the anticipated prior distribution of double difference flux measurements, $N(S_{\mathrm{p}})$, is plotted in the first panel of Fig. \ref{fig:boost}." We have also investigated the ellects of reasonable excursions [rom the assumed: shape of the source. counts., We have also investigated the effects of reasonable excursions from the assumed shape of the source counts. For example. using the Lo error bar values at the bright end of the number counts has less than a 10 per cent. ellect on the resulting Hux estimates.," For example, using the $1\,\sigma$ error bar values at the bright end of the number counts has less than a 10 per cent effect on the resulting flux estimates." The distribution NOS). which is the prior probability that a pixel in the map has cdilferential [ux y. is calculated [rom simulations while our actual map contains noise.," The distribution $N(S_{\mathrm{p}})$, which is the prior probability that a pixel in the map has differential flux $S_{\mathrm{p}}$, is calculated from simulations while our actual map contains noise." " 1 AZ is the statement that we measure Dux Su,ou at some pixel in the map. the probability that the true Lux of that pixel is ορ is obtained [from Bayes’ theorem: where the probability we would measure Sy, when the true Dux is 5, is"," If $M$ is the statement that we measure flux $S_{\mathrm{m}}\pm\,\sigma_{\mathrm{m}}$ at some pixel in the map, the probability that the true flux of that pixel is $S_{\mathrm{p}}$ is obtained from Bayes' theorem: where the probability we would measure $S_{\mathrm{m}}$ when the true flux is $S_{\mathrm{p}}$ is" The EBL is composed of enüssiou from starlight (at optical. ultraviolet. and nemr-infrared. wavelengths) and reradiated thermal dust cussion (at far-infrared) in galaxies.,"The EBL is composed of emission from starlight (at optical, ultraviolet, and near-infrared wavelengths) and reradiated thermal dust emission (at far-infrared) in galaxies." At observed energies bevond the ECRET energv range (but well within the energy range). photons suffer significant attenuation due to pair production interactions with the soft plotons of the EBL Αι.," At observed energies beyond the EGRET energy range (but well within the energy range), photons suffer significant attenuation due to pair production interactions with the soft photons of the EBL \citep{sal98,chen04,kne02,kne04,kne07,ste06,ste07,pri08,gil09,ven09}." Tn 7. we demonstrated that blazars exhibit an absorption feature at the highest energies iu their collective spectrum.," In \citet{ven09}, we demonstrated that blazars exhibit an absorption feature at the highest energies in their collective spectrum." We showed that the streneth of such au absorption feature depends on the blazar CLE with the strongest feature arising for those models that situate more high-huninosity sources at high redshifts., We showed that the strength of such an absorption feature depends on the blazar GLF with the strongest feature arising for those models that situate more high-luminosity sources at high redshifts. We also showed that the shape of the absorption feature depends on the EBL model., We also showed that the shape of the absorption feature depends on the EBL model. Thus. we demoustrated hat if blazars dominate the EGRB. the measurement of he absorption feature at the highest cucreies cau place constraints on the blazar CLF aud the EBL.," Thus, we demonstrated that if blazars dominate the EGRB, the measurement of the absorption feature at the highest energies can place constraints on the blazar GLF and the EBL." We did not. jowever. propagate high energy photous to determine the resulting cascade radiation. which will further alter the shape of the collective unresolved blazar spectrum.," We did not, however, propagate high energy photons to determine the resulting cascade radiation, which will further alter the shape of the collective unresolved blazar spectrum." Iu his paper. we study the effect of the cascades resulting roni propagation on the collective blazar inteusity.," In this paper, we study the effect of the cascades resulting from propagation on the collective blazar intensity." Iu interacting with EBL photous. VITE. gauuna ravs will produce pairs of electrons aud positrous. which will inverse Compton scatter EBL photons to ligh energies.," In interacting with EBL photons, VHE gamma rays will produce pairs of electrons and positrons, which will inverse Compton scatter EBL photons to high energies." " These upscattered photous will. in turn. interact with soft EBL photons through pair production. and this ""EM cascade” process continues uutil the cnereies of the resulting photons are low enoush that pair production is no longer effücieut."," These upscattered photons will, in turn, interact with soft EBL photons through pair production, and this “EM cascade” process continues until the energies of the resulting photons are low enough that pair production is no longer efficient." For amy cosmiological population cluitting eanuua ravs at VIIEs. the effect. of EM cascading results in a flux suppression at the highest euergies and culaneceient at lower energies.," For any cosmological population emitting gamma rays at VHEs, the effect of EM cascading results in a flux suppression at the highest energies and enhancement at lower energies." Ii thle case of blazars. which can comprise a sizable contribution to the ECRB. predictions of the resulting cuhancement at lower energies can lead to the overproduction of the EGRB if the collective ligh-cnerey intensity of blazars is high and/or the EBL is ligh (?)..," In the case of blazars, which can comprise a sizable contribution to the EGRB, predictions of the resulting enhancement at lower energies can lead to the overproduction of the EGRB if the collective high-energy intensity of blazars is high or the EBL is high \citep{cop97}. ." More recently. ? and ? have estimated the contribution of cascade radiation to the EGRB.," More recently, \citet{kne08} and \citet{ino08} have estimated the contribution of cascade radiation to the EGRB." They insighttully demonstrate that in iucludiug radiation from EXD cascades. blazars can account for ucazly all of the EGRD (~ s0%-90% )).," They insightfully demonstrate that in including radiation from EM cascades, blazars can account for nearly all of the EGRB $\sim 80\%$ $90$ )." However. in neither analysis was the blazar SID as determined from either EGRET or data iucluded. and thus. the impact of the population of blazar GeV spectral iudices was not fully cxaminued.," However, in neither analysis was the blazar SID as determined from either EGRET or data included, and thus, the impact of the population of blazar GeV spectral indices was not fully examined." Furthermore. neither analysis wakes use of a Monte Carlo propagation scheme. aud heuce do uot fairly sample secondary electron energies.," Furthermore, neither analysis makes use of a Monte Carlo propagation scheme, and hence do not fairly sample secondary electron energies." " Iu calculating the spectrum of cascade photous. we make use of a Monte Carlo propagation code calledCuscata, which samples secondary clectron energies fro cross-section-weighted distributions (see Section 2? and the Appendix}."," In calculating the spectrum of cascade photons, we make use of a Monte Carlo propagation code called, which samples secondary electron energies from cross-section-weighted distributions (see Section \ref{subsec-propcode} and the Appendix)." Once sampled. the resulting spectrum of EM cascade radiation is then calculated.," Once sampled, the resulting spectrum of EM cascade radiation is then calculated." Iu this manner. calculates à iore fully sampled cascade spectra resulting from a spectrum of primary photons.," In this manner, calculates a more fully sampled cascade spectrum resulting from a spectrum of primary photons." Tu this paper. we revisit the contribution of EM cascade radiation to the ECRB.," In this paper, we revisit the contribution of EM cascade radiation to the EGRB." Specifically. we study the impact of the blazar GLF. the blazar SID. aud the EBL model ou the spectrum of cascade radiation. which. im turn. affects the blazar contribution to the EGRD.," Specifically, we study the impact of the blazar GLF, the blazar SID, and the EBL model on the spectrum of cascade radiation, which, in turn, affects the blazar contribution to the EGRB." All of the aforementioned inputs remain quite uncertain., All of the aforementioned inputs remain quite uncertain. However. if blazars do. in fact. comprise the bulk of the ECRB intensity. then the careful study of EM. (cascades. along with observations cau be used to constrain the inputs of the collective iuteusitv and the nature of the EBL.," However, if blazars do, in fact, comprise the bulk of the EGRB intensity, then the careful study of EM cascades along with observations can be used to constrain the inputs of the collective intensity and the nature of the EBL." Furthermore. as the EXD cascade radiation is SCsitive to the blazar SID. it is also seusitive to possible breaks im blazar spectra bevoud the ECRET energv range (e.g. spectral breaks or eutoffs).," Furthermore, as the EM cascade radiation is sensitive to the blazar SID, it is also sensitive to possible breaks in blazar spectra beyond the EGRET energy range (e.g., spectral breaks or cutoffs)." Thus. the study of EM cascades together with observations of the EGCRB can also provide information about blazar spectra bevoud tens of GeV. which cau. in turn. provide insight iuto the nature of blazar emission.," Thus, the study of EM cascades together with observations of the EGRB can also provide information about blazar spectra beyond tens of GeV, which can, in turn, provide insight into the nature of blazar emission." Tn this paper. we demoustrate that with a Monte Carlo propagation code such as sud indepeudenut| constraints ou the inputs from observatious. as well as those from nuagius atmospheric Clerenukov telescopes TACTs). the blazar contribution to the ECRB will ultimately be determined.," In this paper, we demonstrate that with a Monte Carlo propagation code such as and independent constraints on the inputs from observations, as well as those from imaging atmospheric Cherenkov telescopes (IACTs), the blazar contribution to the EGRB will ultimately be determined." In Section 2. we preseut the formalisin of the calculation of the collective unresolved blazar iutensitv aud a short discussion of the aspects of the code relevant to the propagation of VUE eanuua raves.," In Section 2, we present the formalism of the calculation of the collective unresolved blazar intensity and a short discussion of the aspects of the code relevant to the propagation of VHE gamma rays." In Section 3. we diseuss the inputs of the calculation and their uncertaiutics.," In Section 3, we discuss the inputs of the calculation and their uncertainties." " In Section 4, we present the results of the calculation. aud we discuss these results in Section 5."," In Section 4, we present the results of the calculation, and we discuss these results in Section 5." The contribution to the ECRD due to blazars cau be viewed as the superposition of the collective iuteusitv of blazar spectra and the contribution from the cascade radiation from the interactions of VITEphotous from blazars with the EBL: where the iuteusity. Zg(Ej). is given iu units of photous per mut enerey per mut time per unit area per uuit solid angle emitted at observer frame euergev. £y.," The contribution to the EGRB due to blazars can be viewed as the superposition of the collective intensity of blazar spectra and the contribution from the cascade radiation from the interactions of VHEphotons from blazars with the EBL: where the intensity, $I_E(E_0)$, is given in units of photons per unit energy per unit time per unit area per unit solid angle emitted at observer frame energy, $E_0$." " The collective intensity of blazar spectra including attenuation bv the EBL is eiven by 7) where E, is sone fiducial fraune ΟΠΟΥ: (taken tohe 100 AÍeV)."," The collective intensity of blazar spectra including attenuation by the EBL is given by \citep[for derivation, see ][]{ven09}: : where $E_f$ is some fiducial frame energy (taken tobe $100$ MeV)," nur.) with (he optical depth given bv equ.,"r_s, with the optical depth given by eqn." (2aa) ancl τι by equ., \ref{tau}a a) and $\tau_s$ by eqn. (2bb)., \ref{tau}b b). For the density profileseiven bx eqn. (2)).," For the density profilesgiven by eqn. \ref{NFW}) )," Che relaxation lime goes to zero αἱ the center., the relaxation time goes to zero at the center. This sets a limit to ihe minimum radius. rj. for which the svstem can be considered collisionless. where the relaxation time equals the age of the halo.," This sets a limit to the minimum radius, $r_H$, for which the system can be considered collisionless, where the relaxation time equals the age of the halo." " For the range of scales ancl parameters we consider. r,."," In the final state, the baryons are assumed to dominate the total mass (dark matter plus baryons) $M_f\left(r_f\right)$ in the inner region where the dark matter profile is desired, and this final total mass distribution is taken to be $M_f\sim r_f^{3-\xi}$ corresponding to a total density profile $\rho_{f}\sim r_f^{-\xi}$." " We assume the dark matter density cusp is p;~r;ial belore condensation and p;~r;,"" after. and determine o!—ία.Εξ)."," We assume the dark matter density cusp is $\rho_i \sim r_i^{-\alpha}$ before condensation and $\rho_f \sim r_f^{-\alpha^{\prime}}$ after, and determine $\alpha^{\prime}=f\left(\alpha,\xi\right)$." For the collisionless case. we make (he simplifving approximation that the dark matter parücles are on circular orbits. which is justified since there is more phase space available for nearly circular orbits than for radial ones (Blumenthal et al.," For the collisionless case, we make the simplifying approximation that the dark matter particles are on circular orbits, which is justified since there is more phase space available for nearly circular orbits than for radial ones (Blumenthal et al." 1986: Flores et al., 1986; Flores et al. 1993: Navarro. FrenkWhite 1996).," 1993; Navarro, FrenkWhite 1996)." Conservation of dark matter implies (hat L POTrzdr;-p prptepitightarveni] e, Conservation of dark matter implies that _i r_i^2 _f r_f^2 dr_f . Conservation of dark matter implies (hat L POTrzdr;-p prptepitightarveni] er, Conservation of dark matter implies that _i r_i^2 _f r_f^2 dr_f . Conservation of dark matter implies (hat L POTrzdr;-p prptepitightarveni] ers, Conservation of dark matter implies that _i r_i^2 _f r_f^2 dr_f . considerable distance from the cluster centres.,considerable distance from the cluster centres. We have no heoretical predictions with which to compare these results the predictions by 7. relate to the environment. of the xightest cluster galaxy., We have no theoretical predictions with which to compare these results – the predictions by \citet{West..1995} relate to the environment of the brightest cluster galaxy. Our low LGC count may. be due o the areal limit of our survey. since outside the cluster core the distribution of λος may be non-uniform. mirroring he cluster galaxy clistribution.," Our low IGC count may be due to the areal limit of our survey, since outside the cluster core the distribution of IGCs may be non-uniform, mirroring the cluster galaxy distribution." Our findings suggest. that »opulations of IGC€'s may exist in both clusters. but. that we need to probe a wider area of the intracluster regions o a deeper faint limit in order to further investigate their distribution and origins.," Our findings suggest that populations of IGCs may exist in both clusters, but that we need to probe a wider area of the intracluster regions to a deeper faint limit in order to further investigate their distribution and origins." Active gas-rich galaxy mergers. are observed: το contain close groupings of newlv-condensed star clusters. (suchasthoseobserved.intheAntennaegalaxypair 2).. and numerical simulations (c.g.2) confirm that the largest of these should survive clisruptive tidal forces and merge on relatively short. time-scales (~LOO Myr) to form. stellar superclusters.," Active gas-rich galaxy mergers are observed to contain close groupings of newly-condensed star clusters \citep[such as those observed in the Antennae galaxy pair][]{Kroupa..1998}, and numerical simulations \citep[e.g.][]{Fellhauer..2002} confirm that the largest of these should survive disruptive tidal forces and merge on relatively short time-scales $\sim\!100 \; \mbox{Myr}$ ) to form stellar superclusters." Superclusters with mass of order 107M. may then evolve into present-day bright CSSs. or potentially into EsWheroidal cwarl galaxies with low dark matter content.," Superclusters with mass of order $10^8 \; \mbox{M}_{\odot}$ may then evolve into present-day bright CSSs, or potentially into spheroidal dwarf galaxies with low dark matter content." ‘This mechanism for luminous CSS formation is theoretically supported. by. simulations (22).. whereas their formation as ancient but unusually massive GC's is not well understood.," This mechanism for luminous CSS formation is theoretically supported by simulations \citep{Fellhauer..2002, Fellhauer..2005}, whereas their formation as ancient but unusually massive GCs is not well understood." On the other hand. it is unclear whether stellar superclusters are ejected with enough ellicieney from their formation sites to account for the CSS populations we find in cluster core and intracluster environments.," On the other hand, it is unclear whether stellar superclusters are ejected with enough efficiency from their formation sites to account for the CSS populations we find in cluster core and intracluster environments." The NGC 1316 galaxy merger environment borders our Fornax intracluster field. (see Fig. 8))., The NGC 1316 galaxy merger environment borders our Fornax intracluster field (see Fig. \ref{fig:aaovirgofornax_11}) ). " ??. found evidence of both old and intermediate age (high hydrogen content) iq M ≺∣≺⊳∖∖∖⋎⊔↓⊔⊔⋜⋯↖∖, ὃν. .In ↖∖↓⋅⋖⊾⋃↓∪⊔⊳∖⊔↓⋅↓⋅∪⊔⊔∠⊔⊔⋃↿⇂⊔⊳∖∆∫≻−≺∣∖⇁↓⋅−∪↓∠⇂⋠⋅⊲ merger remnant galaxy. including four exceptionally bright CSSS (My< 12)."," \citet{Goudfrooij..2001a, Goudfrooij..2001b} found evidence of both old and intermediate age (high hydrogen content) GCs within an $8^\prime\times8^\prime$ region surrounding this 3-Gyr-old merger remnant galaxy, including four exceptionally bright CSSs $M_V<-12$ )." Although we racially restrict our definition of the NGC 1316 ealaxy merger environment to «20aremin (130kpc. encompassing the faintest. traces of the ealaxy’s stellar envelope). our ANOmega intracluster field extends cast of NGC 1910 almost 2 (500kpe).," Although we radially restrict our definition of the NGC 1316 galaxy merger environment to $<\!20 \; \mbox{arcmin}$ $130 \; \mbox{kpc}$, encompassing the faintest traces of the galaxy's stellar envelope), our AAOmega intracluster field extends east of NGC 1316 almost $2^\circ$ $800 \; \mbox{kpc}$ )." " Above the relatively bright limit CM,ς 11.7) of our survey. we found no evidence of dispersed. intermediate-age stellar superclusters emanating from the NGC 1316 galaxy merger."," Above the relatively bright limit $M_{b_J}<-11.7$ ) of our survey, we found no evidence of dispersed intermediate-age stellar superclusters emanating from the NGC 1316 galaxy merger." While observing conditions restricted our detection limit to the most. luminous CSSs. we would have expected. to find any ejected stellar superclusters since their initial luminosity (Mle~ 15) should still be above our detection limit after 3Gyr (7)..," While observing conditions restricted our detection limit to the most luminous CSSs, we would have expected to find any ejected stellar superclusters since their initial luminosity $M_B\simeq-15$ ) should still be above our detection limit after $3 \; \mbox{Gyr}$ \citep{Fellhauer..2002}." We conclude that there is no evidence such objects have been dispersed. outside the innermost region of the NGC 1316 galaxy merger or into intracluster space., We conclude that there is no evidence such objects have been dispersed outside the innermost region of the NGC 1316 galaxy merger or into intracluster space. The ealaxy NGC 4438. which has been strongly distorted by interaction with NGC 4435. is marked in big.," The galaxy NGC 4438, which has been strongly distorted by interaction with NGC 4435, is marked in Fig." at the edge of our MS7 field., \ref{fig:aaovirgofornax_11} at the edge of our M87 field. In our survey we found. no overdensity of confirmed foreground or cluster objects that might be associated with these galaxies., In our survey we found no overdensity of confirmed foreground or cluster objects that might be associated with these galaxies. In our search for CSS. we have obtained recishift measurements of colour-selected: point sources in two nearby ealaxy clusters.," In our search for CSS, we have obtained redshift measurements of colour-selected point sources in two nearby galaxy clusters." Our new observations:, Our new observations: first overtone model for the dominant mode. the is an (=+m| mode for an equatorial rotation of 119kkmss7!. and in case of the fourth overtone model. the is an £=+m2 mode for a rotation velocity of kkmss!.,"first overtone model for the dominant mode, the is an $\ell=+m=1$ mode for an equatorial rotation of $^{-1}$, and in case of the fourth overtone model, the is an $\ell=+m=2$ mode for a rotation velocity of $^{-1}$." As can be seen from refbars.. all those cases give a good explanation of the observed frequencies.," As can be seen from \\ref{bars}, all those cases give a good explanation of the observed frequencies." We stress that these are only six out of many good solutions., We stress that these are only six out of many good solutions. We point out that our procedure was not ideal for the three options for with the highest equatorial rotation velocity listed in reffreqs.. for which second-order rotational effects may come into play at a level that can reach values above the theoretical uncertainty we adopted.," We point out that our procedure was not ideal for the three options for with the highest equatorial rotation velocity listed in \\ref{freqs}, for which second-order rotational effects may come into play at a level that can reach values above the theoretical uncertainty we adopted." The estimate of the rotation period from the magnetic field study by Hubrig et (2011) would have allowed us to drop these three options from the start., The estimate of the rotation period from the magnetic field study by Hubrig et (2011) would have allowed us to drop these three options from the start. We preferred not to do so. however. as the derivation of the rotation period. by Hubrig et rrelies on the assumption of dealing with a rigid rotator model and a centred dipole.," We preferred not to do so, however, as the derivation of the rotation period by Hubrig et relies on the assumption of dealing with a rigid rotator model and a centred dipole." While this is a very plausible assumption. and certainly the most obvious one to make. we wanted the seismic modelling to be as independent as possible of this result.," While this is a very plausible assumption, and certainly the most obvious one to make, we wanted the seismic modelling to be as independent as possible of this result." " This implies that our modelling is not optimal for those three options with high Vο,. because we did not consider second-order effects in the rotation when computing the evolutionary models and the pulsation frequencies."," This implies that our modelling is not optimal for those three options with high $V_{\rm eq}$, because we did not consider second-order effects in the rotation when computing the evolutionary models and the pulsation frequencies." Improving this would require a full two-dimensional treatment of the equilibrium nodels and their frequencies. which is beyond the scope of this paper.," Improving this would require a full two-dimensional treatment of the equilibrium models and their frequencies, which is beyond the scope of this paper." There has been good agreement between spectroscopically derived effective temperatures and abundances. and their seismically derived counterparts. from the method of frequency matching that we adopted here.," There has been good agreement between spectroscopically derived effective temperatures and abundances, and their seismically derived counterparts, from the method of frequency matching that we adopted here." This is not necessarily the case for the gravity of the seismically modelled 6 Cep stars.," This is not necessarily the case for the gravity of the seismically modelled $\beta\,$ Cep stars." " While good agreement was found for several stars (e.g..1129929, Dupret et 22004; I2LLac. Desmet et 22009). the spectroscopic logg turned out to be 0.15 dex higher than the seismic logg for the star @Oph (Briquet et 22007)."," While good agreement was found for several stars (e.g.,129929, Dupret et 2004; Lac, Desmet et 2009), the spectroscopic $\log\,g$ turned out to be 0.15 dex higher than the seismic $\log\,g$ for the star $\theta\,$ Oph (Briquet et 2007)." For 446202. the discrepancy even amounted to 0.24 dex (Briquet et 22011).," For 46202, the discrepancy even amounted to 0.24 dex (Briquet et 2011)." Given these previous discrepancies. we prefer not to impose the spectroscopic gravity as a secure constraint in the modelling: this would imply that the dominant mode ts a high overtone (2> 3) while we consider this unlikely.," Given these previous discrepancies, we prefer not to impose the spectroscopic gravity as a secure constraint in the modelling; this would imply that the dominant mode is a high overtone $n\geq 3$ ) while we consider this unlikely." Similarly. the current metallicity of the star measured at its surface Is not necessarily the initial one when the star was born. as effects such as atomic diffusion or unknown mixing may have occurred.," Similarly, the current metallicity of the star measured at its surface is not necessarily the initial one when the star was born, as effects such as atomic diffusion or unknown mixing may have occurred." Thus. we take a conservative attitude and request as an additional constraint from spectroscopy that the models must fulfil the lor error bar in the effective temperature only.," Thus, we take a conservative attitude and request as an additional constraint from spectroscopy that the models must fulfil the $1\sigma$ error bar in the effective temperature only." In refkiel.. all 2541 models surviving the previous section are shown. along with the spectroscopically determined error box in the Kiel diagram.," In \\ref{kiel}, all 2541 models surviving the previous section are shown, along with the spectroscopically determined error box in the Kiel diagram." As can be seen. only two models would survive. if we were to impose the lc error bar for the gravity of the star.," As can be seen, only two models would survive, if we were to impose the $1\sigma$ error bar for the gravity of the star." For these two models. none of the observed non-radial modes is excited (see the following section).," For these two models, none of the observed non-radial modes is excited (see the following section)." " We consider this too restrictive and continued with all the models that fulfil Toy€[23500.25500]K. There are 357 models left after this requirement. with a mass coverage from MM,. to MM..."," We consider this too restrictive and continued with all the models that fulfil $T_{\rm eff} \in [23\,500,25\,500]$ K. There are 357 models left after this requirement, with a mass coverage from $_\odot$ to $_\odot$." This set of models still covers the entire considered range of values for the metallicity. hydrogen fraction. and core overshooting.," This set of models still covers the entire considered range of values for the metallicity, hydrogen fraction, and core overshooting." We subsequently checked the mode excitation of the low-order zonal frequencies for the 357 surviving models with the codeMAD., We subsequently checked the mode excitation of the low-order zonal frequencies for the 357 surviving models with the code. Depending on the model parameters. we found excitation for the first radial overtone near frequency for masses between 9.7 and 13MM... for the £=l. py mode with frequency in [6.0.6.5] for masses between 9 and MM... and for the £=2 f mode with frequency near for masses between 9.4 and MM...," Depending on the model parameters, we found excitation for the first radial overtone near frequency for masses between 9.7 and $_\odot$, for the $\ell=1$, $_1$ mode with frequency in $[6.0,6.5]\,$ for masses between 9 and $_\odot$, and for the $\ell=2$ f mode with frequency near for masses between 9.4 and $_\odot$." For £=3 and £=4. the modes also have their frequency in [6.0.6.5]d and are found to be excited for masses between 9 and MM.. while the £=3 f mode has its frequency near and is excited for masses between 9.7 and MM...," For $\ell=3$ and $\ell=4$, the $_1$ modes also have their frequency in $[6.0,6.5]\,$ and are found to be excited for masses between 9 and $_\odot$ while the $\ell=3$ f mode has its frequency near and is excited for masses between 9.7 and $_\odot$." These rough conclusions about the mode excitation are in qualitative agreement with the results on mode excitation found by Dziembowskt Pamyatnykh (2008). but these authors considered only a few representative models that have frequency spectra similar to those observed for the 5 Cep stars v Eri and LLac. while we considered an entire grid of models.," These rough conclusions about the mode excitation are in qualitative agreement with the results on mode excitation found by Dziembowski Pamyatnykh (2008), but these authors considered only a few representative models that have frequency spectra similar to those observed for the $\beta\,$ Cep stars $\nu\,$ Eri and Lac, while we considered an entire grid of models." To constrain the parameters space for 1180642. we first eliminated the models for which none of the non-radial modes with frequency above that of the dominant radial mode is excited.," To constrain the parameters space for 180642, we first eliminated the models for which none of the non-radial modes with frequency above that of the dominant radial mode is excited." This reduced the number of models to 221 and led to an upper limit in mass of MM..., This reduced the number of models to 221 and led to an upper limit in mass of $_\odot$. In particular. this removed the two models with the fourth overtone as a fit to the dominant frequency.," In particular, this removed the two models with the fourth overtone as a fit to the dominant frequency." Only five models able to predict that the dominant mode is the first overtoe remained., Only five models able to predict that the dominant mode is the first overtone remained. All of these have only one non-radial mode excited in the frequency range [6.9]..," All of these have only one non-radial mode excited in the frequency range $[6,9]\,$." In each case. this corresponds to the £22. pj; mode nearcd.," In each case, this corresponds to the $\ell=2$, $_1$ mode near." . This is insufficient to explain the observed frequency spectrum and we are thus left with models whose fundamental radial mode fits the dominant frequency., This is insufficient to explain the observed frequency spectrum and we are thus left with models whose fundamental radial mode fits the dominant frequency. Among the remaining 22] models. we found five that excite listed in reffreqs..," Among the remaining 221 models, we found five that excite listed in \\ref{freqs}." The properties of these five models are listed in the upper part of refmodels.., The properties of these five models are listed in the upper part of \\ref{models}. . These models are indicated with a cross in and fulfil the spectroscopically determined effective temperature., These models are indicated with a cross in \\ref{hrd} and fulfil the spectroscopically determined effective temperature. The frequency spectra of the two models whose mass Is indicated in italics in were compared with the observed ones in the middle panels of, The frequency spectra of the two models whose mass is indicated in italics in \\ref{models} were compared with the observed ones in the middle panels of density and estimate the distance to each source: in section 4. we discuss our results. before concluding.,"density and estimate the distance to each source; in section \ref{discussion} we discuss our results, before concluding." Preliminary results of our data analysis for AX 0536 and IGR J19140+0951 were published in ?.., Preliminary results of our data analysis for AX J1841.0--0536 and IGR J19140+0951 were published in \citet{nespoli07}. We selected proposed counterparts. choosing sources observed by X-ray missions like XMM or Chandra. which can produce a very small error circle and facilitate the detection of the counterpart.," We selected proposed counterparts, choosing sources observed by X-ray missions like XMM or Chandra, which can produce a very small error circle and facilitate the detection of the counterpart." Data were obtained in visiting mode during two observing runs. in July 2006 and May 2007 respectively. at the European Southern Observatory (ESO).," Data were obtained in visiting mode during two observing runs, in July 2006 and May 2007 respectively, at the European Southern Observatory (ESO)." The employed instrument was the Sofl spectrograph (2).. on the 3.5m New Technology Telescope (NTT) at La Silla. Chile.," The employed instrument was the SofI spectrograph \citep{sofi98}, on the 3.5m New Technology Telescope (NTT) at La Silla, Chile." Table | reports the observation log. including. for each spectrum. the retrieved signal-to-noise ratio (S/N).," Table \ref{table:logobs} reports the observation log, including, for each spectrum, the retrieved signal-to-noise ratio (S/N)." " We used the long slit spectroscopy mode. at medium resolution (R= 1320) with a K, grism and wwidth slit."," We used the long slit spectroscopy mode, at medium resolution $R = 1320$ ) with a $K_{s}$ grism and width slit." The instrument large field objective provided a FOV of 4.92’x4.92’., The instrument large field objective provided a FOV of $4.92' \ \times \ 4.92'$. The sky had thin cirri on 2006 July 14th and 15th. while it was generally clear on 2007 May 26th.," The sky had thin cirri on 2006 July 14th and 15th, while it was generally clear on 2007 May 26th." " Seeing averaged between 0.9"" and 1.2”. with the exception of the observation of IGR J16749-4514 which was performed with a seeing of 1.6"". In order to ensure accurate removal of atmospheric features from the spectra. we followed a strategy similar to that outlined by ?.."," Seeing averaged between $0.9''$ and $1.2''$, with the exception of the observation of IGR J16749–4514 which was performed with a seeing of $1.6''$ In order to ensure accurate removal of atmospheric features from the spectra, we followed a strategy similar to that outlined by \citet{clark2000}." At the telescope. we observed an standard star immediately. before or after each target and a G2-3 V star once per hour in order to obtain very small differences in airmass (differences between 0.01 and 0.04 airmasses were accomplished).," At the telescope, we observed an standard star immediately before or after each target and a G2-3 V star once per hour in order to obtain very small differences in airmass (differences between 0.01 and 0.04 airmasses were accomplished)." To compute the tellurie features in the region of theH121 6661 ((Brackett-y line. or Bry). which is the only non-telluric feature in the A-star spectra. we employed the observed G-star spectra divided by the solar properly degraded in resolution.," To compute the telluric features in the region of the 661 $\gamma$ line, or $\gamma$ ), which is the only non-telluric feature in the A-star spectra, we employed the observed G-star spectra divided by the solar properly degraded in resolution." The dispersion solution obtained for the SofI spectra was also applied and the spectra of the A star. G star and the solar one were aligned in wavelength space.," The dispersion solution obtained for the SofI spectra was also applied and the spectra of the A star, G star and the solar one were aligned in wavelength space." A telluric spectrum for each scientific target was obtained by patching into the A-star spectrum the ratio between the G star and the solar spectrum in the Bry region (we selected the range 5590 - 7739 A))., A telluric spectrum for each scientific target was obtained by patching into the A-star spectrum the ratio between the G star and the solar spectrum in the $\gamma$ region (we selected the range 590 - 739 ). Typical integration times for standard stars were between 3 and 7 Data reduction was performed using the package. following the standard procedure.," Typical integration times for standard stars were between 3 and 7 Data reduction was performed using the package, following the standard procedure." We first corrected for the inter-quadrant row cross-talk. a feature that affects the Sofl detector: we then applied sky subtraction: we employed dome flat-fields and extracted one dimensional spectra.," We first corrected for the inter-quadrant row cross-talk, a feature that affects the SofI detector; we then applied sky subtraction; we employed dome flat-fields and extracted one dimensional spectra." Wavelength calibration was accomplished using Xenon and Neon lamp spectra., Wavelength calibration was accomplished using Xenon and Neon lamp spectra. Spurious features. such às cosmic rays or bad pixels. were removed by interpolation. when necessary.," Spurious features, such as cosmic rays or bad pixels, were removed by interpolation, when necessary." The reduced spectra were normalized by dividing them by a fitted polynomial continuum., The reduced spectra were normalized by dividing them by a fitted polynomial continuum. We corrected for tellurie absorption. dividing each scientific spectrum by its corresponding telluric spectrum. obtained as deseribed above.," We corrected for telluric absorption, dividing each scientific spectrum by its corresponding telluric spectrum, obtained as described above." A scale and a shift factor were applied to the telluric spectrum. to best correct for the airmass difference and the possible wavelength shift: the optimum values for these parameters were obtained using an iterative procedure that minimizes the residual noise.," A scale and a shift factor were applied to the telluric spectrum, to best correct for the airmass difference and the possible wavelength shift; the optimum values for these parameters were obtained using an iterative procedure that minimizes the residual noise." In this section we present the results of spectral classification and analysis for each target., In this section we present the results of spectral classification and analysis for each target. The field of ΝΙΚ spectral classification is still very young and the level of required S/N and resolution to perform a quantitative profile analysis are very high (ΑΔ.-12000 and S/N z 250). especially for young massive stars. as shown by ?..," The field of NIR spectral classification is still very young and the level of required S/N and resolution to perform a quantitative profile analysis are very high $R \sim 12\,000$ and S/N $\gtrsim$ 250), especially for young massive stars, as shown by \citet{hanson05-2}." The difficulty of the analysis depends on the few lines available and the relatively large uncertainty in theirstrength. due to their intrinsic weakness: moreover. some significant spectral regions. specifically through the 205580 He I and the Bry features. pose systematic complications because of the strong telluric absorption.," The difficulty of the analysis depends on the few lines available and the relatively large uncertainty in theirstrength, due to their intrinsic weakness; moreover, some significant spectral regions, specifically through the 580 He I and the $\gamma$ features, pose systematic complications because of the strong telluric absorption." Under this premise. our analysis will be qualitative. based on the comparison with available NIR spectral atlases (??)..," Under this premise, our analysis will be qualitative, based on the comparison with available NIR spectral atlases \citep{hanson96,hanson05}. ." According to our estimation. this approach implies that the," According to our estimation, this approach implies that the" purpose. the data were divided iuto two eroups.,"purpose, the data were divided into two groups." " All data at wavenmlubers between TUO and 1000 (10.7.13.7 pany) were fitted simultaucously. aud data at 12101280 ((uecar 8 jun)) were fitted separately,"," All data at wavenumbers between 700 and 1000 (10.7–13.7 ) were fitted simultaneously, and data at 1240–1280 (near 8 ) were fitted separately." The Marquardt fitting procedure (Bevinetou&Robinsou2003) was used. which minimizes \2. the summed squared deviation normalized by the squared noise. between the data and the model.," The Marquardt fitting procedure \citep{bev03} was used, which minimizes $\chi2$, the summed squared deviation normalized by the squared noise, between the data and the model." Fitting was first attempted with a sinele component for cach molecule. but the residuals suggested that a better fit could be obtained with iiultiple velocity componucuts.," Fitting was first attempted with a single component for each molecule, but the residuals suggested that a better fit could be obtained with multiple velocity components." The model that we used. assiuned that cach molecule is found in one or two absorbing components., The model that we used assumed that each molecule is found in one or two absorbing components. Each component is described by its Doppler shift. Vpag. its Gaussian line width (1/e half width = (2kET/m)E?). & the molecules cohuuu deusitv. NV. the rotational teiiperature of the gas. T. aud the covering factor. C. (the fraction of the backeround continu source covered by the component).," Each component is described by its Doppler shift, $V_{\rm LSR}$, its Gaussian line width $1/e$ half width = $^{1/2}$ ), $b$, the molecule's column density, $N$ , the rotational temperature of the gas, $T$, and the covering factor, $C$, (the fraction of the background continuum source covered by the component)." The fitted coluun density is the average over the partially covered source. so the column density in the covered portion would be A/C.," The fitted column density is the average over the partially covered source, so the column density in the covered portion would be $N/C$." A covering factor of. e... means that lines saturate at of the continuuu flix aud the colin density iu the absorbing coniponenut is ten times the average over the coutimmun source.," A covering factor of, e.g., means that lines saturate at of the continuum flux and the column density in the absorbing component is ten times the average over the continuum source." The effect modeled iu this way could also result from veiling (contiuuunu emission from foreground or surrounding material) or from re-enissiou in the lines by the absorbing molectles., The effect modeled in this way could also result from veiling (continuum emission from foreground or surrounding material) or from re-emission in the lines by the absorbing molecules. The compoucuts were asstuned to overlap by the products of their covering factors (see Fie. 5))., The components were assumed to overlap by the products of their covering factors (see Fig. \ref{fig:comp}) ). " The following equation was used to calculate the observed transmission: where €, aud C5 are the covering factors for tle two conrponeuts.", The following equation was used to calculate the observed transmission: where $C_1$ and $C_2$ are the covering factors for the two components. This results in a ereater absorption iu saturated lues than would result if the optical depths were added first aud then the transmission spectra was calculated frou the optical depth spectra., This results in a greater absorption in saturated lines than would result if the optical depths were added first and then the transmission spectrum was calculated from the optical depth spectrum. This approach was chosen because it gave a better fit to the data than adding the optical depths first aud assmmine he same covering factor. but it assumes that different conrponeuts absorb along different lines of sight to a xwtiallv covered continui source. which may not be he case.," This approach was chosen because it gave a better fit to the data than adding the optical depths first and assuming the same covering factor, but it assumes that different components absorb along different lines of sight to a partially covered continuum source, which may not be the case." A frequency correction was allowed for cach spectral setting observed. to correct for errors in wavelength calibration.," A frequency correction was allowed for each spectral setting observed, to correct for errors in wavelength calibration." With ouly one exception. the correction was ess thana 1lau DDoppler shift.," With only one exception, the correction was less than a 1 Doppler shift." Iu addition. a broadenius of the iustruinental resolution was permitted in the fitting o allow for müiperfect internal instrument focusing. or xossiblv a cimacroturbulent” broadeuing im the absorbing eas.," In addition, a broadening of the instrumental resolution was permitted in the fitting to allow for imperfect internal instrument focusing, or possibly a `macroturbulent' broadening in the absorbing gas." The fitting program chose a resolution a factor of L2 ereater than that derived. from eas cell data., The fitting program chose a resolution a factor of 1.2 greater than that derived from gas cell data. A constant frequency resolution (as opposed to a coustaut Doppler resolution) was used iu cach of the two fitted regions., A constant frequency resolution (as opposed to a constant Doppler resolution) was used in each of the two fitted regions. This represents well the improving resolving power toward shorter wavelengths in the 10.7-13.7 rregion., This represents well the improving resolving power toward shorter wavelengths in the 10.7-13.7 region. Iu addition to these parameters. the continua. slope. and curvature of cach echelon order were varied. to allow correction of the baseline fitting done chiving data reduction.," In addition to these parameters, the continuum, slope, and curvature of each echelon order were varied, to allow correction of the baseline fitting done during data reduction." " The coutinuuuu fittine and frequency correction required about 2300 free. but rather casily determined. parameters,"," The continuum fitting and frequency correction required about 300 free, but rather easily determined, parameters." Fewer parameters are needed to determine the physical conditions such as temperature. cohunn density. line width and covering factor: 70 paraiueters for the L0.7-13.7 sspectra and 21 for the & rregion.," Fewer parameters are needed to determine the physical conditions such as temperature, column density, line width and covering factor: 70 parameters for the 10.7-13.7 spectra and 21 for the 8 region." For the 10-123 iregion. we lave over 3000 points to constrain the 70 paralucters of mterest if we characterize the constrainiug points by the uuuber of lines times the numberof pixcls for cach Ime.," For the 10-13 region, we have over 3000 points to constrain the 70 parameters of interest if we characterize the constraining points by the number of lines times the numberof pixels for each line." For, For High-redshift analogs of local superwinds. Lyman break galaxies. have been seen by Steidel et al. (1996)),"High–redshift analogs of local superwinds, Lyman break galaxies, have been seen by Steidel et al. \nocite{Steidel96}) )" at 2~3.," at $z \sim 3$." A rest-frame ultraviolet spectrum of a lensed Lyman break galaxy. MS 1512-cB58. shows evidence for an outflow of 200 and a star formation rate of ~LOM. 1.," A rest–frame ultraviolet spectrum of a lensed Lyman break galaxy, MS 1512–cB58, shows evidence for an outflow of $\sim 200$ and a star formation rate of $\sim 40$ $^{-1}$." These properties are similar to those we expect for the objects giving rise to the very strong absorbers. indicating that absorption could be used as a tracer of Lyman break galaxies at zo3.," These properties are similar to those we expect for the objects giving rise to the very strong absorbers, indicating that absorption could be used as a tracer of Lyman break galaxies at $z \sim 3$." Using equation | and existing data on Lyman break galaxies. we can estimate the expected redshift number density of absorbers from Lyman break galaxies.," Using equation \ref{eq:dndz} and existing data on Lyman break galaxies, we can estimate the expected redshift number density of absorbers from Lyman break galaxies." If we assume that these objects are like the +~1.3 very strong absorbers and use RU=Ὁ kpe (see Section 5)) as the typical absorption radius. we get o~SU kpc?.," If we assume that these objects are like the $z \sim 1.3$ very strong absorbers and use $R^*=5$ kpc (see Section \ref{sec:dndzlocal}) ) as the typical absorption radius, we get $\sigma \simeq 80$ $^2$." The number density of Lyman break galaxies isn>0.02 Ὁ (Adelbergeretal. 1998))., The number density of Lyman break galaxies is $n \ga 0.02$ $^{-3}$ \cite{Adelberger98}) ). This is a lower limit because it only takes into account those Lyman break galaxies that have been detected using photometric methods., This is a lower limit because it only takes into account those Lyman break galaxies that have been detected using photometric methods. Using equation l.. we get N(:)rpe;=0.05 at 2= 3.," Using equation \ref{eq:dndz}, we get $N(z)_{LBG} \ga 0.05$ at $z=3$ ." The idea that superwinds seen in absorption might constitute a non-negligible fraction of the damped absorbers (DLAs. logV(HI)>20.3 7) in quasar spectrao was first proposed by Nulsen (1998)).," The idea that superwinds seen in absorption might constitute a non–negligible fraction of the damped absorbers (DLAs, $\log N(\HI)>20.3$ ) in quasar spectra was first proposed by Nulsen \nocite{Nulsen98}) )." Based on a rough model of a weakly collimated. biconical outflow. they determined that superwinds could give rise to the majority of DLAs at all redshifts.," Based on a rough model of a weakly collimated, biconical outflow, they determined that superwinds could give rise to the majority of DLAs at all redshifts." We assess Whether the majority of symmetric-inverted (1>1.5 A) profiles that we attribute to superwinds could also be DLAs., We assess whether the majority of symmetric–inverted $W_r>1.8$ ) profiles that we attribute to superwinds could also be DLAs. Ofthe absorbers shown in Figure|. two have measured column densities.," Ofthe absorbers shown in Figure, two have measured column densities." The system in Q1213.—0017 at.=1.55411 was found not to be a DLA (Rao&Turnshek 2000)) from analysis of a HST/FOS spectrum., The system in $1213-0017$ at $z=1.5541$ was found not to be a DLA \cite{Rao00}) ) from analysis of a /FOS spectrum. For the system in Q1225|317 at:=1791s. a limit of N(HI)<5«10/5 was inferred from the lack of damping wings in an/UE spectrum (Bechtold 1987)).," For the system in $1225+317$ at $z=1.7948$, a limit of $N({\HI})<5 \times 10^{18}$ was inferred from the lack of damping wings in an spectrum (Bechtold \nocite{Bechtold87}) )." Thus. 50 of the HIRES/Keck very strong absorption systems have known column densities and both of them are not DLAs.," Thus, $50$ of the HIRES/Keck very strong absorption systems have known column densities and both of them are not DLAs." Rao Turnshek (2000)) searched for DLAs in the HS7/FOS spectra of 57 Meti-absorption systems., Rao Turnshek \nocite{Rao00}) ) searched for DLAs in the /FOS spectra of $87$ –absorption systems. Of the 57 absorbers in their sample. nine of them have IV.>1.58A.," Of the $87$ absorbers in their sample, nine of them have $W_r > 1.8$." Of those nine absorbers. four are at +> 1.," Of those nine absorbers, four are at $z > 1$ ." In total. 1/5 (80 %)) of the :<1 absorbers are DLAs. and 1/1 (25 %)) of the:>1 absorbers are DLAs.," In total, $4/5$ $80$ ) of the $z<1$ absorbers are DLAs, and $1/4$ $25$ ) of the $z>1$ absorbers are DLAs." This suggests not onlythat the ο1 very strong systems are a different population than the 2<1 systems. but that the τν1 population displays a relative paucity of DLAs.," This suggests not onlythat the $z>1$ very strong systems are a different population than the $z<1$ systems, but that the $z>1$ population displays a relative paucity of DLAs." Furthermore. in contrast to both superwinds and very strong absorption systems. DLAs display no significant evolution in Αν) from τ=| to. =0 (Rao&Turnshek.2000:: Churchill2001)).," Furthermore, in contrast to both superwinds and very strong absorption systems, DLAs display no significant evolution in $N(z)$ from $z=4$ to $z=0$ \cite{Rao00}; \cite{cwc01}) )." If. as we hypothesize. superwinds give rise to the majority of ->1. IT.>LaA absorbers. we are compelled to conclude that most DLAs are not superwinds.," If, as we hypothesize, superwinds give rise to the majority of $z > 1$, $W_r > 1.8$ absorbers, we are compelled to conclude that most DLAs are not superwinds." Why might this be the case?, Why might this be the case? Although large amounts of material (~συ yr.+) are expelled in a superwind. the majority of this material is highly ionized (e.g.1993.1994.1998.1998).," Although large amounts of material $\sim 60$ $^{-1}$ ) are expelled in a superwind, the majority of this material is highly ionized (e.g.,)." The only clouds that gives rise to low-ionization. absorption are the dense clouds of entrained material., The only clouds that gives rise to low–ionization absorption are the dense clouds of entrained material. High-equivalent width systems like the ones presented in Figure could be produced with only small numbers of moderate-column density clouds (greater than about five) because the clouds in a superwind have a significant spread in velocity space (~300 7)., High–equivalent width systems like the ones presented in Figure could be produced with only small numbers of moderate–column density clouds (greater than about five) because the clouds in a superwind have a significant spread in velocity space $\sim 300$ ). It has been shown that the majority of DLAs have total velocity spreads less than 200 (Prochaska&Wolfe1999:: Pettinietal.20000). indicating that they are typically produced in environments less active than those which produce the very strong absorbers.," It has been shown that the majority of DLAs have total velocity spreads less than $200$ \cite{Prochaska99}; \cite{Pettini00}) ), indicating that they are typically produced in environments less active than those which produce the very strong absorbers." Figure 3. illustrates these differences.," Figure \ref{fig:DLA} illustrates these differences." The bottom two panels contain high-resolution profiles of two DLAs (Churchilletal. 2000b)) and the top two panels show examples of symmetric-inverted profiles from our sample., The bottom two panels contain high–resolution profiles of two DLAs \cite{archive2}) ) and the top two panels show examples of symmetric–inverted profiles from our sample. " The majority of very strong GT,>Ls A): >1 absorption profiles with high-resolution. spectra show distinctive kinematic features. including a central inversion and a large velocity spread."," The majority of very strong $W_r>1.8$ ), $z>1$ absorption profiles with high–resolution spectra show distinctive kinematic features, including a central inversion and a large velocity spread." All of these features can be explained with a line of sight through à superwind., All of these features can be explained with a line of sight through a superwind. The redshift number density of absorbers expected from superwinds. τὸ. was calculated using parameters observed in local superwinds and was found to be consistent with the Ας) of very strong absorbers.," The redshift number density of absorbers expected from superwinds, $N(z)$, was calculated using parameters observed in local superwinds and was found to be consistent with the $N(z)$ of very strong absorbers." In addition. the absence of very strong absorbers is consistent with the decrease in star formation from 7=1 to thepresent.," In addition, the absence of very strong absorbers is consistent with the decrease in star formation from $z=1$ to thepresent." The number of DLAs. however. ts consistent with no evolution over this redshift range.," The number of DLAs, however, is consistent with no evolution over this redshift range." In addition. the verystrong absorbers at το1 with known column densitiesdisplay a paucity of DLAs as compared with the low-redshift very strong absorbers. suggesting that the majority of DLAs do not arise in superwinds.," In addition, the verystrong absorbers at $z>1$ with known column densitiesdisplay a paucity of DLAs as compared with the low–redshift very strong absorbers, suggesting that the majority of DLAs do not arise in superwinds." (D= 15.7: 2= 0.0411) has displayed some of the most rapid X-ray variability observed in a Seyfert galaxy (Turner 1999: Leighly 19992).,$B=15.7$ ; $z=0.0411$ ) has displayed some of the most rapid X-ray variability observed in a Seyfert galaxy (Turner 1999; Leighly 1999a). " Its X-ray spectrum is steep and shows a strong ""soft excess” (Vaughan 1999: Leighly 1999b) and its optical spectrum shows narrow (FWHM = 1050 km s. Po and strong eemission (Remillard et al.", Its X-ray spectrum is steep and shows a strong “soft excess” (Vaughan 1999; Leighly 1999b) and its optical spectrum shows narrow (FWHM = 1050 km $^{-1}$ ) and strong emission (Remillard et al. 1986. Leighly 1999b). characteristic of many ultrasoft Sevferts.," 1986, Leighly 1999b), characteristic of many ultrasoft Seyferts." On the basis of FWHM is classified as a Narrow-Line Seyfert | (NLSD) galaxy., On the basis of FWHM is classified as a Narrow-Line Seyfert 1 (NLS1) galaxy. Such ultrasoft NLSIs are of particular interest because their extreme properties are most likely produced by an extreme value of an underlying physical parameter (e.g. Pounds. Done Osborne 1995: Boller. Brandt Fink 1996: Brandt Boller 1998: Vaughan 2001).," Such ultrasoft NLS1s are of particular interest because their extreme properties are most likely produced by an extreme value of an underlying physical parameter (e.g. Pounds, Done Osborne 1995; Boller, Brandt Fink 1996; Brandt Boller 1998; Vaughan 2001)." However. with a few exceptions. their timing and spectral properties proved difficult to study in detail with previous X-ray observatories as a result of e.g.. regular light curve interruptions from Earth occultation and limited spectral bandpass.," However, with a few exceptions, their timing and spectral properties proved difficult to study in detail with previous X-ray observatories as a result of e.g., regular light curve interruptions from Earth occultation and limited spectral bandpass." was observed as part of a guaranteed time programme to study the timing and spectral properties of the brightest and most prominent ultrasoft NLSIs usingNewton., was observed as part of a guaranteed time programme to study the timing and spectral properties of the brightest and most prominent ultrasoft NLS1s using. . In this Letter we report the first results from the EPIC data and in particular the detection of an unusual spectral feature at around 7 keV. oobserved on 2000 October 21 during rev., In this Letter we report the first results from the EPIC data and in particular the detection of an unusual spectral feature at around 7 keV. observed on 2000 October 21 during rev. 0159 for a duration of 46 ks. during which all instruments were operating nominally.," 0159 for a duration of 46 ks, during which all instruments were operating nominally." The EPIC pn camera was operated in full-frame mode. and the two MOS cameras were in large-window mode: all three cameras used the medium filters.," The EPIC pn camera was operated in full-frame mode, and the two MOS cameras were in large-window mode; all three cameras used the medium filters." Extraction of science products from the Observation Data Files (ODFs) followed standard procedures using the SScience Analysis System version 5.1.0 y)., Extraction of science products from the Observation Data Files (ODFs) followed standard procedures using the Science Analysis System version 5.1.0 ). The raw MOS and pn data were processed to produce calibrated event lists., The raw MOS and pn data were processed to produce calibrated event lists. Unwanted hot. dead or flickering pixels were removed. likewise events due to electronic noise. and event energies were corrected for charge-transfer losses.," Unwanted hot, dead or flickering pixels were removed, likewise events due to electronic noise, and event energies were corrected for charge-transfer losses." The latest available,The latest available The astronomy and radio astronomy investigations by means of spacecrafts and space missions have extraordinary importance for science ancl mankind. ancl nobody. calls in question now.,"The astronomy and radio astronomy investigations by means of spacecrafts and space missions have extraordinary importance for science and mankind, and nobody calls in question now." Lt is enough to recall about the famous space telescope of Hubble. that eave ancl gives a huge amount of new scientific results., It is enough to recall about the famous space telescope of Hubble that gave and gives a huge amount of new scientific results. Really. its location behind the terrestrial atmosphere allowed one to take olf restrictions due to optic cllects of the atmosphere ancl to open a new page in the exploration of the Universe.," Really, its location behind the terrestrial atmosphere allowed one to take off restrictions due to optic effects of the atmosphere and to open a new page in the exploration of the Universe." In. this connection a natural wish to reach the same success by spacecralts in other frequeney ranges has arisen., In this connection a natural wish to reach the same success by spacecrafts in other frequency ranges has arisen. One of challenges. sulliciently dillicult. for exploring from. the Earth. is the decameter wavelength emission.," One of challenges, sufficiently difficult for exploring from the Earth, is the decameter wavelength emission." Although racdioastronomvy was born at low frequency of 20.5 MIIZ in the 1930s. it rapidly was developed: towards. higher frequencies for higher resolution ancl better. sensitivity.," Although radioastronomy was born at low frequency of 20.5 MHz in the 1930s, it rapidly was developed towards higher frequencies for higher resolution and better sensitivity." Creat many disturbances and interference from various racio broadcast stations. propagat world-wide in this frequeney range. plus undesirable and not-well-precictableed ionospheric ellects pulled up the progress of decameter radio astronomy. though it would answer many very interesting astrophysical problems.," Great many disturbances and interference from various radio broadcast stations, propagated world-wide in this frequency range, plus undesirable and not-well-predictable ionospheric effects pulled up the progress of decameter radio astronomy, though it would answer many very interesting astrophysical problems." However. to launch. the same (in the sense of ellicieney as the telescope of Hubble. ancl similar others) decameter radiotelescope in the near-carth space (or for example. even in the backside of the Moon. just some overbold. heads. proposed: see. for example. Smith 1990: ‘Takahashi 2003) is not quite simple.," However, to launch the same (in the sense of efficiency as the telescope of Hubble and similar others) decameter radiotelescope in the near-earth space (or for example, even in the backside of the Moon, just some overbold heads proposed; see, for example, Smith 1990; Takahashi 2003) is not quite simple." Phe point is that the receiving antenna capability of such a radio telescope depends. in many respects. on its ellective area that. for its turn. depends on a wavelength of the receiving emission.," The point is that the receiving antenna capability of such a radio telescope depends, in many respects, on its effective area that, for its turn, depends on a wavelength of the receiving emission." Lf it is large (in particular. decameters in our case). then the antenna sizes should be corresponding.," If it is large (in particular, decameters in our case), then the antenna sizes should be corresponding." Lt is clear that the facilities of space technology are not boundless., It is clear that the facilities of space technology are not boundless. Therefore. in the present day the space missions (WIND. STEREO and others). carried out radio observations in the decamoeter wavelength range. can permit themselves only some dipoles on their board. as the size of such spacecrafts. and. their weight are restricted.," Therefore, in the present day the space missions (WIND, STEREO and others), carried out radio observations in the decameter wavelength range, can permit themselves only some dipoles on their board, as the size of such spacecrafts and their weight are restricted." How effective is the telescope it?, How effective is the telescope it? OF course. it is not comparable with the capability of the space telescope as Hubble. ete;," Of course, it is not comparable with the capability of the space telescope as Hubble, etc." But it would be useful to estimate its facilities in comparison with erounc-basecl instruments such as. for example. the well-known biggest decameter raciotelescope UTI-2.," But it would be useful to estimate its facilities in comparison with ground-based instruments such as, for example, the well-known biggest decameter radiotelescope UTR-2." The aim of this paper is to answer this posed question., The aim of this paper is to answer this posed question. For this purpose we have carried out simultaneously the radio astronomy observations in the radiotelescope UTIU-2 by two dilferent antennas in the same frequeney. band;, For this purpose we have carried out simultaneously the radio astronomy observations in the radiotelescope UTR-2 by two different antennas in the same frequency band. One of them was an array of 720 dipoles. and another consisted of one.," One of them was an array of 720 dipoles, and another consisted of one." With all this going on the concrete problem was on the agenda: to examine what intensity of solar bursts one, With all this going on the concrete problem was on the agenda: to examine what intensity of solar bursts one For galaxies further than ~ 100Mpc. the usual kinematic tracers of galactic dynamics become increasingly difficult or impossible to use.,"For galaxies further than $\sim100$ Mpc, the usual kinematic tracers of galactic dynamics become increasingly difficult or impossible to use." But at larger distances. nature sometimes provides a very different indicator of galaxy mass—strong lensing of quasars.," But at larger distances, nature sometimes provides a very different indicator of galaxy mass—strong lensing of quasars." Galaxies with a quasar conveniently placed behind them. which they then lens into multiple images. are rare.," Galaxies with a quasar conveniently placed behind them, which they then lens into multiple images, are rare." But for those galaxies it is fairly easy to measure masses. even to z~I.," But for those galaxies it is fairly easy to measure masses, even to $z\sim1$." In recent years there has been progress on estimating the M/L in samples of lensing galaxies (Keeton et 11998. Kochanek et 22000. Rusin et al.," In recent years there has been progress on estimating the $M/L$ in samples of lensing galaxies (Keeton et 1998, Kochanek et 2000, Rusin et al." 2003)., 2003). For a few systems there have been efforts to combine lensing and velocity dispersions (Treu Koopmans 2002a.b. Koopmans Treu 2003).," For a few systems there have been efforts to combine lensing and velocity dispersions (Treu Koopmans 2002a,b, Koopmans Treu 2003)." In this Letter we go beyond simple M/L for a sample of lensing galaxies and try to recover the distribution of stellar and dark mass within galaxies., In this Letter we go beyond simple $M/L$ for a sample of lensing galaxies and try to recover the distribution of stellar and dark mass within galaxies. Our technical innovations are (1) we use observed colors to model the stellar population in detail and hence map the stellar mass. and (11) we use the method of pixelated lens reconstruction to make detailed. profiles of the total mass: we pay particular attention to quantifying the uncertainties in both departments.," Our technical innovations are (i) we use observed colors to model the stellar population in detail and hence map the stellar mass, and (ii) we use the method of pixelated lens reconstruction to make detailed profiles of the total mass; we pay particular attention to quantifying the uncertainties in both departments." Our sample comprises 17 early-type galaxies over a wide range of redshifts (0.310*'ergs""!, r«17.77 mmag and 0.03«z0.2 (median redshift z=0.1)."," The final XMM/SDSS sample used in this paper consists of 175 serendipitous sources with $L_X \rm (2-10) > 10^{41} \, erg \, s^{-1}$, $r<17.77$ mag and $0.0320) XMM observations that became public in June 2004 and overlapped with the second data release of the SDSS., That survey consisted of high Galactic latitude $b > 20$ ) XMM observations that became public in June 2004 and overlapped with the second data release of the SDSS. The original NHS is now superseded by the XMM/SDSS survey(?)., The original NHS is now superseded by the XMM/SDSS survey. ". However, extensive optical spectroscopy has been obtained for X-ray sources in a subset of the original NHS fields (see below)."," However, extensive optical spectroscopy has been obtained for X-ray sources in a subset of the original NHS fields (see below)." " Therefore, we retain that survey in its original format but reanalyse the XMM observations using the pipeline developed for the reduction of the XMM/SDSS survey fields(?)."," Therefore, we retain that survey in its original format but reanalyse the XMM observations using the pipeline developed for the reduction of the XMM/SDSS survey fields." ". As a result the source detection, flux estimation, astrometric corrections, optical identification of the X-ray sources and sensitivity map construction in the updated NHS follow the methodology described in?."," As a result the source detection, flux estimation, astrometric corrections, optical identification of the X-ray sources and sensitivity map construction in the updated NHS follow the methodology described in." . For the subset of the original NHS fields with declination ó« 10ddeg follow-up spectroscopy was carried out at the ESO VLT and NTTtelescopes?., For the subset of the original NHS fields with declination $\delta<10$ deg follow-up spectroscopy was carried out at the ESO VLT and NTT. ". The total area of that subsample, which hereafter willbe referred to as NHS, is 5.6deg”."," The total area of that subsample, which hereafter willbe referred to as NHS, is $\rm 5.6\,deg^2$." All X-ray sources with extended optical light profiles (i.e. optically resolved) in the SDSS and r«20.5 mmag have been observed spectroscopically., All X-ray sources with extended optical light profiles (i.e. optically resolved) in the SDSS and $r<20.5$ mag have been observed spectroscopically. " Because the density of the targets on the sky is low, each source was observed separately with a longslit."," Because the density of the targets on the sky is low, each source was observed separately with a longslit." The observations were carried out between October 2006 and March 2008 in queue mode with the FORS2 (FOcal Reducer and low dispersion Spectrograph) on the VLT (Very Large Telescope) and the EMMI (ESO’s Multimode Instrument) at the NTT (New Technology Telescope)., The observations were carried out between October 2006 and March 2008 in queue mode with the FORS2 (FOcal Reducer and low dispersion Spectrograph) on the VLT (Very Large Telescope) and the EMMI (ESO's Multimode Instrument) at the NTT (New Technology Telescope). The data were reduced using standard routines in IRAF., The data were reduced using standard routines in IRAF. Redshifts were determined for 129 out of 151 targeted sources by visual inspection of the reduced spectra., Redshifts were determined for 129 out of 151 targeted sources by visual inspection of the reduced spectra. The redshift measurements correspond to at least two secure spectral features., The redshift measurements correspond to at least two secure spectral features. Figure 2 presents the redshift distribution of the sample and demonstrates that at the magnitude limit r=20.5 mmag the majority of the sources lie at z<0.5., Figure \ref{fig_zdist} presents the redshift distribution of the sample and demonstrates that at the magnitude limit $r=20.5$ mag the majority of the sources lie at $z\la0.5$. In the updated NHS catalogue there are 126 hard-band 8kkeV) detected sources with r< 20.5mmag and extended optical light profiles., In the updated NHS catalogue there are 126 hard-band keV) detected sources with $r<20.5$ mag and extended optical light profiles. Redshift estimates are available for 100 of them (including one Galactic star)., Redshift estimates are available for 100 of them (including one Galactic star). " The redshift incompleteness is because of (i) featureless spectra, (ii) failure to observe some of the targets and (iii) mismatches between the updated NHS source catalogue and the original one (Georgantopoulos et al."," The redshift incompleteness is because of (i) featureless spectra, (ii) failure to observe some of the targets and (iii) mismatches between the updated NHS source catalogue and the original one (Georgantopoulos et al." 2005) used to construct the target list for follow-up spectroscopy., 2005) used to construct the target list for follow-up spectroscopy. " The sample used in this paper consists of 73 hard X-ray sources with 0.1< 0.5, r«20.5 mmag."," The sample used in this paper consists of 73 hard X-ray sources with $0.1