ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 They are not obviously offset from cach other iu οίIE)., They are not obviously offset from each other in $S_{2}(CH)$.3 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 5466.4 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."5 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."6 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"7enerev 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."8" 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.9 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][]{td1999,10low_berger2003,gibsonetal2006}."11". 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)."12 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."13" 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}) )."14 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}) ).15 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."16 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}) )."17 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."18 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.19 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}20 and panels (b)(d)(f) of Figure \ref{fig11}) ) whose apexes are located in the layer of the most intense current density and heating."21 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."22 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 $J/B > 1/l$ "23As 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."24 Any distortion can then be summarized ow ἃ set of cocllicients., Any distortion can then be summarized by a set of coefficients.25 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."26 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.27 Paper 1. 822 (see eqns.," Paper 1, 2 (see eqns."28 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.29 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.30 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."31 We will begin with the development common to both cases., We will begin with the development common to both cases.32 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}) ).33 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 $(E, \kappa,34\cos\beta)$ in the end."35 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."36 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."37 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."38 This allows cach frequeney to be treated: separately., This allows each frequency to be treated separately.39 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 ${\cal40 M}$ describes the reaction of the galaxy to the perturbation; so the entire response is the sum of both the response and direct forcing, ${\cal M}^{lm}_{jk} + \delta_{jk}$ ."41 We may integrate the equations of motion directly to evaluate στ0., We may integrate the equations of motion directly to evaluate $\bI(\tau+t)$.42" 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}) )."43↕⋯∩⊳∖∖⊽∢⊾⋜↧⊳∖⊳∖⊔⊔↓∢⋅⊳ ∣⋡∙∖⇁⋯⇂∩↓≻↿⊀↓⊔⋏∙≟⇂↓↕∢⊾∣↕↓↥↓∢⊾−⋜↧≻∙∖⇁↓↕↓↓≻⇂∪↿⊲⊔⇍↓⋅⋖⋅⊳∖↓≻∪⊔⊳∖⋖⋅⊔↓⋜∐↓⋰∟∖⋅⋈∣⋯⊲↓⊔∠⇂∢⊾↓⋰↓∖⋰↓⊔⋏∙≟⇂↓⋯↿⇠∕⊲⊥⋜⋯∠⇂∐⊥⋜↧∣⋯∖⇁∢⊾⊳↿⇂⋯↿⊤↕≻↓⋜⊔⋅⋏∙≟∢⊾↓⋅↿↓↥⋜↧↓↕↕↓↕⇂↓⋅↕↓↕≻↕≼∼ ∠⇂∙∖⇁⊔⋜⋯↓⊲⊔⇍⋜↧↓↿⊲↓⊔↓∢⊾⊳∖⊳≼⇍∪⊔⊳∖⊲↓⊳∖∩⋅↓∐∖∖⋰↓∣↓↕∣↓↕⋖⊾∪↓⋅∠⇂∢⊾↓⋰↓⊔⋏∙≟∪⇂⋅⋯," 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."44⊔⋅⊳∖↓∪∖∖⊽⋜⋯∠⊔⋅⋜↧⊳∖⇂↿⊲↓⊔↓∢⊾⊳∖≼⇍⋜↧↓∢⊾⊳∖⋡↓↴↓⋅⋖⋅∖⋰↓∪⊔≱∖∖∖⊽∪↓⋅↳⊳⊀↓⊔≼⇍↓⋯⇂⊲↓⊔⋏∙≟≼∼∪⊔↓↓≻⋜⊔⋰↓≱∖∪⊔↥∪⊔−∣⋡⇜⇂∙∖⇁ ⊳∖⊲↓⊔↓⊔↓⋜∐⊲↓∪⊔⊳∖⊳⊳∖⊔⋏∙≟⋏∙≟∢⊾⊳∖⇂⊳∖⇂↓⋯↿↿↓↥↕≻↕≻⋜↧∖⇁⋖⋅↓⋅∙∖⇁⋏∙≟∪⇜⇂⋜↧↓≻," Previous work, including comparison to n-body simulations, suggests that this is a very good approximation for time scales longer than several crossing times."45↓≻↓⋅∪⇀∖⊲↓⊔↓⋜∐⊀↓∪⊔⇂⋅∪↓⋅↿⊀↓⊔↓∢⊾⊳∖≼⇍⋜↧↓∢⊾⊳∖↓∪⊔⋏∙≟∢⊾↓⋅↿↓⋯⊔⊳∖∢⊾∖⇁⋖⋅↓⋅⋜↧⇂≼⇍↓⋅∪⊳∖⊳∖⊲↓⊔⋏∙≟↿⊀↓⊔↓∢⊾⊳∖⊳↾↓∖↓↥⋖⊾↓⋅∢⋅⊳∖↓≻∪⊔⊳∖⋖⊾ 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.46" 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 $b^{lm}_j(t)$.47" The fiducial stochastic variables are the coellicients 7"" themselves.", The fiducial stochastic variables are the coefficients $b^{lm}_j(t)$ themselves.48 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 therefore49whereda(o)/do.,where.50. 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.51 2002). so that is constrained to be smaller than roughly.," 2002), so that is constrained to be smaller than roughly."52 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."53 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)."54 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."55 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."56 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}) ).57 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.58 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.59 4., 4.60" 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."61. 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."62 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. ("632002).,2002).64 These models also account for the observed level of present Hactuations., These models also account for the observed level of present fluctuations.65 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.66 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."67. 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.68 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"69 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"70(Miles1961:Llowarel1961;Chimonas1970).,"\citep{jwm61,how61,chi70}."71".."" 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."72" 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) ]."73(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."74" 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 $\delta(t) \propto \exp(-i\omega t)$."75 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."76 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."77 Due to the lack of, Due to the lack of781994).. 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."79 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."80 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}) ). ("81This should be the case of £<£.),"This should be the case of $\xi\leq82 \xi_{\rm c}$ .)"83 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 |<r€E., The key point missed in this calculation is that the fine-tuning of $1-\xi^{2}=O(1/E^{2})$ to realize the energy equipartition $\mm^{2}\sim 1$ ) may occur at a radius $x$ in the range $1\ll x\leq E$.84" Then. to discuss the energy conversion in the range 1«or<E. which is called the ""intermediate"" range of a in this paper. we must analvze the evolution of AP without assuming (1—£?)47 to be very large."," Then, to discuss the energy conversion in the range $1\ll x\leq E$, which is called the “intermediate” range of $x$ in this paper, we must analyze the evolution of $\mm^{2}$ without assuming $(1-\xi^{2})x^{2}$ to be very large."85 The existence of the intermediate range ofr is a main feature of highly relativistic outflows with a very large specific enerev (2>> 1)., The existence of the intermediate range of $x$ is a main feature of highly relativistic outflows with a very large specific energy $E\gg 1$ ).86 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-««AP<I/E? to a rough equipartition value of AM?~ Las outllows propagate in (he intermediate region.," Recalling that we obtain $\mm^{2}\simeq e/E$ at the light cylinder surface $x=1$, we expect $\mm^{2}$ to increase from a sub-fast-magnetosonic value in the range $1/E\ll \mm^{2}\ll 1/E^{2/3}$ to a rough equipartition value of $\mm^{2}\sim 1$ as outflows propagate in the intermediate region."87 The last-imagnetosonic point al which we have the value of AP=L/h can be involved in (his region., The fast-magnetosonic point at which we have the value of $\mm^{2}=1/E^{2/3}$ can be involved in this region.88 The usual asvimptotie analysis becomes valid only in (he region 2c»E. where Al? nav increase logarithmically with vr. and our purpose here is to give the more precise treatment valid both in the intermediate and asyanptotic regions.," The usual asymptotic analysis becomes valid only in the region $x\gg E$, where $\mm^{2}$ may increase logarithmically with $x$, and our purpose here is to give the more precise treatment valid both in the intermediate and asymptotic regions."89 The Grad-Shafranov equation can be written in the form if no eravily is included. (see. e.g.. Tomimatsu 1994).," The Grad-Shafranov equation can be written in the form if no gravity is included (see, e.g., Tomimatsu 1994)."90 The source terms sq and s» are given bv and, The source terms $s_{1}$ and $s_{2}$ are given by and91Stellar. pulsations. offer. a unique. opportunity. to constrain. the intrinsicVON parameters of⋅ stars and. by using. asteroscismoloey.. o unveil. their D.inner structure.,"Stellar pulsations offer a unique opportunity to constrain the intrinsic parameters of stars and, by using asteroseismology, to unveil their inner structure."92" In. particular.. the classical. ASset.. variables. are late A-type and carly E-tvpe. stars that ..opulatelate thex TESTinstabilityinstability.AIS stripstSEED""n betweeWEEE mfoeο zero-agezoponame naunmi. sequence and terminal-age main sequence. with 3.0 1.5."," In particular, the classical $\delta$ Sct variables are late A-type and early F-type stars that populate the instability strip between the zero-age main sequence and terminal-age main sequence, with $3.0 \le {\rm M}_V \le 930.5$ ."94 hey. pulsate in mode of low radial order with periods ranging: [rom⋅ about mmin⊀ to hh (seeBreeer5.2000.for⋅a: review).., They pulsate in mode of low radial order with periods ranging from about min to h \citep[see][for a review]{breger00}.95 0 TUSSct stars pulsate in: both radial. and. non-racial. »mmocdes anc gmunmocdes. driven. by the smechanism..in. xwlicular. in. the ⋠⋠ionization zone.," $\delta$ Sct stars pulsate in both radial and non-radial modes and modes, driven by the $\kappa$ -mechanism,in particular in the ionization zone."96 asThe ~ DDor variables.. with. periods. tween about 0.3. and 3dd. are mostly located near he cool edge of the &Sset instability strip (haveοἱal. 1999)..," The $\gamma$ Dor variables, with periods between about 0.3 and d, are mostly located near the cool edge of the $\delta$ Sct instability strip \citep{kaye99}. ."97 heir pulsations are driven by convective blocking, Their pulsations are driven by convective blocking98"dynamical instability. 3,20.27.","dynamical instability, $\beta_d \approx 0.27$."99 This critical value is owed on simulations of cdilferentially rotating polvtropes iwing the jOn—)-distribution of Alaclaurin spheroids., This critical value is based on simulations of differentially rotating polytropes having the $j(m_{\varpi})$ -distribution of Maclaurin spheroids.100 However. recent simulations demonstrate that clillerentially rotating polvtropes having other j(m—)-clistributions can »f dynamically unstable for values of 3 as low as 0.14 uckett.Durisen&Davis1996:Centrellaetal.2000).," However, recent simulations demonstrate that differentially rotating polytropes having other $j(m_{\varpi})$ -distributions can be dynamically unstable for values of $\beta$ as low as 0.14 \cite{pickett96,centrella00}."101. The equilibrium. configurations of some of those unstable stars also contain a low density accretion clisk like structure in vw stars outer lavers., The equilibrium configurations of some of those unstable stars also contain a low density accretion disk like structure in the stars' outer layers.102 This feature is very similar to the equilibrium structure of our models., This feature is very similar to the equilibrium structure of our models.103 Hence a more detailed study has to be carried out to determine whether the cold models are cynamically stable., Hence a more detailed study has to be carried out to determine whether the cold models are dynamically stable.104 The subsequent evolution of a bar-unstable object has been studied. for the past 15 vears (Durisen.Gingold&Imamura.Durisen&Pickett2000:Brown 2000)..," The subsequent evolution of a bar-unstable object has been studied for the past 15 years \cite{durisen86,williams88,houser96,pickett96,smith96,houser98,new99,imamura00,brown00}."105 It is found that a bar-like structure develops in a dynamical timescale., It is found that a bar-like structure develops in a dynamical timescale.106 However. it is still not certain whether the bar structure would be persistent. giving rise to a lone-livecl gravitational wave signal. or material would be shed from the ends of the bar after tens of rotation periods. leaving an axisvmmetric. dynamically bar-stable central star.," However, it is still not certain whether the bar structure would be persistent, giving rise to a long-lived gravitational wave signal, or material would be shed from the ends of the bar after tens of rotation periods, leaving an axisymmetric, dynamically bar-stable central star."107 Even if the colkd neutron stars are dynamically stable. they are subject to various secular instabilities.," Even if the cold neutron stars are dynamically stable, they are subject to various secular instabilities."108 The timescale of the gravitational-wave-cdriven bar-moce instability can be estimated by (Friedman&Schutz1975. 1978).., The timescale of the gravitational-wave-driven bar-mode instability can be estimated by \cite{friedman7578}. .109 In our case. 2zm35km (see Figure 12)). 2=4000rads and 3&024. SO TharUL]s.," In our case, $R\approx 35~\rmn{km}$ (see Figure \ref{ToW}) ), $\Omega\approx 4000~\rmn{rad}~\rmn{s}^{-1}$ and $\beta \approx 0.24$, so $\tau_{\rm bar} \sim 0.1~\rmn{s}$."110 Gravitational waves mav also drive the r- instability (Lindblom.Owen&Morsink.LO9S)., Gravitational waves may also drive the r-mode instability \cite{lindblom98}.111. The timescale is estimated by [or the /=2 r-mode at low temperatures (Lindblom.Alendell&Owen 1999).. where p is the average density.," The timescale is estimated by for the $l=2$ r-mode at low temperatures \cite{lindblom99}, where $\bar{\rho}$ is the average density."112 Inserting p lor the inner 20-kmi cores of the cold. stars. we have 7.zc10«s<>nee.," Inserting $\bar{\rho}$ for the inner 20-km cores of the cold stars, we have $\tau_r \approx 10~\rmn{s}\gg \tau_{\rm bar}$."113 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.114 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}."115. 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.116 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.117 We considered. three models. for. the pre-collapse white chvarts., We considered three models for the pre-collapse white dwarfs.118 All of them are rigiclv rotating at the maximum possible angular velocities., All of them are rigidly rotating at the maximum possible angular velocities.119 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}.120. 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."121 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."122 Two EOS have been used for the collapsed objects., Two EOS have been used for the collapsed objects.123 One of them is one of the standard cold neutron-star LOS., One of them is one of the standard cold neutron-star EOS.124 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."125 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."126 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}) )."127" 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 $4\times 10^{11}~\rmn{g}~\rmn{cm}^{-3} \la \rho \la 1282\times 10^{14}~\rmn{g}~\rmn{cm}^{-3}$ )."129h 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 $\beta$."130 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."131 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)."132 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.133 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.134 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."135 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.136 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."137 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."138 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.139 Ewen if they, Even if they140We estimate 7 and Vz used in Section 4.4..,We estimate $\mathcal{R}$ and $\mathcal{Y}_{Z}$ used in Section \ref{subsec:enrichment}.141" 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 $m$."142 We assume the Salpeter IMF (¢(m)οςm ???) with stellar mass range 0.1Mc;<m100Mo., We assume the Salpeter IMF $\phi (m)\propto m^{-2.35}$ ) with stellar mass range $0.1~\mathrm{M}_{\sun}\leq m\leq 100~\mathrm{M}_{\sun}$.143 The IMF is normalized as where 7n; is the lower mass cutoff of stellar mass., The IMF is normalized as where $m_\mathrm{l}$ is the lower mass cutoff of stellar mass.144" For the remnant mass, we adopt the fitting formula provided by Inoue(2011):: We also adopt the fitting formula for the mass of ejected metals as a function of stellar mass as (Inoue2011) Inoue(2011) (Kennicutt"," For the remnant mass, we adopt the fitting formula provided by \citet{inoue11}: We also adopt the fitting formula for the mass of ejected metals as a function of stellar mass as \citep{inoue11}145 \citet{inoue11} \\ref{fig:returned}, \citep{kennicutt98,gavazzi02}."146chosen to follow the radial density function given by Eq.,chosen to follow the radial density function given by Eq.147 3 oul to à maximun clistance of 350 Ape. and the Iuminosities are chosen to follow either a power law distribution (scenario 1) or to be all equal (scenario 2).," \ref{eq:RadialDensity2} out to a maximum distance of 350 Mpc, and the luminosities are chosen to follow either a power law distribution (scenario 1) or to be all equal (scenario 2)."148 The flux q trom each source is computed. then the relative πας of the brightest source is computed as Q=max[qi.....qxV/sumiqi.....dx }.," The flux $q$ from each source is computed, then the relative flux of the brightest source is computed as $Q = \max\{ q_1,\ldots,q_N \} / \mbox{sum} \{ q_1,\ldots,q_N \}$ ."149 We calculate Q by averaging over 1000 realizations., We calculate $\bar{Q}$ by averaging over 1000 realizations.150 This is repeated for several different source densities., This is repeated for several different source densities.151 We show the results of this analvsis in Fig. 4.., We show the results of this analysis in Fig. \ref{fig:Qbar}.152 The error bars represent the quantiles of each set of realizations., The error bars represent the quantiles of each set of realizations.153 At a source density of 105Ape*. the expected value of Q for scenario Lis and the quantile range is to1056.," At a source density of $10^{-6} \quad\mbox{Mpc}^{-3}$, the expected value of $\bar{Q}$ for scenario 1 is and the quantile range is to."154.. At a source density of 10?.Mpe7. the expected value of Q is and the quantile range is to2654.," At a source density of $10^{-2} \quad\mbox{Mpc}^{-3}$, the expected value of $\bar{Q}$ is and the quantile range is to."155 The numeric results are greater than the analvtical treatment. at all source densities., The numeric results are greater than the analytical treatment at all source densities.156 This is expected since the analvlic treatment is a lower limit., This is expected since the analytic treatment is a lower limit.157 From a source density of 10.*.Mpe tte lO!Mpe*. the nunerical results follow the general trend of the analytic treatment: decreasing by a factor of approximately 4 as (he source densitv increases by a factor of 100.," From a source density of $10^{-6} \quad\mbox{Mpc}^{-3}$ to $10^{-4} \quad\mbox{Mpc}^{-3}$, the numerical results follow the general trend of the analytic treatment: decreasing by a factor of approximately 4 as the source density increases by a factor of 100."158" At source densities greater than 101\IpeI, the numerical results flatten (i.e.. Chev are nearly independent of source densitv)."," At source densities greater than $10^{-4} \quad\mbox{Mpc}^{-3}$, the numerical results flatten (i.e., they are nearly independent of source density)."159 This is the source density above which we expect (he closest sources to be within 10 Alpe and the linear region of Eq., This is the source density above which we expect the closest sources to be within 10 Mpc and the linear region of Eq.160 :) to be important., \ref{eq:RadialDensity2} to be important.161 If no local overdensity is assumed. ie. Eq.," If no local overdensity is assumed, i.e. Eq."162 1 is substituted for Eq. 3.. ," \ref{eq:RadialDensity} is substituted for Eq. \ref{eq:RadialDensity2}, ,"163then the numerical results do not flatten., then the numerical results do not flatten.164 In (hiis case. the expected value of Q lor scenario 1 at a source density of LO2Mpe τὰς£.0%..," In this case, the expected value of $\bar{Q}$ for scenario 1 at a source density of $10^{-2} \quad\mbox{Mpc}^{-3}$ is."165 The relatively weak dependence of Q on source density is caused by two effects which somewhat balance each other., The relatively weak dependence of $\bar{Q}$ on source density is caused by two effects which somewhat balance each other.166 The first is that a greater number of sources will tend to diminish the relative flux of the brightest source by increasing the background., The first is that a greater number of sources will tend to diminish the relative flux of the brightest source by increasing the background.167 The second is (hat a greater number of sources will tend to increase the (lux of the brightest source since (here is a greater probability of a source being relatively close or luminous or both., The second is that a greater number of sources will tend to increase the flux of the brightest source since there is a greater probability of a source being relatively close or luminous or both.168 For the special case dN/drxr. the tendencies exactly balance such that Q is independent of source density.," For the special case $dN/dr \propto r$, the tendencies exactly balance such that $\bar{Q}$ is independent of source density."169 The weak dependence of Q on source density. implies that estimates of source density based solely on event clustering will have a large uncertainty., The weak dependence of $\bar{Q}$ on source density implies that estimates of source density based solely on event clustering will have a large uncertainty.170 Indeed. the recent. CR. source density estimates by Takami&Sato(2009) ancl Cuocoetal.(2008) reflect (his.," Indeed, the recent CR source density estimates by \citet{Takami} and \citet{Cuoco} reflect this."171 In general. scenario | has a greater Q than scenario 2. however the difference is well within the quantile range.," In general, scenario 1 has a greater $\bar{Q}$ than scenario 2, however the difference is well within the quantile range."172 That is. the results are not sensitive to the details of the source luminosity [funcüon.," That is, the results are not sensitive to the details of the source luminosity function."173 Regardless of this. scenario 1 (power-law huminositwv function) is (he more appropriate and the more generalconsideration.," Regardless of this, scenario 1 (power-law luminosity function) is the more appropriate and the more generalconsideration."174 For instance. in scenario 1 the brightestsources are spread. over a relatively large range of distances. whereas in scenario," For instance, in scenario 1 the brightestsources are spread over a relatively large range of distances, whereas in scenario"175case the CPU time does increase dramatically. because it becomes increasingly hard for the aleorithin to fill the nissius pieces of the data stream.,"case the CPU time does increase dramatically, because it becomes increasingly hard for the algorithm to fill the missing pieces of the data stream."176 In this case. the noise covariance matrix condition becomes larger auc larger.," In this case, the noise covariance matrix condition becomes larger and larger."177 We have described and tuplemented ai Bayesian fraanework for cstimating the time-domain noise power spectruuni for uon-ideal CAIB experiments., We have described and implemented a Bayesian framework for estimating the time-domain noise power spectrum for non-ideal CMB experiments.178— This fraanework is conceptually identical to a previously described method for estimating the angular CMD power spectrum from CAIB sky maps (Jewelletal.2001:Wandeltetal.Eriksen 2001).. aud relies heavily on the Cabbs sampling algorithm.," This framework is conceptually identical to a previously described method for estimating the angular CMB power spectrum from CMB sky maps \citep{jewell:2004, wandelt:2004, eriksen:2004}, and relies heavily on the Gibbs sampling algorithm."179 The single imnost iuportaut advantage of this method over existing colpetitors iu the literature derives from the conditional nature of the Cübbs sampler: Additional xusnueters nav be introduced mto the algorithin., The single most important advantage of this method over existing competitors in the literature derives from the conditional nature of the Gibbs sampler: Additional parameters may be introduced into the algorithm.180 This allows for scamless marginalization over Nusance parameters. which otherwise may be dificult to iuteerate.," This allows for seamless marginalization over nuisance parameters, which otherwise may be difficult to integrate."181 A second important advantage of the method is the fact that it provides proper uncertainties on all estimated quantities. which at least in principle later may © propagated iuto final estimates of the uncertainties of he CAIB sky map aud augular power spectra.," A second important advantage of the method is the fact that it provides proper uncertainties on all estimated quantities, which at least in principle later may be propagated into final estimates of the uncertainties of the CMB sky map and angular power spectra."182 Iu this paper we implemented support for two ecnueral eatures that are useful for analvsis of realistic data. wuuely constrained realizations aud template sampling.," In this paper we implemented support for two general features that are useful for analysis of realistic data, namely constrained realizations and template sampling."183 The former is useful whenever there are gaps in the data. or instance due to au iustruneutal elitch. or there are stroug localized sources in the skv that may bias the roise estimate: In these cases. the gaps are refilled with a constrained noise realization with the appropriate noise paralucters. such that the full time stream represeuts a proper sample from a Gaussian distribution with a noise covariance matrix. N.," The former is useful whenever there are gaps in the data, for instance due to an instrumental glitch, or there are strong localized sources in the sky that may bias the noise estimate: In these cases, the gaps are refilled with a constrained noise realization with the appropriate noise parameters, such that the full time stream represents a proper sample from a Gaussian distribution with a noise covariance matrix, $\N$."184 Since the time stream uo longer contains gaps. the Toeplitz svaunietzy of the noise covariance matrix is restored. and matrix multiplieatious iav be performed quickly iu Fourier space.," Since the time stream no longer contains gaps, the Toeplitz symmetry of the noise covariance matrix is restored, and matrix multiplications may be performed quickly in Fourier space."185 The secoud operation. template sampling. is also a powerful and versatile technique for mitigating systematic errors.," The second operation, template sampling, is also a powerful and versatile technique for mitigating systematic errors."186 In this paper we mostly focused on data from the QUIET experiment. for which ground pickup from sidelobes is one significant source of systematics (QUIET2011).," In this paper we mostly focused on data from the QUIET experiment, for which ground pickup from sidelobes is one significant source of systematics \citep{quiet:2011}."187. In a future publication we will apply the same method to simulations of the Planck experiment. for which cosmic rav elitches is au inportaut source of systematic errors.," In a future publication we will apply the same method to simulations of the Planck experiment, for which cosmic ray glitches is an important source of systematic errors."188 As detailed ly Planels(2011b).. these cosmic ravs may be modeled iu ternis of a lanited sot of time domain templates. aud the algorithiis presented in this paper should therefore prove useful for mitieating the effects of these elitches. as well as for propagating the corresponding uncertainties iuto the final noise spectrum parameters.," As detailed by \citet{planck_hfi:2011}, these cosmic rays may be modeled in terms of a limited set of time domain templates, and the algorithms presented in this paper should therefore prove useful for mitigating the effects of these glitches, as well as for propagating the corresponding uncertainties into the final noise spectrum parameters."1890.25 at a size of 327.,0.25 at a size of $32^2$.190 This higher uncertainty for smaller maps prevents any significant conclusion from maps spanning less than «30 pixels., This higher uncertainty for smaller maps prevents any significant conclusion from maps spanning less than $\approx 30$ pixels.191 To demonstrate the influence of the edge treatment on the A-variance spectrum of an object with à pronounced size scale we show in Fig., To demonstrate the influence of the edge treatment on the $\Delta$ -variance spectrum of an object with a pronounced size scale we show in Fig.192 5 the spectra computed for the map containing the filled circle with a diameter of 1/8 of the map size., \ref{fig_circleexample} the spectra computed for the map containing the filled circle with a diameter of 1/8 of the map size.193" The peak of the A-variance spectra at 0.11 falls below the circle diameter of 0.125 but slightly above the average distance between two points on the rim of the circle is probably due to the contributions from the ""empty"" environment of the circle at large lags. also resultingstructures."," The peak of the $\Delta$ -variance spectra at 0.11 falls below the circle diameter of 0.125 but slightly above the average distance between two points on the rim of the circle is probably due to the contributions from the “empty” environment of the circle at large lags, also resulting."194. These contributions are dispersed over a relatively wide range of scales corresponding to the different distances to the map boundary in a non-periodic treatment and to the distances to the next circle in a periodic interpretation of this structure., These contributions are dispersed over a relatively wide range of scales corresponding to the different distances to the map boundary in a non-periodic treatment and to the distances to the next circle in a periodic interpretation of this structure.195 As these variations are mainly assigned to lags exceeding the map size in the periodic treatment. the two curves for the periodic treatment show somewhat lower A-variance values within the map than the filter truncation method where the “empty” region is constrained by the map size.," As these variations are mainly assigned to lags exceeding the map size in the periodic treatment, the two curves for the periodic treatment show somewhat lower $\Delta$ -variance values within the map than the filter truncation method where the “empty” region is constrained by the map size."196 Nevertheless. the total differences between A-variance spectra using the different edge treatment methods are relatively small. so that either method seems to be justified for this case.," Nevertheless, the total differences between $\Delta$ -variance spectra using the different edge treatment methods are relatively small, so that either method seems to be justified for this case."197 The concept of weighting the A-variance computation by different filter significance values can be generalised to deal with data. where the data points in a map are as well characterised by a variable data reliability.," The concept of weighting the $\Delta$ -variance computation by different filter significance values can be generalised to deal with data, where the data points in a map are as well characterised by a variable data reliability."198 This applies e.g. to maps where not all points are observed with the same ntegration time so that they show a different noise level., This applies e.g. to maps where not all points are observed with the same integration time so that they show a different noise level.199 The —averse noise RMS ts an indicator for the significance of the mSata at different points., The inverse noise RMS is an indicator for the significance of the data at different points.200 Many other observational effects may lead to a similar variation in the data reliability across the map., Many other observational effects may lead to a similar variation in the data reliability across the map.201 As long as the reliability can be expressed as a significance umber μμ). between O and | all such maps may be analysed within the concept outlined here., As long as the reliability can be expressed as a significance number $w\sub{data}(\vec{r})$ between 0 and 1 all such maps may be analysed within the concept outlined here.202 The same equations as discussed in the filter truncation are to be applied. but the auxiliary weight map η(η) does no longer consist of the values | inside and 0 outside of the original map.," The same equations as discussed in the filter truncation are to be applied, but the auxiliary weight map $w(\vec{\vec{r}})$ does no longer consist of the values 1 inside and 0 outside of the original map."203 It rather contains the significance values waü(r) ranging continuously from 0 to I., It rather contains the significance values $w\sub{data}(\vec{r})$ ranging continuously from 0 to 1.204" The weighting factors in the A-variance computation W,ur) then contain the integrated significance of the filter-convolvec data at each point."," The weighting factors in the $\Delta$ -variance computation $W\sub{{\it l}, tot}(\vec{r})$ then contain the integrated significance of the filter-convolved data at each point."205 With this generalised concept. the A-variance analysis cai be applied to arbitrary two-dimensional data sets.," With this generalised concept, the $\Delta$ -variance analysis can be applied to arbitrary two-dimensional data sets."206" They must be projected onto some regular grid but they do not need to contain regular boundaries as the corresponding ""empty"" gric points only have to be marked with a zero significance.", They must be projected onto some regular grid but they do not need to contain regular boundaries as the corresponding “empty” grid points only have to be marked with a zero significance.207 Varying noise or other changes in the data reliability can be expressec in the significance function Wear) which has to be constructed for each data set., Varying noise or other changes in the data reliability can be expressed in the significance function $w\sub{data}(\vec{r})$ which has to be constructed for each data set.208 The only remaining requirement for the applicability of the A-variance is the sufficiently large spatial dynamic range in the data., The only remaining requirement for the applicability of the $\Delta$ -variance is the sufficiently large spatial dynamic range in the data.209 The criterion of at least 30 pixels in each direction for reasonable error bars of the A-variance spectrum discussed above has to be extended in the case of a low data significance., The criterion of at least 30 pixels in each direction for reasonable error bars of the $\Delta$ -variance spectrum discussed above has to be extended in the case of a low data significance.210 In paper II we will apply the A-variance analysis to observed data with irregular boundaries and a spatially varying significance., In paper II we will apply the $\Delta$ -variance analysis to observed data with irregular boundaries and a spatially varying significance.211 A] examples given above were computed with the fixed filter function of a French hat with a diameter ratio between the annulus and the core v=43., All examples given above were computed with the fixed filter function of a French hat with a diameter ratio between the annulus and the core $v=3$.212 An obvious question is whether we can improve on the A-variance by using a different diameter ratio and/or a different filter function., An obvious question is whether we can improve on the $\Delta$ -variance by using a different diameter ratio and/or a different filter function.213 Due to its discontinuity in the normal space the French hat has high frequency lobes in Fourier space., Due to its discontinuity in the normal space the French hat has high frequency lobes in Fourier space.214 Alternative approaches should use smoother functions in ordinary space to obtain a better confinement in Fourier space., Alternative approaches should use smoother functions in ordinary space to obtain a better confinement in Fourier space.215" As à smooth example we implemented a ""Mexican hat consisting of two Gaussian functions: where / is the size of the filter and v is the diameter ratio between the annulus and the core of the filter as defined in", As a smooth example we implemented a “Mexican hat” consisting of two Gaussian functions: where $l$ is the size of the filter and $v$ is the diameter ratio between the annulus and the core of the filter as defined in216 The remaining numbered sources. except for 13. have positional correspondences with objects in the USNO star catalog.," The remaining numbered sources, except for 13, have positional correspondences with objects in the USNO star catalog."217 Their R and B magnitudes are included in Table |.(RASS):, Their $R$ and $B$ magnitudes are included in Table 1.:218: In addition to the point sources in Table 1. Figs.," In addition to the point sources in Table 1, Figs."219 1 and 3 also show the locations of faint sources from the RASS catalog (Voges et al., 1 and 3 also show the locations of faint sources from the RASS catalog (Voges et al.220 2000) not detected in the pointed PSPC and HRI data., 2000) not detected in the pointed PSPC and HRI data.221 The RASS field covers the entire EGRET error circle. even the areas not covered or detected by the pointed PSPC and HRI data sets.," The RASS field covers the entire EGRET error circle, even the areas not covered or detected by the pointed PSPC and HRI data sets."222 The RASS sources are marked with crosses and listed in Table 2., The RASS sources are marked with crosses and listed in Table 2.223" Except for the source marked ""f"" all the sources in Table 2 are positionally coimeident with objects from the USNO catalog.", Except for the source marked “f” all the sources in Table 2 are positionally coincident with objects from the USNO catalog.224" Source ""g"" was determined to be a dMe star from spectroscopic observation on the MDM 2.4m. We have searched the NRAO/VLA Sky Survey (NVSS) catalog (Condon et al.", Source “g” was determined to be a dMe star from spectroscopic observation on the MDM 2.4m. We have searched the NRAO/VLA Sky Survey (NVSS) catalog (Condon et al.225 1998) for possible 1.4 GHz radio counterparts to the X-ray point sources., 1998) for possible 1.4 GHz radio counterparts to the X-ray point sources.226 There were 111 radio sources in the field of 3EG J162148203 of which only 10 had integrated radio fluxes 7100 mJy., There were 111 radio sources in the field of 3EG J1621+8203 of which only 10 had integrated radio fluxes $> 100$ mJy.227 These are shown in Fig., These are shown in Fig.228 4 and listed in Table 3., 4 and listed in Table 3.229 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."230 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.231 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."232 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."233 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."234 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."235" 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."236 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."237 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"238The 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."239 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."240 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."241 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 $p \sim 0.082/2\pi =0.013$."242" 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)."243 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).244 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."245.. 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.246 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.247" 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."248 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}.249. 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)."250 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.251 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 2003/12/16.252 Both are eenuine FREDs., Both are genuine FREDs.253 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."254 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."255 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.256 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."257 The result comes from BATSE catalog (Paciesasetal.1999) as, The result comes from BATSE catalog \citep{paciesas99} as258particle acceleration.,particle acceleration.259" Finally, in Sec."," Finally, in Sec."260 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)."261 The results are stummarized in Sec., The results are summarized in Sec.262 5., 5.263 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}.264"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."265" 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."266" 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:."267 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)."268" 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."269 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)."270 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."271 Following Ptuskin ct al. (, Following Ptuskin et al. (2722010). 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."273 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."274 3.3., 3.3.275"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."276 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."277 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."278 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."279" 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."280 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.281 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)."282 We adopt two sets of stellar models in this work., We adopt two sets of stellar models in this work.283 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."284 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."285 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."286 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."287 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)."288 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.289" 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.290 The various masses involved in the“tov model” of Sec.," The various masses involved in the ""toy model"" of Sec."291 2.1 and Fi, \ref{sub:Toy} and Fig.292e.d are providedin Table 2 of LCO6 aux are displaved in Fig.2. left)," \ref{Fig:SNStruct}293 are provided in Table 2 of LC06 and are displayed in Fig.\ref{Fig:SNmasses} )"294 of this work. whereas derived quantities are displaved in Fig.," of this work, whereas derived quantities are displayed in Fig."295 2. left)., \ref{Fig:SNmasses} ).296 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.297 Stars with L30M hhave i Wir," Stars with $>$ 30 have $>$ ,"298 Stars with L30M hhave i Wire," Stars with $>$ 30 have $>$ ,"299 Stars with L30M hhave i WireM," Stars with $>$ 30 have $>$ ,"300 Stars with L30M hhave i WireMg," Stars with $>$ 30 have $>$ ,"301 Stars with L30M hhave i WireMg.," Stars with $>$ 30 have $>$ ,"302reanalyse 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."303 This result is confirmed in Peng et al. (, This result is confirmed in Peng et al. (304Q006b). 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."305 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."306 In Fig., In Fig.307 5 (adapted from Miley De Breuck 2008 following, 5 (adapted from Miley De Breuck 2008 following30810960 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}."309". 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.310 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}311 inversion under the assumption of Milne-Eddington (ME) atmosphere \citep{lando82,skum87}."312. 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."313 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.314 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.315 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."316 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.317 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}."318.. 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.319 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.320 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."321 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.322" 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."323 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 in324"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."325 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."326" 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."327 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."328 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."329 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."330 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}."331 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.)"332 are unable to generate the observed lux (Strongetal.2005:Porterc," are unable to generate the observed flux \citep{strong, portt}."333t2008).. 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.334 Llowever. it is observed. not only in the direction of the GC.," However, it is observed not only in the direction of the GC."335 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.336 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.337 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 $\la3385^\circ$ ), absolutely the same excess in other parts of the disk remains unexplained \citep[see][]{sizun,chern1}."339". ""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."340 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.341 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.342 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."343 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."344" 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}.345. 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}."346. 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 for347detail][]{haya}."348. 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.349 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."350 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."351 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}."352. 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.353 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."354 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}355 we shall show that the condition of non-stationarity is also required to fit radio observations."356 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."357 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.358 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.359 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 $\geq 10^4$ $^{-3}$."360 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."361 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 $^{-3}$.362" 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.363 Phe plasma density was estimated in limits 0.1.0.2 *., The plasma density was estimated in limits $0.1-0.2$ $^{-3}$.364 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.365 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.366 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}) )."367 Itaclio observations of the central regions show that the structure of, Radio observations of the central regions show that the structure of3682006).,.369. 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."370 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."371 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.372 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."373 Section 3. discusses the practical limitations to achieving high-precision timing., Section \ref{practice} discusses the practical limitations to achieving high-precision timing.374 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.375 These should be read and understood by everyone., These should be read and understood by everyone.376 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."377 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)."378 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."379 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."380 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."381 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}."382. This article should be equally applicable in such cases., This article should be equally applicable in such cases.383 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."384" 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."385 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}."386 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."387 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 $\Delta_{C}$.388 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."389 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."390 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."391 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."392 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.393 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."394 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.395 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."396 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.397 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 $\delta$ ),"398According 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."399 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.400" ""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."401 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}."402. 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."403 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}404 and \cite{cru05,cru06} a cold non-Gaussian spot of unknown origin was detected and studied by using the Spherical Mexican Hat Wavelet."405 Non-Caussian signatures have also been found by using dillerent methods:, Non-Gaussian signatures have also been found by using different methods:406eravothermal contraction makes the iuner regions of clusters rouuder as they evolve.,gravothermal contraction makes the inner regions of clusters rounder as they evolve.407 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."408 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."409 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.410 Mergers night produc! highly flattenvcd clusters., Mergers might produce highly flattened clusters.411 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."412 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."413 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."414 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.415" 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.416 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.417 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.418" 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."419 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 1.420 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.421 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).422" 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.423" 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."424 It suffers heavy absorption along its castern edee (van den Bergh 1982a)., It suffers heavy absorption along its eastern edge (van den Bergh 1982a).425 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."426" 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."427 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.428 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.429 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."430" 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."431 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.432 This conclusion strenetlens aud coufiruis, This conclusion strengthens and confirms433The 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.434" 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 $2\eforced$."435" 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."436" 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 $i_N$."437 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.438" 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."439" 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 $e_N$."440 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.441 Fig., Fig.442 8 illustrates the independence of the eccentricity and inclination parameters., \ref{fig:dampboth} illustrates the independence of the eccentricity and inclination parameters.443doown decreasesthe fromx-axis.,own the x-axis.444"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."445" 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 $\delta \equiv \rho/\bar{\rho} = 200$."446" 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."447 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}.448 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.449" 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."450" 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."451" 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."452" Instead, it more closely follows the temperature structure "," Instead, it more closely follows the temperature structure (middle)."453This 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 $\gamma=5/3$ ).454"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."455" 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,456 Clarke:2006aa}."457 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.458 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.459 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.460 These shapes are similar to what is seen in observed radio relics., These shapes are similar to what is seen in observed radio relics.461" 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}."462" 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."463" 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."464" 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."465" 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)."466 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.467 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.468" 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}."469" 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 $\mathrm{log}(P_{1.4GHz}) = \mathrm{A} \mathrm{log}(M_{200}) +470\mathrm{B}$ for all halos with $M_{200} > 10^{13}M_\odot$ and $2\times10^{13}M_\odot$ for the $relic64$ and"471parameters from cosmic shear and galaxy survey data.,parameters from cosmic shear and galaxy survey data.472" 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."473 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.474 This is acceptable given that the surveys do not overlap significantly., This is acceptable given that the surveys do not overlap significantly.475 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.476 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.477 and Eq. [16)), \ref{eq:P_II_halo_general} and Eq. \ref{eq:P_GI_halo_general}) )478 which are projected onto the sky (Eq., which are projected onto the sky (Eq.479 [5] and Eq. [9 , \ref{eq:C_II_fn_of_PEE} and Eq. \ref{eq:C_GI_fn_of_PdgI}) )480and 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}) )481nd the correlation function is calculated by Eq. Bl., and the correlation function is calculated by Eq. \ref{eq:Cl_to_corrfn}.482 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}) )483hich is a inverseHankel transform (Eq. of the [I8)), which is a inverseHankel transform (Eq. \ref{eq:wdeltaplus}) )484relevant IA power spectrum (Eq. , of the relevant IA power spectrum (Eq. \ref{eq:C_GI_fn_of_PdgI}) ).485The 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 $\sigma_8$.486 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.487" 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."488" 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}."489 results are shown in Fig., The results are shown in Fig.490 [ῆ 68% confidence contours Thein og-A parameter space., \ref{fig:Cls_s8_A} as $\%$ confidence contours in $\sigma_8$ $A$ parameter space.491 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).492 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.493" [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."494 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.495" 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 $A$."496" 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."497" 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."498 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.499 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.500 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.501 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.502" 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."503" For the fiducial Qm, Fig."," For the fiducial $\Omega_{\rm m}$, Fig."504 [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.505" This can be understood by examining Fig. D],"," This can be understood by examining Fig. \ref{fig:corrfns_100sqdeg},"506" 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."507 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}.508 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.509" 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."510 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.511" 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."512" 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."513 Indeed we do see the direction reversed in this figure., Indeed we do see the direction reversed in this figure.514" 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."515 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.516 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.517" 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."518" The analysis was repeated, allowing A, 6 and os to vary."," The analysis was repeated, allowing $A$ , $\beta$ and $\sigma_{\rm 8}$ to vary."519 We marginalised over og to produce the results shown, We marginalised over $\sigma_8$ to produce the results shown520suggest 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.521 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.522 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.523 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."524 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.525 ROB acknowledges the support of a SPEC senior fellowship., RGB acknowledges the support of a STFC senior fellowship.526 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.527 AJB acknowledges the support of the Gordon and Betty Moore Foundation., AJB acknowledges the support of the Gordon and Betty Moore Foundation.528 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.529detailed 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."530. 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."531 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."532 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}."533 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}) ).534 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 $\sim5351-3\times10^{32}$ erg $^{-1}$ \cite{bsc96}) ), corresponding to an unabsorbed flux density (0.3–10.0 keV) $f_x \sim536(0.4-4)\times10^{-13}$ erg $^{-2}$ $^{-1}$ for a photometric distance in the range 2.5–4.6 kpc \cite{shmc83}; \cite{are91}) )."537 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.538 What features 1—4 represent is not immediately clear., What features 1–4 represent is not immediately clear.539" 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."540" 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. “"541"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}) )."542 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}) )."543 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}) )."544 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}) ).545 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."546". 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 $r_{\rm knot} \approx 4'' =5470.1$ pc."548 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}) )."549 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."550 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."551 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."552" 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}$$_{\rm knot} = 5530.13(\varepsilon/B_{\rm knot}^3)^{1/2}$ pc."554" Adopting Rin~0.05 pe and s25 keV. we can infer Bia~3 μα. We computedin iv! f refsecyisc.nergythattherateo pairproductioninthe pulsarwindisN,zzÀ«1076 s!."," Adopting $\mathcal{R}$$_{\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 $\dot{N}_\pm \approx5554\times10^{36}$ $^{-1}$."556" 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 $\gamma_1 = 2.6 \times10^6$.557 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. ("558We 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.)"559 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<I (at the termination shock) to occur at r«rij (Coroniti1990:; 1994:: Melatos. private communication).," This low value of $\sigma$ is consistent with the various models for energy transport in the unshocked wind, which generally require the transition from $\sigma \gg 1$ (at the light cylinder) to $\sigma \ll 1$ (at the termination shock) to occur at $r \ll560r_{\rm knot}$ \cite{cor90}; \cite{mic94}; Melatos, private communication)."561 Itis interesting to note that ini the large-amplitude plasma wave model proposed by Melatos (1998). the wind beyond this transition point evolves as aX77.," It is interesting to note that in the large-amplitude plasma wave model proposed by Melatos \nocite{mel98}) ), the wind beyond this transition point evolves as $\sigma \propto r^2$."562 We thus expect σ for feature | to be 20 times smaller than that inferred at the termination shock. a result not inconsistent with our calculations.," We thus expect $\sigma$ for feature 1 to be $\sim$ 20 times smaller than that inferred at the termination shock, a result not inconsistent with our calculations."563 A better insight into the nature of these compact features will require observations of this system at multiple epochs and at longer wavelengths ΠΠ the near-infrared)., A better insight into the nature of these compact features will require observations of this system at multiple epochs and at longer wavelengths in the near-infrared).564 With such data. we will be better able to determine the broadband spectrum and hence total energetics of these sources. can establish whether these features are persistent or transient. and can determine whether any of these sources shows outward proper motion which could associate them directly with outflow from the pulsar.," With such data, we will be better able to determine the broadband spectrum and hence total energetics of these sources, can establish whether these features are persistent or transient, and can determine whether any of these sources shows outward proper motion which could associate them directly with outflow from the pulsar."565 Indeed. hhas identified significant changes in the positions and brightnesses of small-scale structure in the Vela PWN on a time-scale of seven months (Pavlovetal. 2001))," Indeed, has identified significant changes in the positions and brightnesses of small-scale structure in the Vela PWN on a time-scale of seven months \cite{pksg01}) )."566 Our oobservations have confirmed that PSR linteracts with its surroundings in a spectacular and highly anisotropic fashion., Our observations have confirmed that PSR interacts with its surroundings in a spectacular and highly anisotropic fashion.567 Our main results are as follows:, Our main results are as follows:568Recent developments. in. ssengeer observational techniques often make it desirable to calculate the angular clistribution of a dilluse ux expected from sources with a given spatial distribution.,Recent developments in ger observational techniques often make it desirable to calculate the angular distribution of a diffuse flux expected from sources with a given spatial distribution.569 The predicted. Dux. distribution may then be usec for source identification. estimation of the background. etc.," The predicted flux distribution may then be used for source identification, estimation of the background, etc."570 Necessity for. such a calculation arises in the context of ultra-high. energy. cosmic ravs (ULlECTis). neutrino physics. as well as ganima-ray astrononi.," Necessity for such a calculation arises in the context of ultra-high energy cosmic rays (UHECRs), neutrino physics, as well as gamma-ray astronomy."571 lf. the. sources are extragalactic. their space distribution can be derived. from the matter distribution in the Universe.," If the sources are extragalactic, their space distribution can be derived from the matter distribution in the Universe."572" The. latter can be inferred. from. galaxy surveys. e.g. οον, "," The latter can be inferred from galaxy surveys, e.g. \citet{2008ApJS..175..297A, 2006AJ....131.1163S, 2005PASA...22..277J}."573Good. distance determination is required to reconstruct the spatial mass cistribution., Good distance determination is required to reconstruct the spatial mass distribution.574 Special techniques have been developed to minimize the impact of distance errors ancl to suppress the short-scale noise (sec. e... ? and references therein).," Special techniques have been developed to minimize the impact of distance errors and to suppress the short-scale noise (see, e.g., \citet{Erdogdu:2006nd}575 and references therein)."576 The problem of tus caleulation has a number of features that make it) different from (ancl easier than) reconstruction of the full three-dimensional mass distribution: only a two-dimensional projection of the three-dimensional distribution. is needed: contributions of remote sources are suppressed. by the ecometrical factor 7 and. in many cases. by the flux attenuation due to interactions with the ambient matter: the smaller amplitude of inhomogeneities at. larger scales makes the contribution of remote sources essentially isotropic: only the overall normalization of such an isotropic part has to be caleulated.," The problem of flux calculation has a number of features that make it different from (and easier than) reconstruction of the full three-dimensional mass distribution: only a two-dimensional projection of the three-dimensional distribution is needed; contributions of remote sources are suppressed by the geometrical factor $r^{-2}$ and, in many cases, by the flux attenuation due to interactions with the ambient matter; the smaller amplitude of inhomogeneities at larger scales makes the contribution of remote sources essentially isotropic; only the overall normalization of such an isotropic part has to be calculated."577 Phese simplifications result in weaker requirements on the quantity and quality of astronomical data in [lux calculations. which makes it advantageous to by-pass the reconstruction of matter density ane caleulate the Dux distribution directly. [rom he galaxv catalogs.," These simplifications result in weaker requirements on the quantity and quality of astronomical data in flux calculations, which makes it advantageous to by-pass the reconstruction of matter density and calculate the flux distribution directly from the galaxy catalogs."578 Accurate results may. be achieved with substantially smaller input., Accurate results may be achieved with substantially smaller input.579 oth. in the context of mass distribution and in lux calculations. a crucial requirement. is completeness of the underlving galaxy catalog.," Both in the context of mass distribution and in flux calculations, a crucial requirement is completeness of the underlying galaxy catalog."580 That is. a volume-imited sample is needed: which includes all galaxies of a certain kind within a given. volume.," That is, a volume-limited sample is needed which includes all galaxies of a certain kind within a given volume."581 On the contrary. a natural product. of an astronomical survey is a [LIux-imited sample that contains all galaxies up to certain magnitude as set by the instrumental sensitivity and observation time.," On the contrary, a natural product of an astronomical survey is a flux-limited sample that contains all galaxies up to certain magnitude as set by the instrumental sensitivity and observation time."582 Volume-limitecd samples may. be obtained. from a flus-limitecl sample by cutting away objects that are further than a given distance and cdimmoer than a certain magnitude. chosen in such a manner that the resulting sample is complete.," Volume-limited samples may be obtained from a flux-limited sample by cutting away objects that are further than a given distance and dimmer than a certain magnitude, chosen in such a manner that the resulting sample is complete."583 ‘To model adequately the source distribution in the Universe. one requires a galaxy catalog that extencds to sulliciently large. distance (large enough that the," To model adequately the source distribution in the Universe, one requires a galaxy catalog that extends to sufficiently large distance (large enough that the"584 The current favored model for Type Ia superuovae (SNIa) involves burning beginning as a subsonic deflagration near the ceutral region of a Chnaudrasekliarauass white dwarf., The current favored model for Type Ia supernovae (SNIa) involves burning beginning as a subsonic deflagration near the central region of a Chandrasekhar-mass white dwarf.585 Progress has been made in receut vears in understanding the micdle stages of these events through niultiscale reactive flow simulations where the initial burning is prescribed as an initial condition of one or more sizable bubbles already burning material at time zero., Progress has been made in recent years in understanding the middle stages of these events through multiscale reactive flow simulations where the initial burning is prescribed as an initial condition of one or more sizable bubbles already burning material at time zero.586 However. the initial ignition process by which such bubbles beein burning whether enormous 50 kan bubbles (72). or more plivsically motivated smaller igniting points (7???) remains poorly uuderstood.," However, the initial ignition process by which such bubbles begin burning – whether enormous 50 km bubbles \citep{pcl} or more physically motivated smaller igniting points \citep{mpa02,hoeflichstein02,barcelona03} remains poorly understood."587 Further. if later in the evolution there is a transition to a detonation (6.9...2). this iguitfion process. too. must be explained.," Further, if later in the evolution there is a transition to a detonation \citep[\eg{}, this ignition process, too, must be explained."588 Indeed. iguitiou physics will plav a role by determining the location. ummber. aud sizes of the first buruiug points in auv currently viable SNIa model.," Indeed, ignition physics will play a role — by determining the location, number, and sizes of the first burning points — in any currently viable SNIa model."589 However. uutil very receutlv ναν little work has eone iuto examining the iguitiou phlivysics of these eveuts.," However, until very recently \citep[for590example,][]{woosley04,barcelona05} very little work has gone into examining the ignition physics of these events."591 Hore we begeiu examining the ignition process by considering the simplest ieuitious possible — that of a sinele zone — and the possibility of igniting a detonation from a Sedov blast wave lanuched at a single point., Here we begin examining the ignition process by considering the simplest ignitions possible – that of a single zone – and the possibility of igniting a detonation from a Sedov blast wave launched at a single point.592 Astrophysical combustion. like* nost. combustion (forexample.77)... is highly teiiperature-depoenudent: the 5 12€ | 5 10ο reaction.. for. examyde. scales as Tt? near LO? K. Rates for the exothermic reactions which define the burning process are generally expoucutial or uear-expoucutial in temperature (e.g...2).," Astrophysical combustion, like most combustion \citep[for593 example,][]{williams,glassman96}, is highly temperature-dependent; the $^{12}$ C + $^{12}$ C reaction, for example, scales as $T^{12}$ near $^{9}$ K. Rates for the exothermic reactions which define the burning process are generally exponential or near-exponential in temperature \citep[\eg{},."594 Thus a region with a positive temperature perturbation can sit “simmucrine’ for a verv loug time. iuitiallv ouly very slowly consuming fuel aud increasing its teniperature as au expoucutial runaway occurs.," Thus a region with a positive temperature perturbation can sit `simmering' for a very long time, initially only very slowly consuming fuel and increasing its temperature as an exponential runaway occurs."595 This is expecially true in the clectron-degenerate environment of a white chwarf. where the small iucreases in temperature that occur for most of the evolution of he hotspot will have ouly extremely siall bydrodvuamic effects.," This is especially true in the electron-degenerate environment of a white dwarf, where the small increases in temperature that occur for most of the evolution of the hotspot will have only extremely small hydrodynamic effects."596 If fuel depletion aud hvdrodyιασα. effects were ignored. the teuperature of the spot would become infinite after a finite period of time.," If fuel depletion and hydrodynamical effects were ignored, the temperature of the spot would become infinite after a finite period of time."597 This time is called the iguitionoO time. or ignitionOo delay time. or sometinics induction time. rz.," This time is called the ignition time, or ignition delay time, or sometimes induction time, $\tau_i$."598 After ignition sarts. burning proceeds for some leneth of time 75.," After ignition starts, burning proceeds for some length of time $\tau_b$."599 For burning problems of interest. of course. fuel depletion is important. aud no quantities become ifiuite: however. the idea of an ignition deav time still holds (see Fig. 1)).," For burning problems of interest, of course, fuel depletion is important, and no quantities become infinite; however, the idea of an ignition delay time still holds (see Fig. \ref{fig:ignitiondelay}) )."600 If the energy release rate for most of the evolution of the burning is too small to have significant lbydrodvuamical effects. aud if the timescale over which burning “suddenly turus om is mach shorter than aux other bydrocdvuamucal or conductive timescales. then the burning of such a hotspot can be treated. as an excellent approximation. as a step function where," If the energy release rate for most of the evolution of the burning is too small to have significant hydrodynamical effects, and if the timescale over which burning `suddenly turns on' is much shorter than any other hydrodynamical or conductive timescales, then the burning of such a hotspot can be treated, as an excellent approximation, as a step function where"601This may indicate an even higher overall metallicity and/or that a non-solar C-to-O ralio is required.,This may indicate an even higher overall metallicity and/or that a non-solar C-to-O ratio is required.602 A broader exploration of the possible metal abundances for all four planets will be left to a future paper., A broader exploration of the possible metal abundances for all four planets will be left to a future paper.603 In (his letter. we have estimated [or the first tme Che M-band. fluxes of three of the currently four known planets.," In this letter, we have estimated for the first time the M-band fluxes of three of the currently four known planets."604 These detections were made possible due io (he use of an innovative LOCI-based background. subtraction routine that has allowed for a [actor of 3 gain in contrast (factor of 9 in integration time) compared Lo a classical background subtraction using a median., These detections were made possible due to the use of an innovative LOCI-based background subtraction routine that has allowed for a factor of $3$ gain in contrast (factor of $9$ in integration time) compared to a classical background subtraction using a median.605 This new background subtraction routine can be used to subtract the background noise in anv intrared data., This new background subtraction routine can be used to subtract the background noise in any infrared data.606 We have detected8799b.. c and d al δα from 3 to 86.," We have detected, c and d at M-band from 3 to $\sigma$."607 From a IX-L/ and L-M' color diagram. we confirm that the three planets ave located near the end οἱ the L-tvpe sequence. close to (he L- and T-dwarl transition region.," From a K'-L' and L'-M' color diagram, we confirm that the three planets are located near the end of the L-type sequence, close to the L- and T-dwarf transition region."608 We then derived new aü(mosphere model fits for the three planets., We then derived new atmosphere model fits for the three planets.609 For planets ¢ and d. temperatures and surface eravilies are close (o the expected values [rom evolutionary moclels.," For planets c and d, temperatures and surface gravities are close to the expected values from evolutionary models."610 For planet b. the solar abundance mocel fits well the broad band photometry from 1 to 5yon but it requires a very small planetary radius to mate the bolometric mninositv and is thus in contradiction wilh the planet evolution models.," For planet b, the solar abundance model fits well the broad band photometry from $1$ to $5\,\mu$ m but it requires a very small planetary radius to match the bolometric luminosity and is thus in contradiction with the planet evolution models."611 The nelal rich evolution-consistent moclel over-predicts the M-band flux. which max indicate an even higher overall metallicity and/or a non-solar C-to-O ratio.," The metal rich evolution-consistent model over-predicts the M-band flux, which may indicate an even higher overall metallicity and/or a non-solar C-to-O ratio."612 Higher SNR images will help disentangle (he different physical and chemical parameters., Higher SNR images will help disentangle the different physical and chemical parameters.613" The authors wish to thank ο, Leggett for kindly providing the Fig.", The authors wish to thank S. Leggett for kindly providing the Fig.614 3. Ποιά brown cwarf data., \ref{fig : f3} field brown dwarf data.615 Portions of this work performed under (he auspices of the U.S. Depart(inent of Energy by Lawrence Livermore National Laboratory under Contract. DE-ACS52-07NA21344., Portions of this work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.616 The dala presented herein were obtained at the WAL heck Observatory. which is operated as a scientific partnership amone the California Institute of Technology. the University of California and the National Aeronautics ancl Space Administvation.," The data presented herein were obtained at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration."617 The Observatory was made possible by the generous financial support oL the W.M. Ixeck Foundation., The Observatory was made possible by the generous financial support of the W.M. Keck Foundation.618 The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maia hea has always had within the indigenous Hawaiian community., The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community.619 We are most lortunate to have the opportunity to conduct observations [rom this mountain., We are most fortunate to have the opportunity to conduct observations from this mountain.620Iu principle we should be measuring spin-down values at the stellar surface. but there is uncertainty in the stelay iieasurement due to stai-steppiig at the spherical Ίππο boundary on our Cartesia1 eid.,"In principle we should be measuring spin-down values at the stellar surface, but there is uncertainty in the stellar spin-down measurement due to stair-stepping at the spherical inner boundary on our Cartesian grid."621 To avoid this issuc. we ucasure spin-down at the helt evliuder.," To avoid this issue, we measure spin-down at the light cylinder."622 Dissipation of Povuting Hux inside the light exlinder artificially suppresses our spin-down estimates lueastred at the lieht cvlinder. though.," Dissipation of Poynting flux inside the light cylinder artificially suppresses our spin-down estimates measured at the light cylinder, though."623 We quautifv these uncertainties by computing the spin-down values measured both ou the star aud at the light exlinder., We quantify these uncertainties by computing the force-free spin-down values measured both on the star and at the light cylinder.624 T‘he true force-free spin-down Iuinosity ikelv falls within the shaded erev region in Fig., The true force-free spin-down luminosity likely falls within the shaded grey region in Fig.625" 2 bounded by the stellar aux| πο exliuder spin-down values,", \ref{dipole} bounded by the stellar and light cylinder spin-down values.626 There is also a cleviation frou f1ο vacuum Deutsch solution for our zero conducivity solution (compare dashed line to (0/Q)?=0 line)., There is also a deviation from the vacuum Deutsch solution for our zero conductivity solution (compare dashed line to $(\sigma/\Omega)^2=0$ line).627 This difference is due to our boundary conditions at the star., This difference is due to our boundary conditions at the star.628 The sinoothiung of the fic‘lds across he stair-stepped boundary leads to small charge bleed-off from the inside of he star to the outside., The smoothing of the fields across the stair-stepped boundary leads to small charge bleed-off from the inside of the star to the outside.629 The first term in equation (3)) is then uot identically zero just outside the star even in the 6=0 case., The first term in equation \ref{current}) ) is then not identically zero just outside the star even in the $\sigma=0$ case.630 This ummerical artifact docs not affect the solutions with hieh conductivity when the plivsical current exceeds the mmumerical smoothing current. but low (0/97D=LsE10? Bocit can influenceB the felda structure and sleltly. modifyIq the spin-down+ power.," This numerical artifact does not affect the solutions with high conductivity when the physical current exceeds the numerical smoothing current, but below $(\sigma/\Omega)^2=4\times10^{-3}$ it can influence the field structure and slightly modify the spin-down power."631 To better understand these nuuerical issues it is helpful to look at the run «of Povuting flux with radius., To better understand these numerical issues it is helpful to look at the run of Poynting flux with radius.632 In Fig., In Fig.633 D6 we show the Povuting flux inteerated over spherical shells of varving radii for force-free. vacuum and a range of resistive solutions with a=607.," \ref{poynt} we show the Poynting flux integrated over spherical shells of varying radii for force-free, vacuum and a range of resistive solutions with $\alpha =63460^\circ$."635 The results are normalized to the force-free value a he star. located at R.=O.375Ree. aud we show the run of Povutiug fux with spherical radius out to 2.25Rpe.," The results are normalized to the force-free value at the star, located at $R_*=0.375R_{LC}$, and we show the run of Poynting flux with spherical radius out to $2.25R_{LC}$."636 The vacuum and (0/0)=0 curves are flat. iudicatiug neselieibleOo dissipation of Povutiue flux with increasing radius. nut there is an offset between he curves that we attributeC» to our imperfect immer boundary.," The vacuum and $(\sigma/\Omega)^2=0$ curves are flat, indicating negligible dissipation of Poynting flux with increasing radius, but there is an offset between the curves that we attribute to our imperfect inner boundary."637 Force-free is in. priuciple dissipationless aud should have the ru f Povutiug flux flat with raditSS, Force-free is in principle dissipationless and should have the run of Poynting flux flat with radius.638 As was argued above. our method for cleuune parallel electric feld iu force-free sinulations is resistive and causes Povuting fux to slope dowuwards with iicreasine radius.," As was argued above, our method for cleaning parallel electric field in force-free simulations is resistive and causes Poynting flux to slope downwards with increasing radius."639 Inside the ligl cvliuder. the drop is due to artificial volume j:E dissipation above the polar caps.," Inside the light cylinder, the drop is due to artificial volume $\vec{j}\cdot\vec{E}$ dissipation above the polar caps."640 This dissipation varies with nmuagnetic inclination angle aud is respousibe for the varving width of the exav eror leid with anele for force-free xdutious nu Fie. 2.., This dissipation varies with magnetic inclination angle and is responsible for the varying width of the gray error band with angle for force-free solutions in Fig. \ref{dipole}.641 Outside the Iight οντικer. the drop in Povutiug flux is due to it disappearing iuto the current shees.," Outside the light cylinder, the drop in Poynting flux is due to it disappearing into the current sheets."642 BG 2 , \ref{poynt} \ref{dipole} 643On the other hand. from the observational side. we now have many candidates of dense structures al various scales.,"On the other hand, from the observational side, we now have many candidates of dense structures at various scales."644 The most massive example is a huge dark matter distribution ol the cluster of galaxies. AIGS9. reported recently by Broadhurstetal.(2005a.b).," The most massive example is a huge dark matter distribution of the cluster of galaxies, A1689, reported recently by \citet{TB05a,TB05b}."645. They obtained the mass column density distribution of the cluster of galaxies. 1689 by gravitational lensing.," They obtained the mass column density distribution of the cluster of galaxies, A1689 by gravitational lensing."646 The column density. profile has a fIat-top ancl we suspected Chat this f[Iat-top nature might be due to the degeneracy pressure of fermions., The column density profile has a flat-top and we suspected that this flat-top nature might be due to the degeneracy pressure of fermions.647 We derive a volume density profile from the observed column density profile assuming spherical symmetry and compare the observed 3D encircled mass profile with our model profile of an FEDES., We derive a volume density profile from the observed column density profile assuming spherical symmetry and compare the observed 3D encircled mass profile with our model profile of an FDFS.648 The condense structure made from the fully degenerate fermion is not restricted to a center of a cluster of galaxies., The condense structure made from the fully degenerate fermion is not restricted to a center of a cluster of galaxies.649 If we consider more massive neutrinos. such as sterile neutrinos. (he similar structures are realized in scaled-down form as in Eq.(1)).," If we consider more massive neutrinos, such as sterile neutrinos, the similar structures are realized in scaled-down form as in \ref{Mfermi}) )."650 If this structure is universal. we will find groups of black holes which have (typical masses directly. characterized by fermion masses.," If this structure is universal, we will find groups of black holes which have typical masses directly characterized by fermion masses."651 The paper is organized as follows., The paper is organized as follows.652 The formalism by Oppenheimer&Volkoll(1939). is introduced and equilibrium solutions are discussed in 822., The formalism by \citet{OV39} is introduced and equilibrium solutions are discussed in 2.653 Reaclers who are not interested in (he derivation of the solutions. are advised to skip to 822.3 where the properties of the solutions are discussed.," Readers who are not interested in the derivation of the solutions, are advised to skip to 2.3 where the properties of the solutions are discussed."654" The application of a nonrelativistic FDES to the cluster of galaxies Α1050, is discussed in 833."," The application of a nonrelativistic FDFS to the cluster of galaxies A1689, is discussed in 3."655 The possible relation between the mass hierarchies of black holes and sterile neutrinos are considered in 844., The possible relation between the mass hierarchies of black holes and sterile neutrinos are considered in 4.656 llere we review the derivation of the general relativistic equilibrium equations following Tolman(1934). ancl Oppenheimer&Volkolf(1939)., Here we review the derivation of the general relativistic equilibrium equations following \citet{RT34} and \citet{OV39}.657. The most general static line element exhibiting spherical sviumetry may be expressed in the form If the matter supports no traverse stresses and has no mass motion. then ils enerev momentum tenor is given by," The most general static line element exhibiting spherical symmetry may be expressed in the form If the matter supports no traverse stresses and has no mass motion, then its energy momentum tenor is given by"658nucleus towards the west side of the image and continues to wrap around the nucleus until it closes in a ring.,nucleus towards the west side of the image and continues to wrap around the nucleus until it closes in a ring.659 This ring appears more continuous and. broader in the northern part than in the south where it looks patchy., This ring appears more continuous and broader in the northern part than in the south where it looks patchy.660 Phe feature seen in our NIR colour index map cannot be an artifact of combining two images with slightly dillerent spatial resolution. because such an artifact would show up as a complete ring. whereas the observed. red. feature is not at constant galactocentric racius.," The feature seen in our NIR colour index map cannot be an artifact of combining two images with slightly different spatial resolution, because such an artifact would show up as a complete ring, whereas the observed red feature is not at constant galactocentric radius."661" Pogee (1989a) saw an incomplete nuclear ring in eemission with a number of distinct ""hot spots"".", Pogge (1989a) saw an incomplete nuclear ring in emission with a number of distinct “hot spots”.662 TheHST' H-band image resolves the nuclear ring into a series of tightly wound. spiral armlets. outlined. in dust and stellar populations.," The $H$ -band image resolves the nuclear ring into a series of tightly wound spiral armlets, outlined in dust and stellar populations."663 The ring region is of a relatively low amplitude compared to the central bulge component. in contrast to nuclear rings in other objects. e.g. NGC 3351. as can be observed in Fig.," The ring region is of a relatively low amplitude compared to the central bulge component, in contrast to nuclear rings in other objects, e.g. NGC 3351, as can be observed in Fig."664 1., 1.665 The location of the ring corresponds to a bump in all racial profiles (1.0.. surface brightness. colour. cllipticity and position angle).," The location of the ring corresponds to a bump in all radial profiles (i.e., surface brightness, colour, ellipticity and position angle)."666 Phe JA colour of the ring is redder by 0.1. magnitudes than the background., The $J-K$ colour of the ring is redder by 0.1 magnitudes than the background.667 No isophotal twists are seen in the ellipticity and position angle profiles or in the contour map of the A-band image., No isophotal twists are seen in the ellipticity and position angle profiles or in the contour map of the $K$ -band image.668 Thus we confirm that there is no evidence for a nuclear bar (Regan Elmegreen 1991)., Thus we confirm that there is no evidence for a nuclear bar (Regan Elmegreen 1997).669 We find very well-defined mini-spiral structure in the central region of this galaxy. (Fig., We find very well-defined mini-spiral structure in the central region of this galaxy (Fig.670 2b)., 2b).671 Revnaud Downes (1997: see also Revnaucl Downes 1998. 1999) sugeest that the molecular gas distribution in the central 5 kpe of this galaxy is concentrated along are-like shock features.," Reynaud Downes (1997; see also Reynaud Downes 1998, 1999) suggest that the molecular gas distribution in the central 5 kpc of this galaxy is concentrated along arc-like shock features."672 Our JA image shows that these ares are part of a well-defined nuclear spiral structure., Our $J-K$ image shows that these arcs are part of a well-defined nuclear spiral structure.673 Furthermore. Revnaucd Downes suggest. that a patchy molecular ring may lic inside these shock fronts. possibly connected to them.," Furthermore, Reynaud Downes suggest that a patchy molecular ring may lie inside these shock fronts, possibly connected to them."674 Fig., Fig.675 2b reveals that the spiral structure forms a pseudoring around the nucleus., 2b reveals that the spiral structure forms a pseudoring around the nucleus.676 Leven the broad-band image shows considerable structure in the CNR., Even the broad-band image shows considerable structure in the CNR.677 No isophote twists can be seen in the position angle plot., No isophote twists can be seen in the position angle plot.678 Distinct regions. presumably of enhanced SE. can be noticed along the mini-spiral in the broacd-bancl NLR images.," Distinct regions, presumably of enhanced SF, can be noticed along the mini-spiral in the broad-band NIR images."679 These regions coincide in position with the dark (red) lanes seen to outline the mini-spiral in the Jdv image., These regions coincide in position with the dark (red) lanes seen to outline the mini-spiral in the $J-K$ image.680 This implies that the mini-spiral in J.—-A is not necessarily a dust spiral (as would have been tempting to conclude from the colour index image alone) but mav well be delineated by either emission [rom voung stars (e.g. red supergiants). or from hot dust.," This implies that the mini-spiral in $J-K$ is not necessarily a dust spiral (as would have been tempting to conclude from the colour index image alone) but may well be delineated by either emission from young stars (e.g. red supergiants), or from hot dust."681 We conclude that we see a minisxral in the NLR. outlines by emission from SE and dust.," We conclude that we see a mini-spiral in the NIR, outlined by emission from SF and dust."682 This mini-spiral is well trace also on theHST H-band image (Fig., This mini-spiral is well traced also on the $H$ -band image (Fig.683 1) as a collection of distinct. Luminous regions outlining the armlets. which are accompanied by clust lanes.," 1) as a collection of distinct luminous regions outlining the armlets, which are accompanied by dust lanes."684 Like in the case of NGC 1300. a bump in the raclia profiles is visible at the location of the ring.," Like in the case of NGC 1300, a bump in the radial profiles is visible at the location of the ring."685 Phe JA colour of the ring is 0.05 magnitudes redder than the backerounc colour., The $J-K$ colour of the ring is 0.05 magnitudes redder than the background colour.686 No pronounced change of slope is detected in. the IH -band surface brightness profile. which overall decreases more smoothly than in the other galaxies discussed here.," No pronounced change of slope is detected in the $H$ -band surface brightness profile, which overall decreases more smoothly than in the other galaxies discussed here."687 Fig., Fig.688 2e shows several peaks of SE in the ΝΑ. of this starburst galaxy. which. as expected. are resolved in much more detail in theZ57 NICMOS image we obtained [rom the£57 archive (Fig.," 2c shows several peaks of SF in the CNR of this starburst galaxy, which, as expected, are resolved in much more detail in the NICMOS image we obtained from the archive (Fig."689 1)., 1).690 These peculiar “hot spots’ in the nuclear region have been identified and described in cilferent ways by various authors., These peculiar `hot spots' in the nuclear region have been identified and described in different ways by various authors.691" Marcelin. Boulesteix CGoeorgelin (1983) found six ""hot spots’ forming a linear μαructure that crosses the central region."," Marcelin, Boulesteix Georgelin (1983) found six `hot spots' forming a linear structure that crosses the central region."692 A later study in --=irarecd and radio by WynnWilliams Becklin (1985) showed that bursts of SE were not confined to the visible hot μα»ots., A later study in infrared and radio by Wynn–Williams Becklin (1985) showed that bursts of SF were not confined to the visible hot spots.693 Simons et al. (, Simons et al. (694LOSS) noticed the presence of organized dust structure in the CNR. using NI and optical imaging.,1988) noticed the presence of organized dust structure in the CNR using NIR and optical imaging.695 We see patches of dust. in our images. but. no coherent structure.," We see patches of dust in our images, but no coherent structure."696 ltegan Elmeereen (1997) found that this galaxy has an isophotal twist. using a {ραπ image of the inner bar region. although the results from an earlier. study. by Elmeercen et al. (," Regan Elmegreen (1997) found that this galaxy has an isophotal twist, using a $K$ -band image of the inner bar region, although the results from an earlier study by Elmegreen et al. ("6971996) were ambiguous.,1996) were ambiguous.698 Similar twists have been interpreted as nuclear bars or triaxial structures (e.g. Shaw et al.," Similar twists have been interpreted as nuclear bars or triaxial structures (e.g., Shaw et al."699 1995: Eriedli Alartinet 1993: Wozniak οἱ al., 1995; Friedli Martinet 1993; Wozniak et al.700 1995)., 1995).701 However. our images show such an abundance of structure that it is hard to imagine that the measured changes in the radial behaviour of ellipticitv or PA would have any significance in this respect.," However, our images show such an abundance of structure that it is hard to imagine that the measured changes in the radial behaviour of ellipticity or PA would have any significance in this respect."702 For that reason. we set the ellipticity and the PA to fixed values corresponding," For that reason, we set the ellipticity and the PA to fixed values corresponding"703oblique shock.,oblique shock.704 By svunuetiy the results for azimuthal angeles 2257. 2707. and 315° are identical to results for 1357. 907. and 15? respectively. except that the different angles sample different projections of the random field component. aud so the differences in cimergeut radiation for the three pairs of ruus provide insight iuto variatious to be expected from differeut realizations.," By symmetry the results for azimuthal angles $225\arcdeg$ , $270\arcdeg$ , and $315\arcdeg$ are identical to results for $135\arcdeg$, $90\arcdeg$, and $45\arcdeg$ respectively, except that the different angles sample different projections of the random field component, and so the differences in emergent radiation for the three pairs of runs provide insight into variations to be expected from different realizations."705 At all azimuthal augles. total inteusitv curves are identical. as are those for percentage polarization. but during outburst there are small differences in EWPA as a function of frequency: this is ercatest at the first time shown. the quiesceut state. because of the low level of polarized cussion then.," At all azimuthal angles, total intensity curves are identical, as are those for percentage polarization, but during outburst there are small differences in EVPA as a function of frequency; this is greatest at the first time shown, the quiescent state, because of the low level of polarized emission then."706 As discussed above. ordered. and in particular ‘helical’. magnetic fields have received much attention over the last decade.," As discussed above, ordered, and in particular `helical', magnetic fields have received much attention over the last decade."707 Iu order to include the most plivysicallvy plausible ordered field component. with the least παπα” of free paralucters. a force-free. minim enerev configuration is adopted.," In order to include the most physically plausible ordered field component, with the least number of free parameters, a force-free, minimum energy configuration is adopted."708 Ou the sub-pursec scale of interest hore. the flow is far enough from the central cugine that local evolutionary effects should domunate over the iuflueuce of the eugime's creosphere or iuner accretion disk.," On the sub-parsec scale of interest here, the flow is far enough from the central engine that local evolutionary effects should dominate over the influence of the engine's ergosphere or inner accretion disk."709 Tudeed. lone-teria changes in the character of a larec-scale inagnetic field are possible. if jets are subjected to turbulence aud a dissipative dynamo process.," Indeed, long-term changes in the character of a large-scale magnetic field are possible, if jets are subjected to turbulence and a dissipative dynamo process."710 Turbulence could be driven throughout the body of the flow due to their ultra-hieh. Revuolds number., Turbulence could be driven throughout the body of the flow due to their ultra-high Reynolds number.711 Alcan field cdyvuaiuos i sheared. turbulent flows are known to occur (Rosachevski&Wleeorin2003). aud although the process has not been explored im cylindrical ecometry. it can be speculated that the mean field then takes a form simular to that of a force-free flux tube.," Mean field dynamos in sheared, turbulent flows are known to occur \citep{rk03}, and although the process has not been explored in cylindrical geometry, it can be speculated that the mean field then takes a form similar to that of a force-free flux tube."712 This field exists in what would be the asviuptotie region discussed by MeIxiuney(2006).. aud its svuuuetry is thus unrelated to the anenlar momentum of the ceutral cneine’.," This field exists in what would be the asymptotic region discussed by \citet{mac06}, and its symmetry is thus unrelated to the angular momentum of the `central engine'."713 Although the process of field reversal is different from that exhibited by the solarterrestrial field beiug stochastic rather than periodic — recent simulations— (Yousefetal.2007) have shown such behavior. aud it would naturally explain the observed circular polarization ‘fips’.," Although the process of field reversal is different from that exhibited by the solar-terrestrial field – being stochastic rather than periodic – recent simulations \citep{you08} have shown such behavior, and it would naturally explain the observed circular polarization `flips'."714 Whether the field evolves due to dynamo action or relaxation. a likely cud point is a force-free configuration V.B=cB (Eik&Iughes 1991)..," Whether the field evolves due to dynamo action or relaxation, a likely end point is a force-free configuration $\nabla\times {\bf B}=\sigma{\bf715B}$ \citep{eh91}. ."716 It has been shown by Ikóniel&Choudlur(1985). that in ονΙσσα] ecolctry. oulv the modes a=0 and i»=1 coutribute o the general solution to the force-free equation iu the uiiminmn enerev state.," It has been shown by \citet{kc85} that in cylindrical geometry, only the modes $m=0$ and $m=1$ contribute to the general solution to the force-free equation in the minimum energy state."717 For a rauge of jet aud ambieut uediun parameters. aud for zu paraiecters leading toa jet with small deviation from axisvuuuetry. oulv the a= Yanode need be considered.," For a range of jet and ambient medium parameters, and for any parameters leading to a jet with small deviation from axisymmetry, only the $m=0$ mode need be considered."718 Then. by the diverecuce-tree constraint V:B—0. the axial waveuuniber &= 0.," Then, by the divergence-free constraint $\nabla\cdot{\bf B}=0$, the axial wavenumber $k=0$ ."719 Iu circular exlindiical coordinates. (p.o.+). this leads o a field coufiguratiou where the J are Bessel functions of iteger order. aud A ds a coustaut that must be determined.," In circular cylindrical coordinates, $\left(\rho,\phi,z\right)$, this leads to a field configuration where the $J$ are Bessel functions of integer order, and $K$ is a constant that must be determined."720 The oulv physical boundary condition is that the radial coniponenut of B vanish there. but as this is identically zero for the a=0 mode. this boundary condition provides uo coustraiut.," The only physical boundary condition is that the radial component of ${\bf B}$ vanish there, but as this is identically zero for the $m=0$ mode, this boundary condition provides no constraint."721 By choosiug A=2.11/1(2). with +(2) the jet radius. the axial field goes through a null at the boundary (Lundquist1950).," By choosing $K=2.41/r\left(z\right)$, with $r\left(z\right)$ the jet radius, the axial field goes through a null at the boundary \citep{lun50}."722.. While it is in principle permissible for the axial field to reverse sign inside the jet. the adopted value preveuts that. and is consistent with the simple field topology selected by evolution to a force-free. nmiünimuun cucrey state.," While it is in principle permissible for the axial field to reverse sign inside the jet, the adopted value prevents that, and is consistent with the simple field topology selected by evolution to a force-free, minimum energy state."723 This field is adopted ‘locally. in that the jet radius increases due to flow divergence. but note that it is not built self-cousisteutly iuto the prescription of the magnetic field.," This field is adopted `locally', in that the jet radius increases due to flow divergence, but note that it is not built self-consistently into the prescription of the magnetic field."724 The coustant By is varied to model flow divereeuce and shock compression., The constant $B_0$ is varied to model flow divergence and shock compression.725" The streneth of the random coumonent is established by scaling so that «B2,> is a specified multiple of the ordered feld strength."," The strength of the random component is established by scaling so that $<{\bf726B}^2_{\rm ran}>$ is a specified multiple of the ordered field strength."727 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)."728" Both approaches have Όσοι tried. revealing that the choice has no dmupact on the final results. merely chaneing the precise value of FP=<BL,>~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."729 It is extraordinarily dificult to define a quiesceut state from data., It is extraordinarily difficult to define a quiescent state from data.730 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."731 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."732 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."733 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}."734. 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}.735 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."736" This establishes a defined EVPA in the quiesceut state,", This establishes a well-defined EVPA in the quiescent state.737 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"738The 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."739 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 $\chi^{2}/\nu = 792/594$."740 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 $L_{\rm Edd}$."741 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."742 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."743 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}."744. 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 $b$ )."745 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}."746". 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."747 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 339–4.748 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."749 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 25.750 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."751" 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."752 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."753 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."754 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."755" 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 $J\propto r^{-q}$."756Although 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."757 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}."758. 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}.759. 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 $i = 18^{\circ}$."760" 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."761" 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 $R_{\rm in} = 2.4$ $R_{g}$.762 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."763 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."764 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."765" 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 $R_{g}$ ."766 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.767" 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)."768 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."769" For example. at /= 30°. the limit is Rj,7 ΕΝ."," For example, at $i = 30^{\circ}$ , the limit is $R_{\rm in} > 175 R_{g}$ ."770" There are at least two reasons why our limits on Aj, are", There are at least two reasons why our limits on $R_{\rm in}$ are771We 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.772 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.773 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.774 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."775 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.776 We thank II. Spruit and. C. Smith for useful cdisceussions., We thank H. Spruit and G. Smith for useful discussions.777 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. ("7781909).,1909).779 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."780 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)."781 They analyzed the photoelectric light curves of Broglia et al. (, They analyzed the two-color photoelectric light curves of Broglia et al. (7821955) using the WININ model (Wood 1972) and,1955) using the WINK model (Wood 1972) and783"↴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 $k=-2$."784 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."785 We denote these eigenvectors by το).," We denote these eigenvectors by $|\chi_{\,j,\,k,\,m}\rangle $ ."786 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}787 "788We 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."789 Wo turns out that the LED arbitrary functions assume their RW form., It turns out that the LTB arbitrary functions assume their RW form.790 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.791 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.792 These RW relations are and respectively., These RW relations are and respectively.793 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 $q_0 < {1 794\over 2}$ ) to obtain We continue by solving the first order linear differential equation for $M(z)$ (the effective gravitational mass) \ref{eq:M}) )."795 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 that796A 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[][ private797communication]{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."798 This ephemeris was used to phase all of our data., This ephemeris was used to phase all of our data.799" 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 $\Delta\phi = \phi_{we} -800\phi_{wi}$ : The shape of the system does not depend on the orbital separation $a$; this just determines the scale."801 “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).802" 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 $10^{4}$.803" ""Phis assumes that the gas stream follows a ballistic path.", This assumes that the gas stream follows a ballistic path.804 Figure 3. shows a theoretical eas stream for q=0.175., Figure \ref{mass} shows a theoretical gas stream for $q=0.175$.805 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.806 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."807 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.808 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."809 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.810 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 $\phi_{e}$."811 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.812 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 $q$.813 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.814 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 $R_{d}/a$."815 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 $\Delta\phi = 0.041585$.816 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.817 Figures 4. and ο show the eclipse constraints on the structure of the bright spot.," Figures \ref{bs_horizontal}818 and \ref{bs_vertical} show the eclipse constraints on the structure of the bright spot."819 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 vertical820where 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 $A=\sum_i^{557}{(\mu^{\rm data}-\mu^{\rm821th})^2}/{\sigma^2_i}~, B=\sum_i^{557}{\mu^{\rm data}-\mu^{\rm822th}}/{\sigma^2_i}~, C=\sum_i^{557}{1}/{\sigma^2_i}$ $\mu^{\rm823data}$ is the distance modulus obtained from observations and $\sigma_i$ is the total uncertainty of SNe Ia data."824 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.825 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}.826". 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."827 1., 1.828 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}.829 With the /(z) data only (Fig., With the $H(z)$ data only (Fig.830" 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 $\gamma_m=0.22$."831 With H(2)2-DAO--CMD (Fig., With $H(z)$ +BAO+CMB (Fig.832" Lb). (he best-fit values at1-0 are wy=—1.10Pet. 54,=—0.013.(t."," 1b), the best-fit values at$\sigma$ are $w_X=-1.10_{-0.17}^{+0.16}$, $\gamma_m=-0.013_{-0.011}^{+0.013}$."833 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."834 Le., 1c.835" 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 $\gamma_m=-0.009_{-0.012}^{+0.013}$.836 In Fig., In Fig.837" 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 $\gamma_m=-0.011_{-0.011}^{+0.012}$."838 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.839 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 ."840" 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"841quite 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.842 We therefore calculate Fur) in a numerical fashion., We therefore calculate $F_{\mathrm{ss}}(r)$ in a numerical fashion.843" 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."844 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.845" 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."846" 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."847" 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.848" 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."849 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).850 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.851 '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.852 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.853 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 $\gamma= 2.06 \pm 0.21$.854" 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."855" 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."856 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 $\fgal$.857" 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."858" 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."859 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.860 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).861" 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 $\fgal$."862" 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 $\gamma = -2.17\pm 0.12$."863" 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 $\Mone$."864" 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 $c = 4.25$ ."865 Applying our 1-σ range for implies that cgaj~0.1 —4.1., Applying our $\sigma$ range for $\fgal$ implies that $\Cgal\sim 0.1 - 4.1$ .866" 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."867" 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."868" 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."869" 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}."870" 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."871 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.872" 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}."873". 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."874 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.875 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.876 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.877" 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."878" 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."879 It is difficult to model this regime because simulations must, It is difficult to model this regime because simulations must880model to represent the disk SFR.,model to represent the disk SFR.881" 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 $_{882\odot}$ /yr for $10^{10}$ yrs with a Gaussian tail with $\sigma=0.6$."883" For tgx10. the second component is given by while lor tg>10 a Gaussian tail with σι,=0.6 was assiuned."," For $_{9}884\leq10$, the second component is given by while for $_{9}>10$ a Gaussian tail with $\sigma_{t_{9}}=0.6$ was assumed."885 The sum of these two components is shown in Figure d., The sum of these two components is shown in Figure 4.886" 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."887 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)."888 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.889 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."890 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.891 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."892S 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)."893" 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 $_{t,red}$ $_{t,blue}894$ which from Table 1 is $\sim2.4$."895 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."896 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."897 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).898»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.899 1999. Nevalainen et al.," 1999, Nevalainen et al."900 2000. Finoguenoy et al.," 2000, Finoguenov et al."901 2001. FOL hereafter) and BeppoSAX data (Ettori. De Grandi Alolendi 2002).," 2001, F01 hereafter) and Beppo–SAX data (Ettori, De Grandi Molendi 2002)."902 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."903 Ettori et al., Ettori et al.904 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."905 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."906 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.907 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."908 Finoguenoy et al. (, Finoguenov et al. (9092001. 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."910 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."911 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)."912 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."913 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.914 Ettort et al. (, Ettori et al. (9152002) 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."916 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."917 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.918 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."919 “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.920 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.921 Dremsstrahlung emissivity predicts LxκAlpray17.," Bremsstrahlung emissivity predicts $L_X\propto M\rho_{\rm922gas}T^{1/2}$."923" '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."924" 1998. for an extension to £9,, cosmologies)."," 1998, for an extension to $\Omega_m$ cosmologies)."925 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."926 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, $L_X\propto927M^\alpha$ with $\alpha\simeq 1.8\pm 0.1$ (Reiprich Böhhringer 2002)."928 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.929 1993. White. Jones Forman 1997).," 1993, White, Jones Forman 1997)."930 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."931 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"932 , 933"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}.934. 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}.935. 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.936 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.937" 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}."938. 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}."939". 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."940" 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}."941" 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."942 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.943" 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}."944". 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}."945". 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}."946 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.947" 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}."948". 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."949 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.950 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.951" 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."952 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.953 We summarise our results in Section 4.., We summarise our results in Section \ref{conclusion}.954" 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 $\dot M_{\rm a}$.955 The jet is modelled withMc a conical shape as shown in Fig., The jet is modelled with a conical shape as shown in Fig.956 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.957" 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 $N_{\rm e} = \int_{\gamma_{\rm min}}^{\gamma_{\rm max}} N_{\rm e} (\gamma) \, d\gamma$ ."958" 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."959" 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}. ."960" 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"961integration 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}) )"962 aud (8)). we get where z(f/)=(L-e7)!/?sinf/(124-6cosf).," and \ref{Ef}) ), we get where $z(f)=(1-e^2)^{1/2}\sin f/(1+e\cos f )$."963 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."964 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."965 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 $m=2$."966" 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 $t_{\rm open}\approx Re_{\rm {crit}}({\Delta967r}/{\rtrunc})^2\Porb/2\pi$ as in \citet{art94}, where $Re_{\rm968crit}=\alpha_{\rm crit}^{-1} ({H}/{r})^{-2}$ denotes the Reynolds number for which the gap is opened from $\rtrunc$."969" 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."970" 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}971 where $\velr_{\rm max}\sim 0.1 \cs$ and $\dlo=(0.500-0.227\lg972\qx)a(1-e)$ - 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."973enission 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."974 (ακομα ct al. (, Ghisellini et al. (9751998). 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"976colors.,colors.977" The nuclear color is the color of the inner10"".", The nuclear color is the color of the inner.978. 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.979 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.980" 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."981 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.982 Table 3 gives total colors of our sample., Table \ref{colors} gives total colors of our sample.983 The estimated errors are ~0.1 mag., The estimated errors are $\sim 0.1$ mag.984 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.985" 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."986 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).987 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.988 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.989 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 = 0.59.990 We thus, We thus991instability 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}) )."992 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}) ).993 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.994 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."995 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."996 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."997 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},"998we 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.999 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.1000 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.1001" 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 $L_{\rm X}\approx 5\times100210^{29}$ erg and is stationary over $\approx 100$ yrs."1003 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.1004 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 $7\%$."1005 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."1006 The melt upper paucl in Fie., The right upper panel in Fig.1007 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.1008 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)."1009 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.1010 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},"1011can  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.1012 We rescaled the svuthetic X-ray image shown in Fie., We rescaled the synthetic X-ray image shown in Fig.1013 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}) ).1014 The cussion within the nozzle is assumed to be totally absorbed., The emission within the nozzle is assumed to be totally absorbed.1015 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.1016 In Fig., In Fig.1017" 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)."1018 The 2001 image coutour Is superimposed ou the modeled source., The 2001 image contour is superimposed on the modeled source.1019 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.1020 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.1021 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 $T > 7\times102210^{6}$ 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."1023 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."1024 13 in Bonitoetal. 2008))., 13 in \citealt{bff08}) ).1025" 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 $P.A.\approx270^{\circ}$."1026 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.1027 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."1028 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}."1029. 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.1030 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}, ,"1031 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"1032causally connected.,causally connected.1033 We will assume that this is the accretion disc., We will assume that this is the accretion disc.1034 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.1035 This is consistent with the Ilux-Ilux. plots presented in Figure 3., This is consistent with the flux-flux plots presented in Figure 3.1036 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.1037 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.1038 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."1039 We need to understand. the different slopes. however.," We need to understand the different slopes, however."1040 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 $\propto1041R^{-3}$ for large $R$."1042 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 $\propto1043R^{-3}$."1044 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)."1045 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."1046 One possible explanation is a wavelength dependent albedo., One possible explanation is a wavelength dependent albedo.1047 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."1048 ]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 $7.5\times10^{-15} \la f_{B} \la104910^{-14}$ $^2$."1050" 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."1051 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."1052 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."1053 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."1054 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."1055 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 5.2.1056 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."1057 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."1058 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."1059 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."1060 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."1061 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."1062 For the H-band we tried delays, For the H-band we tried delays1063assume 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."1064 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."1065 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."1066 For 47 Tuc all three cases are equally possible., For 47 Tuc all three cases are equally possible.1067 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.1068 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.1069" 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 $10^{-12} \rm erg/cm^3$."1070 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 $10^{26}\rm cm^2/s$."1071 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)."1072" 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 the1073When (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."1074 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}."1075 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}."1076 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."1077 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}. ."1078stellar flux.,stellar flux.1079 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}) ).1080 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."1081" 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."1082 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.1083 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."1084 A ciagram of CUIbis orbit is preseuted iu Figure 2.., A diagram of GJ43b's orbit is presented in Figure \ref{orbit_fig}. .1085 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."1086 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."1087 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."1088 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.1089 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}.1090 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.1091 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.1092 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}1093 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."1094 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.1095 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."1096 RMS wind speeds typically reach ~1 kan ! at plotosphere levels., RMS wind speeds typically reach $\sim$ 1 km $^{-1}$ at photosphere levels.1097 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.1098 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.1099 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.1100" 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."1101 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.1102 Additionally.theoretical light curves aud. spectra," Additionally,theoretical light curves and spectra"1103ealaxy 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."1104 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.1105 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.1106 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.1107 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.1108 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.1109 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."1110 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)."1111 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."1112 This wind power is cissipatec as reat in the surrounding medium., This wind power is dissipated as heat in the surrounding medium.1113 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 $z\sim 1-2$ ."1114 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."1115 L thank the referee for comments and Phe Roval Society [or support., I thank the referee for comments and The Royal Society for support.1116relative 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.1117 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."1118 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}1119 where $h_M = (M/3M_*)^{1/3}$ is the reduced Hill radius of the embryo and $\tilde e = e/h_M$."1120 Equation (8)) is derived under the two-body approximation., Equation \ref{eq:atm_cap}) ) is derived under the two-body approximation.1121 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.1122 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 $r$.1123 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}) )1124as 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},"1125 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}.1126". 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."1127 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 $\propto1128(R_{\rm e}/R)^{1/2}$ ; see Equation \ref{eq:pcol_low}) )), this discrepancy produces insignificant errors."1129" 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.1130" 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, $\tilde b1131(2M/3M_*)^{1/3} a$, where $\tilde b \simeq 10$ is \citep{kokubo00,kokubo02}."1132" 2002).. WANT Wass Or ""jsolatiou lass” is ALA,=Iwπα”ΟΛΗ,TOMEBIND."," The maximum mass or “isolation mass” is $M_{\rm iso} = 2 \pi a^2 (2M_{\rm1133iso}/3M_*)^{1/3}\tilde b \Sigma_{\rm s,0}$."1134 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.1135 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}. ."1136 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}. ."1137The 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 ${\bf E}=\{x_0, y_0, \mu, \eta_+,1138\eta_\times\}$ 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}) )."1139 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}) )."1140 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 ${\bf1141 E}_0$ 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."1142 These matrices are fixed by the choice of basis functions {ey}., These matrices are fixed by the choice of basis functions $\{\psi_i\}$.1143 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.1144" 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 $\infty\times N$."1145 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."1146" 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 $\delta\boldb = ({\bf1147 G}^T\boldb_0)\cdot \delta{\bf E}$ (with some abuse of notation here)."1148 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."1149. We use the Causs-LaeucrreOo decomposition iu our shape measurements., We use the Gauss-Laguerre decomposition in our shape measurements.1150 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."1151 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."1152" The functions are equivalent to the ""polar shapelets” of Masseyetal.(200L)..", The functions are equivalent to the “polar shapelets” of \citet{Massey}..1153The 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."1154equation (29)) and equation (40)) (taking Mp=0).,equation \ref{hdel}) ) and equation \ref{gdel}) ) (taking $\dot{M}_D = 0$ ).1155 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. Lyppl<rq)=ip.," We can define a half-light radius $r_{1/2}$, within which the energy radiated per unit time by the disk is one half of the total power of the disk, i.e. ${\cal L}_{HD}(<r_{1/2}) = {1\over 2} {\cal L}_{HD}$."1156" From equation (46)). for a non-accretion disk magnetically coupled to a black hole. r4;5 can be solved from Sinlarly. for a standard accretion disk. (he energy. radiated per unit time from the region inside a circle of radius r>rj, 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 ${\cal L}_{acc} = \dot{M}_D \left(1-1157E_{ms}^+\right)\,$."1158" 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 ${\cal L}_{acc}(<r_{1/2}) = {1\over 2} {\cal L}_{acc}$, can be solved from where $f$ is give by equation (15n) of \citet{pag74}."1159. We have calculated the hall-Hlisht radius of a disk magnetically coupled to a Ixerr black hole. assuming the disk has no accretion and the magnetic field touches the disk at the inner boundary.," We have calculated the half-light radius of a disk magnetically coupled to a Kerr black hole, assuming the disk has no accretion and the magnetic field touches the disk at the inner boundary."1160 The results are shown in Fig. 6.., The results are shown in Fig. \ref{fig5}.1161 For comparison. we have also calculated. the half-light. radius of a standard accretion disk around a Nerv black hole. the results are also shown in Fig.," For comparison, we have also calculated the half-light radius of a standard accretion disk around a Kerr black hole, the results are also shown in Fig."1162 6 with the dashed curve., \ref{fig5} with the dashed curve.1163 From these resul(s we see that. lor à non-accretion disk magnetically coupled to a Ixerr black hole with the magnetic Ποιά touching the disk al the inner boundary. most energy radiated by the disk comes from a region closer to the center of the disk. compared to the case of a standard accretion disk.," From these results we see that, for a non-accretion disk magnetically coupled to a Kerr black hole with the magnetic field touching the disk at the inner boundary, most energy radiated by the disk comes from a region closer to the center of the disk, compared to the case of a standard accretion disk."1164 A similar figure is shown by Agol and Ixvolik (2000. Fig.," A similar figure is shown by Agol and Krolik (2000, Fig."1165 1). ancl verv similar results are obtained by them for a disk magnelically coupled to the material in (he transition region.," 1), and very similar results are obtained by them for a disk magnetically coupled to the material in the transition region."1166 Bul we empliasize (hat in (heir model à state with a zero accretion rate and a finite power can never be realized. since in (heir model in order (ο extract energy. from a black hole material with negative energy must [all into the black hole.," But we emphasize that in their model a state with a zero accretion rate and a finite power can never be realized, since in their model in order to extract energy from a black hole material with negative energy must fall into the black hole."1167 And. in our figure the curve is broken at 0/3;=0.3594 for the non-accretion disk. while in Agol and Ixrolik's figure the curve is drawn without broken.," And, in our figure the curve is broken at $a/M_H = 11680.3594$ for the non-accretion disk, while in Agol and Krolik's figure the curve is drawn without broken."1169 Suppose a Ixerr black hole loses its energy ancl angular momentum through (he magnetic coupling to a thin Weplerian disk with no accretion. wilh the magnetic field lines touching the disk at a circle of radius r= ry.," Suppose a Kerr black hole loses its energy and angular momentum through the magnetic coupling to a thin Keplerian disk with no accretion, with the magnetic field lines touching the disk at a circle of radius $r=r_0$ ."1170 Then. the evolution of the black hole spin," Then, the evolution of the black hole spin"1171integration volume.,integration volume.1172 The best method for recovering the local orientation in the well resolved region in this case is S2 tightly followed by S1 and $3., The best method for recovering the local orientation in the well resolved region in this case is S2 tightly followed by S1 and S3.1173" The deviations for the semi-major axis a, 6,, are the largest."," The deviations for the semi-major axis $a$ , $\delta_a$, are the largest."1174" The deviations are smallest for the semi-minor axis c, i.e. we have shown the worst case in Figure 4.."," The deviations are smallest for the semi-minor axis $c$, i.e. we have shown the worst case in Figure \ref{fig:changing_axis_ratio_changing_orientation_da}."1175" We have experimented with many more mass density, shape and orientation profiles as well as different resolutions than shown here."," We have experimented with many more mass density, shape and orientation profiles as well as different resolutions than shown here."1176 The findings are always the same: using an ellipsoidal shell as an integration volume without or with rap weighting (methods $1 and $3) gives results that are closest to the expected value under controlled conditions in regions where the mass distribution is well resolved and the density contrast is high enough (i.e. no flat mass density profiles)., The findings are always the same: using an ellipsoidal shell as an integration volume without or with $r_\mathrm{ell}^{-2}$ weighting (methods S1 and S3) gives results that are closest to the expected value under controlled conditions in regions where the mass distribution is well resolved and the density contrast is high enough (i.e. no flat mass density profiles).1177" Methods S1 and $3 agree, since the weighting by rab in each shell is like dividing by a different constant in each shell, which does not affect the axis ratios."," Methods S1 and S3 agree, since the weighting by $r_\mathrm{ell}^{-2}$ in each shell is like dividing by a different constant in each shell, which does not affect the axis ratios."1178 The absolute values of the eigenvalues of the shape tensor for method S3 change of course., The absolute values of the eigenvalues of the shape tensor for method S3 change of course.1179" Hence, our preferred method is the pure form without any weighting, i.e. method S1."," Hence, our preferred method is the pure form without any weighting, i.e. method S1."1180" All other methods lead to significant deviations that in detail depend on the mass density, shape and orientation profile."," All other methods lead to significant deviations that in detail depend on the mass density, shape and orientation profile."1181 This makes it also impossible to come up with a correction scheme that works in all cases that would allow to convert the measured axis ratios between different methods., This makes it also impossible to come up with a correction scheme that works in all cases that would allow to convert the measured axis ratios between different methods.1182 Now we turn to a study of halos in cosmological structure formation simulations., Now we turn to a study of halos in cosmological structure formation simulations.1183" In these halos, in addition to the change of the axis ratios and the orientation of the principal axes as a function of distance, we also have subhalos."," In these halos, in addition to the change of the axis ratios and the orientation of the principal axes as a function of distance, we also have subhalos."1184" 'The data are from a cosmological structure formation simulation, where we simulated several objects that will end up as Milky Way-sized objects at redshift z— 0."," The data are from a cosmological structure formation simulation, where we simulated several objects that will end up as Milky Way-sized objects at redshift $z=0$ ."1185 The simulations were run with the latest version of the gas dynamics and N-body adaptive refinement tree (ART) code (????)..," The simulations were run with the latest version of the gas dynamics and $N$ -body adaptive refinement tree (ART) code \citep{1997ApJS..111...73K,1999PhDT........25K,2002ApJ...571..563K,2008ApJ...672...19R}."1186 ART includes 3-dimensional radiative transfer of ultraviolet (UV) radiation from individual stellar particles using the optically thin variable Eddington tensor (OTVET) approximation (?).. , ART includes 3-dimensional radiative transfer of ultraviolet (UV) radiation from individual stellar particles using the optically thin variable Eddington tensor (OTVET) approximation \citep{2001NewA....6..437G}. .1187"It includes a non-equilibrium chemical network of hydrogentextsci, and H3) and heliumtextsci, and as well as non-equilibrium cooling and heating rates, textsciii))which use the local abundances of atomic, molecular and ionic species as well as the local UV intensity (?).."," It includes a non-equilibrium chemical network of hydrogen, and $_2$ ) and helium, and ) as well as non-equilibrium cooling and heating rates, which use the local abundances of atomic, molecular and ionic species as well as the local UV intensity \citep{2011ApJ...728...88G}."1188 All these properties are followed self-consistently during the course of a simulation., All these properties are followed self-consistently during the course of a simulation.1189 An empirical model for the formation and shielding of molecular hydrogen on the interstellar dust allows for more realistic star formation recipes based on the local density of molecular hydrogen (?).., An empirical model for the formation and shielding of molecular hydrogen on the interstellar dust allows for more realistic star formation recipes based on the local density of molecular hydrogen \citep{2011ApJ...728...88G}.1190 Also included in ART is metal enrichment and thermal feedback due to the Type II and Type Ia supernovae (?) as well as stellar feedback , Also included in ART is metal enrichment and thermal feedback due to the Type II and Type Ia supernovae \citep{2003ApJ...590L...1K} as well as stellar feedback \citep{2005ApJ...623..650K}.1191"Here, we use data at ze2 from a simulation that(?)..includes cooling and star formation(simulation series A)."," Here, we use data at $z \approx 2$ from a simulation thatincludes cooling and star formation(simulation series A)."1192 Further details are presented in an accompanying paper (?).., Further details are presented in an accompanying paper \citep{2011ZempBaryonicImpact}. .1193Were typicalv accurate to O5aaresce.,were typically accurate to arcsec.1194 Source detection used the package (Bertin Arnouts 1996)., Source detection used the package (Bertin Arnouts 1996).1195 Comparing the number counts from these observations with oevious studies we estimate a completeness limit of A8zm15 mma., Comparing the number counts from these observations with previous studies we estimate a completeness limit of $Ks\approx18$ mag.1196 Finally we note that thePhocnix/XAIAI-Nevw/on field xuwtlv overlaps with the deep optical CVRL photometric data presented by Sullivan et al. (, Finally we note that the field partly overlaps with the deep optical $UBVRI$ photometric data presented by Sullivan et al. (11972004).,2004).1198" These observations use the Wide Field Imager at the ANT CDVRE bands) ancl he C""PIO-4m telescopes and reach limiting magnitudes {7z24 and Cz24 mimiag.", These observations use the Wide Field Imager at the AAT $BVRI$ bands) and the CTIO-4m telescopes and reach limiting magnitudes $R\approx24$ and $U\approx24$ mag.1199 When available we use these deeper data rather than the shallower observations from either the ESO 2.2m (C-band) or our previous ANT survey of the PDS (V A-bands)., When available we use these deeper data rather than the shallower observations from either the ESO 2.2m $U$ -band) or our previous AAT survey of the PDS $VR$ -bands).1200 The magnitudeὃν ogiven in this study are in the Vega system., The magnitude given in this study are in the Vega system.

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