ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 In order to model the prompt GRB observation with CPA. the simulated. You distribution. must be ᾱ goodapproximationof the observed. one. where Zoo is the time needed to accumulate from 5 to 95 of observed photon," In order to model the prompt GRB observation with CTA, the simulated $T_{90}$ distribution must be a goodapproximationof the observed one, where $T_{90}$ is the time needed to accumulate from 5 to 95 of observed photon"3| Opt = 9pt,= 9pt = 9pt4Given that the surface. brightness distribution of the original galaxy image is statistically isotropic. we have οο)—0 and ffs)=0.,"Given that the surface brightness distribution of the original galaxy image is statistically isotropic, we have $\langle\epsilon_{1,2}^S\rangle=0$ and $\langle\epsilon_1^S\epsilon_2^S\rangle=0$."5 Therefore. we find This result. I2q.(10)). clearly shows that e; and e» are unbiased shear estimators. as (c7)2) and (c2)? in the multiplicative factors depend on the galaxy morphology distribution. ancl cannot be reduced. to constant factors. (," Therefore, we find This result, \ref{q5}) ), clearly shows that $\epsilon_1$ and $\epsilon_2$ are unbiased shear estimators, as $\langle\left(\epsilon_1^S\right)^2\rangle$ and $\langle\left(\epsilon_2^S\right)^2\rangle$ in the multiplicative factors depend on the galaxy morphology distribution, and cannot be reduced to constant factors. ("6Also see. 124.(3.29). of Bernstein Jarvis (2002). or 154.(9.5.26) of Weinberg (2008).),"Also see Eq.(3.29) of Bernstein Jarvis (2002), or Eq.(9.5.26) of Weinberg (2008).)"7" One can construct an unbiased estimator of the shear. if one keeps three quantities from each lensed galaxy image: QuΦου. 2€». and (Qj,|Qee. and use the ratios of their averages."," One can construct an unbiased estimator of the shear, if one keeps three quantities from each lensed galaxy image: $Q_{11}-Q_{22}$, $2Q_{12}$, and $Q_{11}+Q_{22}$, and use the ratios of their averages."8 Assuming statistical isotropy of intrinsic galaxy shapes in eq.(6)). and keeping up to first. order in shear/convergence. we have (also see Eq.(9.5.30) of Weinberg (2008)): This form of shear estimators is not conventional. as one has to keep more than one quantities from cach galaxy image for cach shear component.," Assuming statistical isotropy of intrinsic galaxy shapes in \ref{q3}) ), and keeping up to first order in shear/convergence, we have (also see Eq.(9.5.30) of Weinberg (2008)): This form of shear estimators is not conventional, as one has to keep more than one quantities from each galaxy image for each shear component."9 Lt is this class of estimators we shall discuss in this paper in detail., It is this class of estimators we shall discuss in this paper in detail.10 One may wonder whether unbiased shear estimators in the conventional formi ever exist., One may wonder whether unbiased shear estimators in the conventional form ever exist.11 The answer is ves. at least when the PSE is absent.," The answer is yes, at least when the PSF is absent."12 For example. we find the following unbiased shear estimators: 154.(12)) can be checked by applying Taylor expansion of In(1|e;)/(1o) 0G= L2) to the first order in shear/convergence using eq.(8)). Eq.(12))," For example, we find the following unbiased shear estimators: \ref{q7}) ) can be checked by applying Taylor expansion of $\ln[(1+\epsilon_i)/(1-\epsilon_i)]$ $i=1, 2$ ) to the first order in shear/convergence using \ref{q4}) ). \ref{q7}) )"13 defines a special tvpe of conventional shear estimators that are accidentally found bv us., defines a special type of conventional shear estimators that are accidentally found by us.14 Lt is now immediately. interesting to ask if there exist other types of unbiased shear estimators in the conventional form., It is now immediately interesting to ask if there exist other types of unbiased shear estimators in the conventional form.15 We study this issue specifically. in the next two sections., We study this issue specifically in the next two sections.16 Lf the readers wish to go directly to the relevant sections on the new estimator. read on from refalternatives..," If the readers wish to go directly to the relevant sections on the new estimator, read on from \\ref{alternatives}."17" For notational convenience. we shall abbreviate ""conventional shear estimator"" as “CSE” in the rest of the paper."," For notational convenience, we shall abbreviate “conventional shear estimator” as “CSE” in the rest of the paper."18 Once again. by CSE we mean the shear estimators that are made of just one number measured from a galaxy image for each shear component.," Once again, by CSE we mean the shear estimators that are made of just one number measured from a galaxy image for each shear component."19 In preparation for our main theme of this section. we discuss the spin properties of cosmic shears and their estimators in refcoor;pin..," In preparation for our main theme of this section, we discuss the spin properties of cosmic shears and their estimators in \\ref{coor_spin}."20M'ethenstudglheformsofC'SEsinlheabsenccofthe D sli., We then study the forms of CSEs in the absence of the PSF in \\ref{spin_2_esti}.21 ‘To study the forms of the CSEs. it is useful to first consider their properties under coordinate rotations.," To study the forms of the CSEs, it is useful to first consider their properties under coordinate rotations."22 Suppose we rotate the coordinates Grey) clockwise by an angle 6.," Suppose we rotate the coordinates $(x, y)$ clockwise by an angle $\theta$."23 The new coordinates (r.94) ave related to the old one via the Following relation: Η we write the position vector as a complex number of the former |iy. where Lis the complex unit. the coordinate transformation uncer rotation can then be written as: For notational brevity. we shall generally use XY? to denote the salue of any quantity NV in the new coordinates that are rotated clockwise by an angle 6 with respect to the original coordinates.," The new coordinates $(x^{\theta}, y^{\theta})$ are related to the old one via the following relation: If we write the position vector as a complex number of the form $x+\ima y$, where $\ima$ is the complex unit, the coordinate transformation under rotation can then be written as: For notational brevity, we shall generally use $X^{\theta}$ to denote the value of any quantity $X$ in the new coordinates that are rotated clockwise by an angle $\theta$ with respect to the original coordinates."24 Let us now cliscuss how cosmic shears and their (SEs transform under coordinate rotation., Let us now discuss how cosmic shears and their CSEs transform under coordinate rotation.25 The definitions of the shear components (shown in the beginning of refelassic)) involve spatial derivatives: thus. their transformation| rules under coordinate— rotation can be found from the chain rule: From eq.(13)). we get: 'Pherefore. we have: ‘Taking the square of eq.(17)). we find: Therefore. the shear components. which are 2nd order derivatives of the lensing potential 9. also transform: under coordinate rotation as: Because of this property. we usually say that cosnic shears form a spin-2 quantity.," The definitions of the shear components (shown in the beginning of \\ref{classic}) ) involve spatial derivatives; thus, their transformation rules under coordinate rotation can be found from the chain rule: From \ref{coor_trans}) ), we get: Therefore, we have: Taking the square of \ref{coor_trans_complex_2}) ), we find: Therefore, the shear components, which are 2nd order derivatives of the lensing potential $\Phi$, also transform under coordinate rotation as: Because of this property, we usually say that cosmic shears form a spin-2 quantity."26 In general. a complex quantity. sav HL is called a spin-n quantity if ittransforms as H=ILexp(in8) under a clockwise coordinate rotation of angle8.," In general, a complex quantity, say $\Pi$, is called a $n$ quantity if ittransforms as $\Pi^{\theta}=\Pi\exp(\ima n\theta)$ under a clockwise coordinate rotation of angle$\theta$."27 Now let us discuss shear cstimators., Now let us discuss shear estimators.28 Lt is straightforward to see that the CSEs —defined in eq.(12)) do notform a spin-2 quantity., It is straightforward to see that the CSEs defined in \ref{q7}) ) do notform a spin-2 quantity.29" More. generally. assuming that Vy and E» are the CSEs for 5, and τοι respectively. then. ,| ine. Py|ike is not necessarily a spin-2 quantity."," More generally, assuming that $\Gamma_1$ and $\Gamma_2$ are the CSEs for $\gamma_1$ and $\gamma_2$ , respectively, then, unlike $\gamma_1+\ima\gamma_2$ , $\Gamma_1+\ima\Gamma_2$ is not necessarily a spin-2 quantity."30 tibtibaslHlowever. it turns out that we can regularize any CSEs by," However, it turns out that we can regularize any CSEs by"31profile for our cight targets and overplot the generic examples of Starburst99 model spectra described above.,profile for our eight targets and overplot the generic examples of Starburst99 model spectra described above.32 We defer to a future paper a detailed discussion of the properties of the stellar populations in the LBAs., We defer to a future paper a detailed discussion of the properties of the stellar populations in the LBAs.33 Tere we mnerely point out that the far-UV spectra of the LBAs are all consistent with a normal population of ioniziug stars expected for a strong starburst., Here we merely point out that the far-UV spectra of the LBAs are all consistent with a normal population of ionizing stars expected for a strong starburst.34 Tn Fieve Lowe show the CTIAL331.5 absorption-line profiles for our COS data on cight LBAs., In Figure 4 we show the $\lambda$ 1334.5 absorption-line profiles for our COS data on eight LBAs.35 The correspouding profiles for the CTIAL036.3 Lue from the FUSE data can be found in ΠΟ and C9., The corresponding profiles for the $\lambda$ 1036.3 line from the FUSE data can be found in H01 and G09.36 À striking result is that there is a significant residual intensity iu the absorption-line profiles in four LBAs (LBA0213|12. LDAUsQS|39. LDAO921115. aud LBA0N926|15).," A striking result is that there is a significant residual intensity in the absorption-line profiles in four LBAs (LBA0213+12, LBA0808+39, LBA0921+45, and LBA0926+45)."37 The first three objects all contain a DCO., The first three objects all contain a DCO.38 These results contrast strouely with the results in IHIOl and C09 in which the CITAT036.3 absorption-line in the FUSE data is black or nearly black at line ceuter in all cases., These results contrast strongly with the results in H01 and G09 in which the $\lambda$ 1036.3 absorption-line in the FUSE data is black or nearly black at line center in all cases.39 To understand. our approach in‘ using. the CII line. as a probe of the Lyman coutimuun. let us consider two limiting idealized cases.," To understand our approach in using the CII line as a probe of the Lyman continuum, let us consider two limiting idealized cases."40 In the first. we assume a picket-foeuce model im which the far-UV source is surrounded by," In the first, we assume a picket-fence model in which the far-UV source is surrounded by"41he filaments coalesce cach other to form larger onc.,the filaments coalesce each other to form larger one.42 Although each filament is small (its initial radius is roughly equal to a few electron skin depth). the detailed xoperties of this structure. articlec.g.the correlation length of the magnetic field. the energv distribution. aud the time evolution. mav affect the macroscopic vchaviors of the transition laver of a collisionless shock.," Although each filament is small (its initial radius is roughly equal to a few electron skin depth), the detailed properties of this structure, e.g., the correlation length of the magnetic field, the particle energy distribution, and the time evolution, may affect the macroscopic behaviors of the transition layer of a collisionless shock."43 For example. \ledvedey(2000) pointed out a possibility hat ultrarelativistic clectrous accelerated by lightly ionuniforni small scale magnetic fields cuit radiations different from a svuchrotrou radiation ciuitted hy electrous in uniforii magnetic fields.," For example, \cite{m00} pointed out a possibility that ultrarelativistic electrons accelerated by highly nonuniform small scale magnetic fields emit radiations different from a synchrotron radiation emitted by electrons in uniform magnetic fields."44 Subsequently some investigations iuto the fllameutary structure have Όσσα performed., Subsequently some investigations into the filamentary structure have been performed.45" From the conservation of cucrey. Cauzinov(2001) predicted that the magnetic field energy decreases as ftft, Ch"," From the conservation of energy, \cite{g01} predicted that the magnetic field energy decreases as $t^{-1}$."46angetal.(2008) cousidered a variaut of Laudau damping (a process dissipating the energv of electromagnetic fields iuto the kinetic energy of particles) and reached a simular result for the evolution of the magnetic fields., \cite{csa08} considered a variant of Landau damping (a process dissipating the energy of electromagnetic fields into the kinetic energy of particles) and reached a similar result for the evolution of the magnetic fields.47 They asstmed straight orbits of particles because of weak magnetic fields. though them PIC siuulatious reveal that there exist some regions where strong imaenetic fields bend the orbits of particles.," They assumed straight orbits of particles because of weak magnetic fields, though their PIC simulations reveal that there exist some regions where strong magnetic fields bend the orbits of particles."48 Medvedevetal.(2005) investigated the coalescence of the fibuneuts by using a two-dimensional toy model., \cite{m05} investigated the coalescence of the filaments by using a two-dimensional toy model.49 They pointed out that the correlation leneth of the naenetic field grows exponentially at first aud then iucarlv with time., They pointed out that the correlation length of the magnetic field grows exponentially at first and then linearly with time.50 Achterbereetal.(2007) reexamine he tov model including the effect of screening currents of he backeround plasma and predict that the coalescence slows down when the separation of the filaments becomes arecr than the skin depth of the backerouncl plasma., \cite{awn07} reexamine the toy model including the effect of screening currents of the background plasma and predict that the coalescence slows down when the separation of the filaments becomes larger than the skin depth of the background plasma.51 But their analysis docs not predict whether there exists a critical scale leugth above which the coalescence does rot proceed., But their analysis does not predict whether there exists a critical scale length above which the coalescence does not proceed.52 Furthermore. their simple model ignores ucro processes such as the dissipation of the magnetic energv iuto the kinetic energv by the reconnection of he magnetic field.," Furthermore, their simple model ignores micro processes such as the dissipation of the magnetic energy into the kinetic energy by the reconnection of the magnetic field."53 On the other haud. Milosavljevió&Naker(2006). treated the filamentary structure in the yamework of the maguetolhydrodvuamics(," On the other hand, \cite{m06} treated the filamentary structure in the framework of the magnetohydrodynamics(MHD)."54 They areuc that oessure-driven ΑΠΟ instability MID).destroys he filament aud the strong magnetic field generated in he transition laver is short-lived., They argue that a pressure-driven MHD instability destroys the filament and the strong magnetic field generated in the transition layer is short-lived.55 That is. the couseusus is vet to be reached regarding the long-term: evolution of the Weibel filaments.," That is, the consensus is yet to be reached regarding the long-term evolution of the Weibel filaments."56 Especially. it is unclear whether he tov mocel aud the MIID model are appropriate to nocel the filaments.," Especially, it is unclear whether the toy model and the MHD model are appropriate to model the filaments."57 To settle such uuresolved problems. we use a kinetic Vlasov code.," To settle such unresolved problems, we use a kinetic Vlasov code."58 This approach enables us to investigate he structure of the filaments and their coalescence and las the advantage that the accuracy. of the calculated velocity distribution docs not depend ou the density of plasinas at cach poiut iu the plysical space. while it does in PIC simulations.," This approach enables us to investigate the structure of the filaments and their coalescence and has the advantage that the accuracy of the calculated velocity distribution does not depend on the density of plasmas at each point in the physical space, while it does in PIC simulations."59 However. there are some conrputational constrains on Vlasov codes.," However, there are some computational constrains on Vlasov codes."60 The most serious one is its stall dvnamic range in both plysical and velocity spaces., The most serious one is its small dynamic range in both physical and velocity spaces.61 Due to the defect. we caunot treat the formation of a shock from two plasma flows or relativistic motions of particles.," Due to the defect, we cannot treat the formation of a shock from two plasma flows or relativistic motions of particles."62 Thus. in this work. we concentrate ou the coalescence of filaments forming as a result of the nou-relativistic Weibel iustabilitv.," Thus, in this work, we concentrate on the coalescence of filaments forming as a result of the non-relativistic Weibel instability."63 The saturation of the relativistic Weibel instability is realized bv the same mechauisia as that of the non-relativistic Weibel instability (Nato&Takabe2008)., The saturation of the relativistic Weibel instability is realized by the same mechanism as that of the non-relativistic Weibel instability \citep{kt08}.64. Therefore. if we can construct a reliable model of the filameuts by analyzing the non-linear behavior of the non-relativistic Weibel instability in detail it may provide a general insight into some essential processes operating in the transition laver of a collisionless shock aud predict their long-term evolution bevoud the reach of the simulation.," Therefore, if we can construct a reliable model of the filaments by analyzing the non-linear behavior of the non-relativistic Weibel instability in detail, it may provide a general insight into some essential processes operating in the transition layer of a collisionless shock and predict their long-term evolution beyond the reach of the simulation."65 This paper is organized as follows., This paper is organized as follows.66 Iu the next section. we describe the strateey for the muuerical simulation.," In the next section, we describe the strategy for the numerical simulation."67 The results are shown in 53., The results are shown in $\S$ 3.68 In 51 . we coustruct an analytic model for the filaments aud address romaine problems.," In $\S$ 4, we construct an analytic model for the filaments and address remaining problems."69 We conclude this paper iu 55., We conclude this paper in $\S$ 5.70 Iu this section. we describe the governing equations. sole assiuniptions. aud au initial setup for the umumerical simulation.," In this section, we describe the governing equations, some assumptions, and an initial setup for the numerical simulation."71 The equatious describing the behavior of rarefied plasmas are the Vilasov-Masxwell system (sec.e...," The equations describing the behavior of rarefied plasmas are the Vlasov-Maxwell system \citep[see, e.g.,][]{s94}."72 The Viasov equation e@overus the time evolution of the distribution. —function of species jC) for ious aud « forFin electrons)δ," The Vlasov equation governs the time evolution of the distribution function $f_j(t,x,y,z,v_x,v_y,v_z)$ of species $j$ $i$ for ions and $e$ for electrons)."73ντνΌχι ty.ereος}. the cartesian coordinates are Grey.2]. and the corresponding coordinates in the velocity space are (60.0g.0:).," Here the cartesian coordinates are $(x,y,z)$ and the corresponding coordinates in the velocity space are $(v_x,v_y,v_z)$."74 The Maxwell. equations govern the time evolution of the electromagnetic fields E aud B., The Maxwell equations govern the time evolution of the electromagnetic fields ${\bf E}$ and ${\bf B}$.75 We impose two assumptious., We impose two assumptions.76 One is that the plasma is homogeneous iu the + direction. which males the Vlasov equation to take the following forix: where di aud ai; are the charge and the mass of species j. and «is the speed of helt.," One is that the plasma is homogeneous in the $z$ direction, which makes the Vlasov equation to take the following form; where $q_j$ and $m_j$ are the charge and the mass of species $j$, and $c$ is the speed of light."77 E and B are expresseME N introducing the scalar aud the vector poteutials. off...4) and A(f..e.g) as The time evolution of the poteutials is described by the wave equations: where p and j ave the electric density and the electric current density. which satisfy the Lorenz condition: The other assuniptiou is that the plasima consists of 1ος and electrons with the same charge but with the opposite ni (q;=qe c)," ${\bf E}$ and ${\bf B}$ are expressed by introducing the scalar and the vector potentials, $\phi(t,x,y)$ and ${\bf A}(t,x,y)$ as The time evolution of the potentials is described by the wave equations; where $\rho$ and ${\bf j}$ are the electric density and the electric current density, which satisfy the Lorenz condition; The other assumption is that the plasma consists of ions and electrons with the same charge but with the opposite sign $q_i=-q_e=e$ )."78 So the source terms iu Equation (3)jj) are expressed in terms of fj as We define some values characterizing the plysical quantities: l/w. as the time scale. efw. as the," So the source terms in Equation \ref{wave}) ) are expressed in terms of $f_j$ as We define some values characterizing the physical quantities; $1/\omega_\mathrm{e}$ as the time scale, $c/\omega_\mathrm{e}$ as the"79Correlations between the elobal X-ray properties of galaxy clusters have proven to be important probes of the intracluster mecium (ICAL).,Correlations between the global X-ray properties of galaxy clusters have proven to be important probes of the intracluster medium (ICM).80 Studies of the relation between the X-rav luminosity (Ly) aud the oenuüssion-weighted temperature (Ly) have been particularly powerful., Studies of the relation between the X-ray luminosity $L_X$ ) and the emission-weighted temperature $T_X$ ) have been particularly powerful.81" Numerical simulations aud analytic models that take iuto account the effects of eravity aud shock heating of the eas oulv (ie. the so-called ""self-inübu models) predict that LyxTX for uassive clusters. vet the observed relation is auch steeper: LyxTiHU (ee. Abwkeviteh 1995: Allen Fabian 1998: Arnaud Evi 1999)."," Numerical simulations and analytic models that take into account the effects of gravity and shock heating of the gas only (i.e., the so-called “self-similar” models) predict that $L_X \propto T_X^2$ for massive clusters, yet the observed relation is much steeper; $L_X \propto T_X^{2.6-3.0}$ (e.g., Markevitch 1998; Allen Fabian 1998; Arnaud Evrard 1999)."82 A umber of other observed N-vav scaling relations. for exaauple the total cluster mass (CAM) Ty aud total TCA nass )-Ey velatious. have also receutlv. been shown to deviate(Aga. from thei predicted scalings (6.8... Horner et al.," A number of other observed X-ray scaling relations, for example the total cluster mass $M_{tot}$ $T_X$ and total ICM mass $M_{gas}$ $T_X$ relations, have also recently been shown to deviate from their predicted scalings (e.g., Horner et al."83 1999: Ettori Fabian 1999: Mohr et al., 1999; Ettori Fabian 1999; Mohr et al.84 1999: Vikhlinin et al., 1999; Vikhlinin et al.85 1999: Nevalainen et al., 1999; Nevalainen et al.86 2000: Finogueuov et al., 2000; Finoguenov et al.87 2001: MeCarthyv et al., 2001; McCarthy et al.88 2002. hereafter MDDU2).," 2002, hereafter MBB02)."89 These diserepaucies between theory aud observations have motivated a ummber of authors to examine the poteutial role of “additional” gas plivsics., These discrepancies between theory and observations have motivated a number of authors to examine the potential role of “additional” gas physics.90 For example. the heating of the ICAL by ealactic winds and/or quasar outflows has been investigated by Kaiser (1991) aud also by a whole host of subsequent authors (c.g.. Evrard Ieurx 1991: Bower 1997: Balogh et al.," For example, the heating of the ICM by galactic winds and/or quasar outflows has been investigated by Kaiser (1991) and also by a whole host of subsequent authors (e.g., Evrard Henry 1991; Bower 1997; Balogh et al."91 1999: Wu et al., 1999; Wu et al.92 2000: Loewenstein 2000: Tozzi Norman 2001: Dorsani ct al., 2000; Loewenstein 2000; Tozzi Norman 2001; Borgani et al.93 2001: Babul et al., 2001; Babul et al.94 2002. hereafter DBLDP02: MDD02: Nath Rovchowdlury 2002: Lloyd-Davies et al.," 2002, hereafter BBLP02; MBB02; Nath Roychowdhury 2002; Lloyd-Davies et al."95 2002)., 2002).96 Receutly. the effects of radiative cooling ou N-rav scaling relations have also been explored (c.g.. Bryan 2000: Voit Bryan 2001: Wu Xue 2002: Thomas et al.," Recently, the effects of radiative cooling on X-ray scaling relations have also been explored (e.g., Bryan 2000; Voit Bryan 2001; Wu Xue 2002; Thomas et al."97 2002: Voit et al., 2002; Voit et al.98 2002: Dave et al., 2002; Davé et al.99 2002)., 2002).100 These studies fiud hat both heating aud cooling cau act in ao similar uanner. by raising the mean eutropv of the iutracluster eas and. in some cases; establishing a core in the eutropy motile.," These studies find that both heating and cooling can act in a similar manner, by raising the mean entropy of the intracluster gas and, in some cases, establishing a core in the entropy profile."101 This. iu turn. modifies the X-ray scaling relations of clusters and amelorates. or possibly clinunates. the discrepancies between theory aud observations.," This, in turn, modifies the X-ray scaling relations of clusters and ameliorates, or possibly eliminates, the discrepancies between theory and observations."102 It also xteutiallv explains the cmereie observational evidence or an “entropy floor” in nearbv erowps and low nass clusters (Pomman et al., It also potentially explains the emerging observational evidence for an “entropy floor” in nearby groups and low mass clusters (Ponman et al.103 1999: Llovd-Davics et al., 1999; Lloyd-Davies et al.104 2000)., 2000).105 Thus far. X-ray observations alone lave provided evidence for the entropy floor and it has come alimost entirely from low redshift (2= 0.2) groups/clusters.," Thus far, X-ray observations alone have provided evidence for the entropy floor and it has come almost entirely from low redshift $z \lesssim 0.2$ ) groups/clusters."106 Observations of higher redshift clusters are hindered by cosinological dinuuing [the bolometric N-ray surface brightuess of a cluster scales as (112) !., Observations of higher redshift clusters are hindered by cosmological dimming [the bolometric X-ray surface brightness of a cluster scales as $(1+z)^{-4}$ ].107 An additional.independent. probe which could be used to confirm the presence of this excess cutropy in low/intermediate redshift clisters aud also provide new tests for their high redshift counterparts would be quite useful.," An additional, probe which could be used to confirm the presence of this excess entropy in low/intermediate redshift clusters and also provide new tests for their high redshift counterparts would be quite useful."108" Here. we show that scaling relations based ou the thorial Suuvaev-Zeldovich effect (Suunvaev Zelcovich 1972: 1980) - hereafter referred to as the ""SZ effect™ - cau provide such a probe."," Here, we show that scaling relations based on the thermal Sunyaev-Zeldovich effect (Sunyaev Zeldovich 1972; 1980) - hereafter referred to as the “SZ effect” - can provide such a probe."109 The SZ effect is a fractional change in the teiiperature/iutensitv οἳ the cosnüc nücrowave background (CAIB) caused by. the inverse-Compton scattering of CAIB photous off high. cuerey olectrous in the ICAL, The SZ effect is a fractional change in the temperature/intensity of the cosmic microwave background (CMB) caused by the inverse-Compton scattering of CMB photons off high energy electrons in the ICM.110 On average. the plotous eain a small iunouut of this energv from the scatterings and this results iu a slight spectral distortion of the CMD towards clusters.," On average, the photons gain a small amount of this energy from the scatterings and this results in a slight spectral distortion of the CMB towards clusters."111We reproduce the relevant linear theory velocity predictions here. but generalised to linearly biased tracers with bias Ph: where pe=6P denotes the angle between the LOS and the pair separation vector and o is the one-dimensional velocity dispersion. +(v(x):V(X)).,"We reproduce the relevant linear theory velocity predictions here, but generalised to linearly biased tracers with bias $b$: where $\mu = \hat{\ell} \cdot \hat{r}$ denotes the angle between the LOS and the pair separation vector and $\sigma_v^2$ is the one-dimensional velocity dispersion, $\frac{1}{3}\left\langle{\bf v}({\bf x}) \cdot {\bf v}({\bf x})\right\rangle$."112" Our Fourier convention is derived the linear theory redshift space distortion limit in configuration space under the assumption that the density and velocity fields are Gaussian. which amounts to evaluating the following expression: where oj» and vj,» are the density and LOS velocity at two points with real space separation v along the LOS and 7. perpendicular to the LOS. and 6? is the Dirac delta function ensuring that the pair is mapped to redshift space separation Ες."," Our Fourier convention is derived the linear theory redshift space distortion limit in configuration space under the assumption that the density and velocity fields are Gaussian, which amounts to evaluating the following expression: where $\delta_{1/2}$ and $v_{1/2}$ are the density and LOS velocity at two points with real space separation $y$ along the LOS and $r_{\sigma}$ perpendicular to the LOS, and $\delta^D$ is the Dirac delta function ensuring that the pair is mapped to redshift space separation $r_{\pi}$."113 We can then re-express 0? and compute the expectation. value. assuming Gaussian statistics190511: If we expand Eq.," We can then re-express $\delta^D$ and compute the expectation value, assuming Gaussian statistics: If we expand Eq."114 15. to linear order. the redshift space correlation function is equivalent to where εν)=ῥ is the real space linear galaxy correlation function evaluated at redshift space separation s=ησε απ r=rtt+vds the real space separation of the pair.," \ref{eq:exactgaussian} to linear order, the redshift space correlation function is equivalent to where $\xi_g^r(s) = b^2 \xi_m^r(s)$ is the real space linear galaxy correlation function evaluated at redshift space separation $s^2=r_\sigma^2 + r_\pi^2$ and $r^2 = r_{\sigma}^2 + y^2$ is the real space separation of the pair."115 We expand the last two terms to elucidate the contribution from different halo velocity statistics as a function of angle and separation., We expand the last two terms to elucidate the contribution from different halo velocity statistics as a function of angle and separation.116 The terms proportional to 5/ in Eq., The terms proportional to $bf$ in Eq.117 6 arise from the pairwise infall and its derivative as a function of separation r (denoted with ’ throughout). and terms proportional to f° arise from the pairwise velocity dispersion and its first and second derivatives: Since the theoretical prediction for the redshift space correlation function depends on first and second derivatives of velocity statistics. scale-dependent errors on a theoretical model for these functions can translate into large errors on &.," \ref{pkkaiser} arise from the pairwise infall and its derivative as a function of separation $r$ (denoted with $'$ throughout), and terms proportional to $f^2$ arise from the pairwise velocity dispersion and its first and second derivatives: Since the theoretical prediction for the redshift space correlation function depends on first and second derivatives of velocity statistics, scale-dependent errors on a theoretical model for these functions can translate into large errors on $\xi^{s}$."118 Eg., Eq.119" 18. also demonstrates that at linear order. any constant. isotropic velocity dispersion does not alter the redshift space correlation function. since only the difference T,(7)—I(ry enters. along with derivatives of those functions."," \ref{vdispexpand} also demonstrates that at linear order, any constant, isotropic velocity dispersion does not alter the redshift space correlation function, since only the difference $\Psi_{\perp}(r) - \Psi_{\parallel}(r)$ enters, along with derivatives of those functions."120 It is standard practise to expand the dependence of PCR) or £s) on the LOS angle in Legendre polynomials. which we here write as L; to avoid confusion with the power spectrum moments: The power spectrum moments are given by In linear theory. only €= 0. 2. and4 are non-zero.," It is standard practise to expand the dependence of $P(\mathbf{k})$ or $\xi(\mathbf{s})$ on the LOS angle in Legendre polynomials, which we here write as $L_\ell$ to avoid confusion with the power spectrum moments: The power spectrum moments are given by In linear theory, only $\ell =$ 0, 2, and4 are non-zero."121" The power spectrum is particularly simple because the &-dependencies of the Legendre moments P;(4) are identical. and the relative amplitudes depend only on the sample bias 6 and the rate of structure growth """," The power spectrum is particularly simple because the $k$ -dependencies of the Legendre moments $P_\ell(k)$ are identical, and the relative amplitudes depend only on the sample bias $b$ and the rate of structure growth $f$ ."122 Fourier transforming to configuration space gives, Fourier transforming to configuration space gives123Iu order to understand the dynamics of a galaxy it is crucial to know propertics of its radio population.,In order to understand the dynamics of a galaxy it is crucial to know properties of its radio population.124 ADuch has been learned about the Milkv Wav frou radio observations of the supernova remmanuts (SNRs). regions. aud pulsars detected within it.," Much has been learned about the Milky Way from radio observations of the supernova remnants (SNRs), regions, and pulsars detected within it."125 However. a conrplete census of radio sources in the Milkv Way is difficult to obtain because of source confusion.," However, a complete census of radio sources in the Milky Way is difficult to obtain because of source confusion."126 Iu addition. since the distances to these sources are often extremely uncertain. it is difficult to determine their properties.," In addition, since the distances to these sources are often extremely uncertain, it is difficult to determine their properties."127 As a result. it is advantageous to observe exterual galaxies to learn about the dvuamics and properties of “ioral” ealaxies.," As a result, it is advantageous to observe external galaxies to learn about the dynamics and properties of “normal” galaxies."128 The first step of this process is to obtain a census of radio populations in a galaxy. aud it is for this reason that we have surveyed the radio population of M31. the nearest spiral galaxy.," The first step of this process is to obtain a census of radio populations in a galaxy, and it is for this reason that we have surveyed the radio population of M31, the nearest spiral galaxy."129 ADAE has been surveyed in the radio before. both as parts of larger surveys such as the WENSS (2). aud NVSS (7) survers. and as the focus of dedicated surveys such as the SOW (2).. 37W (2). and Braun (7). surveys. the propertics of all of which are sunuuarized in Table ??7..," M31 has been surveyed in the radio before, both as parts of larger surveys such as the WENSS \citep{wenss} and NVSS \citep{nvss} surveys, and as the focus of dedicated surveys such as the 36W \citep{36w}, 37W \citep{37w}, and Braun \citep{braun} surveys, the properties of all of which are summarized in Table \ref{catprop}."130 Despite its prosimuty to the Milkv Was. mapping MOI is dithicult because its large aneular size on the skv (27) requires inauy poiutiugs at higher radio frequeucies (7z1 CGIIz) to fully cover.," Despite its proximity to the Milky Way, mapping M31 is difficult because its large angular size on the sky $>$ $^\circ$ ) requires many pointings at higher radio frequencies $\nu \ga 1$ GHz) to fully cover."131 As a result. existing survevs of M31 are either deep but cover ouly a πια] region of M31. or cover the entire optical disk of N31 with relatively poor seusitivitv. as shown iu Table ?? and Figure L..," As a result, existing surveys of M31 are either deep but cover only a small region of M31, or cover the entire optical disk of M31 with relatively poor sensitivity, as shown in Table \ref{catprop} and Figure \ref{pbeam}."132 Because of this. the radio population of discrete sources in AL31 is not well uuderstood.," Because of this, the radio population of discrete sources in M31 is not well understood."133 To rectify this situation. we have surveved ADM with the Very Large (VLA) at 325 ΛΠΙΣ (\=90 cn) using the A-confieuration. achieving a lo sensitivity less than a indy with a resolution of (~20 pe at the distance of NI. assiuued to be τοῦ kpe: ?. 2)) over the entire optical disk of M31 because of the large size of the VLAs primary beam at this frequency.," To rectify this situation, we have surveyed M31 with the Very Large (VLA) at 325 MHz $\lambda=90~\mbox{cm}$ ) using the A-configuration, achieving a $\sigma$ sensitivity less than a mJy with a resolution of $\sim$ 20 pc at the distance of M31, assumed to be 780 kpc; \citeauthor{stanek} \citeyear{stanek}) ) over the entire optical disk of M31 because of the large size of the VLA's primary beam at this frequency."134 Using the A-configuration has the advantage that exteuded emissiou from M31 was resolved out. allowing us to better determine the properties of the compact radio population.," Using the A-configuration has the advantage that extended emission from M31 was resolved out, allowing us to better determine the properties of the compact radio population."135 As secu in Table ??.. the survey presented here does very well iu resolution (0ο) vs. field of view (FOV) when compared to past survevs of M31. aud has a similar scusitivity to that of previous higher frequency survevs.," As seen in Table \ref{catprop}, the survey presented here does very well in resolution $\theta_{res}$ ) vs. field of view (FOV) when compared to past surveys of M31, and has a similar sensitivity to that of previous higher frequency surveys."136 This paper describes the observations. the data reduction process that led to the final source list. aud the statistical properties of the detected sources.," This paper describes the observations, the data reduction process that led to the final source list, and the statistical properties of the detected sources."137 This paper is structured as follows: Section 2. describes the observations, This paper is structured as follows: Section \ref{analysis} describes the observations138or voids than for the backeround.,for voids than for the background.139 As a result. a small growth in structure results iu the production of (fractionallv) many nore galaxies at high masses.," As a result, a small growth in structure results in the production of (fractionally) many more galaxies at high masses."140 Finally. we can ask. “Wow much matter las any galaxy accreted since a previous epoch?”," Finally, we can ask, “How much matter has any galaxy accreted since a previous epoch?”"141 We may set a density hreshold. aud ask. for a given epoch. for what mass is the cumulative mass fiction equal to that density?," We may set a density threshold, and ask, for a given epoch, for what mass is the cumulative mass function equal to that density?"142 The bottom ΠΟ] in Fie., The bottom panel in Fig.143 3 shows the evolution of this fuuctiou for 1019 aud 101275.TAL..., \ref{fg:evolve} shows the evolution of this function for $10^{10}$ and $10^{12} h^{-1}M_\odot$.144" The fact that in the backeround a 10195.TAL, ealaxy achieves a ΙΑΝ mass around 2z1.5 sugeests that a significant fraction of this mass accretion is in the form of iiergers.", The fact that in the background a $10^{10}h^{-1}M_\odot$ galaxy achieves a maximum mass around $z\simeq 1.5$ suggests that a significant fraction of this mass accretion is in the form of mergers.145 This simple picture suggests that for the few high mass galaxies in voids. we would expect a relatively high yaction of recent mass accretion.," This simple picture suggests that for the few high mass galaxies in voids, we would expect a relatively high fraction of recent mass accretion."146 This is consistent with the result found by Rojas et al. (, This is consistent with the result found by Rojas et al. (1472001b) who fouud a relatively Heh specific star formation rate in voids compared to wall regions.,2004b) who found a relatively high specific star formation rate in voids compared to wall regions.148 Iu Figure d we show the estimated SDSS void galaxy mass fuuctiou for Dark Matter Scale Factors. $=2.5 aud 10.," In Figure \ref{fg:massfunc} we show the estimated SDSS void galaxy mass function for Dark Matter Scale Factors, $S=$ 2, 5 and 10."149" For coluparison. we also show the expected Press-Schechter mass functions for 0,=0.9 (observed mean galaxy uuiderdeusity) and ὃς=0 (background) euvirouiments. aud determine the best value of ὃν for each value of S. by matching the cumulative munber density of objects at [ times the mass detection limit."," For comparison, we also show the expected Press-Schechter mass functions for $\delta_v=-0.9$ (observed mean galaxy underdensity) and $\delta_v=0$ (background) environments, and determine the best value of $\delta_v$ for each value of $S$, by matching the cumulative number density of objects at 4 times the mass detection limit."150 We note that the mimimatin value of Roy observed in the spiral sample is approximately 2 kpc. and that the maxima observable absolute magnitude is -18.," We note that the minimum value of $R_{90}$ observed in the spiral sample is approximately 2 kpc, and that the maximum observable absolute magnitude is -18."151 Combining these results. we find a uuimiunua detectable mass of S«6«10°TAL...," Combining these results, we find a minimum detectable mass of $S\times 6\times 10^{9} h^{-1} M_\odot$."152 This mass detection limit is shown bv a vertical dashed line in the bottom panels of Fig. b.., This mass detection limit is shown by a vertical dashed line in the bottom panels of Fig. \ref{fg:massfunc}.153 The mass detection limit is determined by relating the fliux-liuited minim velocity estimate with a fit relation between size aud. Iuninosity., The mass detection limit is determined by relating the flux-limited minimum velocity estimate with a fit relation between size and luminosity.154 It should be noted that the mass function does uot flatten out considerably bevoud this limit., It should be noted that the mass function does not flatten out considerably beyond this limit.155 In other words. we do not see a deficit of low mass/low luuinosity galaxies in voids bevond what is expected by Press-Schecliter analysis aud our detection limit.," In other words, we do not see a deficit of low mass/low luminosity galaxies in voids beyond what is expected by Press-Schechter analysis and our detection limit."156 Tn addition to plotting the mass function for all galaxies. we subclivide our sample into ellipticals aud spirals in Fie. L.," In addition to plotting the mass function for all galaxies, we subdivide our sample into ellipticals and spirals in Fig. \ref{fg:massfunc}."157 Ellipticals clearly cousitute the high-mass end of the spectrum. and their distribution tends to be much flatter than the distribution of spirals. which dominate at low aud intermediate mass.," Ellipticals clearly consitute the high-mass end of the spectrum, and their distribution tends to be much flatter than the distribution of spirals, which dominate at low and intermediate mass."158 For comparison. we plot a dass function estimated from the stellar mass distribution elven by Kauffmann et al. (," For comparison, we plot a mass function estimated from the stellar mass distribution given by Kauffmann et al. ("1592003) from the SDSS First Data Release (Abazajian ct al.,2003) from the SDSS First Data Release (Abazajian et al.160 2003)., 2003).161 To turn these iuto total mass distributions. we assume a constant mass-stellay mass ratio of 3. as estimated for cllipticals by Padmanabhan et al.," To turn these into total mass distributions, we assume a constant mass-stellar mass ratio of 3, as estimated for ellipticals by Padmanabhan et al."162 2001., 2004.163 The mass-stellar mass ratio of spirals is expected to be larger than for ellipticals. even if the barvon ratio for both is the same. since spirals are expected to be more gas rich.," The mass-stellar mass ratio of spirals is expected to be larger than for ellipticals, even if the baryon ratio for both is the same, since spirals are expected to be more gas rich."164 It is clear. however. that this simple estimate of the mass function does not produce a good fit to the slope of the Press-Schechter mass fuuctious.," It is clear, however, that this simple estimate of the mass function does not produce a good fit to the slope of the Press-Schechter mass functions."165 For our “dynamical” mass estimates. lower values of S appear to produce a better fit to the shape of a Press-Schechter function.," For our “dynamical” mass estimates, lower values of S appear to produce a better fit to the shape of a Press-Schechter mass function."166" This"". is ↴∙∙confirmed via⋅ a∙ series of∙ 47 ⊳⋅≻tests.", This is confirmed via a series of $\chi^2$ tests.167" For ο =⊲2.5.10.+the⋅ fits tod,↘ = T(0.82.0,c =-.0.73.andmass 6. =0.62.respectively, produce q per degree of freedom of 3.3. 8.2 and 11.7."," For $S=2,5,10$ , the fits to $\delta_v=-0.82$, $\delta_v=-0.73$, and $\delta_v=-0.62$, respectively, produce $\chi^2$ per degree of freedom of $3.3$, $8.2$ and $14.7$."168 Note that we only model this fit out to masses of 5«1012AL..., Note that we only model this fit out to masses of $5\times 10^{12}M_\odot$.169 Bevoud that. all three models produce at most 1 ealaxy per bin. in cach case. an Elliptical.," Beyond that, all three models produce at most 1 galaxy per bin, in each case, an Elliptical."170 Since these galaxy nmniasses are somewhat uureasonablv large. it may be that we have simply uuderestimated the uncertainty in velocity measurement for the Ellipticals.," Since these galaxy masses are somewhat unreasonably large, it may be that we have simply underestimated the uncertainty in velocity measurement for the Ellipticals."171" Since in all cases we measure 4?21. it is clear that despite au excellent ""chi-by-eye; we have not correctly characterized either our uncertainties or our mass nieasurenieuts,"," Since in all cases we measure $\chi^2 > 1$, it is clear that despite an excellent “chi-by-eye,” we have not correctly characterized either our uncertainties or our mass measurements."172; Oue of the most likely culprits is that the halo extent parameter. 9. is an explicit function of mass.," One of the most likely culprits is that the halo extent parameter, $S$, is an explicit function of mass."173 Civenu the other uucertaimties in our measurements. it is unrealisticallv optimistic to try to claim a functional form of this term with any confidence.," Given the other uncertainties in our measurements, it is unrealistically optimistic to try to claim a functional form of this term with any confidence."174 Since a given value of 5 implies an uuderdeusitv in Dark Matter for the cusemble of voids. we show. in Fig.," Since a given value of $S$ implies an underdensity in Dark Matter for the ensemble of voids, we show, in Fig."175 5 the explicit relationship between these two terms., \ref{fg:bias} the explicit relationship between these two terms.176" Moreover. a simple calculation of the “typical” galaxy density within our selected void sauple ΠΡΟΣ of observed galaxies. divided by total void volume). viclds 04,,;,—0.77."," Moreover, a simple calculation of the “typical” galaxy density within our selected void sample (number of observed galaxies, divided by total void volume), yields $\delta_{v,gal}=-0.77$."177 Since lower values of S are eeucrally preferred Grom a 4? poiut of view). we that voids may. in fact. be nearly wibiased tracers of dark matter.," Since lower values of $S$ are generally preferred (from a $\chi^2$ point of view), we that voids may, in fact, be nearly unbiased tracers of dark matter."178 Even for larger values of 5=10. we find 5=1.21. consistent with typical bias relations found im the universe at laree.," Even for larger values of $S=10$, we find $b=1.24$, consistent with typical bias relations found in the universe at large."179 There remain several untested assumptions in this study., There remain several untested assumptions in this study.180 For example. though compact halos are most consistent witli our theoretical mass function models. Press-Schechter has not been tested against observations in very low density void regions.," For example, though compact halos are most consistent with our theoretical mass function models, Press-Schechter has not been tested against observations in very low density void regions."181 Moreover. we asstuned that the TF relation in the field would necessarily hold for void galaxies as well.," Moreover, we assumed that the TF relation in the field would necessarily hold for void galaxies as well."182 However. ax Rojas et al. (," However, as Rojas et al. ("1832001a) has shown. the photometric properties of void ealaxies differ from those of wall galaxies. aud thus we would not be surprised to find a ciffereut TF relation.,"2004a) has shown, the photometric properties of void galaxies differ from those of wall galaxies, and thus we would not be surprised to find a different TF relation."184 Future prospects for work in this direction include more systematic estimates of the rotation curves of void spirals., Future prospects for work in this direction include more systematic estimates of the rotation curves of void spirals.185 Ideally. followup observations using loue-slit spectroscopy could potentially vield a TF relation for voids which differs sjeuificautlv from wall regions.," Ideally, followup observations using long-slit spectroscopy could potentially yield a TF relation for voids which differs significantly from wall regions."186 Additionally. as the numbers of uown void galaxies increase. galaxy-ealaxy eravitational leusiug will become a potentially powerful probe for mieasumiug mass profiles aud halo exteuts.," Additionally, as the numbers of known void galaxies increase, galaxy-galaxy gravitational lensing will become a potentially powerful probe for measuring mass profiles and halo extents."187 Since the separation between a lens aud a source galaxy is much larger than the scale of a void (A+20.5 in many cases) au isolated void ealaxy lens may still have many potential sources tolens., Since the separation between a lens and a source galaxy is much larger than the scale of a void $\Delta z\simeq 0.5$ in many cases) an isolated void galaxy lens may still have many potential sources tolens.188 DMCG acknowledges support from NSF evant AST-0205080., DMG acknowledges support from NSF grant AST-0205080.189 MSV acknowledecs support from NSF eraut. AST-0071201., MSV acknowledges support from NSF grant AST-0071201.190detected inνο and longer wavelength baud).,detected in$K_S$ and longer wavelength bands).191 Region C. on the north-west side. has a long tail coutainiug bright red clusters as well.," Region C, on the north-west side, has a long tail containing bright red clusters as well."192 Dust is clearly appareut in this inagoe. as shown by the red fibuneuts observed to the south-cast side between A and D. These appear to be blown away from the central region. rapidly dissolviug in 22-10's interstellar inediui.," Dust is clearly apparent in this image, as shown by the red filaments observed to the south-east side between A and B. These appear to be blown away from the central region, rapidly dissolving in 2-10's interstellar medium."193 Assuniug for the dust clouds a velocity equal to the typical sound speed iu the ISAL ie. 10 —10 knees . hence a growing rate of ~ ρολ the present radi of curvature of the filaments ~50| I00ppe vield dviuuical ages of 5. 10M.," Assuming for the dust clouds a velocity equal to the typical sound speed in the ISM, i.e. 10 $\sim 10$ $\cdot$ $^{-1}$, hence a growing rate of $\sim10$ $/$ Myr, the present radii of curvature of the filaments $\sim 50-100$ pc yield dynamical ages of $~5-10$ Myr."194 Reeion A is also flanked by two compact red sources that are ouly visible at As aud longer wavelengths., Region A is also flanked by two compact red sources that are only visible at $K_S$ and longer wavelengths.195 These two sources eet brighter with longer wavelcugths. as shown iu Figure 3..," These two sources get brighter with longer wavelengths, as shown in Figure \ref{figmulti}."196 The various colors of the sources hint at a lighly heterogeueous dust content. aud possibly age differences among the cluster population.," The various colors of the sources hint at a highly heterogeneous dust content, and possibly age differences among the cluster population."197 Recent observations in the optical. IR. and radio. have brought new exciting facts.," Recent observations in the optical, IR, and radio, have brought new exciting facts."198 First. the vouth of the starburst event in the center was confirmed by STIS analysis of the brightest UVoptical kuots by Chandarctal.(2003) which vielded a coeval formation age of 1-5 Myr for all optical clusters.," First, the youth of the starburst event in the center was confirmed by STIS analysis of the brightest UV/optical knots by \citet{chandar03} which yielded a coeval formation age of 4-5 Myr for all optical clusters."199 Second. the presence and importance of dust in the central region was confirmed bw high-resolution iunid-infrared observations (Sauvageetal.1997:Beck2001:Vacca 2002):: the majority )) of the MIR. eiission is confined to a 5 reeion. compatible iu size with the location of the observed starburst.," Second, the presence and importance of dust in the central region was confirmed by high-resolution mid-infrared observations \citep{sauvage97,beck01,vacca02}: the majority ) of the MIR emission is confined to a $\sim5""$ region, compatible in size with the location of the observed starburst."200 However the intrinsically large uncertainties in MIB. astrometry preveuted a clear of ideutificatiou theMIR sources., However the intrinsically large uncertainties in MIR astrometry prevented a clear identification of the MIR sources.201 Finally. the radio observatious of RkobuluickvJohnson(1999.2000)— evidenced 5 compact radio sources (hereafter called the radio kuots) characterized by mostly thermal spectra.," Finally, the radio observations of \citet{kobulnicky99,kobulnicky00} evidenced 5 compact radio sources (hereafter called the radio knots) characterized by mostly thermal spectra."202 The striking norphological resemblance between the radio kuots and the MIB cunission allowed to tie down the location of the MIR. sources precisely (Becketal.2001)., The striking morphological resemblance between the radio knots and the MIR emission allowed to tie down the location of the MIR sources precisely \citep{beck01}.203. Furthermore. comparing with UST images. IKobuluickv&Johuson(1999.2000) argue that most of these radio-MIBR sources were off-centered. oei the dusty area between region A aud D. Thev thus attributed this enuüssjon to voung (4 «Myr) ultra dense (UD) IIT regious with ongoing star formation hidden m deuse molecular clouds.," Furthermore, comparing with HST images, \citet{kobulnicky99,kobulnicky00} argued that most of these radio-MIR sources were off-centered, in the dusty area between region A and B. They thus attributed this emission to young $1<$ Myr) ultra dense (UD) HII regions with ongoing star formation hidden in dense molecular clouds."204 Following this iuterpretation.(2001).. froin. 1μι observations.derived that up to 10! OTV stars (equivalent to 1079. Lyinan pliotous:s 1j anust be hidden in these dense cocoons. and Vaccaetal.(2002)... from 10.5jn observations. computed that LOCAL. of dust aud eas nmst be surrounding the UD ΠΠ regions aud estimated the bolometric hnuuinositv of the brightest MIR region overlapping with radio knot Lto be as nimcli as 2«L0°L... Jolinso," Following this interpretation, from $11.7\mu$ m observations,derived that up to $10^4$ O7V stars (equivalent to $10^{49}$ Lyman $\cdot$ $^{-1}$ ) must be hidden in these dense cocoons, and \citet{vacca02}, from $10.8\,\mu$ m observations, computed that $10^7 M_\odot$ of dust and gas must be surrounding the UD HII regions and estimated the bolometric luminosity of the brightest MIR region overlapping with radio knot 4 to be as much as $2\times10^9 L_\odot$."205u&Kobul-nicky(2003) extended the racio observations aud refined the measurement of plivsical properties of the UD WIT regions. iu particular au anomalous low mass ΠΠ coutent o28 SLOPML was found. attributed to the extreme vouth of the objects.," \citet{johnson03} extended the radio observations and refined the measurement of physical properties of the UD HII regions, in particular an anomalous low mass HII content of $\times10^3 M_\odot$ was found, attributed to the extreme youth of the objects."206 Therefore. as of today. 22-10 appears as a spectacular case of a starburst galaxy where a laree fraction of its most curent star formation activity lies completely buried in dust. aud has absolutely uo visible counterpart.," Therefore, as of today, 2-10 appears as a spectacular case of a starburst galaxy where a large fraction of its most current star formation activity lies completely buried in dust, and has absolutely no visible counterpart."207 We present here high-resolution observations iu Ivy (2.2gnuj with VLT/ISAAC 270.B-50116A))). £7 Cj). aac AL (i8pau) bands with the Adaptive Optics CCONICA ))) that eive the highes resolution to date of the nucleus of 22-10 in the NIR. a waveleugth τοσο adequately located between the stellar optical regime iux the dust thermal regine.," We present here high-resolution observations in $K_S$ $2.2\mu$ m) with VLT/ISAAC ), $L'$ $\mu$ m), and $M'$ $\mu$ m) bands with the Adaptive Optics CONICA ) that give the highest resolution to date of the nucleus of 2-10 in the NIR, a wavelength regime adequately located between the stellar optical regime and the dust thermal regime."208 The high quality of the observations allows the identification.for the first time. of bright £7 resions which correlate with radio knots (Iobuluickv&Jolson1999).. aud Ivy regions that correlate with the optically bright cluster. thus bridging the existing wavelength gap.," The high quality of the observations allows the identification,for the first time, of bright $L'$ regions which correlate with radio knots \citep{kobulnicky99}, and $K_S$ regions that correlate with the optically bright cluster, thus bridging the existing wavelength gap."209" We observed 22-10 in Ns using ISAAC at the ESO VLT/Autu uuder 0.3” seeing (Figure 1)). aud in Z aud AL with the adaptive optics system NAOS-CONICA at the ESO VLT/Yepun. reaching a corrected PSE full width at halt naxumnunn (FWIIM) of 0.12""."," We observed 2-10 in $K_S$ using ISAAC at the ESO VLT/Antu under $\arcsec\,$ seeing (Figure \ref{figKs}) ), and in $L'$ and $M'$ with the adaptive optics system NAOS-CONICA at the ESO VLT/Yepun, reaching a corrected PSF full width at half maximum (FWHM) of $\arcsec$ ."210 The observations were obtained iu service mode iu 2003-2001., The observations were obtained in service mode in 2003-2004.211 We used standard observing strategies., We used standard observing strategies.212" In Γι we alternated exposures between the object aud the sky in 15 ABBA sequences with a throw of 10"".", In $L'$ we alternated exposures between the object and the sky in 15 ABBA sequences with a throw of .213", Object cubes (vespectively sky cubes) cousisted of 220 (110) raucdom ss jitter for a total", Object cubes (respectively sky cubes) consisted of 220 (110) random s jitter for a total214can also be found in single galaxies to explain their flat rotation curves.,can also be found in single galaxies to explain their flat rotation curves.215 The second proposal results in the modified Newtonian dvnamics (MOND). proposed by Milgrom. based on a modification of Newtons second law of motion (Milgrom. 1933).," The second proposal results in the modified Newtonian dynamics (MOND), proposed by Milgrom, based on a modification of Newton's second law of motion (Milgrom, 1983)."216 This well known law states that an object of mass m subject to a force F undergoes an acceleration e bv the simple equation F=me., This well known law states that an object of mass $m$ subject to a force $F$ undergoes an acceleration $a$ by the simple equation $F=ma$.217 However. it has never been verified [or extremely small accelerations which are happening at the scale of galaxies.," However, it has never been verified for extremely small accelerations which are happening at the scale of galaxies."218 The modification proposed by Milgrom was the following where ay=1.2x10.imis7 is a proposed new constant., The modification proposed by Milgrom was the following where $a_0=1.2\times10^{-10} ms^{-2}$ is a proposed new constant.219 The acceleration e is usually much greater than ej for all physical effects in evervday life. therefore ία/ag)—1. and Fo-—ma as usual.," The acceleration $a$ is usually much greater than $a_0$ for all physical effects in everyday life, therefore $\mu(a/a_0)$ =1 and $F=ma$ as usual."220 However. at the galactic scale where à~ay we have the moclilied dvnamics F—m) leading to a constant velocity of stars on a circular orbit [ar from the center of galaxies.," However, at the galactic scale where $a \sim a_0$ we have the modified dynamics $F=m(\frac{a^2}{a_0})$ leading to a constant velocity of stars on a circular orbit far from the center of galaxies."221 Another interesting model in this direction has been recently proposed by Sanders., Another interesting model in this direction has been recently proposed by Sanders.222 In (his model. it is assumed that gravitational attraction force becomes more like 1/r bevond some galactic scale (Sanders. 2003).," In this model, it is assumed that gravitational attraction force becomes more like $1/r$ beyond some galactic scale (Sanders, 2003)."223 A test particle at a distance r [rom a large mass AL is subject to the acceleration where C is the Newlonian constant. ry is of the order of the sizes of galaxies and," A test particle at a distance $r$ from a large mass $M$ is subject to the acceleration where $G$ is the Newtonian constant, $r_0$ is of the order of the sizes of galaxies and"224(shown in Fig. 7)),(shown in Fig. \ref{fpdb}) )225" is now much more similar to that of BEL04, demonstrating how the apparent morphology of the emission may depend significantly on the resolution."," is now much more similar to that of BEL04, demonstrating how the apparent morphology of the emission may depend significantly on the resolution."226" Given the larger number of antennas and more circular beam, we believe that our SMA images reproduce the structure of the emission more faithfully than the old maps by BEL04 and BELOS."," Given the larger number of antennas and more circular beam, we believe that our SMA images reproduce the structure of the emission more faithfully than the old maps by BEL04 and BEL05."227 One of the purposes of the present study was to compare the structure and kinematics of the HMC with those of a possible bipolar outflow associated with it., One of the purposes of the present study was to compare the structure and kinematics of the HMC with those of a possible bipolar outflow associated with it.228" The existence of such an outflow had been suggested by Olmi et al. (1996)),"," The existence of such an outflow had been suggested by Olmi et al. \cite{olmi96b}) ),"229 whose, whose230decreasing too quickly with respect to the X-ray brightness.,decreasing too quickly with respect to the X-ray brightness.231" This reflects the point raised in the previous Section, ie. that the slope of the radial distribution of the synchrotron emission in our secondary-generated radio halos is too steep."," This reflects the point raised in the previous Section, i.e. that the slope of the radial distribution of the synchrotron emission in our secondary-generated radio halos is too steep."232" In particular, the adoption of the cosmic ray scaling function (models 2 and 3) causes the emission to decrease in the innermost five patches, which can be seen in the plots as a bending at high brightness."," In particular, the adoption of the cosmic ray scaling function (models 2 and 3) causes the emission to decrease in the innermost five patches, which can be seen in the plots as a bending at high brightness."233" The magnetic field scaling (model 3) adds more power to the outmost regions, resulting in a flattening of the correlation, but still the obtained slope is steeper than found in observations."," The magnetic field scaling (model 3) adds more power to the outmost regions, resulting in a flattening of the correlation, but still the obtained slope is steeper than found in observations."234" There are several observed correlations for radio halos that relate thermal and non-thermal properties of the IGM: those between the radio power at 1.4 GHz, Pi, and the X-ray luminosity, Lx, temperature, and cluster mass (???).."," There are several observed correlations for radio halos that relate thermal and non-thermal properties of the IGM: those between the radio power at 1.4 GHz, $P_{1.4}$, and the X-ray luminosity, $L_X$, temperature, and cluster mass \citep{2000ApJ...544..686L,2001A&A...369..441G,2006MNRAS.369.1577C}."235" In addition, by making use of a sample of 14 giant radio halos, ?) found new scaling relations that connect the radio power, Pr, of halos to the size of the emitting region, Ry (seealso?),, and to the total cluster mass within Ry, My; a geometrical scaling was also found between My and Rx."," In addition, by making use of a sample of 14 giant radio halos, \citet{2007MNRAS.378.1565C} found new scaling relations that connect the radio power, $P_{\mathrm{R}}$, of halos to the size of the emitting region, $R_{\mathrm{H}}$ \citep[see also][]{2009A&A...499..679M}, and to the total cluster mass within $R_{\mathrm{H}}$, $M_{\mathrm{H}}$ ; a geometrical scaling was also found between $M_{\mathrm{H}}$ and $R_{\mathrm{H}}$."236" The observed scalings from ?) are: Specifically, Mi was computed from X-ray observations under the assumption of hydrostatic equilibrium and spherical symmetry."," The observed scalings from \citet{2007MNRAS.378.1565C} are: Specifically, $M_{\mathrm{H}}$ was computed from X-ray observations under the assumption of hydrostatic equilibrium and spherical symmetry."237" This procedure may lead to errors as large as in mass (?) which are expected to be not dependent on cluster mass, so that these errors might introduce considerable scatter without affecting the real trend of the correlation."," This procedure may lead to errors as large as in mass \citep{2006MNRAS.369.2013R} which are expected to be not dependent on cluster mass, so that these errors might introduce considerable scatter without affecting the real trend of the correlation."238" Ry was measured on the radio images, Ry=XRinRmax, where Rmin and Rmax are the minimum and maximum radii measured on the 3c radio isophotes."," $R_{\mathrm{H}}$ was measured on the radio images, $R_{\mathrm{H}}=\sqrt{R_{\mathrm{min}}\times R_{\mathrm{max}}}$, where $R_{\mathrm{min}}$ and $R_{\mathrm{max}}$ are the minimum and maximum radii measured on the $\sigma$ radio isophotes."239" We stress that Ry provides a simple, but viable estimate of the physical size of radio halos, indeed a one-to-one correlation has been found between Ry and the size containing the of the radio halo flux, Rgs, derived from the observed brightness profiles of halos (?).."," We stress that $R_{\mathrm{H}}$ provides a simple, but viable estimate of the physical size of radio halos, indeed a one-to-one correlation has been found between $R_{\mathrm{H}}$ and the size containing the of the radio halo flux, $R_{85}$, derived from the observed brightness profiles of halos \citep{2007MNRAS.378.1565C}."240" A scaling was also found between the size of radio halos and the virial radius of clusters, RyxR2,0?ος (2).."," A scaling was also found between the size of radio halos and the virial radius of clusters, $R_{\mathrm{H}}\propto R_{\mathrm{vir}}^{2.63\pm0.50}$ \citep{2007MNRAS.378.1565C}."241" Given that massive clusters are almost self similar (e.g.?) one might have expected that Ry scales with R,ir and that the radial profiles of the radio emission are self-similar.", Given that massive clusters are almost self similar \citep[e.g.][]{2002ARA&A..40..539R} one might have expected that $R_{\mathrm{H}}$ scales with $R_{\mathrm{vir}}$ and that the radial profiles of the radio emission are self-similar.242" On the contrary, this result proves that self-similarity is broken in the case of the non-thermal cluster components, as first noted by (?).."," On the contrary, this result proves that self-similarity is broken in the case of the non-thermal cluster components, as first noted by \citep{2001ApJ...548..639K}."243" As the synchrotron power depends on both magnetic field scaling and CRe scaling with density, it is unclear what is responsible for the break in the observed properties."," As the synchrotron power depends on both magnetic field scaling and CRe scaling with density, it is unclear what is responsible for the break in the observed properties."244" On the other hand we know from previous work (?) that the magnetic field scaling (with temperature or mass) flattens out for the largest clusters in our simulation, that would imply an expected break of self similarity in the thermal vs non-thermal propertiesof our simulated clusters."," On the other hand we know from previous work \citep{2008arXiv0808.0919D} that the magnetic field scaling (with temperature or mass) flattens out for the largest clusters in our simulation, that would imply an expected break of self similarity in the thermal vs non-thermal propertiesof our simulated clusters."245" ?) showed that all the correlations explored so far for radio halos can be derived by combining the Ry—R, and Pj.4—Ry ", \citet{2007MNRAS.378.1565C} showed that all the correlations explored so far for radio halos can be derived by combining the $R_H-R_v$ and $P_{1.4}-R_H$ 246"Following Colbergetal(2005),, our void finding algorithm consists of two steps: the identification of spherical proto-voids and mergers of proto-voids to form voids of arbitrary shape (all through this paper proto-voids and voids are different things and are not to be confused).","Following \citet{csdgy}, our void finding algorithm consists of two steps: the identification of spherical proto-voids and mergers of proto-voids to form voids of arbitrary shape (all through this paper proto-voids and voids are different things and are not to be confused)."247 The proto-voids are spherical regions in which the average of the density contrast 6=p/p—1 is below some predefined threshold δν.," The proto-voids are spherical regions in which the average of the density contrast $\delta=248\rho/\bar{\rho}-1$ is below some predefined threshold $\delta_v$."249" As shown by Colbergetal (2005),, voids very clearly correspond to the troughs of the initial density field, justifying the assumption that voids grow gravitationally from the initial negative overdensities."," As shown by \citet{csdgy}, voids very clearly correspond to the troughs of the initial density field, justifying the assumption that voids grow gravitationally from the initial negative overdensities."250" Assuming spherical evolution model for the voids (Gunn&Gott1972;aDubinskietal 1993),, the growth of the voids can be studied analytically, and it is found that at the time of shell-crossing the overdensity inside the spherical reaches —0.8."," Assuming a spherical evolution model for the voids \citep{gg, ddglp}, the growth of the voids can be studied analytically, and it is found that at the time of shell-crossing the overdensity inside the spherical proto-void reaches $-0.8$."251" Although this is the result for Einstein-de Sitter cosmology (Colbergetal2005),, we shall adopt it as a guidance and set ó,——0.8 in the coupled scalar field models as well."," Although this is the result for Einstein-de Sitter cosmology \citep{csdgy}, we shall adopt it as a guidance and set $\delta_v=-0.8$ in the coupled scalar field models as well."252" Our void finding algorithm is similar to that of Colbergal (2005),, but it differs from the latter in various details, particularly the treatment of the mergers of proto-voids."," Our void finding algorithm is similar to that of \citet{csdgy}, but it differs from the latter in various details, particularly the treatment of the mergers of proto-voids."253" 'To be clear and self-contained, here we briefly describe our algorithm in separate steps: (1) A regular 128x mesh is set up and the particle densities on this mesh are computed using the Triangular-shaped Cloud (TSC) scheme."," To be clear and self-contained, here we briefly describe our algorithm in separate steps: (1) A regular $128\times128\times128$ mesh is set up and the particle densities on this mesh are computed using the Triangular-shaped Cloud ) scheme."254 This scheme ensures that the density interpolation is smoother than the usually used Cloud-in-Cloud scheme. (, This scheme ensures that the density interpolation is smoother than the usually used Cloud-in-Cloud scheme. (255"2) The local minima in the density field are located, and these are considered as the centres of the proto-voids (vandeWaygaert&vanKampen1993).","2) The local minima in the density field are located, and these are considered as the centres of the proto-voids \citep{wk1993}."256". Top-hat spherical windows with large enough radii so that the smoothed density contrasts inside are greater than 6, are then placed at these minima, and the radii are gradually decreased until the density contrast drops below 6,."," Top-hat spherical windows with large enough radii so that the smoothed density contrasts inside are greater than $\delta_v$ are then placed at these minima, and the radii are gradually decreased until the density contrast drops below $\delta_v$."257 These minima and radii are then taken as the centres and sizes of the proto-voids respectively., These minima and radii are then taken as the centres and sizes of the proto-voids respectively.258" One can also do this for all grid points on our mesh set up a top-had window on each grid point, decrease the radii of the windows until the overdensity at a grid point falls below ó,) as in Keselman,Nusser&Pee-bles(2010),, but this is more time-consuming and we have checked that the two methods lead to compatible results. ("," One can also do this for all grid points on our mesh set up a top-had window on each grid point, decrease the radii of the windows until the overdensity at a grid point falls below $\delta_v$ ) as in \citet{knp2010}, but this is more time-consuming and we have checked that the two methods lead to compatible results. ("2593) The above identified proto-voids are merged as appropriate to form the final voids of arbitrary shapes.,3) The above identified proto-voids are merged as appropriate to form the final voids of arbitrary shapes.260" It is well known that voids occupy the majority of the space, with islands of matter (dark matter halos and galaxies) interconnected by the narrow filaments which go through them."," It is well known that voids occupy the majority of the space, with islands of matter (dark matter halos and galaxies) interconnected by the narrow filaments which go through them."261" As a result, the merging criteria must be chosen carefully: for example, the dumbbell-shaped configurations are better to be avoided (Colbergetal2005) to prevent the proto-voids from all being merged to form a single void as big as the simulation box."," As a result, the merging criteria must be chosen carefully: for example, the dumbbell-shaped configurations are better to be avoided \citep{csdgy} to prevent the proto-voids from all being merged to form a single void as big as the simulation box."262" To this end let's adopt a variant of the merging criterion proposed by Colbergetal(2005),, which consists of the following steps:"," To this end let's adopt a variant of the merging criterion proposed by \citet{csdgy}, , which consists of the following steps:"263empirically [οι for loug period CVs aud implied by magnetic brakiug (Patterson1981).,empirically found for long period CVs and implied by magnetic braking \citep{patterson84}.264. While there is the small probability that V105 Pee is a previously detached white dwarl/M-dwarl binary just establishing contact. it is more likely that it lias been a normal CV in the dant temporarily accreting at a low rate.," While there is the small probability that V405 Peg is a previously detached white dwarf/M-dwarf binary just establishing contact, it is more likely that it has been a normal CV in the past temporarily accreting at a low rate."265 One possiblity is that it is in an extencled state of hibernation 19560).., One possiblity is that it is in an extended state of hibernation \citep{shara86}.266 Such long-term cyclic chauges of the mass trausler rate are believed to be the resporse of a CV to the ellects of a nova explosion aud might be the underlyiug cause lor tle large observed spreacl in inass trausfer raes of CVs at a given orbital period., Such long-term cyclic changes of the mass transfer rate are believed to be the response of a CV to the effects of a nova explosion and might be the underlying cause for the large observed spread in mass transfer rates of CVs at a given orbital period.267 However. broader acceptance of this hypothesis still suffers [rou the difficulty of confirming a decline in the mass-trausler rate in any oL the recorded post novae.," However, broader acceptance of this hypothesis still suffers from the difficulty of confirming a decline in the mass-transfer rate in any of the recorded post novae."268 The discovery of V105 Pee. together with the recent icentification of a number of DA-dM. bina‘ies with alinost-attachecd secondaries (O'Donoghueetal.2003.. etal. 2002.. Gausickeetal.2001)) in the perioc| rauge preferentially occupied by ok 10vae is a first indication that a substantial uumber of hibernating CVs may exist.," The discovery of V405 Peg, together with the recent identification of a number of DA-dM binaries with almost-attached secondaries \citealt{ODonoghue03}, \citealt{Kawka02}, \citealt{Gaensicke04}) ) in the period range preferentially occupied by old novae \citep{Warner02} is a first indication that a substantial number of hibernating CVs may exist."269 Iu contrast to the DÀ-dM. binaries which show 1io obvious sigus of accretion. V105 Pee woid. be the first candidate system occasionally accreting at a low rate.," In contrast to the DA-dM binaries which show no obvious signs of accretion, V405 Peg would be the first candidate system occasionally accreting at a low rate."270 Au alternate hypothesis woud be that VI05 Peg is a CV of the VY Sculytoris sub-class currently stallecl in au exteuded lowel., An alternate hypothesis would be that V405 Peg is a CV of the VY Sculptoris sub-class currently stalled in an extended low.271 In these high-M. nova-like CVs. which preferentially cluster at orbital periods between 3 aud 1: ber. lass transfer is temporarily interrupted at random intervals.," In these $\dot M$, nova-like CVs, which preferentially cluster at orbital periods between 3 and 4 hr, mass transfer is temporarily interrupted at random intervals."272 However. the white cdwarls iu hese systems are very hot with ζω in the range of 10 to 50 klk (Hamilton&Sion2008).. in conrast to the upper limit of 17 klx for V105 Peg set by the GALEN fluxes.," However, the white dwarfs in these systems are very hot with $T_{\rm eff}$ in the range of 40 to 50 kK \citep{Hamilton08}, in contrast to the upper limit of 17 kK for V405 Peg set by the GALEX fluxes."273 The timescale for coolie the heated envelope of the white dwarf to an ellective temperature of 17 klx is 5x107 vr (Towusley&Causicke2009).. which provides a roteh estimate for the time since its last uova erruptlo or the period speut ina VY Sel type low-st:de.," The timescale for cooling the heated envelope of the white dwarf to an effective temperature of 17 kK is $5\times 10^4$ yr \citep{Townsley09}, which provides a rough estimate for the time since its last nova erruption or the period spent in a VY Scl type low-state."274 Because ol the loug implied cooling 1116. we COLclude that V102 Peg is unlikely to be a loug«ornant VY Scl star.," Because of the long implied cooling time, we conclude that V405 Peg is unlikely to be a long-dormant VY Scl star."275 V105 Peg exhibits two features tha suggest it is a 1uagnetic CV. namely (1 frequent changes jetweenu episodes of residual accretion and complete olf states. aud (2) a photometric signal unrelated o the orbital period.," V405 Peg exhibits two features that suggest it is a magnetic CV, namely (1) frequent changes between episodes of residual accretion and complete off states, and (2) a photometric signal unrelated to the orbital period."276 The later could be interpreted as a sigual of au asyuchrouotsly rotating white diwarl., The latter could be interpreted as a signal of an asynchronously rotating white dwarf.277 However. the lalla‘k of such a system would be a truly stable period. wlich our extensive shotometric data fail to show.," However, the hallmark of such a system would be a truly stable period, which our extensive photometric data fail to show."278 Either the accretion process is Liehly uustable iu V105 Pee. whicl would be unusual for such a low accretion rate system. or the sampliug of our data is still not sullicient.," Either the accretion process is highly unstable in V405 Peg, which would be unusual for such a low accretion rate system, or the sampling of our data is still not sufficient."279 Also. most magnetic cataclysimics sow strouger Hell A L686 than seen here. though ii ow states all the emission lines can be much recluced (e.g.. Masonetal. 2007)).," Also, most magnetic cataclysmics show stronger HeII $\lambda$ 4686 than seen here, though in low states all the emission lines can be much reduced (e.g., \citealt{mason07}) )."280 The spectral euergy. cistribution unfortuately does not help to coustrain the likely type of CV., The spectral energy distribution unfortunately does not help to constrain the likely type of CV.281 If the object is strongly magnetic. Le. of a polar type. what would be the field streugth?," If the object is strongly magnetic, i.e. of a polar type, what would be the field strength?"282 Ii which part of the spectrum would the eyclotro spectrum be located?, In which part of the spectrum would the cyclotron spectrum be located?283 The abseuce of a unique spit period equaling the orbital period argues agalst the polar interpretation., The absence of a unique spin period equaling the orbital period argues against the polar interpretation.284 Ou the other hand. the," On the other hand, the"285Tocchini-Valentini (2002).,Tocchini-Valentini (2002).286 In principle. (he coupling could be seen also in astrophysical objects like galaxy clusters by comparing the forces felt by dark matter halos aud barvons (for instance. barvons in the intracluster gas). ie. as an astrophysical test of the violation of the equivalence principle.," In principle, the coupling could be seen also in astrophysical objects like galaxy clusters by comparing the forces felt by dark matter halos and baryons (for instance, baryons in the intracluster gas), i.e. as an astrophysical test of the violation of the equivalence principle."287 This approach. discussed in detail in Gracdwohl Frieman (1992). requires several assumptions on the distribution of dark haloes.," This approach, discussed in detail in Gradwohl Frieman (1992), requires several assumptions on the distribution of dark haloes."288 As emphasized bv Peebles (2002). however. it has the potentiality to open unexplored paths in cosmoloey.," As emphasized by Peebles (2002), however, it has the potentiality to open unexplored paths in cosmology."289 Amendola L. Phys., Amendola L. Phys.290 Rev.D62.. 043511 Amendola L. and D. Tocehini-Valentini. Phys.," Rev., 043511 Amendola L. and D. Tocchini-Valentini, Phys."291 Rev.D64.. 043509," Rev., 043509"292In this paper. we investigate the evolution of non-thermal electrons and Langmuir waves using weak-turbulence theory in a collisional. inhomogeneous solar coronal plasma.,"In this paper, we investigate the evolution of non-thermal electrons and Langmuir waves using weak-turbulence theory in a collisional, inhomogeneous solar coronal plasma."293 We show that the evolution of the Langmuir wave spectrum caused by plasma inhomogeneities and wave-wave processes leads to effective acceleration of high energy electrons., We show that the evolution of the Langmuir wave spectrum caused by plasma inhomogeneities and wave-wave processes leads to effective acceleration of high energy electrons.294 The resulting HXR spectrum is found to be strongly affected by the evolution of Langmuir turbulence. so that if the HXR spectrum is interpreted in terms of a collisional model. the accelerated electron spectrum will be overestimated.," The resulting HXR spectrum is found to be strongly affected by the evolution of Langmuir turbulence, so that if the HXR spectrum is interpreted in terms of a collisional model, the accelerated electron spectrum will be overestimated."295 The weakly turbulent collisional relaxation of an energetic electron population is considered in a collisional plasma typical for the solar corona., The weakly turbulent collisional relaxation of an energetic electron population is considered in a collisional plasma typical for the solar corona.296 The evolution of energetic electrons is described using weak turbulence theory including wave-particle and wave-wave interactions in non-uniform plasma., The evolution of energetic electrons is described using weak turbulence theory including wave-particle and wave-wave interactions in non-uniform plasma.297" The corresponding equations (???) governing the electron distribution funetion ftv.) [electrons em (cm/s)! | and the spectral energy densities of Langmuir W,. and ion-sound waves Wj ergs cm | are as in 2: where the spectral energy density is normalized such. that fW.dk is the energy density of the waves [erg cm?|."," The corresponding equations \citep{1963JETP...16..682V,1967PlPh....9..719V,1995lnlp.book.....T}298 governing the electron distribution function $f({\mr v},t)$ [electrons $^{-3}$ $^{-1}$ ] and the spectral energy densities of Langmuir $W_k$, and ion-sound waves $W_k^s$ [ergs $^{-2}$ ] are as in \citet{2002PhRvE..65f6408K}: : where the spectral energy density is normalized such, that $\int W_k\, dk$ is the energy density of the waves [erg $^{-3}$ ]."299 The system of equations (2--5)) describes the weakly turbulent evolution of electrons and Langmuir waves in the presence of density inhomogeneities and/or 10n-sound waves., The system of equations \ref{eqk1}- \ref{alphaL}) ) describes the weakly turbulent evolution of electrons and Langmuir waves in the presence of density inhomogeneities and/or ion-sound waves.300 The spontaneous emission of Langmuir waves has been treated as in 992? and the system was numerically integrated using a numerical scheme as in ?.. ," The spontaneous emission of Langmuir waves has been treated as in \citet{2009ApJ...707L..45H,2011A&A...529A..66R} and the system was numerically integrated using a numerical scheme as in \citet{2001CoPhC.138..222K}. ."301As we are interested in the evolution of the system at time- f>>τι. the collisional operator (e.g.?) 1s included to account for the binary collisions where the first RHS term describes the systematic drag on energetic particles and the second term diffusion in velocity space due to binary collisions.," As we are interested in the evolution of the system at time-scales $t\gg \tau _{col}$, the collisional operator \citep[e.g.][]{1981phki.book.....L} is included to account for the binary collisions where the first RHS term describes the systematic drag on energetic particles and the second term diffusion in velocity space due to binary collisions."302 We note that the collisional drag is larger than energy losses due to spontaneous emission of Langmuir waves [second term in the right hand side of Eq. (2))], We note that the collisional drag is larger than energy losses due to spontaneous emission of Langmuir waves [second term in the right hand side of Eq. \ref{eqk1}) )]303 by a non-thermal electron in a plasma., by a non-thermal electron in a plasma.304 In other words. only a small part of the energy lost by an electron with velocity v goes into spontaneously generated Langmuir waves given by Eq. (3)).," In other words, only a small part of the energy lost by an electron with velocity ${\mr v}$ goes into spontaneously generated Langmuir waves given by Eq. \ref{eqk2}) )."305 Finally. the collisional damping rate for Langmuir waves γιοί=F/Avj.. is added to Eq. (3)).," Finally, the collisional damping rate for Langmuir waves $\gamma_{col} \simeq \Gamma/4{\mr v}_{Te}^3$ is added to Eq. \ref{eqk2}) )."306 Let us consider the evolution. of a non-thermal electron population with the initial electron distribution go(v) in a Maxwellian plasma (Fig. 1)):, Let us consider the evolution of a non-thermal electron population with the initial electron distribution $g_0({\mr v})$ in a Maxwellian plasma (Fig. \ref{fig:collisions}) ):307" the non-thermal particlere distributionNiet go(v) is initiallywhere a power law f(v.t =0)~v7for v >vy=LOvy,and flattens at low velocities v <IOvy,:2p ὁ is the power law index for the energetic particles in energy space. 1 the number density of non-thermal electrons. Ap<<n. and T(x) denotes the gamma function."," where the non-thermal particle distribution $g_0({\mr v})$ is initially a power law $f({\mr v},t=0)\sim {\mr v}^{-2\delta}$ for ${\mr v}> {\mr v}_b=10{\mr v}_{Te}$ and flattens at low velocities ${\mr v}<10{\mr v}_{Te}$; where $\delta$ is the power law index for the energetic particles in energy space, $n_{b}$ the number density of non-thermal electrons, $n_{b}<<n$, and $\Gamma (x)$ denotes the gamma function."308 The initial electron distribution is normalized to the electron. number density [electrons em 7]. so that The initial level of Langmuir waves can be calculated assuming an equilibrium with Maxwellian electron distribution function. ignoring all non-linear terms and setting dW;/dr=0 in Eq. (35) ," The initial electron distribution is normalized to the electron number density [electrons $^{-3}$ ], so that The initial level of Langmuir waves can be calculated assuming an equilibrium with Maxwellian electron distribution function, ignoring all non-linear terms and setting $dW_k/dt=0$ in Eq. \ref{eqk2}) )"309"where &, is Boltzmann constant. 7,=HIN; the electron temperature of the plasma. and 2p.=vro, is the Debye length."," where $k_b$ is Boltzmann constant, $T_e=m{\mr v}_{Te}^2$ the electron temperature of the plasma, and $\lambda_{De}={\mr v}_{Te}/\omega _{pe}$ is the Debye length."310" The equation (10)) can be reduced to W(kK.f=0)uae in the collistonless limit for y,,;—0. which is the thermal Inge)level of plasma waves in a collisionless Maxwellian plasma (??).."," The equation \ref{eq:W_t0}) ) can be reduced to $W(k, t=0)\simeq \frac{k_b T_e}{4 \pi^2}{k^2\ln(\frac{1}{k\lambda_{de}})}$ in the collisionless limit for $\gamma _{col}\rightarrow 0$, which is the thermal level of plasma waves in a collisionless Maxwellian plasma \citep{1973plas.book.....K,1995lnlp.book.....T}."311 For the problem considered. the exact initial level of plasma waves is not important. as the governing equations quickly establish a balanced level. which is a few orders of magnitudeless than the level driven by the instability.," For the problem considered, the exact initial level of plasma waves is not important, as the governing equations quickly establish a balanced level, which is a few orders of magnitudeless than the level driven by the instability."312" We assume a background plasma similar to the solar corona. with plasma frequency of fj,=Wpe/2a2 GHz and an electron and ion temperature of 7;=7,| MK."," We assume a background plasma similar to the solar corona, with plasma frequency of $f_{pe}=\omega _{pe}/2\pi =2$ GHz and an electron and ion temperature of $T_i=T_e=1$ MK."313 The corresponding plasmadensity is then 5.0x 10'!em7 and the, The corresponding plasmadensity is then $5.0\times 10^{10} $ $^{-3}$ and the314"supersvmnmetric particle [or example ancl if (hey are born sullicientlv late (hen the initial velocities of (he resulGing daughter particles can be sufficiently high to vield a free streaming length comparable to that found from the Lyva forest analvsis but with Q, orders of magnitude lower than above (i.e. Q,LO?—10.5) and a correspondingly much higher dark halo mass limit.",supersymmetric particle for example and if they are born sufficiently late then the initial velocities of the resulting daughter particles can be sufficiently high to yield a free streaming length comparable to that found from the $\alpha$ forest analysis but with $_{p}$ orders of magnitude lower than above (i.e. $_{p}\sim10^{-5}-10^{-6}$ ) and a correspondingly much higher dark halo mass limit.315 This picture has the additional feature that itis hierarchical in the conventional CDM sense since (he parent particles are born cold and being bosons they. are not subject to the ultimate phase space density restriction., This picture has the additional feature that it is hierarchical in the conventional CDM sense since the parent particles are born cold and being bosons they are not subject to the ultimate phase space density restriction.316 Future results from experimental particle physics and even more sophisticated cosmological simulations should lead to a fuller understanding of the dark matter problem and the viability of the model., Future results from experimental particle physics and even more sophisticated cosmological simulations should lead to a fuller understanding of the dark matter problem and the viability of the model.317 The author wishes to thank Drs., The author wishes to thank Drs.318 Julio Navarro. Tony Burke and Andi Mabedavi for useful discussions. Dr. Greg Poole for introducing me to x-ray observations of galaxy clusters and the releree lor a constructive report.," Julio Navarro, Tony Burke and Andi Mahdavi for useful discussions, Dr. Greg Poole for introducing me to x-ray observations of galaxy clusters and the referee for a constructive report."319Previous5. works suggest that the most. [uminous. extended emission.⋠⋠ linc. regions. (IZELIts)HEN around type 1 quasars (QSOs); at redshiftD. 2 550.5. exist.. preferentially⋅: associated: withM steep-speetrum radio-loudT. QSOs. with.v [uminous. OLUJA5007- nuclear emission.20. and low broad. line.. region. metallicities (Z Z0.6Z.).,Previous works suggest that the most luminous extended emission line regions (EELRs) around type 1 quasars (QSOs) at redshift $z\la$ 0.5 exist preferentially associated with steep-spectrum radio-loud QSOs with luminous $\lambda$ 5007 nuclear emission and low broad line region metallicities $Z\la$ $Z_{\odot}$ ).320 These ELLRs have low metallicities as well and seem especially prevalent in QSOs showing signs of strongDp interaction., These EELRs have low metallicities as well and seem especially prevalent in QSOs showing signs of strong interaction.321: The origin? of these nebulae is oecontroversial. whether cold. accretion of intergalactic. eas. tidal. debris ⋠⋅from a galactic. merger or remnants of⋅ ealactic⊀ superwinds⊀ (for⋅ a review. see Fu: Stockton 2009: Stockton. Fu Canalizo 2006).," The origin of these nebulae is controversial, whether cold accretion of intergalactic gas, tidal debris from a galactic merger or remnants of galactic superwinds (for a review see Fu Stockton 2009; Stockton, Fu Canalizo 2006)."322 Very [little is known about the existence. of EELRs associated with tvpe 2 quasars (e.g. Humphrey. οἱ al., Very little is known about the existence of EELRs associated with type 2 quasars (e.g. Humphrey et al.323 2009: Gandhi. Fabian. Crawford. 1996).," 2009; Gandhi, Fabian Crawford 1996)."324 Phese objects cre unique laboratories to/ investigate the existence. and properties. of⋅ quasar IEELIV., These objects are unique laboratories to investigate the existence and properties of quasar EELR.325" ↔≽⊳∖The fortuitous⋅. occultation. of the active. galactic. nucleus. (AGN)ae acts like. a .""natural coronograph""M. allowing. a detailed. study of⋅ many properties. of⋅ the surrounding⊀ medium.⊀ without⊀ the problems associated. with the bright quasar point spread function."," The fortuitous occultation of the active galactic nucleus (AGN) acts like a “natural coronograph”, allowing a detailed study of many properties of the surrounding medium, without the problems associated with the bright quasar point spread function."326 On the other hand. due to their much lower racio Luminosity. distortions imprinted by the radio activity on the properties of the underlving. nebulae are less important. than in. radio-loud. objectobjects.," On the other hand, due to their much lower radio luminosity, distortions imprinted by the radio activity on the properties of the underlying nebulae are less important than in radio-loud objects."327 For. these reasons. we are undertaking. a project. based on imagine. long-slit and. integral field. data obtained. with FORS2/VLT. the integral field spectrograph PALAS on the 3.5m telescope at C'alar Alto Observatory (Humphrey ct al.," For these reasons, we are undertaking a project based on imaging, long-slit and integral field data obtained with FORS2/VLT, the integral field spectrograph PMAS on the 3.5m telescope at Calar Alto Observatory (Humphrey et al."328 2009). and the tunable filter OSIRIS on the GLC.," 2009), and the tunable filter OSIRIS on the GTC."329 These are being used to investigate the existence of ELLE. associated with Sloan Digital Sky Survey (SDSS) type 2 quasars at 2o0.3-0.4 and characterize their morphological. ionization and kinematic properties.," These are being used to investigate the existence of EELR associated with Sloan Digital Sky Survey (SDSS) type 2 quasars at $z\sim$ 0.3-0.4 and characterize their morphological, ionization and kinematic properties."330 In this paper we present results on the tvpe 2 quasar SDSS J012341.47|004435.9 (SDSS JO0123|00 hereafter) at, In this paper we present results on the type 2 quasar SDSS J012341.47+004435.9 (SDSS J0123+00 hereafter) at331"for birth frequencies between kklIz and ΚΙ. the search is sensitive to €Z1.9.10 ""and Dzs.100 GG. We note that these estimates. derived [from the limits on (Qj, and Qe. assume the standard values for the neutron star mass and radius. Ad,=L4. and ἐν=lO kkm.","for birth frequencies between kHz and kHz, the search is sensitive to $\epsilon \gtrsim 7.9 \times 10^{-5}$ and $B \lesssim 0.8 \times 10^{11}$ G. We note that these estimates, derived from the limits on $Q_1$ and $Q_2$, assume the standard values for the neutron star mass and radius, $M_\star = 1.4 M_\odot$ and $R_\star = 10$ km."332" It is possible that SNIU LOSTA contains à low-mass neutron star with AZ,zz0.134. (Imshenik.1992).. in which case the limit on the ellipticity. for ο=1.00 kklIIz. would. be em25.104"," It is possible that SNR 1987A contains a low-mass neutron star with $M_\star \approx 0.13 M_\odot$ \citep{imshenik92}, in which case the limit on the ellipticity, for $\nu_b = 1.00$ kHz, would be $\epsilon \gtrsim 2.5 \times 10^{-4}$."333 We now comment briellv on the relevance. of. these limits., We now comment briefly on the relevance of these limits.334 The range of D listed in Table 1 is within the expected theoretical range discussed in Section 2. (Michel1994:Ogelman&Alpar 2004).," The range of $B$ listed in Table \ref{tab:results} is within the expected theoretical range discussed in Section \ref{sn1987Adetails} \citep{michel94, ogelman04}."335. The range of c listed. in ‘Table 1.. however. is larger than the maximum ellipticity sustainable by the unmagnetized neutron star crust for many equations of state.," The range of $\epsilon$ listed in Table \ref{tab:results}, however, is larger than the maximum ellipticity sustainable by the unmagnetized neutron star crust for many equations of state."336" For example. conventional neutron stars are expected to support. €10"". while hybrid quark-barvon or meson-condensate stars can support c<10 (Ushomiurskyetal.2000:Owen2005:Horowitz&Ixacdau 2009).."," For example, conventional neutron stars are expected to support $\epsilon \leq 10^{-6}$, while hybrid quark-baryon or meson-condensate stars can support $\epsilon \leq 10^{-5}$ \citep{ushomirsky00, owen05, horowitz09}. ."337 LLowever. some exotic models cdo allow for. larger ellipticities.," However, some exotic models do allow for larger ellipticities."338 Solid. strange quark stars are. predicted. to be able to sustain οx610 (Owen2005)., Solid strange quark stars are predicted to be able to sustain $\epsilon \leq 6 \times 10^{-4}$ \citep{owen05}.339. Lor mass neutron stars. the limit is €xο10 (Lmshenik 2010).," For low-mass neutron stars, the limit is $\epsilon \leq 5 \times 10^{-3}$ \citep{imshenik92, horowitz10}."340. We note also that these limits apply only to clastically supported: deformations: magnetically supported deformations can be larger (Alelatos2007:Akgün&Wasserman2008:Haskell 2008).," We note also that these limits apply only to elastically supported deformations; magnetically supported deformations can be larger \citep{melatos07, akgun08, haskell08}."341. Therefore. even placing the relatively large upper limit of€<10! on the putative neutron star in SNR. 1987X will be useful to some degree in constraining its mass and/or equation of state.," Therefore, even placing the relatively large upper limit of $\epsilon \lesssim 10^{-4}$ on the putative neutron star in SNR 1987A will be useful to some degree in constraining its mass and/or equation of state."342 In this paper. we describe the steps taken to quantify the astrophysical significance of a cross-correlation search for the supernova remnant. SNR. LOSTA in LIGO $5 data.," In this paper, we describe the steps taken to quantify the astrophysical significance of a cross-correlation search for the supernova remnant SNR 1987A in LIGO S5 data."343 With the required. template spacing and current computational capabilities discussed in Section 6.2.. we will be able to search up to approximately. 107n templates.," With the required template spacing and current computational capabilities discussed in Section \ref{sec:templates}, we will be able to search up to approximately $10^{9}$ templates."344 In the event of a non-detection. considering the parameter range discussed in this paper ancl assuming the standard neutron star mass and radius. we expect to place the following limits on the pulsars ellipticity ancl magnetic lield: cx8SS107. Bom209107 GG. The search. is also expected to be sensitive to electromagnetic braking indices 2.3xn3.0.," In the event of a non-detection, considering the parameter range discussed in this paper and assuming the standard neutron star mass and radius, we expect to place the following limits on the pulsar's ellipticity and magnetic field: $\epsilon \leq 8 \times 10^{-5}$, $B \geq 2.0 \times 10^{11}$ G. The search is also expected to be sensitive to electromagnetic braking indices $2.3 \leq n \leq 3.0$."345 lis greatest weakness remains that it assumes 7 to be constant throughout the semi-coherent integration., Its greatest weakness remains that it assumes $n$ to be constant throughout the semi-coherent integration.346 Constant 7 is the simplest possible astrophysical scenario. and it certainly deserves to be considered in its own right. in view of the overwhelming computational cost of a variable-n search.," Constant $n$ is the simplest possible astrophysical scenario, and it certainly deserves to be considered in its own right, in view of the overwhelming computational cost of a $n$ search."347 Nevertheless. it is vital to recognize that the constant-7 hypothesis covers a small fraction of the astrophysical parameter space.," Nevertheless, it is vital to recognize that the $n$ hypothesis covers a small fraction of the astrophysical parameter space."348" A search using gravitational wave data is anticipated to begin soon and. would be the first application of the correlation method to a continuous wave search,", A search using gravitational wave data is anticipated to begin soon and would be the first application of the cross-correlation method to a continuous wave search.349 CC acknowledges the support of an Australian Postgraduate Award and the Albert Shimmins. Memorial. Fund., CC acknowledges the support of an Australian Postgraduate Award and the Albert Shimmins Memorial Fund.350 JEN acknowledges the support of NSE erant. PIIY-0855494. the College of Science at Rochester Institute of Technology. aud the German AerospaceCenter (DLR).," JTW acknowledges the support of NSF grant PHY-0855494, the College of Science at Rochester Institute of Technology, and the German AerospaceCenter (DLR)."351 This paper has been designated LIGO Document No., This paper has been designated LIGO Document No.352 LIGO-PI000089-V3., LIGO-P1000089-v3.353üunplicitly. as the uncle‘ying agent which is responsible.,"implicitly, as the underlying agent which is responsible."354 There has been extensive work ou rotational muinine in bxrth low aicL high mass main sequence stars (Michaια&Charbonneaual.1997)... aud phenouenological work on ixiug in evolved stars has recently. been uudertakeu by several groups (Claronnel1995:Swele:irt1997).," There has been extensive work on rotational mixing in both low and high mass main sequence stars \citep{MC91,TZMM97}, and phenomenological work on mixing in evolved stars has recently been undertaken by several groups \citep{C95,S97}."355. However. detailed pliysical moclels of giant braucl uixiug have p“OVeu to be a signiicat challenge to theo‘ists.," However, detailed physical models of giant branch mixing have proven to be a significant challenge to theorists."356" Tie largest uicerainty. iLou view. been the lack of constraiuts ou the augular momentum evolutiou from the ανα] seq,lence to t ib ascent giant branch. the horizontal branch. and beyond."," The largest uncertainty, in our view, has been the lack of constraints on the angular momentum evolution from the main sequence to the first ascent giant branch, the horizontal branch, and beyond."357 LIIn tils paper we exalline the im»licatious of ineasured surface ‘olation rates of horizontal braucl Se for anguliP Inoueutum evolt10 on the giant branch., In this paper we examine the implications of measured surface rotation rates of horizontal branch stars for angular momentum evolution on the giant branch.358 We willshow that the combination oL rapid lhorizontal brauch roatiou aud slow main sequence rotation paces strong constraints on the auglar noueitum evoluion of giarS., We will show that the combination of rapid horizontal branch rotation and slow main sequence rotation places strong constraints on the angular momentum evolution of giants.359 The 10ueeriug work of Sweigart&Meugel(1979) ‘elnaius the single best physical analysis of rotati umüxiug iu evolved stars., The pioneering work of \cite{SM79} remains the single best physical analysis of rotational mixing in evolved stars.360 They investigated the link between classical meridional d the CNO anomalies in giants. aud stressed he initial angularOm momentum budgetOm aud the rotation aw in the couvectiou zoue.," They investigated the link between classical meridional circulation and the CNO anomalies in giants, and stressed the initial angular momentum budget and the rotation law in the convection zone."361 They concluded hat meridional circulation was generally cousistent with the observational data. provided that the rotaion rate on the giant brauch was sullicienly high.," They concluded that meridional circulation was generally consistent with the observational data, provided that the rotation rate on the giant branch was sufficiently high."362" The necessary rotation rates ou the giait branchicl require a rapidly rotating core on the main sequence. aid the convective envelope of a giait brauch""al star cannot be rotating[n]) as a solid body. since the 'equired maii sequeuce rotation raes WOlId be inich highe‘than observed."," The necessary rotation rates on the giant branch require a rapidly rotating core on the main sequence, and the convective envelope of a giant branch star cannot be rotating as a solid body, since the required main sequence rotation rates would be much higher than observed."363 This st«ly neglected he 1rulxiug of elements caused by diffe‘ential rotation with depth in the star. and clicl not iuclude t1je. effects of mass loss.," This study neglected the mixing of elements caused by differential rotation with depth in the star, and did not include the effects of mass loss."364 Icleally. we woulc like to study tje rotation rates of [n]o]:it branch stars directly.," Ideally, we would like to study the rotation rates of giant branch stars directly."365 These stars show tle slronges evidence for i0n-stancdard mixiug. aux ilir evolution froin main sequence stars is clirect ancl well Εςerstood.," These stars show the strongest evidence for non-standard mixing, and their evolution from main sequence stars is direct and well understood."366 By loosing at die rotation rrates of giants at different. luminosities ou the giant bratch. we shouk be alle to cleermine their initial angular momentum profile as angular momentutu is credged 1p by tie deepering convection zone.," By looking at the rotation rates of giants at different luminosities on the giant branch, we should be able to determine their initial angular momentum profile as angular momentum is dredged up by the deepening convection zone."367 We should also be able to test the precdicted cor'elations betweeu cdiferent iuernal rotation velocities aud the observed. surface abundances., We should also be able to test the predicted correlations between different internal rotation velocities and the observed surface abundances.368 However. since giai| brauch stars are so large. their surface rotation rates are predicted to be very stuall. 1vuch less than 1 kms. |.," However, since giant branch stars are so large, their surface rotation rates are predicted to be very small, much less than 1 km $^{-1}$."369 The s»ectral resolutiou required to observe such velocities is far beyond what cau be done today. althougl gravitational microleusiug may make this possible (Coud1997).," The spectral resolution required to observe such velocities is far beyond what can be done today, although gravitational microlensing may make this possible \citep{G97}."370. Fortuiately. horizontal ranch stars Lave observable rotatiou raes. aud they provide Insight into the iteriors of giant stars.," Fortunately, horizontal branch stars have observable rotation rates, and they provide insight into the interiors of giant stars."371 Siuce stars lose mass on the giau brauch. the surface of the horizontal ranch star was OLce iuside the giant brauch star.," Since stars lose mass on the giant branch, the surface of the horizontal branch star was once inside the giant branch star."372 Stars at dli[Iereut effective temperatures ou the horizoutal branch have lost different. amount of mass. and trerefore cau. be used to test the angular inoinentuiu cist‘bution within giants.," Stars at different effective temperatures on the horizontal branch have lost different amount of mass, and therefore can be used to test the angular momentum distribution within giants."373 The rotation of stars ou tle horizontal brauch tlierefore p'ovides au Ποος test of the internal rotation of the same stars in p'evious evolutionary stages., The rotation of stars on the horizontal branch therefore provides an indirect test of the internal rotation of the same stars in previous evolutionary stages.374"to obtain ng,~0.1 (equation (2)).",to obtain $n_{\bar{\nu}_\mathrm{e}} \sim 0.1$ (equation (2)).375" For the standard model (r«,=300 km and νο= 2.19), the maximum production factor in Table is obtained at ?9Ru (nuc(fmax) in Table 1), (fmaxa daughter 1)nucleus of δρα (N= 50) on the vp-process pathway."," For the standard model $r_\mathrm{wt} = 300$ km and $T_\mathrm{wt, 9} = 2.19$ ), the maximum production factor $f_\mathrm{max}$ in Table 1) is obtained at $^{96}$ Ru $\mathrm{nuc}(f_\mathrm{max})$ in Table 1), a daughter nucleus of $^{96}$ Pd $N=50$ ) on the $\nu$ p-process pathway."376 We have the optimal production (logfmax=7.67 at with Twt.9=2.65 when the termination point is set to 19604)ry_=231 km.," We have the optimal production $\log f_\mathrm{max} = 7.67$ at $^{106}$ Cd) with $T_\mathrm{wt, 9} = 2.65$ when the termination point is set to $r_\mathrm{wt} = 231$ km."377" In Table 1, the nuclide with the largest mass number Amax With f>fmax/10 is also shown (e.g., !99Cd for the standard model; nuc(Amax) in Table which is taken to be the largest A of the p-nuclei synthesized1), by the vp-process."," In Table 1, the nuclide with the largest mass number $A_\mathrm{max}$ with $f > f_\mathrm{max}/10$ is also shown (e.g., $^{106}$ Cd for the standard model; $\mathrm{nuc}(A_\mathrm{max})$ in Table 1), which is taken to be the largest $A$ of the p-nuclei synthesized by the $\nu378$ p-process."379" Given that our standard model represents a typical supernova condition, this implies that the vp-process can be the source of the solar p-abundances up to A~110 (see 6 for more detail)."," Given that our standard model represents a typical supernova condition, this implies that the $\nu$ p-process can be the source of the solar p-abundances up to $A \sim 110$ (see 6 for more detail)."380" However, this favorable condition is not robust against a variation of rwt thus the outflows with ry.=200 km (Twt.9(and=2.95)"" Tyt);and ry.>500 km (Tio« 1.55) end up with Amax=84 (84Sr; Table 1)."," However, this favorable condition is not robust against a variation of $r_\mathrm{wt}$ (and thus $T_\mathrm{wt}$ ); the outflows with $r_\mathrm{wt} = 200$ km $T_\mathrm{wt, 9} =3812.95$ and $r_\mathrm{wt} \ge 500$ km $T_\mathrm{wt, 9} < 1.55$ ) end up with $A_\mathrm{max} = 84$ $^{84}$ Sr; Table 1)."382 Note that the outflow with ry;=1000 km leads to a similar result as that without wind termination (black line in Figure 2; T«c=oo in Table 1).," Note that the outflow with $r_\mathrm{wt} =3831000$ km leads to a similar result as that without wind termination (black line in Figure 2; $r_\mathrm{wt} = \infty$ in Table 1)."384" This indicates that the role of wind termination is unimportant for Tyt,9«1.5."," This indicates that the role of wind termination is unimportant for $T_\mathrm{wt, 9} < 1.5$."385 We find no substantial vp-processing for the outflow with ryt=100 km (Figure 2)., We find no substantial $\nu$ p-processing for the outflow with $r_\mathrm{wt} = 100$ km (Figure 2).386" This is due to the substantially smaller Y, at the beginning of the vp- (Tg=3), ος=0.509 (only slightly proton-rich), than those for the other cases (0.550; Table 1)."," This is due to the substantially smaller $Y_\mathrm{e}$ at the beginning of the $\nu$ p-process $T_9 =3873$ ), $Y_\mathrm{e, 3} = 0.509$ (only slightly proton-rich), than those for the other cases (0.550; Table 1)."388" As a result, Yp/Yn at Tg=3 is only 1.78, resulting in a small A, (=0.24) in spite of the largest np, among the various ry models presented here."," As a result, $Y_\mathrm{p}/Y_\mathrm{h}$ at $T_9 = 3$ is only 1.78, resulting in a small $\Delta_\mathrm{n}$ $=0.24$ ) in spite of the largest $n_{\bar{\nu}_\mathrm{e}}$ among the various $r_\mathrm{wt}$ models presented here."389" It should be noted that Y,3 is always lower than Y,,9 (=0.600 in the present cases)."," It should be noted that $Y_\mathrm{e, 3}$ is always lower than $Y_\mathrm{e, 9}$ $= 0.600$ in the present cases)."390 This is due to a couple of neutrino effects., This is due to a couple of neutrino effects.391" One is that the asymptotic equilibrium value of Y, in the non-degenerate matter consisting of free nucleons, which is subject to neutrino capture, is *0.56 (see,e.g.Qian&Woosley1996) with theYo, neutrino luminosities and energies taken in this study."," One is that the asymptotic equilibrium value of $Y_\mathrm{e}$ in the non-degenerate matter consisting of free nucleons, which is subject to neutrino capture, is $Y_\mathrm{e, a} \approx 0.56$ \citep[see, e.g.,][]{Qian1996} with the neutrino luminosities and energies taken in this study."392" Hence, the value starts relaxing from Y.9 toward Y,,4 as soon as the calculation initiates."," Hence, the value starts relaxing from $Y_\mathrm{e, 9}$ toward $Y_\mathrm{e, a}$ as soon as the calculation initiates."393" The other effect is due to the continuous a- particle formation (Tg«7) from inter-converting free protons and free neutrons that is subject to neutrino capture, which drives Y, towards 0.5 Meyer,McLaughlin,&Fuller 1998a)."," The other effect is due to the continuous $\alpha$ -particle formation $T_9 < 7$ ) from inter-converting free protons and free neutrons that is subject to neutrino capture, which drives $Y_\mathrm{e}$ towards 0.5 \citep[``$\alpha$-effect'',][]{Meye1998}."394". In the ry:(“a-effect”,=100 km case, the wind-termination takes place at high temperature (Twt,9= 5.19) and thus the long τι (=359 ms) leads to the low Υο5 owing to the neutrino effects."," In the $r_\mathrm{wt} =395100$ km case, the wind-termination takes place at high temperature $T_\mathrm{wt, 9} = 5.19$ ) and thus the long $\tau_1$ $= 359$ ms) leads to the low $Y_\mathrm{e, 3}$ owing to the neutrino effects."396" In summary, our exploration here elucidates a crucial role of wind termination on the vp-process."," In summary, our exploration here elucidates a crucial role of wind termination on the $\nu$ p-process."397" On one hand, a fast expansion above the temperature T9~3 (more precisely, Το=2.65 in the considered is favored to obtain a high proton-to-seed ratioconditions) at the onset of the vp-process."," On one hand, a fast expansion above the temperature $T_9 \sim 3$ (more precisely, $T_9 = 2.65$ in the considered conditions) is favored to obtain a high proton-to-seed ratio at the onset of the $\nu$ p-process."398" On the other hand, a slow expansion below this temperature, owing to wind termination, is needed to obtain A,~10 for efficient vp-processing."," On the other hand, a slow expansion below this temperature, owing to wind termination, is needed to obtain $\Delta_\mathrm{n} \sim 10$ for efficient $\nu$ p-processing."399 We presume that the reason for somewhat different outcomes in previous studies of the vp-process described in 1 is largely due to their different behaviors of wind termination., We presume that the reason for somewhat different outcomes in previous studies of the $\nu$ p-process described in 1 is largely due to their different behaviors of wind termination.400" The temperature histories of trajectories taken by Pruetetal.(2006,anexploding15Mstar),, similar to our models with r,,=100—230 (Twi= lead to the production of p-nuclei up to Ac 100. 5."," The temperature histories of trajectories taken by \citet[][an exploding $15 M_\odot$401star]{Prue2006}, similar to our models with $r_\mathrm{wt} = 100-230$ $T_\mathrm{wt, 9} = 2.7-5.2$ ), lead to the production of p-nuclei up to $A \sim 100$ ."402"2),The reason of weak vp-processing in Frohlich may be rather due to the moderate proton-richness (up to Y,~ in their simulations (see 4.4 and Figure "," The reason of weak $\nu$ p-processing in \citet[][a403$20 M_\odot$ explosion]{Froe2006} may be rather due to the moderate proton-richness (up to $Y_\mathrm{e} \sim 0.54$ ) in their simulations (see 4.4 and Figure 6)."404"In contrast,0.54) negligible production of p-nuclei in the electron-capture6). supernova of a 9Mo star (Wanajoetal.2009,also8. is due to the absence of a wind-termination shock within the relevant temperature range (Tg— 1.5—3) owing to the steep density gradient of the oxygen-neon-magnesium core progenitors surrounded by a diluted outer H/He envelope."," In contrast, negligible production of p-nuclei in the electron-capture supernova of a $9 M_\odot$ star \citep[][also S. Wanajo et al., in preparation]{Wana2009} is due to the absence of a wind-termination shock within the relevant temperature range $T_9 = 1.5-3$ ) owing to the steep density gradient of the oxygen-neon-magnesium core progenitors surrounded by a diluted outer H/He envelope."405" Theneutrino luminosity L, decreases with time from its initial value of a few 10°? erg s! to ~10°! erg s! during the first 10 s", Theneutrino luminosity $L_\nu$ decreases with time from its initial value of a few $10^{52}$ erg $^{-1}$ to $\sim 10^{51}$ erg $^{-1}$ during the first 10 s406indeed they should by construction.,indeed they should by construction.407 When we combine the various grids. however. an interesting thing happens.," When we combine the various grids, however, an interesting thing happens."408 Column 10. shows the number of separate. non-overlapping). overdense blocks in the combined grid.," Column 10 shows the number of separate, non-overlapping), overdense blocks in the combined grid."409 At high overdensity all the halos we have identified are distinct (they exceed. the threshold for just one position of the smoothing eric)., At high overdensity all the halos we have identified are distinct (they exceed the threshold for just one position of the smoothing grid).410 Phe total number of halos is therefore greatly in excess of the PS prediction and far closer to that given by. Peaks Theory., The total number of halos is therefore greatly in excess of the PS prediction and far closer to that given by Peaks Theory.411 For η=2 the excess is approximately a factor of three which brings them into agreement once the PS prediction has the extra factor of two applied., For $n=-2$ the excess is approximately a factor of three which brings them into agreement once the PS prediction has the extra factor of two applied.412 For n=0. however. the dillerence is much larger and the number of peaks is a factor of 3-4 larger than even the corrected. PS estimate.," For $n=0$, however, the difference is much larger and the number of peaks is a factor of 3-4 larger than even the corrected PS estimate."413 This goes in some wav to explaining the dilference between the PS prediction and. the measured. cumulative mass function in 4.., This goes in some way to explaining the difference between the PS prediction and the measured cumulative mass function in \ref{fig:cummf}.414 At lower overdensity the disagreement is much less severe., At lower overdensity the disagreement is much less severe.415 One should note that for n=2 there is a gross underestimate of la peaks compared to the values obtained in each sub-grid., One should note that for $n=-2$ there is a gross underestimate of $1\sigma$ peaks compared to the values obtained in each sub-grid.416 Εις is simply a consequence ofthe Peaks methodology., This is simply a consequence of the Peaks methodology.417 Itemember that for cach sub-grid we are just measuring the fraction of the total number of blocks above the threshold. while in the case of combined grids we simply count the number of peaks.," Remember that for each sub-grid we are just measuring the fraction of the total number of blocks above the threshold, while in the case of combined grids we simply count the number of peaks."418 Because for n=2 the peaks are larger and more clustered. there is a great chance of linding blocks sitting next each other which are above the imposed threshold.," Because for $n=-2$ the peaks are larger and more clustered, there is a great chance of finding blocks sitting next each other which are above the imposed threshold."419 Consequently. if we are only selecting the peaks many of those blocks will be discarded.," Consequently, if we are only selecting the peaks many of those blocks will be discarded."420 This situation does not arise for n=O0. where the peaks are smaller and more evenly distributed.," This situation does not arise for $n=0$, where the peaks are smaller and more evenly distributed."421 Our use of overlapping grids is therefore crucial., Our use of overlapping grids is therefore crucial.422 They ensure that all halos are approximately centred. within one of the grid. cells., They ensure that all halos are approximately centred within one of the grid cells.423 Other methods. such as theAlodel.. which have fixed borders between mass cells. have cilliculty. in detecting structures that cross eell boundaries and are. by construction. forced to agree with Press-Schechter.," Other methods, such as the, which have fixed borders between mass cells, have difficulty in detecting structures that cross cell boundaries and are, by construction, forced to agree with Press-Schechter."424 Fhis can lead to a gross underestimate of the number of rare. high-mass peaks. especially for steep spectra.," This can lead to a gross underestimate of the number of rare, high-mass peaks, especially for steep spectra."425 We are not saving that our method. necessarily gives a better description of the erowth of structure in the Universe because all these theoretical models are highly. idealized., We are not saying that our method necessarily gives a better description of the growth of structure in the Universe because all these theoretical models are highly idealized.426 Substructure may lengthen collapse times and tidal field may need to be taken into account., Substructure may lengthen collapse times and tidal field may need to be taken into account.427 Nevertheless. given the simplified prescription which we have adopted. our method does at least seen to detect. the correct. number of high-mass halos. and. many more than other moethocs.," Nevertheless, given the simplified prescription which we have adopted, our method does at least seem to detect the correct number of high-mass halos, and many more than other methods."428 We have presented a new method of constructing a hierarchical merger tree based on actual realizations of the linear density Ποια., We have presented a new method of constructing a hierarchical merger tree based on actual realizations of the linear density field.429 We smooth on a set of interlacect. cubical erids on a variety of mass scales. then order. in decreasing density.," We smooth on a set of interlaced, cubical grids on a variety of mass scales, then order in decreasing density."430 We run down the resulting list. merging together overlapping blocks to form. collapsed. halos.," We run down the resulting list, merging together overlapping blocks to form collapsed halos."431 The main properties of our model are as follows:, The main properties of our model are as follows:432"To illustrate our point we consider a mock galaxy sample, with characteristics similar to an L, sample, at z~0.1, and try to analyze this in two cosmologies that only differ in the normalization of the primordial power spectrum: og=0.8 and 1.0.","To illustrate our point we consider a mock galaxy sample, with characteristics similar to an $L_\star$ sample, at $z\sim 0.1$, and try to analyze this in two cosmologies that only differ in the normalization of the primordial power spectrum: $\sigma_8=0.8$ and $1.0$."433" In both cosmologies a good fit to the function can be found (Fig. 1)),"," In both cosmologies a good fit to the 2-point function can be found (Fig. \ref{fig:xir}) ),"434 but the HOD differs (Fig. 2)), but the HOD differs (Fig. \ref{fig:hod}) )435 because the halo mass function is different in the two cosmologies., because the halo mass function is different in the two cosmologies.436" The fiducial galaxy sample was generated, and the fits were done, by populating N-body simulations with galaxies using an HOD prescription."," The fiducial galaxy sample was generated, and the fits were done, by populating N-body simulations with galaxies using an HOD prescription."437 We use a halo model which distinguishes between central and satellite galaxies with a mean occupancy of halos: N(M)=(Nga(Mnaio))., We use a halo model which distinguishes between central and satellite galaxies with a mean occupancy of halos: $N(M)\equiv\left\langle N_{\rm gal}(M_{\rm halo})\right\rangle$.438" Each halo either hosts a central galaxy or does not, while the number of satellites is Poisson distributed about a mean Neat."," Each halo either hosts a central galaxy or does not, while the number of satellites is Poisson distributed about a mean $N_{\rm sat}$."439 We parameterize N(M)=Neen+Neat with 5 parameters (e.g.Zhengetal.2005) and for M>(Mas)Mc and zero otherwise.," We parameterize $N(M)=N_{\rm cen}+N_{\rm sat}$ with 5 parameters \citep[e.g.][]{Zheng05}440 and for $M>M_{\rm cut}$ and zero otherwise."441" Different functional forms have been proposed in the literature, but the current form is flexible enough for our purposes here."," Different functional forms have been proposed in the literature, but the current form is flexible enough for our purposes here."442 The fiducial galaxy sample is generated from the og=0.8 simulation., The fiducial galaxy sample is generated from the $\sigma_8=0.8$ simulation.443 It has a number density of 1.5x107?5?Mpc? and a correlation length of about 7h! Mpc.," It has a number density of $1.5\times 10^{-3}\,h^3\,{\rm Mpc}^{-3}$ and a correlation length of about $7\,h^{-1}$ Mpc."444" All errors are computed by Monte-Carlo methods, dividing the simulation into disjoint regions."," All errors are computed by Monte-Carlo methods, dividing the simulation into disjoint regions."445" For definiteness we consider a survey of volume (250h!Mpc)?~1.6x10’h-?Mpc?, similar to the corresponding Sloan Digital Sky Survey sample, and scale the covariance matrices to that volume."," For definiteness we consider a survey of volume $(250\,h^{-1}{\rm Mpc})^3\simeq 1.6\times 10^7\,h^{-3}{\rm Mpc}^3$ , similar to the corresponding Sloan Digital Sky Survey sample, and scale the covariance matrices to that volume."446 This yields diagonal errors on €(r) of around 5—10% and bin-to-bin of15-80%., This yields diagonal errors on $\xi(r)$ of around $5-10\%$ and bin-to-bin of.447". When fitting HOD models to these data the best fits are “good” fits, and the parameter values are well within the range of HOD parameters seen for similar galaxy samples, and so both cosmologies are acceptablepriori."," When fitting HOD models to these data the best fits are “good” fits, and the parameter values are well within the range of HOD parameters seen for similar galaxy samples, and so both cosmologies are acceptable."448 It is clear (Fig. 1)), It is clear (Fig. \ref{fig:xir}) )449 that the two-point correlation function by itself cannot distinguish between the two models - Ax?« for 8 data points., that the two-point correlation function by itself cannot distinguish between the two models - $\Delta\chi^2<1$ for 8 data points.450" The next sections demonstrate that a simple1 density mark, measurable from the spatial distribution of galaxies strongly discriminates between these models."," The next sections demonstrate that a simple density mark, measurable from the spatial distribution of galaxies strongly discriminates between these models."451 The marked correlation function generalizes the standard correlation function by weighting galaxies by a numerical “mark”., The marked correlation function generalizes the standard correlation function by weighting galaxies by a numerical “mark”.452" If the mark of the i object is m;, then the marked correlation function is defined as (e.g.Sheth,Connolly,Skibba2005,Eq.3) where the sum is over all pairs of objects (1,1). with separation r;;=r, n(r) is the number of pairs, and the mean mark, 7n, is calculated over all objects in the sample."," If the mark of the $i^{th}$ object is $m_{i}$, then the marked correlation function is defined as \citep[e.g.][Eq.~3]{SheConSki05}453 where the sum is over all pairs of objects $(i,j)$ with separation $r_{ij}=r$, $n(r)$ is the number of pairs, and the mean mark, $\bar{m}$, is calculated over all objects in the sample."454" Note that, unlike €, wp, or w, no random catalog is needed in the computation of M(r)."," Note that, unlike $\xi$, $w_p$ or $w$, no random catalog is needed in the computation of $M(r)$."455 It is convenient to divide out the clustering of the average sample since M(r)#1 then implies a difference in clustering by objects with different marks., It is convenient to divide out the clustering of the average sample since $M(r)\ne 1$ then implies a difference in clustering by objects with different marks.456" The above expression can be applied in 2D or 3D, with angular or linear bins."," The above expression can be applied in 2D or 3D, with angular or linear bins."457 The choice of mark depends on the application., The choice of mark depends on the application.458 In, In459bbeing considered varies.,being considered varies.460a roughly spherical or ellipsoidal shape. uulike clusters with a positive specific heat which may be more nreeular.,"a roughly spherical or ellipsoidal shape, unlike clusters with a positive specific heat which may be more irregular."461 The small nuuber of “particles” in a cell suggest that an effective description of a cell aud. hence of a cluster of galaxies is the nunuber aud detailed positious of its subclusters., The small number of “particles” in a cell suggest that an effective description of a cell and hence of a cluster of galaxies is the number and detailed positions of its subclusters.462 Using this description. compact clusters have a single dominant subcluster. iiediuni compact clusters have uniltiple subchisters aud loose clusters have a single diffuse subcluster that is most likely to be wuvirializect.," Using this description, compact clusters have a single dominant subcluster, medium compact clusters have multiple subclusters and loose clusters have a single diffuse subcluster that is most likely to be unvirialized."463 Based on this classification. compact clusters are best represented as spherical with a density profile.," Based on this classification, compact clusters are best represented as spherical with a density profile."464 Loose unvinalized clusters are likely to be rare. and have fewer galaxies.," Loose unvirialized clusters are likely to be rare, and have fewer galaxies."465 Such clusters are better represented as a collection of galaxies., Such clusters are better represented as a collection of galaxies.466 Finally. medium compact clusters. having inultiple pronounced coucentrations. are best described as a collection of uearly virialized subcelusters.," Finally, medium compact clusters, having multiple pronounced concentrations, are best described as a collection of nearly virialized subclusters."467 With this in munud. we can decompose a rich cluster iuto a ΗΕ nunber of nearly virialized subclusters.," With this in mind, we can decompose a rich cluster into a small number of nearly virialized subclusters."468 These subclusters are simple. ucarly spherical objects with density profiles which are casily characterized.," These subclusters are simple, nearly spherical objects with density profiles which are easily characterized."469 Sparser regions of space nav be similarly decomposed although thev may have differeut scales., Sparser regions of space may be similarly decomposed although they may have different scales.470 From the detailed positious aud velocities of the subchisters in a cell. we can calculate the iustantancous energy aud virial ratio of the cell.," From the detailed positions and velocities of the subclusters in a cell, we can calculate the instantaneous energy and virial ratio of the cell."471 These cueregics represent a snapshot of a cell that is more closely related. to its local dynamics than to its average thermodynamics., These energies represent a snapshot of a cell that is more closely related to its local dynamics than to its average thermodynamics.472 The cnereies fluctuate about the quasi-equilibriun eusenible averages as particles muove about the cell., The energies fluctuate about the quasi-equilibrium ensemble averages as particles move about the cell.473 Therefore a measured iustautaucous virial ratio corresponds to a range of quasi-cquilibritim virial ratios., Therefore a measured instantaneous virial ratio corresponds to a range of quasi-equilibrium virial ratios.474 These factuations have been measured to be up to 20% πι N-hacky simulations (Aarseth&Saslaw1972)... so we use a range of 20% about the measured virial ratio.," These fluctuations have been measured to be up to $20\%$ in $N$ -body simulations \citep{1972ApJ...172...17A}, so we use a range of $20\%$ about the measured virial ratio."475 This eives us a ranee over which to integrate equation(15).. so that the probability that a cell has a measured virial ratio cds This probability. although related to the configuration of a cell. is not the probability that a cell las a similar configuration.," This gives us a range over which to integrate equation, so that the probability that a cell has a measured virial ratio $\psi$ is This probability, although related to the configuration of a cell, is not the probability that a cell has a similar configuration."476 This is because different coufiguratious nav have the same energv and virial ratio., This is because different configurations may have the same energy and virial ratio.477 In fact. because galaxies in a cell πόνο about. the detailed spatial configuration of a cell is not static.," In fact, because galaxies in a cell move about, the detailed spatial configuration of a cell is not static."478 For this reason. we asstune that all configurations with the same virial ratio are equally probable because they are likely to be chance occurrences as galaxies and subclusters move around a cell.," For this reason, we assume that all configurations with the same virial ratio are equally probable because they are likely to be chance occurrences as galaxies and subclusters move around a cell."479 Under this assumption. we can compare different configurations and study how much mere likely a cell is to have one configuration rather than another.," Under this assumption, we can compare different configurations and study how much more likely a cell is to have one configuration rather than another."480 For a cell iu which we can measure both T. and W.. the measured virial ratio c d8 easily computed.," For a cell in which we can measure both $T_*$ and $W_*$, the measured virial ratio $\psi$ is easily computed."481 However. for a cellin which we ouly have the spatial configuration (οιο observations with uo radial velocity iuformation). we need to make additional assumptions in order to iter a value of T..," However, for a cell in which we only have the spatial configuration (e.g. observations with no radial velocity information), we need to make additional assumptions in order to infer a value of $T_*$."482 Since cells that are not iu quasi-equilibrimu are likely to relax iuto quasi-equilibrimm rapidly. we may asstune that the cell is in quasi-cquilibrimm to eet the most probable value of T..," Since cells that are not in quasi-equilibrium are likely to relax into quasi-equilibrium rapidly, we may assume that the cell is in quasi-equilibrium to get the most probable value of $T_*$ ."483" This means that we can use equations and to estimate 7. and c from au observed value of ο,", This means that we can use equations and to estimate $T_*$ and $\psi$ from an observed value of $W_*$.484 Thus andl from which we cau use equation to calculate a probability., Thus and from which we can use equation to calculate a probability.485 Another application of the range of probabilities is to determine if a specific coufiguration is likely to be bound. uubouud or virialized.," Another application of the range of probabilities is to determine if a specific configuration is likely to be bound, unbound or virialized."486 This is useful for niu cases., This is useful for many cases.487 Ilowever. in the case 0.86x0<0.999 a cluster las a neeative specific heat because most spatial configurations have a value of c that falls within the negative specific heat branch of E.[o] in fieure L.," However, in the case $0.86 \leq \overline{\psi} \leq 0.999$ a cluster has a negative specific heat because most spatial configurations have a value of $\psi$ that falls within the negative specific heat branch of $\overline{E}_*[\overline{\psi}]$ in figure \ref{fig-ivar}."488 Then the variation in c caus that we inteerate over the eutire uegative specific heat branch., Then the variation in $\psi$ means that we integrate over the entire negative specific heat branch.489 This suggests that when a cell is virialized. its spatial configuration can take almost amy shape.," This suggests that when a cell is virialized, its spatial configuration can take almost any shape."490 To illustrate this procedure. we compare the two hiehlv idealized configurations of a line aud a ring where we focus on the spatial configuration.," To illustrate this procedure, we compare the two highly idealized configurations of a line and a ring where we focus on the spatial configuration."491 To reduce the uunber of iudependent variables. we ignore the kinetic enerev information aud use equations and to estimate the virial ratio.," To reduce the number of independent variables, we ignore the kinetic energy information and use equations and to estimate the virial ratio."492 In these configurations. particles are regularly spaced so it is easy to compute the poteutial euergv. by a simple μπαμπάΊο.," In these configurations, particles are regularly spaced so it is easy to compute the potential energy by a simple summation."493 The cases are different since the line configuration is a l-dinieusional configuration. and the rug is a Πατ 2-dineusional configuration.," The cases are different since the line configuration is a 1-dimensional configuration, and the ring is a flat 2-dimensional configuration."494 The simplest I-dimensional configuration is a line with particles spaced at regular intervals., The simplest 1-dimensional configuration is a line with particles spaced at regular intervals.495 For a cell with ΝΑ particles and radius FR. the spacing between each adjacent pair of particles is 2R/CN1).," For a cell with $N$ particles and radius $R$, the spacing between each adjacent pair of particles is $2R/(N-1)$."496 This configuration is infinitesimally thin. aud hence the axis ratios are infinite.," This configuration is infinitesimally thin, and hence the axis ratios are infinite."497 Because particles are arranged m a line. particle { has £0] particles to its left aud NU/ particles to its right.," Because particles are arranged in a line, particle $i$ has $i-1$ particles to its left and $N-i$ particles to its right."498 Therefore WW. obtained from equation is A simple case for a 2-dimensional configuration is where particles are arranged in a ring about their conimion center-ofinass., Therefore $W_*$ obtained from equation is A simple case for a 2-dimensional configuration is where particles are arranged in a ring about their common center-of-mass.499 The particles are spaced eveulv around the circumtercnce of a circle so that the distance between particles { aud j is 2Rsin(atiPN)., The particles are spaced evenly around the circumference of a circle so that the distance between particles $i$ and $j$ is $2R \sin(\pi(i-j)/N)$.500 From the svuunetry of the ring. the total poteutial enerev on auv particle in the cbluster is the same for all particles.," From the symmetry of the ring, the total potential energy on any particle in the cluster is the same for all particles."501 Therefore W. for the ringconfiguration is To compare these cases. we plot T. against NV iu figure Lo which shows that that a line configuration caunot be," Therefore $W_*$ for the ringconfiguration is To compare these cases, we plot $W_*$ against $N$ in figure \ref{fig-Wsconf} which shows that that a line configuration cannot be"502a relativistic jet.,a relativistic jet.503 The high-lrequency (X-ray 5-rav) enussion could either be produced via Compton upscattering of low Irequency radiation by the same electrons responsible for the svuchrotron emission (leptonicjetmodels:forarecentreviewsee.e.g..Dóttcher2001a).. or due to hadronic processes initiated by relativistic protons co-accelerated with the electrons (hadronicmodels.lorarecentdiscussionsee.e.g..Miicke&Protheroe 2003).," The high-frequency (X-ray – $\gamma$ -ray) emission could either be produced via Compton upscattering of low frequency radiation by the same electrons responsible for the synchrotron emission \citep[leptonic504jet models; for a recent review see, e.g.,][]{boettcher07a}, or due to hadronic processes initiated by relativistic protons co-accelerated with the electrons \citep[hadronic models, for 505a recent discussion see, e.g.,][]{muecke01,muecke03}."506. Several authors have modeled broadband SEDs of 3C279 in various states (e.g..etal.2001:HartmanοἱMoclerski 2003).," Several authors have modeled broadband SEDs of 3C279 in various states \citep[e.g.,][]{bednarek98,sikora01,hartman01,moderski03}."507. A consistent picture emerges that (he X-ray soft. y-ray portion of the SED might be dominated. by svuchrotron sell-C'ómpton. (SSC) emission. while theEGRET emission mieht require an additional component. most likely external Compton eniission.," A consistent picture emerges that the X-ray – soft $\gamma$ -ray portion of the SED might be dominated by synchrotron self-Compton (SSC) emission, while the emission might require an additional component, most likely external Compton emission."508 Slandarcl leptonic models of blazar emission generally assume that a relativistic plasmoid containing ultrarelativistic nonthermal electrons moves with constant bulk Lorentz [actor E along a jel. directed al a small angle with respect to our line of sight.," Standard leptonic models of blazar emission generally assume that a relativistic plasmoid containing ultrarelativistic nonthermal electrons moves with constant bulk Lorentz factor $\Gamma$ along a jet, directed at a small angle with respect to our line of sight."509 However. for several blazars. in particular high-frequency. peakecl BL Lac objects detected: al =100 GeV - such models sometimes require unexpectedly large bulk Lorentz factors (DZ50) and accordingly small viewing angles in order to explain their SEDs and variability (BeeelmanGhisellini&Taveechio2008:Finkeetal. 2008).," However, for several blazars, in particular high-frequency peaked BL Lac objects detected at $> 100$ GeV $\gamma$ -rays, such models sometimes require unexpectedly large bulk Lorentz factors $\Gamma 510\gtrsim 50$ ) and accordingly small viewing angles in order to explain their SEDs and variability \citep{bfr08,gt08,finke08}."511. Such large Lorentz [actors and small viewing angles pose serious problems for AGN unification schemes. according to which FR. I radio galaxies are believed to be the unbeamecl equivalents of BL Lac objects.," Such large Lorentz factors and small viewing angles pose serious problems for AGN unification schemes, according to which FR I radio galaxies are believed to be the unbeamed equivalents of BL Lac objects."512 A possible solution to this dilemma might lie in the deceleration of the emission region (Georganopoulos&Ixazanas2003a.b) [rom sub-pe scales. at which the optical = X-ray -paw emission is produced. (towards pe and kpe scales. which can be resolved with VLBA / VLBI techniques.," A possible solution to this dilemma might lie in the deceleration of the emission region \citep{gk03a,gk03b} from sub-pc scales, at which the optical – X-ray – $\gamma$ -ray emission is produced, towards pc and kpc scales, which can be resolved with VLBA / VLBI techniques."513 At those scales. superluminal speeds of individual jet components of are characteristically observed in most cases. providing an estimate of the Lorentz factor of jet components at those scales of D10.," At those scales, superluminal speeds of individual jet components of $\beta_{\rm app} \lesssim 10$ are characteristically observed in most cases, providing an estimate of the Lorentz factor of jet components at those scales of $\Gamma 514\sim 10$."515 In fact. extreme deceleration of a radio-emitting plasmoil (component C3) in the jet of 3C 279 may already. habe been directly. observed in space VLBI monitoring observations (Dineretal.2000).. although the identification of (his component over multiple observing epochs with different instruments/arravs is highly uncertain.," In fact, extreme deceleration of a radio-emitting plasmoid (component C3) in the jet of 3C 279 may already habe been directly observed in space VLBI monitoring observations \citep{piner00}, although the identification of this component over multiple observing epochs with different instruments/arrays is highly uncertain."516 In (his paper. we propose a model analogous to the relativistic blast wave model which has successfully predicted and explained the smooth. self-similar light curves of X-ray and optical afterglows of 5-rav bursts (Paczviiski&Roads1993:Mészáros&Dermer 1999).," In this paper, we propose a model analogous to the relativistic blast wave model which has successfully predicted and explained the smooth, self-similar light curves of X-ray and optical afterglows of $\gamma$ -ray bursts \citep{pr93,mr97,cd99}."517. We adapt Chis model lor the specifie situation in blazars., We adapt this model for the specific situation in blazars.518 la particular. we include sell-consistentlv radiative losses and radiation drag from Comptonization of external radiation fields.," In particular, we include self-consistently radiative losses and radiation drag from Comptonization of external radiation fields."519 A similar study. with emphasis on the details of the isotropization of particle distributions in the plasmoid and on spectral features from various leptonic and hadronic processes. has been performed by Pohl&Schlickeiser (2000).. who find &ood agreement of," A similar study, with emphasis on the details of the isotropization of particle distributions in the plasmoid and on spectral features from various leptonic and hadronic processes, has been performed by \cite{ps00}, , who find good agreement of"520will be small.,will be small.521" The azimuthal extent of a bright patch in a nonaxisvnuuelric mode with wavenumber n is ew/in,", The azimuthal extent of a bright patch in a nonaxisymmetric mode with wavenumber $m$ is $\sim\pi/m$.522" The radial extent also has an m-dependence. since away from (he magnetospheric radius (he perturbation solutions decay with radius as ~r="" (84.1)."," The radial extent also has an $m$ -dependence, since away from the magnetospheric radius the perturbation solutions decay with radius as $\sim r^{\pm m}$ (4.1)."523 For bot reasons. low-in modes have patches with the largest area ancl hence are most promising.," For both reasons, $m$ modes have patches with the largest area and hence are most promising."524" The area occupied by a bright patch. defined to correspond to an annular region in the disk bounded by a radius where the perturbation amplitude is half the peak. is estimated to be ο~(πετniο) V"")."," The area occupied by a bright patch, defined to correspond to an annular region in the disk bounded by a radius where the perturbation amplitude is half the peak, is estimated to be $S \sim (\pi r_m^2/2m) (4^{1/m}-4^{-1/m})$ ."525" For m=1.2.32 we have S~L815z17,.0.315217, 0.16z77,. respectively."," For $m526=1, 2, 3$ we have $S \sim 1.875\pi r_m^2, 0.375 \pi r_m^2, 0.16 \pi r_m^2$ , respectively."527 For large m. 5 approaches zero according to 5ο(1n2/117).," For large $m$, $S$ approaches zero according to $S\sim5282\pi r_m^2 (\ln 2/m^2)$."529 The scaling clearly shows that low-n modes clominate by a large factor., The scaling clearly shows that $m$ modes dominate by a large factor.530 In addition. as we argued earlier. low- modes are likely to saturate with substantially larger amplitudes (han high-; modes.," In addition, as we argued earlier, $m$ modes are likely to saturate with substantially larger amplitudes than $m$ modes."531 This is vel another reason why only the lowest order few modes are expected to cause a cliscernible signal in the observations., This is yet another reason why only the lowest order few modes are expected to cause a discernible signal in the observations.532 Apart from demonstrating that unstable modes exist and that mode frequencies in the ratio 2:3 are possible. (he model does not really explain any of (he many puzzling features seen in the observations (see the summary in 81).," Apart from demonstrating that unstable modes exist and that mode frequencies in the ratio 2:3 are possible, the model does not really explain any of the many puzzling features seen in the observations (see the summary in )."533 For instance. the model does not explain why the frequency difference between (win kIIz QPOs in neutron star svstenis is often roughly of order the neutron star spin frequency. (van der Wiis 2000) or sometimes half the spin frequency (Wijnands et al.," For instance, the model does not explain why the frequency difference between twin kHz QPOs in neutron star systems is often roughly of order the neutron star spin frequency (van der Klis 2000) or sometimes half the spin frequency (Wijnands et al."534 2003)., 2003).535 Even though the version of the model described in 85 appears to have (he necessary ingredients lor the beat frequency model to operate. namely gas orbiling at IXeplerian Ireequency around a magnetosphere (hat rotates at the stellar frequency. jever(lieless our analvsis does not reveal any. beat phenomenon.," Even though the version of the model described in 5 appears to have the necessary ingredients for the beat frequency model to operate, namely gas orbiting at Keplerian frequency around a magnetosphere that rotates at the stellar frequency, nevertheless our analysis does not reveal any beat phenomenon."536 Clearly. additional plivsies is needed bevond what we have considered here.," Clearly, additional physics is needed beyond what we have considered here."537 A Rayleigh-Tavlor-like process has been studied extensively by Titareluk and collaborators in a sub-Ixeplerian transition region of a disk around a black hole or a weakly magnetized jeutron star2003)., A Rayleigh-Taylor-like process has been studied extensively by Titarchuk and collaborators in a sub-Keplerian transition region of a disk around a black hole or a weakly magnetized neutron star.538 These authors focus only on stable nodes and suggest that their model eai explain (he observed correlation between (he (win kilohertz Irequencies aud the horizontal branch. QPO frequency2003)., These authors focus only on stable modes and suggest that their model can explain the observed correlation between the twin kilohertz frequencies and the horizontal branch QPO frequency.539 In their model. the dynamical effect of the magnetic field is always assumed to be unimportant. so the fluid is described purely within hyvdrodynamics.," In their model, the dynamical effect of the magnetic field is always assumed to be unimportant, so the fluid is described purely within hydrodynamics."540 The model assumes (he existence of a Chin sub-Ixeplerian (ransilion region in (he vicinity of the compact central object where the accreting matter adjusts itself either to the surface ol a rotating neutron star or to the innermost boundary of the accretion disk1998)., The model assumes the existence of a thin sub-Keplerian transition region in the vicinity of the compact central object where the accreting matter adjusts itself either to the surface of a rotating neutron star or to the innermost boundary of the accretion disk.541 But the origin of the transition laver is not explained. especially considering that the magnetic fieldis assumed to be weak.," But the origin of the transition layer is not explained, especially considering that the magnetic fieldis assumed to be weak."542In the lower panel of Figure 9. we divided clusters into inner ( < 10 kpc) and outer groups.,"In the lower panel of Figure 9, we divided clusters into inner ( $<$ 10 kpc) and outer groups."543 The corresponding gradients are —0.040 + 0.022. aand. —0.047 + 0.023L|. respectively.," The corresponding gradients are $-$ 0.040 $\pm$ 0.022 and $-$ 0.047 $\pm$ 0.023, respectively."544 We can see that the inner disk exhibits roughly the same (or a bit smaller) gradient as the outer part., We can see that the inner disk exhibits roughly the same (or a bit smaller) gradient as the outer part.545 This result is also consistent will the abundance eradient determined by using Cepheid in the solar neighborhood (Andrievskyetal.2002)., This result is also consistent with the abundance gradient determined by using Cepheid in the solar neighborhood \citep{and02}.546. llowever. in our CAT 1. the inner most cluster is located at a galactocentrie distance about 6.8 kpc. il is necessary (to have more inner clusters data (between 3 kpe ancl 7 kpe ) in order to further check the gradient behavior for the inner disk.," However, in our CAT 1, the inner most cluster is located at a galactocentric distance about 6.8 kpc, it is necessary to have more inner clusters data (between 3 kpc and 7 kpc ) in order to further check the gradient behavior for the inner disk."547 If the Galactic bar does play the role. (hen (he inner gradient could be more flat compared wilh outer part.," If the Galactic bar does play the role, then the inner gradient could be more flat compared with outer part."548 Our cluster sample is nearly 50% more than that of TAA97. and we did not find evidence ol any abrupt discontinuity.," Our cluster sample is nearly 50 $\%$ more than that of TAA97, and we did not find evidence of any abrupt discontinuity."549 A similar conclusion was reached bv Friel(1999).. using high resolution abundance determinations for metallicity calibration.," A similar conclusion was reached by \citet{fri99}, using high resolution abundance determinations for metallicity calibration."550 The age-metallicity relationAMIR) for the Galactic disk provides useful clues about the chemical evolution history of the Milky Waxy. and also pul an important constraint on the theoretical models of the disk.," The age-metallicity relation(AMR) for the Galactic disk provides useful clues about the chemical evolution history of the Milky Way, and also put an important constraint on the theoretical models of the disk."551 The observed abundance data generally show a decrease of the stellar metallicity with increasing stellar age. indicating a continuous growth of (he metals in the ISM during the life of the Galaxy.," The observed abundance data generally show a decrease of the stellar metallicity with increasing stellar age, indicating a continuous growth of the metals in the ISM during the life of the Galaxy."552 The early study on AMRB for nearby stars by [found that the mean metallicity of the disk increased by a factor of live between 12 and 5 billion vear ago and has increased only slightly since then., The early study on AMR for nearby stars by \citet{twa80} found that the mean metallicity of the disk increased by a factor of five between 12 and 5 billion year ago and has increased only slightly since then.553 This was also confirmed by latter photometric survey of Meusingeretal.(1991)., This was also confirmed by latter photometric survey of \citet{meu91}.554. With the high resolution spectroscopic data. Edvardssonetal.(1993). showed a plot of iron abundance versus relative ages [or the 139 stars in the solar neighborhood.," With the high resolution spectroscopic data, \citet{edv93} showed a plot of iron abundance versus relative ages for the 189 stars in the solar neighborhood."555 The overall trend of a slowly increasing abundance wilh decreasing age was consistent with the previous photometric results., The overall trend of a slowly increasing abundance with decreasing age was consistent with the previous photometric results.556 ILowever. (he most striking feature of their result is the large scatter around the average trend. which marks a weak correlation between age ancl metallicity.," However, the most striking feature of their result is the large scatter around the average trend, which marks a weak correlation between age and metallicity."557 This spread was. as thev pointed out. in part due to selection bias for the programme stars. and al least partly intrinsic. since the mean errors in [Fe/H] measurement and logarithmic age derivation are much less (han (he scatter.," This spread was, as they pointed out, in part due to selection bias for the programme stars, and at least partly intrinsic, since the mean errors in [Fe/H] measurement and logarithmic age derivation are much less than the scatter."558 In a recent paper. Feltzingetal.(2001) have re-examined the Galactic AMR in the solar neighborhood based on a sample of 5828 dwarls ancl sub-cdwarfs [rom IHipparcos Catalogue.," In a recent paper, \citet{fel01} have re-examined the Galactic AMR in the solar neighborhood based on a sample of 5828 dwarfs and sub-dwarfs from Hipparcos Catalogue."559 Thev found that the solar neighborhood. age-anetallicity diagram is well populated. at all ages and especially Chat old. metalrich stars do exist. which have been omitted in previous samples.," They found that the solar neighborhood age-metallicity diagram is well populated at all ages and especially that old, metal-rich stars do exist, which have been omitted in previous samples."560 This indicates a complete lack of enrichment over the age of Galactic disk among (he fields stars in (he solar neighborhood., This indicates a complete lack of enrichment over the age of Galactic disk among the fields stars in the solar neighborhood.561be real.,be real.562 One possible explanation for the trend with magnitude could be that range svslematically samples more massive stars. which are also expected to be more centrally segregated.," One possible explanation for the trend with magnitude could be that range systematically samples more massive stars, which are also expected to be more centrally segregated."563 In order (o estimate the overall binary content of M10. independently of the value of q. we also computed the (Spor).," In order to estimate the overall binary content of M10, independently of the value of $q$, we also computed the $\xi_{TOT}$ )."564 This requires us to perform simulations of single and binary star populations assuming dillerent input values of the global binary fraction (£5) aud then determining «ο Irom the comparison between (he artificial and the observed CALDs: the value of £j that provides the best match between the two CAIDs is adopted as the global binary. Traction £roy (see Bellazzini et al., This requires us to perform simulations of single and binary star populations assuming different input values of the global binary fraction $\xi_{\rm in}$ ) and then determining $\xi_{TOT}$ from the comparison between the artificial and the observed CMDs: the value of $\xi_{\rm in}$ that provides the best match between the two CMDs is adopted as the global binary fraction $\xi_{TOT}$ (see Bellazzini et al.565 2002 and SOT lor a detailed description of the procedure)., 2002 and S07 for a detailed description of the procedure).566" Once we assumed an input. value of the binary fraction (£u). for each of the considered racial and magnitude bins we have built a sample of Nyy and No, stars. wilh Ny),=INE. A being the number of observed. objects (alter having taken into accout the number of contaminating field stars. discussed in Sect. ??))"," Once we assumed an input value of the binary fraction $\xi_{\rm in}$ ), for each of the considered radial and magnitude bins we have built a sample of $N_{\rm MS}$ and $N_{bin}$ stars, with $N_{bin}= N567\xi_{\rm in}$, $N$ being the number of observed objects (after having taken into accout the number of contaminating field stars, discussed in Sect. \ref{analysis}) )"568 in that bin. ancl Nyy being NCL—Sj)).," in that bin, and $N_{\rm MS}$ being $N(1-\xi_{min})$."569 The MS stars have been simulated by randomly. extracting Nyy values of the mass from the present-day cluster mass function derived by101. and transforming the masses into luminosities hy using the Daraffeetal.(1997) isochrones.," The MS stars have been simulated by randomly extracting $N_{\rm MS}$ values of the mass from the present-day cluster mass function derived by, and transforming the masses into luminosities by using the \citet{baraf97} isochrones."570 Then. from the artificial-star catalogue previously described. we have randomly selected an object with similar (AJ«0.1) magnitude ancl. il recovered. we assigned its output J aud V. magnitudes (to (he considered MS star.," Then, from the artificial-star catalogue previously described, we have randomly selected an object with similar $\Delta I<0.1$ ) magnitude and, if recovered, we assigned its output $I$ and $V$ magnitudes to the considered MS star."571" In order to simulate the binary svstems we randomly extracted N,;, values of the mass of the primary component Irom the INyoupa.(2002). iniGal mass function. aud Ny;,, values of the binary mass ratio from the f/(q) distvibution observed by Fisheretal.(2005) in the solar neighborhood. thus also obtaining the mass of the secondary."," In order to simulate the binary systems we randomly extracted $N_{bin}$ values of the mass of the primary component from the \citet{kroupa02} initial mass function, and $N_{bin}$ values of the binary mass ratio from the $f(q)$ distribution observed by \citet{fisher05} in the solar neighborhood, thus also obtaining the mass of the secondary."572 After transforming masses into luminosities and summing up the fluxes of the two components. an object wilh similar magnitude was randomly extracted from the artificial-star catalogue and. if recovered by the photometric analvsis. (he shifts between its input. and output magnitudes were assigned {ο the considered binary svstem.," After transforming masses into luminosities and summing up the fluxes of the two components, an object with similar magnitude was randomly extracted from the artificial-star catalogue and, if recovered by the photometric analysis, the shifts between its input and output magnitudes were assigned to the considered binary system."573 Finally. the field stars were added to the sample.," Finally, the field stars were added to the sample."574 The result, The result575cannot be accessed easily.,cannot be accessed easily.576 The required. fuunctious are located within thetoollsit?.. aud are designed to create a 2D projection out of a 3D scene.," The required functions are located within the, and are designed to create a 2D projection out of a 3D scene."577 Specifically. the instance. creating the plotting area. takes in two paraicters. the elevation 0 aud the azuuuth o. both iu deerees.," Specifically, the instance, creating the plotting area, takes in two parameters, the elevation $\theta$ and the azimuth $\phi$, both in degrees."578 Creating an sTi stereo pair is then a Desteps process: This nethoc is a trade-off: Toc-in or Offset stereo pairs cannot preseutly be created with easilv. unlike sTi stereo pairs.," Creating an sTi stereo pair is then a 3-steps process: This method is a trade-off: Toe-in or Offset stereo pairs cannot presently be created with easily, unlike sTi stereo pairs."579 Especially. implementing the Toe-in mehod requires the modification of the source code of thefiction”.," Especially, implementing the Toe-in method requires the modification of the source code of the."580. But the sTi simplicity comes at a price., But the sTi simplicity comes at a price.581 For viewpoints with no elevation (69= QU the sTi method is ideutica to the Toc-in technique.," For viewpoints with no elevation $\theta_0=0^{\circ}$ ), the sTi method is identical to the Toe-in technique."582 However. errors both in the LIIS/RIIS images oricutation. as well as iu their azinuthal separation. are introduced with increasing values of |y].," However, errors both in the LHS/RHS images orientation, as well as in their azimuthal separation, are introduced with increasing values of $|\theta_0|$."583 For completeness. we describe those issues in detail in the Appendix ??.. and compare sTi stereo pairs with Του and Offset stereo pairs for different elevatious.," For completeness, we describe those issues in detail in the Appendix \ref{App}, and compare sTi stereo pairs with Toe-in and Offset stereo pairs for different elevations."584 The comparisons show that the STi methoc delivers very simular results to the Του iethod or elevation as high as [00~507., The comparisons show that the sTi method delivers very similar results to the Toe-in method for elevation as high as $|\theta_0|\sim50^{\circ}$.585 Devon this linut. the depth perception is reduced compared to the Toc-iu nethod.," Beyond this limit, the depth perception is reduced compared to the Toe-in method."586 Comparing with the Offset metlo« reveals tha the 3D structure of the οject is mereasec aud better revealed in he sTi method. which makes the latter nore suitable for the publication of iulti-dimensional data sets.," Comparing with the Offset method reveals that the 3D structure of the object is increased and better revealed in the sTi method, which makes the latter more suitable for the publication of multi-dimensional data sets."587 Iu other words. if the objec appears. with the Off«e technique. to be of the screen. it docs iof coutain iself πιο. depth information.," In other words, if the object appears, with the Offset technique, to be of the screen, it does not contain itself much depth information."588 Peterkaetal.(2009) reached a simular conclusion when building a stereoscopic movie of 3D sinulatious of a core-collapse supernova 2003) information.” Teuce. the Toe-in. aud in our case the STi technique. is recouuncucded for the creation of stereo pairs in Astroplysics.," \cite{Peterka09} reached a similar conclusion when building a stereoscopic movie of 3D simulations of a core-collapse supernova \citep[][]{Blondin03} : "" "" Hence, the Toe-in, and in our case the sTi technique, is recommended for the creation of stereo pairs in Astrophysics."589 It is: The hard-coded parameters within cause uo visible vertical parallax or other visual detects in sTi stereo pairs., It is: The hard-coded parameters within cause no visible vertical parallax or other visual defects in sTi stereo pairs.590 We have asked some students and astronomers at the Mount Stromlo Observatory to test our sTi stereo pairs., We have asked some students and astronomers at the Mount Stromlo Observatory to test our sTi stereo pairs.591 None of them found the sTi pais more tiring x difficult to visualize. with a very satisfactory depth oeupression.," None of them found the sTi pairs more tiring or difficult to visualize, with a very satisfactory depth impression."592 Most of thei also noted that even if the epth perception in «ΤΙ pairs is degraded beyoud [09]~507 compared to Tocdn pairs. it does uot vanishes completely.," Most of them also noted that even if the depth perception in sTi pairs is degraded beyond $|\theta_0|\sim50^{\circ}$ compared to Toe-in pairs, it does not vanishes completely."593" Tn that scuse. our suggested sTi method can be used for auv viewpoint with satisfactory depth Hupression and reasonable coutort for the viewer,"," In that sense, our suggested sTi method can be used for any viewpoint with satisfactory depth impression and reasonable comfort for the viewer."594 We illustrate the role that stereoscopy. in the form of stereo pairs. can play in a publication with three exanrples: conceptual. observational. and theoretical.," We illustrate the role that stereoscopy, in the form of stereo pairs, can play in a publication with three examples; conceptual, observational, and theoretical."595 Clearly. the range of applicatious for stereoscopy iu Astroplivsies is much lareer than those we are about to present. and the publications meutioned in Sec.," Clearly, the range of applications for stereoscopy in Astrophysics is much larger than those we are about to present, and the publications mentioned in Sec."596 ?? üehlieht. the fact that stereo pairs can be used for aluost any type of multidineusional data set. e.g.àY 3D imays aud structures. 3D iso-surfaces. N-body sa.ulations and trajectories. cosmological simulations. magnetic aud other feld maps. 3D function fitting. color-magnitude diagrams. lydrodvuamic simulatious and complex (e.g. turbulent) structures.," \ref{Sec:intro} highlight the fact that stereo pairs can be used for almost any type of multi-dimensional data set, e.g., 3D maps and structures, 3D iso-surfaces, N-body simulations and trajectories, cosmological simulations, magnetic and other field maps, 3D function fitting, color-magnitude diagrams, hydrodynamic simulations and complex (e.g. turbulent) structures."597 As mieutioned in Section ??.. stereoscopy. in tliis case in the form of stereo pairs. is different froin standard plots iu flat it πασάτς a fecling of depth to the viewer.," As mentioned in Section \ref{Sec:intro}, stereoscopy, in this case in the form of stereo pairs, is different from standard plots in that it transmits a feeling of depth to the viewer."598 Le us illustrate this advantage with a practical example., Let us illustrate this advantage with a practical example.599 In Fig. 3..," In Fig. \ref{fig:spheres},"600 we present three stereo pairs of the sale object. two intersecting spleres of differcut radius.," we present three stereo pairs of the same object, two intersecting spheres of different radius."601 Tn cach case. the two spheres’ sviunietry axis is in the NZ plane. aud tilted by 15 degrees with respect to the Z axis.," In each case, the two spheres' symmetry axis is in the XZ plane, and tilted by 45 degrees with respect to the Z axis."602normalised the eequivalent widths by the equivalent width of the Lào Lline (Table 2.. column 3).,"normalised the equivalent widths by the equivalent width of the $\alpha$ line (Table \ref{tab:fits}, column 3)."603 The results show a smooth variation with phase: both transitions are of similar strength. except for the abrupt reversal in the phase O spectrum. when the AT065 line becomes significantly weaker than the A6678 line.," The results show a smooth variation with phase; both transitions are of similar strength, except for the abrupt reversal in the phase 0 spectrum, when the $\lambda$ 7065 line becomes significantly weaker than the $\lambda$ 6678 line."604 The measured. velocities of the emission line do not. seem to conform to any sensible pattern., The measured velocities of the emission line do not seem to conform to any sensible pattern.605 In. particular. there is no discernible signature of orbital. motion over most of the orbit.," In particular, there is no discernible signature of orbital motion over most of the orbit."606 This implies that the site of the emission is changing throughout the orbit. ancl possibly over the one vear spanning our observations — see Section 4 for a discussion of the implications for à mocdel for the system.," This implies that the site of the emission is changing throughout the orbit, and possibly over the one year spanning our observations – see Section \ref{sec:discussion} for a discussion of the implications for a model for the system."607 llowever. we do see significant orbital motion in the data taken near periastron.," However, we do see significant orbital motion in the data taken near periastron."608 We divided the data taken on 2000 Alay 22 into four equal segments of 7200 s duration and performed the same analysis on cach segment., We divided the data taken on 2000 May 22 into four equal segments of 7200 s duration and performed the same analysis on each segment.609 Theresults are shown in Fig. 5.., Theresults are shown in Fig. \ref{fig:peri-v}.610 3oth components of the Ha [line as well as the A6678 line (not plotted). show an increase in velocity. of oover six hours.," Both components of the $\alpha$ line, as well as the $\lambda$ 6678 line (not plotted), show an increase in velocity of over six hours."611 This certainly implies that at this point in the orbit the emission line is tracking the orbital motion: in à highly elliptical orbit. nearly all the velocity swing happens right near periastron (Claurisetal.1999).," This certainly implies that at this point in the orbit the emission line is tracking the orbital motion; in a highly elliptical orbit, nearly all the velocity swing happens right near periastron \cite{tfh+99}."612 With only four velocity. points. we cannot place any interesting constraints on the orbital parameters.," With only four velocity points, we cannot place any interesting constraints on the orbital parameters."613 Two representative curves are plotted: with the observed. points: it can be seen that there is essentially no constraint on the orbital inclination. though the eccentricity must be high to produce the observed sharp swing in velocity.," Two representative curves are plotted with the observed points; it can be seen that there is essentially no constraint on the orbital inclination, though the eccentricity must be high to produce the observed sharp swing in velocity."614 Lt is important to note that the phases have been caleulated sing the ephemeris of Stewart et al. (1991)., It is important to note that the phases have been calculated using the ephemeris of Stewart et al. \shortcite{snp+91}.615.. Phase 0 refers o the onset of racio Hares. and how this relates to the X-ray ips observed by lis not clear.," Phase 0 refers to the onset of radio flares, and how this relates to the X-ray dips observed by is not clear."616 We have examined the quick-look results ovided by the RAPESM team to see if we can compare 10 observed. times of the N-ray. dips with the predicted imes from the Stewart et al., We have examined the quick-look results provided by the RXTE/ASM team to see if we can compare the observed times of the X-ray dips with the predicted times from the Stewart et al.617 ephemeris., ephemeris.618 The. periastron xwsage on 2000 Alay 22 did not have good ASAI coverage: »Àh the preceding and the following X-ray clips appear to jwe occurred. θε0.5 d later than the phase O predicted w the Stewart et al., The periastron passage on 2000 May 22 did not have good ASM coverage; both the preceding and the following X-ray dips appear to have occurred 0.4–0.5 d later than the phase 0 predicted by the Stewart et al.619 ephemeris. corresponding to a shift of 1.0240.03 in phase.," ephemeris, corresponding to a shift of 0.024–0.03 in phase."620 Given that the ephemeris was based on radio Hares. and that the X-ray light. curve changes so cdrematicallv. this agreement is reasonably good.," Given that the ephemeris was based on radio flares, and that the X-ray light curve changes so dramatically, this agreement is reasonably good."621 In future work we hope to further investigate the exact. relationship between the X-ray. radio and optical behaviour.," In future work we hope to further investigate the exact relationship between the X-ray, radio and optical behaviour."622 In Paper L we proposed a theoretical model for Cir X-l.," In Paper I, we proposed a theoretical model for Cir X-1."623 Phe binary is a low-mass neutron-star binary with an ultra-eccentric binary orbit (ez 0.7. possibly as high as," The binary is a low-mass neutron-star binary with an ultra-eccentric binary orbit $e \ga 0.7$ , possibly as high as"624The sources of the extragalactic cosmüe rays with euereies in excess of «1015 ceW roniain a mystery. but oue of the best motivated cauclicates is Ganuma-ray bursts (GRBs).,"The sources of the extragalactic cosmic rays with energies in excess of $\sim$ $\times$ $^{18}$ eV remain a mystery, but one of the best motivated candidates is gamma-ray bursts (GRBs)."625 Large cosuiic-rav euergies can be achieved iu the prompt phase of the CRD fireball where internal shocks have the potential to accelerate charged particles up to —10?eeV. (Vietri1995... Waxman 19953).," Large cosmic-ray energies can be achieved in the prompt phase of the GRB fireball where internal shocks have the potential to accelerate charged particles up to $\sim$ $^{21}$ eV \citealt{vietri_1995}, \citealt{waxman_1995}) )."626 Additionally. the total cnerey deusitv in the Universe of cosnüc ravs uaust be matched bv a sutiicicutly high hadronic energy deusitv iu the QGRD with puoi©Per GRB.," Additionally, the total energy density in the Universe of cosmic rays must be matched by a sufficiently high hadronic energy density in the GRB with $\rho_{\mbox{\tiny{had,\,GRB}}}\approx\rho_{\mbox{\tiny{CR}}}$."627" observatious identify svuchrotron photous produced bv the clectrous acceleratedin the fireball with an energy εως dU cores. where Exo, is the total enerev released by the burst."," GRB observations identify synchrotron photons produced by the electrons acceleratedin the fireball with an energy $\epsilon_e\mbox{E}_{\mbox{\tiny{TOT}}}\sim\,$ $^{53}$ ergs, where $_{\mbox{\tiny{TOT}}}$ is the total energy released by the burst."628" CRB fireballs also carry enerev ερων, iu the form of magnetic fields. aud. if they are the sources of cosmic rays. euerey ej,E4 iu protons."," GRB fireballs also carry energy $\epsilon_B\mbox{E}_{\mbox{\tiny{TOT}}}$ in the form of magnetic fields, and, if they are the sources of cosmic rays, energy $\epsilon_p\mbox{E}_{\mbox{\tiny{TOT}}}$ in protons."629" Asstuiue equipartition. epce, ande,|e,ep=."," Assuming equipartition, $\epsilon_B\simeq\,\epsilon_e$ and $\epsilon_e+\epsilon_p+\epsilon_B=1$."630" GRBs emerge as credible sources for the ultra hnieh-energev cosnüc rays because their observed flux can be acconuunodated with an euergv deusity in protons that is simular to that iu electrons. or €,7m 6."," GRBs emerge as credible sources for the ultra high-energy cosmic rays because their observed flux can be accommodated with an energy density in protons that is similar to that in electrons, or $\epsilon_p\,\simeq\,\epsilon_e$ ."631 Recent estimates of the local rate of, Recent estimates of the local rate of632Systematic df line observations of the nearby (2<10 Alpe) galaxies have been recently conducted. at the 62m elescope of the Special Astrophysical Observatory. Russian Academy of Sciences. (SAQ RAS) in order to determine yw rate of star formation in them (??7?7?7)..,"Systematic $H\alpha$ line observations of the nearby $D<10$ Mpc) galaxies have been recently conducted at the 6-m telescope of the Special Astrophysical Observatory, Russian Academy of Sciences (SAO RAS) in order to determine the rate of star formation in them \citep{k05,kk06,kk08,kai07,kk07,kk10}."633 Unlike other similar programs (2222?).. we did not restrict our program o any selected morphological tvpes of galaxies.," Unlike other similar programs \citep{hun93,bk01,jam04,hun04,ken08}, we did not restrict our program to any selected morphological types of galaxies."634" With almost je same enthusiasm we observe both the gas-rich spiral. unrregular ancl blue compact. galaxies. as well as the ""dead elliptical. lenticular and dwarf spheroidal galaxies. where he current rates of star formation are assumed to be close o zero."," With almost the same enthusiasm we observe both the gas-rich spiral, irregular and blue compact galaxies, as well as the “dead” elliptical, lenticular and dwarf spheroidal galaxies, where the current rates of star formation are assumed to be close to zero."635 Such non-selective approach to the compilation of target. list has led to detection of a circumnuclear Lfa emission [from a number of isolated. LE. SO. galaxies. (?).. indicating the ongoing quast-stationary process of accretion of the intergalactic gas onto the central parts of galaxies.," Such non-selective approach to the compilation of target list has led to detection of a circumnuclear $H\alpha$ emission from a number of isolated E, S0 galaxies \citep{mois10}, indicating the ongoing quasi-stationary process of accretion of the intergalactic gas onto the central parts of galaxies."636" Another unexpected: result of our. survey was. the discovery in some dSph galaxies of small emission clumps. which we designated. as ""sparks."," Another unexpected result of our survey was the discovery in some dSph galaxies of small emission clumps, which we designated as “sparks”."637 As it is known. the neighboring group around the giant spiral SSI is rather rich in dwarf spheroidal svstems.," As it is known, the neighboring group around the giant spiral 81 is rather rich in dwarf spheroidal systems."638 Some of them: BASN. DBINXGN. FALL. USN. το do not show any signs of emission in the //a line. and the optical bodies of others 444. 778. FSDI. 663) reveal fine structural details after the subtraction of continuum.," Some of them: BK5N, BK6N, FM1, IKN, 70 do not show any signs of emission in the $H\alpha$ line, and the optical bodies of others 44, 78, F8D1, 63) reveal fine structural details after the subtraction of continuum."639 Such details may be the result. of an incomplete subtraction of the continuum of very red stars. or an artifact from cosmic ravs.," Such details may be the result of an incomplete subtraction of the continuum of very red stars, or an artifact from cosmic rays."640" Lt seems unlikely that the ole. ""bale. devoid of neutral hydrogen. spheroidal cwarls contain small sites of star formation."," It seems unlikely that the old, “bald”, devoid of neutral hydrogen spheroidal dwarfs contain small sites of star formation."641 do verify the nature of the hypothesized emission clumps in dSph galaxies. we carried out spectral observations. the results of which are given in this article.," To verify the nature of the hypothesized emission clumps in dSph galaxies, we carried out spectral observations, the results of which are given in this article."642 As shown bv 777. the region of the MSSI group is illed with filament structures of neutral hverogen. which connect SSI with the neighboring bright galaxies 8S2. 33077 and 22976.," As shown by \citet{app81,yun97,boyce01}, the region of the 81 group is filled with filament structures of neutral hydrogen, which connect 81 with the neighboring bright galaxies 82, 3077 and 2976."643 Lt is assumed that this complex LIL pattern was formed. as a result. of tidal interaction of he brightest group members., It is assumed that this complex HI pattern was formed as a result of tidal interaction of the brightest group members.644 In the most cense parts of he LU filaments. the process of star formation is already uncerway.," In the most dense parts of the HI filaments, the process of star formation is already underway."645 Lt ded to the formation of tidal ears: Garland. LEX. loop CX0958|66) and BIN3N (?2).. where he old (22 Gyr) stellar population is absent.," It led to the formation of tidal dwarfs: Garland, IX, loop (A0958+66) and BK3N \citep{mak02}, , where the old $T>2$ Gyr) stellar population is absent."646 ? and ? have found in the SSI group a significant number of small LL-clouds with masses of ~10°10AL.. [rec-Doating roween bright galaxies.," \citet{bri08}647 and \citet{chy11} have found in the 81 group a significant number of small HI-clouds with masses of $\sim10^5-10^6 M_{\odot}$, free-floating between bright galaxies."648" Some of them coincide in position with the dSph να, galaxies. for example. 557"," Some of them coincide in position with the dSph dwarf galaxies, for example, 57."649 7 obtained deep images with MegaC'am at the CELUT in the ve” andl i filters of an area sized. ~1 square degree: between MSSI and at subareseconel secing., \citet{mouh10} obtained deep images with MegaCam at the CFHT in the “g” and “i” filters of an area sized $\sim 1$ square degree between 81 and 3077 at subarcsecond seeing.650 On these images the authors 33077.found. three knots: clump I. clump EL and clump LI. resolved. into blue stars.," On these images the authors found three knots: clump I, clump II, and clump III, resolved into blue stars."651 All of them are located. approximately along the LIE arm. connecting SSI and 33077.," All of them are located approximately along the HI arm, connecting 81 and 3077."652 These bluishclumps are, These bluishclumps are653"SEDs directly shows that the 25044n/500;,22. ratio is sienificautly lower iu the tidal feature comwed to the main body of 33077. reflecting a lower teniperature in the tidal region.","SEDs directly shows that the $\mu$ $\mu$ m ratio is significantly lower in the tidal feature compared to the main body of 3077, reflecting a lower temperature in the tidal region."654 Caven the lower teiiperature iu the tidal aru aud the comparable total fluxes 11i the SPIRE bauds this iniuediatelv implies that the dus lass in the tidal feature is larger than in NCOC33077 itself (366 more detailed discussion in Sec., Given the lower temperature in the tidal arm and the comparable total fluxes in the SPIRE bands this immediately implies that the dust mass in the tidal feature is larger than in 3077 itself (see more detailed discussion in Sec.655 3.6)., 3.6).656 We have attempted to use Spitzer 3IPS 160jnu nuaeime to further constrain the SED towards shorter wavelengths., We have attempted to use Spitzer MIPS $\mu$ m imaging to further constrain the SED towards shorter wavelengths.657 The main body of NGCOJ3077 is very might. aud we plot the corresponding flux density in Fie.," The main body of 3077 is very bright, and we plot the corresponding flux density in Fig."658 2., 2.659 Because of coverage iux extended cimus CLUISSIOL. he background of the NIPS Ίσθμια is however vadly behaved at the fux levels of interest. leading ο. significant OYTOT lius in the flux determination.," Because of coverage and extended cirrus emission, the background of the MIPS $\mu$ m is however badly behaved at the flux levels of interest, leading to significant error bars in the flux determination."660 We nevertheless derived a 160;12 flux density for the xiehtest aperture (44110. the error bar is dominated by he background. unucertaimties) the complete SED for lis aperture is also plotted iu Fig.," We nevertheless derived a $\mu$ m flux density for the brightest aperture 10, the error bar is dominated by the background uncertainties) — the complete SED for this aperture is also plotted in Fig."661 2 OY conarison., 2 for comparison.662 We have 1sed a blackbody fif. aud the Li Draine (2001) dust chussivity (equivalent to a modified blackbody wit1 0=2) to derive temperatures aud dust masses., We have used a blackbody fit and the Li Draine (2001) dust emissivity (equivalent to a modified blackbody with $\beta$ =2) to derive temperatures and dust masses.663 The temperature for NCOC33077 (aperture #11) is 30.642 NIN aud is in aerecment with high telmpcratures expected for starbursts and the ceutral teniperatures ¢erived for a sub.sample of the KINGFISII ealaxies preseuted bx Eugelbracht et ((2010) of Teor 25.71 KK. The temperature in the tidal feature is uuuch lower.," The temperature for 3077 (aperture 1) is $\pm$ K and is in agreement with high temperatures expected for starbursts and the central temperatures derived for a sub–sample of the KINGFISH galaxies presented by Engelbracht et (2010) of $_{\rm664center}$ $\pm$ K. The temperature in the tidal feature is much lower."665 Based on the SPIRE data only. we derive an average teniperature of T=12.0+1 Kh. Iu he brightes aperture of the tidal feature (4110) he addition of the l60;ün flux estimate increases the cluperature sliebtly IKIS). but is consistent. with he “SPIREoulv vauc.," Based on the SPIRE data only, we derive an average temperature of $\pm$ K. In the brightest aperture of the tidal feature 10) the addition of the $\mu$ m flux estimate increases the temperature slightly K), but is consistent with the `SPIRE–only' value."666 Changing ο) to a value of 1.5 increases the temperature by ~3 ISIN (see dashed SED fits iu Fie., Changing $\beta$ to a value of 1.5 increases the temperature by $\sim$ K (see dashed SED fits in Fig.667 2)., 2).668 In the following we will adopt 532 aud T=12.642 for the tical feature apertures but note that he temperature (ancl the corresponding masses) depend on the exact choice ο: dust mioctel., In the following we will adopt $\beta$ =2 and $\pm$ 2 for the tidal feature apertures but note that the temperature (and the corresponding masses) depend on the exact choice of dust model.669 Finding low chist feuperatures may not be unexpected as the intensity of the radiation field iu the tida arn ds prestunably low: the total star formation in the eutire tidal feature is οuly 2.3410. MM | (based ou In observations. Widter et al.," Finding low dust temperatures may not be unexpected as the intensity of the radiation field in the tidal arm is presumably low: the total star formation in the entire tidal feature is only $\times$ $^{-3}$ $_\odot$ $^{-1}$ (based on $\alpha$ observations, Walter et al."670 2006)., 2006).671 This SER is cousisteut with the rate decrumiued in Weisz et ((2008) through stellar populaticma studies. and CALEN measurements lat cover 1οσ1οus #110 aud #111. implying that the SFR in the tical feature was roughly constant over ie recent past (few hundred Πο vears).," This SFR is consistent with the rate determined in Weisz et (2008) through stellar population studies, and GALEX measurements that cover regions 10 and 11, implying that the SFR in the tidal feature was roughly constant over the recent past (few hundred million years)."672 For those ipertures that iiiclude lYOglons We πιin up their Ilo Lbhunimosities using 1ο values elven in Walter et ((2006) and eive 1C star formalon rate surface densities (averaged OVCT the size of our apertures) in Tab., For those apertures that include regions we sum up their $\alpha$ luminosities using the values given in Walter et (2006) and give the star formation rate surface densities (averaged over the size of our apertures) in Tab.673 1., 1.674 We plot je. 2504025004020. ratios for these aperatures as a, We plot the $\mu$ $\mu$ m ratios for these aperatures as a675have higher-mass disces. as do the objects in binary systems (i.c. names ending in A. D. N or 8).,"have higher-mass discs, as do the objects in binary systems (i.e. names ending in A, B, N or S)."676 Llowever. most. of the short-wavelength data happens to be for the single systems. so these could simply have disc masses that are. estimated due to dust opacity.," However, most of the short-wavelength data happens to be for the single systems, so these could simply have disc masses that are under-estimated due to dust opacity."677 One problem. with the idea of forming planets. early on via clise fragmentation is that theoretical calculations. both semi-analvtic (Alatzner&Levin200:5:Ralikoy2005:Rice&Armitage2009;Clarke2009) and numerical (Boleyetal.2006:Stamatellos&Whitworth2008) suggest that planctary mass bodies will not. form. inside ~50r AU.," One problem with the idea of forming planets early on via disc fragmentation is that theoretical calculations, both semi-analytic \citep{matzner05,rafikov05, rice09,clarke09} and numerical \citep{boley06,stamatellos08}, suggest that planetary mass bodies will not form inside $\sim 50$ AU."678 lt is likely that these extremely massive Class 0. clises would instead become globally unstable (Lodato&Rice 2005).. moving large amounts of mass to large radii. where ragmentation could produce substellar. or even stellar. mass companions(Stamatellos&Whitworth20n.," It is likely that these extremely massive Class 0 discs would instead become globally unstable \citep{lodato05}, moving large amounts of mass to large radii, where fragmentation could produce substellar, or even stellar, mass companions \citep{stamatellos09}."679 Llowever. the orescence of spiral structures in the massive could help to collect together solid particles (Llaghighipour&Boss2003:ticeetal.2004) and thus accelerate planet. formation. via he mechanism of core accretion.," However, the presence of spiral structures in the massive disc could help to collect together solid particles \citep{haghighipour03, rice04} and thus accelerate planet formation via the mechanism of core accretion."680" ""hus massive clises at very carly times may still be a promising signpost to abundant planetary systems around. mature nmaln-sequence stars.", Thus massive discs at very early times may still be a promising signpost to abundant planetary systems around mature main-sequence stars.681 The compilation of millimetre data for circumstellar clises in 1-2 Alvr-okd star formation regions confirms that the mass reservoirs are small. at these snapshots in time.," The compilation of millimetre data for circumstellar discs in 1-2 Myr-old star formation regions confirms that the mass reservoirs are small, at these snapshots in time."682 The fraction of discsapparently capable of forming eas giants by core accretion is generically less than the fraction of observed. exo-planet svstems., The fraction of discs capable of forming gas giants by core accretion is generically less than the fraction of observed exo-planet systems.683 An early start to planetary growth is favoured. as the fractions of exo-planets and suitable proto-planctary dises do match in the Class I stage.," An early start to planetary growth is favoured, as the fractions of exo-planets and suitable proto-planetary discs do match in the Class I stage."684" We also considered: other solutions to the ""missing mass’ problem.", We also considered other solutions to the `missing mass' problem.685 Sweeping up the disc material elliciently into planets has both observational ancl theoretical dilliculties., Sweeping up the disc material efficiently into planets has both observational and theoretical difficulties.686 Alore promisinglv. viscous evolution through disc sell-gravity could. produce a central concentration of mass that would be optically thick even in the millimetre. ancl so essentially invisible.," More promisingly, viscous evolution through disc self-gravity could produce a central concentration of mass that would be optically thick even in the millimetre, and so essentially invisible."687 At very early. times (Class 0). the discs are both massive and at a high mass-fraction with respect to the star. so growth into larger bodies could even start at this very carly phase when the star is only. part-completed.," At very early times (Class 0), the discs are both massive and at a high mass-fraction with respect to the star, so growth into larger bodies could even start at this very early phase when the star is only part-completed."688 La conclusion. most of the We thank STEC and SUPA for support. and Ixenny. Wood for insightful remarks that inspired the carly stages of this project.," In conclusion, most of the We thank STFC and SUPA for support, and Kenny Wood for insightful remarks that inspired the early stages of this project."689where A; is the mass number (protons+neutrons) and Z; the number of electrons.,where $A_{i}$ is the mass number (protons+neutrons) and $Z_{i}$ the number of electrons.690" From (34)) we can thus derive the following advection/diffusion equation for the horizontal fluctuation of the molecular weight A;=μμ: ∣↳↿∣⋅∕↳⊓∏∣≱∣∐⋯↿⋔⊜∣∪∶↔↾⋅≏∐⋪⇈∣↴⋯≣∁∶↔⊺∣⋪∐↳∐⊜∏↾∇∩∶↳⊓∏⇂−∣∕↳⊓∏∣≱↜⊤∣↴≣⋋ H, e", From \ref{c-tilde}) ) we can thus derive the following advection/diffusion equation for the horizontal fluctuation of the molecular weight $\Lambda_{l}=\widetilde{\mu_{l}}/\overline{\mu}$: where we have introduced the pressure scale-height $H_{p}=|{\rm d} r/{\rm d} \ln P |$ and the logarithmic gradient $\nabla_{\mu}={\rm d} \ln\overline{\mu}/ {\rm d}\ln P$.691quation will play a key role in the derivation of the meridional circulation. which we shall discuss in $66.," This equation will play a key role in the derivation of the meridional circulation, which we shall discuss in 6."692 In our case where we take a non-uniform and a non-eylindrical rotation law. the centrifugal force does not derive from a potential.," In our case where we take a non-uniform and a non-cylindrical rotation law, the centrifugal force does not derive from a potential."693 We are in the baroclinic configuration. where the isobars and the surfaces of constant density do not coincide anymore.," We are in the baroclinic configuration, where the isobars and the surfaces of constant density do not coincide anymore."694 To find how the density varies on an isobar. we start from the hydrostatic equation: where ὁ 1s the gravitational potential. and where the local effective gravity g includes the centrifugal force 7(o.," To find how the density varies on an isobar, we start from the hydrostatic equation: where $\phi$ is the gravitational potential, and where the local effective gravity $\vec g$ includes the centrifugal force $\vec{\mathcal F}_{\mathcal{C}}$."695 Taking the curl of this equation. we get which to first order takes the form with (tP being the variation of the density on the isobar. which we write as Likewise we expand Q7 in spherical harmonies: since (cf. 15.. 185) ," Taking the curl of this equation, we get which to first order takes the form with $\rho'$ being the variation of the density on the isobar, which we write as Likewise we expand $\Omega^2$ in spherical harmonics; since (cf. \ref{omega-expand}, \ref{fal}) )"696Wehave where we kept only the terms linear in. Qj., we have where we kept only the terms linear in $\Omega_l$.697 We expect the largest departures from shellular rotation to occur in the tachoclines. where they are enforced by the differential rotation of the adjacent convection zone: judging by the solar case. such departures should be rather small. of the order of 1/10. thus justifying the linear approximation.," We expect the largest departures from shellular rotation to occur in the tachoclines, where they are enforced by the differential rotation of the adjacent convection zone; judging by the solar case, such departures should be rather small, of the order of 1/10, thus justifying the linear approximation."698 Inserting these expansions in (42)). we reach after some algebra the following expression for the modal amplitudes of the relative density fluctuation on an isobar where g is the horizontal average. on the isobar. of the modulus of g. and All numerical coefhcients involved (AT.B.C).DI.G?HN?) are given in Appendix A. We shall display here the result for /=2.4. where we keep only the first term €» of the expansion of M For ¢23:= Owe recover the expression given in Zahn (1992): pjp=ΑθQD.," Inserting these expansions in \ref{barocline}) ), we reach after some algebra the following expression for the modal amplitudes of the relative density fluctuation on an isobar where $\overline{g}$ is the horizontal average, on the isobar, of the modulus of $\vec g$, and All numerical coefficients involved $A^0_l, B^0_l, C^0_l, D^0_l, G^0_l, H^0_l, \mathcal{N}^0_l$ ) are given in Appendix A. We shall display here the result for $l=2, 4$, where we keep only the first term $\Omega_{2}$ of the expansion of $\Omega$: For $\Omega_2=0$ we recover the expression given in Zahn (1992): $\widetilde{\rho}_{2}/\overline\rho = (r^2/ 3\overline g) \partial_r \overline{\Omega}^{2}$."699 This baroclinic equation (46 - 47)) plays a key role in linking the density fluctuation on an isobar with the rotation profile., This baroclinic equation \ref{baro1} - \ref{baro2}) ) plays a key role in linking the density fluctuation on an isobar with the rotation profile.700 It will allow us to close the system formed by the equation for the transport of angular momentum. that for the transport of the chemical species and that for the transport of heat. which we shall establish in $66.. Next we examine the redistribution of masses by the centrifugal force and its effect on the gravity inside the star.," It will allow us to close the system formed by the equation for the transport of angular momentum, that for the transport of the chemical species and that for the transport of heat, which we shall establish in 6.. Next we examine the redistribution of masses by the centrifugal force and its effect on the gravity inside the star."701 As all other scalars. we expand the gravity as: The goal of this section is to determine the amplitude of the fluctuation on an isobar. gj.," As all other scalars, we expand the gravity as: The goal of this section is to determine the amplitude of the fluctuation on an isobar, $\widetilde{g}_{l}$."702 The first step will be to calculate the perturbation of the gravitational potential ὁ on the sphere of radius r. and thus to calculate the functions yr).jr where we have expanded ó as: We follow the method of linearization developed in Sweet (1950). and expand the pressure and the density around the sphere in the same way as 6: Then. we take the hydrostatic equation (using the classical definition of a potential. contrary to . 1992): which we expand to first order We eliminate the pressure fluctuation by taking the curl of the latter equation. which gives us:," The first step will be to calculate the perturbation of the gravitational potential $\phi$ on the sphere of radius $r$, and thus to calculate the functions $\widehat \phi_{l}(r)$, where we have expanded $\phi$ as: We follow the method of linearization developed in Sweet (1950), and expand the pressure and the density around the sphere in the same way as $\phi$: Then, we take the hydrostatic equation (using the classical definition of a potential, contrary to Zahn 1992): which we expand to first order: We eliminate the pressure fluctuation by taking the curl of the latter equation, which gives us:"703variation caused by sound waves in the high plasma j limit may amplify the shear Alfvénn Waves.,variation caused by sound waves in the high plasma $\beta$ limit may amplify the shear Alfvénn waves.704 Then. Zagarashvili&Roberts(2002) showed the resonant οπσον trausfter from fast lagnet¢)»ucotstic waves propagating across the unperturbed imaenetic field to Alfvéóun Waves propagating along the field.," Then, \citet{zaq1} showed the resonant energy transfer from fast magneto-acoustic waves propagating across the unperturbed magnetic field to Alfvénn waves propagating along the field."705 The cucrey transfer is relative to the velocity component- of resonat Alfvéóuu waves normal to both magnetic field and direction of propagation of the maeuctoacoustic waves., The energy transfer is relative to the velocity component of resonant Alfvénn waves normal to both magnetic field and direction of propagation of the magnetoacoustic waves.706 In both papers the temporal behaviour of Alfvénu waves was found to be governed by Mathieu equation., In both papers the temporal behaviour of Alfvénn waves was found to be governed by Mathieu equation.707 Thus the frequency of resonant Alfvén waves was the half frequency of the diiviug compressible oscillations., Thus the frequency of resonant Alfvénn waves was the half frequency of the driving compressible oscillations.708 The natural astroplivsical suggestion was that stellar pulsation iu the fundamental mode may azplity torsional Alfvénn waves in a seed magnetic field (Zaqarashvilictal.2002)., The natural astrophysical suggestion was that stellar pulsation in the fundamental mode may amplify torsional Alfvénn waves in a seed magnetic field \citep{zaq3}.709. The process cau be of nuportance in stellar claromospheres aud coronas as the Alfvénn waves propagate upwards carving enerev and imonmeutuni and so may contribute to chromospheric and coronal heating., The process can be of importance in stellar chromospheres and coronas as the Alfvénn waves propagate upwards carrying energy and momentum and so may contribute to chromospheric and coronal heating.710 Also the waves niv propagate up to the stellarwind and recently ZaqarashviliaudDelvedere.(2005) sugeested them as a source for loug period Alfvén- oscillations (with periods of few hours) observea by ULYSSES in the solar wiud., Also the waves may propagate up to the stellarwind and recently \citet{zaq5} suggested them as a source for long period Alfvénn oscillations (with periods of few hours) observed by ULYSSES in the solar wind.711 Ou another haud. the fundamental frequency of stellar pulsation is too high for resonant torsional Alfvén waves to eive rise fo large-scale torsional oscillations iu a stellar interior.," On another hand, the fundamental frequency of stellar pulsation is too high for resonant torsional Alfvénn waves to give rise to large-scale torsional oscillations in a stellar interior."712 Therefore oue needs a longer period pulsation iu order to sugeest them as an energy source for torsional oscillatious., Therefore one needs a longer period pulsation in order to suggest them as an energy source for torsional oscillations.713 Tere we sugecst that the slow magnetoacoustic waves propagating along the magnetic field iu the lieh plasma .? limit are nonlinearly coupled to the torsional Alfvénn waves propagatingo in the same direction., Here we suggest that the slow magnetoacoustic waves propagating along the magnetic field in the high plasma $\beta$ limit are nonlinearly coupled to the torsional Alfvénn waves propagating in the same direction.714 The velocity polarization of VAOw Inaenetoacoustic waves propagating along a y.raight uniforii magnetic field is along the radial direction iu the case of a cvliudical coordinate system (the waves have a velocity component along the magnetic field as well)., The velocity polarization of slow magnetoacoustic waves propagating along a straight uniform magnetic field is along the radial direction in the case of a cylindrical coordinate system (the waves have a velocity component along the magnetic field as well).715 Therefore fixing the bouudaries along the axis of the cvlindrical svstena originates a standing pattern of waves leading to the pulsation of the magnetic cvlinder with a spatial scale which corresponds to the first or second cigenmode., Therefore fixing the boundaries along the axis of the cylindrical system originates a standing pattern of waves leading to the pulsation of the magnetic cylinder with a spatial scale which corresponds to the first or second eigenmode.716 Iu the case of stars with a poloidal maguetic field in the interior. he fundamental mode of slow magnetoacoustic waves has a very low frequency due to the siall phase speed (note. that the slow magnuetoacoustic waves propagate with the Alfvéóuu speed iui ugh 3 huit)," In the case of stars with a poloidal magnetic field in the interior, the fundamental mode of slow magnetoacoustic waves has a very low frequency due to the small phase speed (note, that the slow magnetoacoustic waves propagate with the Alfvénn speed in high $\beta$ limit)."717 So it will ead to long period stellar pulsation., So it will lead to long period stellar pulsation.718 Since tlic velocity. of the slow nagnetoacoustic waves las the radial direction. anv force (gravity. radiation pressure ete) may support this oscillation.," Since the velocity of the slow magnetoacoustic waves has the radial direction, any force (gravity, radiation pressure etc) may support this oscillation."719 If the oscillation transfers οποίον to torsional Alfvénn waves. then they will lead to the set up of torsional oscillations. as their wavelength will comparable to the stellar radius.," If the oscillation transfers energy to torsional Alfvénn waves, then they will lead to the set up of torsional oscillations, as their wavelength will comparable to the stellar radius."720 So the torsional oscillations will gain cucrey from the radial pulsation aud thus can be sustained against damping., So the torsional oscillations will gain energy from the radial pulsation and thus can be sustained against damping.721 Here we consider a simple case of wave coupling in anu wuiform magnetic evliuder. which can be accounted as the simplest inodel of a nou-rotating star with a poloidal maeuetic field.," Here we consider a simple case of wave coupling in an uniform magnetic cylinder, which can be accounted as the simplest model of a non-rotating star with a poloidal magnetic field."722 We consider a nou-turbuleut iuediun with zero viscosity. infinite conductivity auc negligible displacement current. which cau be described by the magnuetolbydrodvuamic (MIID) equations: where p ds the medium density. P is the pressure. V ds the velocity. B is the magnetic field and ge is the magnetic permeability.," We consider a non-turbulent medium with zero viscosity, infinite conductivity and negligible displacement current, which can be described by the magnetohydrodynamic (MHD) equations: where $\rho$ is the medium density, $P$ is the pressure, ${\bf V}$ is the velocity, $\bf B$ is the magnetic field and $\mu$ is the magnetic permeability."723 To this system we add the acdabatic equation of state where py and py are the unperturbed pressure auc density. while 4 is the ratio of specific heats.," To this system we add the adiabatic equation of state where $p_0$ and $\rho_0$ are the unperturbed pressure and density, while $\gamma$ is the ratio of specific heats."724 We adopt a cylindrical coordinate svsteni GR. o. Z) aud for simplicity consider only the axisviunietrie problem. so everwhere 0/00=0 is assuned.," We adopt a cylindrical coordinate system $R$, $\phi$, $Z$ ) and for simplicity consider only the axisymmetric problem, so everywhere ${{\partial725}/{\partial {\phi}}}=0$ is assumed."726 We suppose that an uniforiii magnetic field is directed along the Z axis so B=(0.0. By).," We suppose that an uniform magnetic field is directed along the $Z$ axis so $B=(0,0,B_0)$ ."727revealing that the real data is only about above the photon noise level. increasing to above the photon noise in the 5]|2-s part.,"revealing that the real data is only about above the photon noise level, increasing to above the photon noise in the 512-s part."728 An inspection of the 2MASS plates reveals that the star has a close companion 3.5 mags fainter in V. whose flux falls completely inside the aperture mask.," An inspection of the 2MASS plates reveals that the star has a close companion 3.5 mags fainter in $V$, whose flux falls completely inside the aperture mask."729 We therefore subtracted a constant value of of the median level of the curve before normalizing it. as in Alonsoetal.(2008)..," We therefore subtracted a constant value of of the median level of the curve before normalizing it, as in \cite{alo08a}."730 The two most remarkable features of the light curve of CoRoT-2 are the transits by its companion and the modulation caused by the stellar activity and rotation., The two most remarkable features of the light curve of CoRoT-2 are the transits by its companion and the modulation caused by the stellar activity and rotation.731 Both features tend to hide any secondary eclipse in the light curve: therefore. in. this section we explain our efforts to filter these two features. while avoiding to dilute or erase the signal of the secondary eclipse.," Both features tend to hide any secondary eclipse in the light curve; therefore, in this section we explain our efforts to filter these two features, while avoiding to dilute or erase the signal of the secondary eclipse."732 To filter out the primary transit we could ignore the data points inside the transit., To filter out the primary transit we could ignore the data points inside the transit.733 However. inclusion of data gaps at the orbital period of the transiting planet might result in spurious signals at this pertod and its harmonies. risking an effect on the signal of secondary eclipse.," However, inclusion of data gaps at the orbital period of the transiting planet might result in spurious signals at this period and its harmonics, risking an effect on the signal of secondary eclipse."734 To reduce this risk. we subtractec the best fit solution of Alonsoetal.(2008) from the curve. instead of cutting the parts of the light curves where the transits are detected.," To reduce this risk, we subtracted the best fit solution of \cite{alo08a} from the curve, instead of cutting the parts of the light curves where the transits are detected."735 We plot the light curve with the transits removec this way in Fig. 1..., We plot the light curve with the transits removed this way in Fig. \ref{fig:curve}.736 As noted by Valoetal.(2009).. the residuals in the individual transits show the effect of occulted spots during the transit. so they might add some high frequencies 11 a very short phase of the planet's orbit.," As noted by \cite{valio}, the residuals in the individual transits show the effect of occulted spots during the transit, so they might add some high frequencies in a very short phase of the planet's orbit."737 To filter out the stellar activity signal.we pre-whitened the light curve using (Lenz&Breger.2005).. a well-known and tested technique for identifying periodic signals in variable stars.," To filter out the stellar activity signal,we pre-whitened the light curve using \citep{lenz05}, a well-known and tested technique for identifying periodic signals in variable stars."738 Basically. it consists of successively locating the highest amplitude in the Fourier power spectrum and fitting a combination of sinusoids to the data that contain the frequency with the highest amplitude and all the previously identified frequencies.," Basically, it consists of successively locating the highest amplitude in the Fourier power spectrum and fitting a combination of sinusoids to the data that contain the frequency with the highest amplitude and all the previously identified frequencies."739 Before performing the pre-whitening of the data. we averaged them into 30-min bins.," Before performing the pre-whitening of the data, we averaged them into 30-min bins."740 We searched for frequencies between 0 and 24 c/d (cycles per day)., We searched for frequencies between 0 and 24 c/d (cycles per day).741 The amplitude spectra before and after filtering the low frequencies are plotted in Fig. 2..," The amplitude spectra before and after filtering the low frequencies are plotted in Fig. \ref{fig:fig2},"742 and the mean noise level in the 0-24 c/d range in the filtered spectum is of 6.1% 1079. with a dispersion of 4.2x10 5.," and the mean noise level in the 0-24 c/d range in the filtered spectum is of $\times$ $^{-6}$, with a dispersion of $\times$ $^{-6}$."743 The search for the secondary eclipse was performed using the same techniques as described in Alonsoetal. (2009b).., The search for the secondary eclipse was performed using the same techniques as described in \cite{alo09b}. .744 Briefly. the search consisted of:," Briefly, the search consisted of:"745mechanism which hides luminous LSBs vet allows cwarl ealaxies of similar surface brightness to be detected within the same volume.,mechanism which hides luminous LSBGs yet allows dwarf galaxies of similar surface brightness to be detected within the same volume.746 The implications are that these galaxy types (Iuminous-LSDCs) are rare with ensities less than 10! galaxies Mpe7., The implications are that these galaxy types (luminous-LSBGs) are rare with densities less than $10^{-4}$ galaxies $^{-3}$.747 Phis result is important as it clirectly aclelresses the issues raised in the introduction and. implies that existing surveys have missed. large populations of luminous low surface brightness galaxies., This result is important as it directly addresses the issues raised in the introduction and implies that existing surveys have missed large populations of luminous low surface brightness galaxies.748 Perhaps more importantly it confirms that the 2dEGIU is complete for giant galaxies and that the postulate that the Universe night be dominated by luminous LSBCGs (Disney 1976) is ruled out., Perhaps more importantly it confirms that the 2dFGRS is complete for giant galaxies and that the postulate that the Universe might be dominated by luminous LSBGs (Disney 1976) is ruled out.749 One caveat however is that. luminous-LSBCs could. be nmiasquerading as dwarfs., One caveat however is that luminous-LSBGs could be masquerading as dwarfs.750" For example consider the case of Alalin 1 (Bothun LOST) which has a huge extended disk (55 kpc seale-length) of very. low surface. brightness (p,= 26.5).", For example consider the case of Malin 1 (Bothun 1987) which has a huge extended disk $55$ kpc scale-length) of very low surface brightness $\mu_o = 26.5$ ).751 This system is actually readily detectable because of its high surface brightness active core. however within the 2dPORS limits it would have been miss-classified asa dwarf svstem with AJ=17.9. pi.=21.8.," This system is actually readily detectable because of its high surface brightness active core, however within the 2dFGRS limits it would have been miss-classified asa dwarf system with $M=-17.9$, $\mu_e=21.8$."752 Hence Figs 11 12 rule out luminous disk svstems only., Hence Figs 11 12 rule out luminous disk systems only.753 To determine whether objects such as Malin. 1 are hidden amongst. the dwarf population will require either ultra-deep CCD imaging Or Cross-correlation with Ll-surveys which would exhibit very high LE mass-to-light ratios for such systems., To determine whether objects such as Malin 1 are hidden amongst the dwarf population will require either ultra-deep CCD imaging or cross-correlation with HI-surveys which would exhibit very high HI mass-to-light ratios for such systems.754 The galaxy population shows a steady increase in number-density with decreasing Luminosity., The galaxy population shows a steady increase in number-density with decreasing luminosity.755 This continues to the survey limits at A=16. whereupon the volume limit and surface brightness selection elfects impinge upon our sample.," This continues to the survey limits at $M=-16$, whereupon the volume limit and surface brightness selection effects impinge upon our sample."756 The expectation is that the distribution continues to rise and hence the location of the peak in the number-density distribution remains unknown., The expectation is that the distribution continues to rise and hence the location of the peak in the number-density distribution remains unknown.757 However we do note that the increase seen within our selection limits is insullicient. [or the dwarf population to dominate the Iuminositv-density as shown in the next section., However we do note that the increase seen within our selection limits is insufficient for the dwarf population to dominate the luminosity-density as shown in the next section.758 Perhaps more surprising is the lack of sub-structure indicating either a continuity between the giant anc cbwarf populations or that any sub-strueture is erased by. the random errors., Perhaps more surprising is the lack of sub-structure indicating either a continuity between the giant and dwarf populations or that any sub-structure is erased by the random errors.759 “The former case is strongly indicative of a hierarchical merger scenario for galaxy. formation which one expects to lead: towards a smooth number-density clistribution between the cwarf and giant svstems (White ltees. 1978).," The former case is strongly indicative of a hierarchical merger scenario for galaxy formation which one expects to lead towards a smooth number-density distribution between the dwarf and giant systems (White Rees, 1978)."760 This is contrary to the change in the luminosity distribution of galaxies seen in cluster environments. (e.g. Smith. Driver. Phillipps 1997).," This is contrary to the change in the luminosity distribution of galaxies seen in cluster environments (e.g. Smith, Driver, Phillipps 1997)."761 In a later paper we intend to explore the dependeney of the BBDupon environment., In a later paper we intend to explore the dependency of the BBDupon environment.762 The luminosity density matrix. jGM.ji) is constructed from L(AM.p) in units of L. and is shown as bie.," The luminosity density matrix, $j(M,\mu)$ is constructed from $L\,\Phi(M,\mu)$ in units of $L_{\odot}$ $^{-3}$ and is shown as Fig."763 13., 13.764" The distribution is strongly peaked close to the conventional Al, parameter derived in previous surveys (see Table 1).", The distribution is strongly peaked close to the conventional $M_{*}$ parameter derived in previous surveys (see Table 1).765 The peak lies at AL=19.5 mag and µ=22.12 mag 7., The peak lies at $M = -19.5 $ mag and $\mu_e = 22.12$ mag $^{-2}$.766" The final value obtained is je=(249+)20)l05,444L. ?.", The final value obtained is $j_B=(2.49 \pm 0.20) \times 10^{8} h_{100} L_{\odot}$ $^{-3}$.767 The sharp peak sits firmly. in he centre. of our observable region of the 2dEC€ 1191) ancl drops rapidly olf on all sides. towards the 2dbCGRS BBD boundaries., The sharp peak sits firmly in the centre of our observable region of the 2dFGRS BBD and drops rapidly off on all sides towards the 2dFGRS BBD boundaries.768 This implies that while the δα does not survey the entire. parameter space of the known BB it does ellectively contain the full galaxy contribution o the local luminosity density., This implies that while the 2dFGRS does not survey the entire parameter space of the known BBD it does effectively contain the full galaxy contribution to the local luminosity density.769" ltedoing the calculations using galaxies with redshifts also results in je=(2404120)«LO5,041. 7."," Redoing the calculations using galaxies with redshifts also results in $j_B=(2.49 \pm 0.20) \times 10^{8} 770h_{100} L_{\odot}$ $^{-3}$."771 Lhis demonstrates that there is no dependeney of the results upon the assumption mace for he distribution of galaxies without recshilts., This demonstrates that there is no dependency of the results upon the assumption made for the distribution of galaxies without redshifts.772 We note that j. derived. via a direct pumL estimate. without any surface brightness or clustering corrections. (Eqn 1)) gives a value of j=1.8240.07«1075ool.," We note that $j$ derived via a direct $\frac{1}{V_{max}}$ estimate, without any surface brightness or clustering corrections, (Eqn \ref{eq:j}) ) gives a value of $j=1.82\pm0.07\times 77310^{8} h_{100} L_{\odot}$ $^{-3}$."774 Including the isophotal magnitude correction only leads to a value of j=2:28d0.09.107ρω. 7.," Including the isophotal magnitude correction only leads to a value of $j=2.28\pm0.09\times10^{8} h_{100} 775L_{\odot}$ $^{-3}$."776 Hence a more detailed: analvsis leads to a increase in j. of this36.8%... is due to the isophotal correction. is due to the Malmiequist bias correction anc is due to the clustering correction.," Hence a more detailed analysis leads to a increase in $j$, of this, is due to the isophotal correction, is due to the Malmquist bias correction and is due to the clustering correction."777 The final value agrees well with that obtained. fron the recent ESO Slice Project. (Zuccea 1997)., The final value agrees well with that obtained from the recent ESO Slice Project (Zucca 1997).778 The method. that they used: corrects. for clustering. but. not surface brightness although their photometry dis. based on aperture rather than isophotal magnitudes.," The method that they used corrects for clustering, but not surface brightness — although their photometry is based on aperture rather than isophotal magnitudes."779 However it is worth pointing out that j is sensitive to the exact. value ob prias., However it is worth pointing out that $j$ is sensitive to the exact value of $\mu_{lim}$.780" Phe quoted error in fifi, is £0.38 or plate-to-plate variations. Aletcalle et al 1995: Pimblett et al 2000)."," The quoted error in $\mu_{lim}$ is $\pm 0.3$ (for plate-to-plate variations, Metcalfe et al 1995; Pimblett et al 2000)."781 Table 3 shows à summary. of results when repeating the entire analvsis using the upper and lower error limits., Table 3 shows a summary of results when repeating the entire analysis using the upper and lower error limits.782 Le therefore seems likely that a of surface brightness biases ancl large scale structure can indeed. lead. to the type of variations seen in Table 1., It therefore seems likely that a of surface brightness biases and large scale structure can indeed lead to the type of variations seen in Table 1.783 Finally following the method of Carlberg.. Yee Ellingson (1997) we can obtain a crude ball-park figure for the total local mass density by adopting a universal mass-to-light ratio based on that observed in clusters.," Finally following the method of Carlberg, Yee Ellingson (1997) we can obtain a crude ball-park figure for the total local mass density by adopting a universal mass-to-light ratio based on that observed in clusters."784 While this method neelects biasing (White. Pully Davis. 1988) it cloes provide a useful erudeupper limit to the mass density.," While this method neglects biasing (White, Tully Davis, 1988) it does provide a useful crude limit to the mass density."785 From Carlberg. (1997)- wo find:. MLopss=.289xΡοM.," From Carlberg (1997) we find: $\frac{{\cal M}_{Dyn}}{L_R} = 289\pm50 h_{100} 786\frac{{\cal M}_{\odot}}{L_{\odot}}$."787 Assuminge a mean colour o£ (D.I)=1.1 and a solar colour index. of 1.17 ⋅−⋠this converts to: ae⇁∖⊿⊓=⋅−2147h-iFM.," Assuming a mean colour of $(B-R)=1.1$ and a solar colour index of 1.17 this converts to: $\frac{{\cal M}_{Dyn}}{L_B} = 271\pm47 h_{100}788\frac{{\cal M}_{\odot}}{L_{\odot}}$."789" Alultiplving the luminosity density by the mass-to-light ratio vields a value for the local mass-densitv of Qa,zz0.24.", Multiplying the luminosity density by the mass-to-light ratio yields a value for the local mass-density of $\Omega_{M} \approx 0.24 $.790 We note that this is consistent with the current constraints from the combination of Sn la results with the recent Boomerang and Maxima-1 results (Balbi 2000: de Bernarclis 2000)., We note that this is consistent with the current constraints from the combination of Sn Ia results with the recent Boomerang and Maxima-1 results (Balbi 2000; de Bernardis 2000).791 As this work represents the first. detailed: measure of the field BBD there is no previous work with which to compare., As this work represents the first detailed measure of the field BBD there is no previous work with which to compare.792 lloweveras mentioned earlier it is trivial to convert. the, Howeveras mentioned earlier it is trivial to convert the793The 34 photometric candidates were then examined to finc their proper motion.,The 34 photometric candidates were then examined to find their proper motion.794 Proper motions were calculated: using the query shown in appendix A. The dillerence in position of the objects in the GCS and 2ALASS catalogues is obtainec in milliarcseconds., Proper motions were calculated using the query shown in appendix A. The difference in position of the objects in the GCS and 2MASS catalogues is obtained in milliarcseconds.795 This is then divided by the cillerence in the two epochs. converted from Julian dates to vears.," This is then divided by the difference in the two epochs, converted from Julian dates to years."796 The lines in the query that list their results “as pmRA” ane vas pmDEC™ perform this task., The lines in the query that list their results “as pmRA” and “as pmDEC” perform this task.797 Phe resulting vector poin diagram. is shown in figure 3., The resulting vector point diagram is shown in figure 3.798" The known proper motions of UpsSco in right ascension and. declination are about lmas/vr and -25mas/vr respectively (deBruijneetal.1997:""Pepbbischetal."," The known proper motions of UpSco in right ascension and declination are about -11mas/yr and -25mas/yr respectively \citep{deb97,pre98}."799 2002).. OL the 34 candidates. Lo was too zünt to be recorded in 2ALASS leaving 33 candidates with oper motion data calculated.," Of the 34 candidates, 1 was too faint to be recorded in 2MASS leaving 33 candidates with proper motion data calculated."800 Phe remaining 33 candidates included G with proper motions greater than the range of igure 3 (Table 2)., The remaining 33 candidates included 6 with proper motions greater than the range of figure 3 (Table 2).801 These 6 objects might be red or brown chwarts located much closer to the Sun than Upseo., These 6 objects might be red or brown dwarfs located much closer to the Sun than UpSco.802 deBrui-jne(1099) notes that the velocity. dispersion in. UpsSco is very small at. 13kms. corresponding to about 2mas/vr.," \citet{deb99} notes that the velocity dispersion in UpSco is very small at 1.3km/s, corresponding to about 2mas/yr."803 The greatest contribution to the spread in the proper motions therefore comes [rom errors in UIXIDSS and 2ALASS measurements., The greatest contribution to the spread in the proper motions therefore comes from errors in UKIDSS and 2MASS measurements.804 To assess the errors the original selection of 282.938 objects had their proper motions examined.," To assess the errors the original selection of 282,938 objects had their proper motions examined."805 The proper motions were found to have a normal distribution about the origin with a standard. deviation of 10.2mas/vr in both right ascension ancl declination., The proper motions were found to have a normal distribution about the origin with a standard deviation of 10.2mas/yr in both right ascension and declination.806 Factoring this error back into the deBruijne(1999). figure noted. above showed that a 2e selection circle for UpSco members would have a radius of 20.8mas/vr., Factoring this error back into the \citet{deb99} figure noted above showed that a $\sigma$ selection circle for UpSco members would have a radius of 20.8mas/yr.807 This error has only a slight dependence on magnitude for objects with a magnitude in Z between 14.0 and. 17.0., This error has only a slight dependence on magnitude for objects with a magnitude in Z between 14.0 and 17.0.808 For the objects fainter than this the standard. deviation is zz20mas/vr., For the objects fainter than this the standard deviation is $\approx$ 20mas/yr.809 There are 3 objects among the final 27 candidates with magnitudes in Z greater than 17.0., There are 3 objects among the final 27 candidates with magnitudes in Z greater than 17.0.810 All 27 candidates shown in figure 32 are predominantly centred around the (-11.-25) position.," All 27 candidates shown in figure 3 are predominantly centred around the (-11,-25) position."811 The 3 candidates with magnitudes in Z greater than 17.0 noted above are marke: in red., The 3 candidates with magnitudes in Z greater than 17.0 noted above are marked in red.812 There is no clustering of objects around the (0.0 position indicating that the sample is not. contaminate bv more distant objects e.g. AGB stars which have similar surface temperatures and colours to brown ενας. but much ercater intrinsic luminosities.," There is no clustering of objects around the (0,0) position indicating that the sample is not contaminated by more distant objects e.g. AGB stars which have similar surface temperatures and colours to brown dwarfs, but much greater intrinsic luminosities."813 The 19 candidates within the 20 selection circle were then classified as members of UpSco., The 19 candidates within the $\sigma$ selection circle were then classified as members of UpSco.814 These objects so selected Clable 1) have the photometric and proper motion characteristics of à 5 Myr old brown cdwarl member of Upseo., These objects so selected (Table 1) have the photometric and proper motion characteristics of a 5 Myr old brown dwarf member of UpSco.815 Given that there are 19 objects within the 20 selection circle statistically it is to be expected that possibly 1 of the S objects outside is also a brown cdwarl member of UpSco., Given that there are 19 objects within the $\sigma$ selection circle statistically it is to be expected that possibly 1 of the 8 objects outside is also a brown dwarf member of UpSco.816 However all of the other 8 objects shown in [ligure 3 are clustered immediately outside the 20 selection circle ancl not scattered. around. the vector. point diagram as would be expected. for random: contaminants., However all of the other 8 objects shown in figure 3 are clustered immediately outside the $\sigma$ selection circle and not scattered around the vector point diagram as would be expected for random contaminants.817 As these S objects have the same range of magnitudes as the 19 within the selection circle. (Table 1) they are not subject to anv systemically larger proper motion errors caused. by being fainter., As these 8 objects have the same range of magnitudes as the 19 within the selection circle (Table 1) they are not subject to any systemically larger proper motion errors caused by being fainter.818 Thus it is likely that these 8 objects are also members of Upseo with slightly higher dispersion velocity., Thus it is likely that these 8 objects are also members of UpSco with slightly higher dispersion velocity.819 Finally we note that none of the brown dwarf cancliclates listed here have been identified before in previous surveys., Finally we note that none of the brown dwarf candidates listed here have been identified before in previous surveys.820 Given the low contamination in our sample with proper motions. the one object which is not detected. in 2ALASS (Table 1) has a high likelihood of being a brown cwarl in UpSco as well (28/34. ic. S24).," Given the low contamination in our sample with proper motions, the one object which is not detected in 2MASS (Table 1) has a high likelihood of being a brown dwarf in UpSco as well (28/34, i.e. )."821 In order to be certain that the candidates found in this studs are in [fact brown dwarfs spectra. should. be obtained., In order to be certain that the candidates found in this study are in fact brown dwarfs spectra should be obtained.822 However. figure 3 indicates that there is negligible contamination from background stars among the sample.," However, figure 3 indicates that there is negligible contamination from background stars among the sample."823 As a further test. of the method outlined above. it was also used to investigate the cddeg? area covered o» UIXIDSS in the two areas shown to the north of figure .," As a further test of the method outlined above, it was also used to investigate the $^2$ area covered by UKIDSS in the two areas shown to the north of figure 1."824 Phe area is also part. of UpSco (deZeeuwetal.1999) and therefore any brown dwarf. here. will share similar whotometric and proper motion eharacteristies of those [rom he area to the south., The area is also part of UpSco \citep{dez99} and therefore any brown dwarf here will share similar photometric and proper motion characteristics of those from the area to the south.825 After the analysis of the ddeg? area was complete. 49 objects in it were identified as possible own cwarfs.," After the analysis of the $^2$ area was complete, 49 objects in it were identified as possible brown dwarfs."826 All 49 were previously identified by Lodieuetal.(2007.2008) as brown dwarf candidates.," All 49 were previously identified by \citet{lodieu07,lodieu08} as brown dwarf candidates."827 Spectra jwe been taken of 26 of the 49 objects (Martinetal.2004:Slesnickοἱal.2006:Loclicuet2008.2011) and all 26 have en confirmed. as brown cwarfs.," Spectra have been taken of 26 of the 49 objects \citep{mar04,sle06,lodieu08,lodieu11} and all 26 have been confirmed as brown dwarfs."828 This result underlines the reliability of the method as a means of discriminating brown dwarls from other objects in Upsco., This result underlines the reliability of the method as a means of discriminating brown dwarfs from other objects in UpSco.829 In order to estimate completeness levels in all passbancds he data from the original 282.938 objects was analysed.," In order to estimate completeness levels in all passbands the data from the original 282,938 objects was analysed."830 Objects were erouped in bins of 0.1 magnitude and examined o see where numbers detected. in each bin began to all., Objects were grouped in bins of 0.1 magnitude and examined to see where numbers detected in each bin began to fall.831 The resulting estimates of completeness were: 25-15.0. Y-17.4. J—17.2. H1—16.2. Ix-16.1.," The resulting estimates of completeness were: Z=18.0, Y=17.4, J=17.2, H=16.2, K=16.1."832 In the Z and J xissbands these would be the expected magnitudes of Upsco member objects in the 0.01 - 0.02A47; mass range., In the Z and J passbands these would be the expected magnitudes of UpSco member objects in the 0.01 - $M_{\sun}$ mass range.833 The istograms in all five passbands showed that completeness ell gradually. at. these. magnitudes anc was still at an level another magnitude deeper., The histograms in all five passbands showed that completeness fell gradually at these magnitudes and was still at an level another magnitude deeper.834 Note that the lower mass range achieved in this survey is not limited by the completeness of UINIDSS but by that of 2ALASS (Je&16) due to the need for proper motion measurements., Note that the lower mass range achieved in this survey is not limited by the completeness of UKIDSS but by that of 2MASS $\approx$ 16) due to the need for proper motion measurements.835 Llowever. of the 34 photometric candidates. only one object was [fainter than the sensitivity. limit of 2ALASS ancl did not have its proper motion calculated.," However, of the 34 photometric candidates, only one object was fainter than the sensitivity limit of 2MASS and did not have its proper motion calculated."836 We re-examined the 19 high probability members. listed in Table 1 in the (Z-J.Z) colour magnitude diagram. and assigned masses based on their Z band magnitude.," We re-examined the 19 high probability members listed in Table 1 in the (Z-J,Z) colour magnitude diagram and assigned masses based on their Z band magnitude."837 They cover a mass range from 0.01 to 0.0047... 7 are below (0.0344; and 2 of those are below 0.0244;.," They cover a mass range from 0.01 to $M_{\sun}$, 7 are below $M_{\sun}$ and 2 of those are below $M_{\sun}$."838 The completeness limit in the Z and JJ passhancls corresponds to a mass of less than 0.02475., The completeness limit in the Z and J passbands corresponds to a mass of less than $M_{\sun}$.839 At O.OLAL: the photometric survey is still at least complete., At $M_{\sun}$ the photometric survey is still at least complete.840 Andersenctal.(2008). performed a combined analysis of the low-mass LALP in seven star forming regions. not including UpSco.," \citet{and08} performed a combined analysis of the low-mass IMF in seven star forming regions, not including UpSco."841 The method. used. a ratio of stars with masses 0.08 - LOÀZ; to brown cwarfs with masses 0.03 - O.OSAL. (30 - SOAL)) from each region to allow for cirect comparison., The method used a ratio of stars with masses 0.08 - $M_{\sun}$ to brown dwarfs with masses 0.03 - $M_{\sun}$ (30 - $M_{\rm J}$ ) from each region to allow for direct comparison.842an AGN.,an AGN.843" ""Table 1 lists the emission. features. detected. in the spectrum. rest-frame equivalent widths ancl EWILN estimated: via gaussian fitting with 90 per cent errors anc corrected. for spectral dispersion."," Table 1 lists the emission features detected in the spectrum, rest-frame equivalent widths and FWHM estimated via gaussian fitting with 90 per cent errors and corrected for spectral dispersion."844 The semi-forbidden CHI] line is clearly detected: anc narrow (see Table 1)., The semi-forbidden CIII] line is clearly detected and narrow (see Table 1).845 Since this line is predicted to be broac in a tvpe 1 AGN. the implication is that the broacd-line region in this AGN is obscured.," Since this line is predicted to be broad in a type 1 AGN, the implication is that the broad-line region in this AGN is obscured."846 The CIV. and Hell lines appear also narrow. but in a low signal to noise part of the spectrum.," The CIV and HeII lines appear also narrow, but in a low signal to noise part of the spectrum."847 The Mgll line is probably broad. but. with an equivalent width normalised to the equivalent width of he narrow lines significantly smaller (10.20 times) than is vpically found in tvpe 1 AXGN (Francis et al 1991).," The MgII line is probably broad, but with an equivalent width normalised to the equivalent width of the narrow lines significantly smaller (10–20 times) than is typically found in type 1 AGN (Francis et al 1991)."848 Broad AMell has been found in Ht hyperluminous galaxies (Hines Wills 1993: Lines et al 1995) and high-redshift raciiogalaxies (di Serego Alighieri. Cimati Fosbury. 1994: Stockton. Ixellogg Ridgeway 1995) and jw been interpreted: as scattered. emission [rom a hidden ype 1 ΔΟΝ.," Broad MgII has been found in IR hyperluminous galaxies (Hines Wills 1993; Hines et al 1995) and high-redshift radiogalaxies (di Serego Alighieri, Cimati Fosbury 1994; Stockton, Kellogg Ridgway 1995) and has been interpreted as scattered emission from a hidden type 1 AGN."849 We searched. in various archives for radio observations of our source., We searched in various archives for radio observations of our source.850 There are a number of detections. the most relevant of which are the Westerbork Northern Sky Survey (Reneclink et al 1997) at 326 Mllz. the Texas Survey (Douglas et al 1996) at 365 MlIz. the FIRST survey (White ct al 1997) at L4 CGllz and the Green Bank Gem survey (Gregory ct al 1996) at 4.85 Cllz.," There are a number of detections, the most relevant of which are the Westerbork Northern Sky Survey (Rengelink et al 1997) at 326 MHz, the Texas Survey (Douglas et al 1996) at 365 MHz, the FIRST survey (White et al 1997) at 1.4 GHz and the Green Bank 6cm survey (Gregory et al 1996) at 4.85 GHz."851 Both the ‘Toxas and the FIRST surveys resolve the source into two components aligned approximately N-S. “Phe N component is the brightest in the FURST cata (0.000 Jy. compared. to the 0.071 Jv of the S component)., Both the Texas and the FIRST surveys resolve the source into two components aligned approximately N-S. The N component is the brightest in the FIRST data (0.090 Jy compared to the 0.071 Jy of the S component).852 The optical position lies in between both components (see Fie., The optical position lies in between both components (see Fig.853 5)., 5).854" The separation between the components is LL” at 14 Gilg and ~15"" at 365 MlIz.", The separation between the components is $\sim 11''$ at 1.4 GHz and $\sim 15''$ at 365 MHz.855 The integrated. radio fluxes. together with the measurements at optical and. N-rav. frequencies are shown in Fie., The integrated radio fluxes together with the measurements at optical and X-ray frequencies are shown in Fig.856 6 in the form of a spectral energy. distribution., 6 in the form of a spectral energy distribution.857" The radio spectrum has aS,x&Uo garape [rom 326 Alllz to 4.85 Cllz. which is typical of lobe-dominated radio sources."," The radio spectrum has a $S_{\nu}\propto \nu^{-0.9}$ shape from 326 MHz to 4.85 GHz, which is typical of lobe-dominated radio sources."858 Although from the spatial information at the various frequencies it is not completely. clear that this is, Although from the spatial information at the various frequencies it is not completely clear that this is859the predicted number.,the predicted number.860" Figure B1 shows this: accumulated number of bursts vs. log peak flux, the linear fit and our fit."," Figure \ref{fig:bursts_count} shows this: accumulated number of bursts vs. log peak flux, the linear fit and our fit."861 with the parameters found: Redshifts are measured only for a moderate fraction of the detected bursts., with the parameters found: Redshifts are measured only for a moderate fraction of the detected bursts.862" A few (5-10%)) are too weak, some don’t have a clear redshift signature and some are not measured because of lack of observational resources."," A few ) are too weak, some don't have a clear redshift signature and some are not measured because of lack of observational resources."863" When we consider the fraction of redshift-measured GRBs to the total number of GRBs detected, we see a trend of increase in this fraction with the measured peak number flux of photons in the detectors main band: 15keV—150keV, p (see figure B2))."," When we consider the fraction of redshift-measured GRBs to the total number of GRBs detected, we see a trend of increase in this fraction with the measured peak number flux of photons in the detectors main band: $15keV - 150keV$, p (see figure \ref{fig:zdetprob_ap}) )."864" We used a linear regression to approximate the relation: Where, 0.(p) is the detection probability and 6,(p) is the probability that a redshift will be"," We used a linear regression to approximate the relation: Where, $\theta_{\gamma}(p)$ is the detection probability and $\theta_{z}(p)$ is the probability that a redshift will be"865"(iii): D—4 For this case we have Therefore, the expression for time delay becomes Thus, from the above case studies one can observe that the maximum time delay will occur when D—2, i.e., forthe usual 4- Schwarzschild space-time.","(iii): $D=4$ For this case we have Therefore, the expression for time delay becomes Thus, from the above case studies one can observe that the maximum time delay will occur when $D=2$, i.e., forthe usual $4$ -dimensional Schwarzschild space-time."866 Time delay decreases due to increase dimensions., Time delay decreases due to increase dimensions.867 This can be shown easily by assuming To««r4 and ro<<r3., This can be shown easily by assuming $r_0<<r_1$ and $r_0<<r_2$.868 Let us consider a test particle having mass m which is moving in the gravitational field of a D4- 2-dimensional spacetime described by the metric (1)., Let us consider a test particle having mass $m$ which is moving in the gravitational field of a $D+2$ -dimensional spacetime described by the metric (1).869" So, theHamilton-Jacobi (HJ) equation for the test particle is (Chakraborty1996;Chakraborty&BiswasRahamanetal.2005b) where gi; are the classical background field and S is the Hamilton's characteristic function."," So, theHamilton-Jacobi (HJ) equation for the test particle is \citep{Chakraborty1996,Biswas1996,Rahaman2005b}870 where $g_{ik}$ are the classical background field and $S$ is the Hamilton's characteristic function."871" For the metric (1) the explicit form of HJ equation (51) now takes the form as where 71,2,.......,&p—z are the independent coordinates on the surface of the unit (D—2) sphere such that and f is given by f(r)=1—u/rP-! as introduced earlier."," For the metric (1) the explicit form of HJ equation (51) now takes the form as where $x_1, x_2 ,.......,x_{D - 2}$ are the independent coordinates on the surface of the unit $(D - 2)$ sphere such that and $f$ is given by $f(r)=1-\mu/r^{D-1}$ as introduced earlier."872" In order to solve the above partial differential equation (52), let us choose the HJ function S as where E is identified as the energy of the particle and Di,pa,eee;PD-2 are the momenta of the particle along different axes on the (D—2) sphere with the resulting momentum of the particle, p=\/p}+4- s."," In order to solve the above partial differential equation (52), let us choose the HJ function $S$ as where $E$ is identified as the energy of the particle and $p_1, p_2 ,......, p_{D - 2}$ are the momenta of the particle along different axes on the $( D - 2 )$ sphere with the resulting momentum of the particle, $p = \sqrt{ p_1^2 + p_2^2 + ...... + p_{D - 2}^2}$ ."873" Now, substitution of the ansatz (54) in equation (52) provides the following expression for the unknown function S; which is"," Now, substitution of the (54) in equation (52) provides the following expression for the unknown function $S_1$ which is"874" 2006).. z>1.5 (NIR), z>1 2011).z>1.5 1.5«z3. z~2 z~0 >lo f>2.5x10-1? s~! cm~? 2/1x271 jum 1 with the G141 grism at various redshift ranges.", $z>1.5$ $z>1$ $z>1.5$ $1.5<z<3$ $z \sim 2$ $z \sim 0$ $>1\sigma$ $f>2.5 \times 10^{-18}$ $^{-1}$ $^{-2}$ $2\farcm1 \times 2\farcm1$ $\mu$ \ref{fig:grismlines} with the G141 grism at various redshift ranges.875" Star formation processes were quite different at z>1 than in the local universe2011),, and so it is not clear if the emission-line diagnostics used to characterize local galaxies can be directly applied to z>1 systems."," Star formation processes were quite different at $z>1$ than in the local universe, and so it is not clear if the emission-line diagnostics used to characterize local galaxies can be directly applied to $z>1$ systems."876" For example, the bulk of z~2 galaxies have higher ratios of collisionally excited to recombination lines ([Ou1]/H8 and [Nu]/Ha) than local galaxies2007)."," For example, the bulk of $z \sim 2$ galaxies have higher ratios of collisionally excited to recombination lines $\OIII/\Hb$ and $\NII/\Ha$ ) than local galaxies."877". Local galaxies with high SFR tend to have higher emission-line ratios than galaxies with lower SFR, suggesting that rapid star formation leads to different ionization properties2008)."," Local galaxies with high SFR tend to have higher emission-line ratios than galaxies with lower SFR, suggesting that rapid star formation leads to different ionization properties."878". Since z>1 galaxies typically have higher SFR than local analogs of the same mass2005),, their higher line ratios may simply be the result of their higher SFR."," Since $z>1$ galaxies typically have higher SFR than local analogs of the same mass, their higher line ratios may simply be the result of their higher SFR."879" However used spatially resolved spectroscopy of one galaxy(2010) at z—1.6 to show that these line ratios increase in the center of the galaxy, with normal star-forming (SF) line ratios at outer apertures."," However used spatially resolved spectroscopy of one galaxy at $z=1.6$ to show that these line ratios increase in the center of the galaxy, with normal star-forming (SF) line ratios at outer apertures."880" This suggests that weak or obscured active galactic nucleus (AGN) activity may be the cause of higher line ratios in z~2 galaxies, perhaps because AGN activity is correlated with SFR as observed locally2009)."," This suggests that weak or obscured active galactic nucleus (AGN) activity may be the cause of higher line ratios in $z881\sim 2$ galaxies, perhaps because AGN activity is correlated with SFR as observed locally."882". There are many predictions for the density of obscured and Compton-thick (CT, Ng=1075 cm?) AGNs at 1.5«z3 from the X-ray background and from IR-excess(Gilli galaxy counts and X- stacking2011),, but to date only three CT AGNs have been individually confirmed at z~22008).."," There are many predictions for the density of obscured and Compton-thick (CT, $N_H \gtrsim88310^{24}$ $^2$ ) AGNs at $1.5<z<3$ from the X-ray background and from IR-excess galaxy counts and X-ray stacking, but to date only three CT AGNs have been individually confirmed at $z \sim 2$."884" Obscured AGNs are missed by even the deepest X-ray surveys, but can still exhibit the narrow emission-line signature of an AGN2011)."," Obscured AGNs are missed by even the deepest X-ray surveys, but can still exhibit the narrow emission-line signature of an AGN."885. Measuring the density of obscured AGNS at z~2 is especially important to reveal how much black hole growth occurs in an enshrouded phase., Measuring the density of obscured AGNs at $z \sim 2$ is especially important to reveal how much black hole growth occurs in an enshrouded phase.886 Here we use 8.5 orbits of WFC3 G141 spectroscopy to study the properties of emission-line galaxies at 13«z24 in the Hubble Ultra Deep Field2006)., Here we use 8.5 orbits of WFC3 G141 spectroscopy to study the properties of emission-line galaxies at $1.3<z<2.4$ in the Hubble Ultra Deep Field.887 These data were taken as part of the supernova follow-up program in the Cosmic Assembly Near-Infrared Deep Extragalactic Legacy Survey2011)., These data were taken as part of the supernova follow-up program in the Cosmic Assembly Near-Infrared Deep Extragalactic Legacy Survey.888" The (CANDELS?5,,supernova candidate identified in the HUDF region is described by and this work makes use of the spectra that were serendipitously(2011),, obtained for hundreds of other targets in the 2.1’x field."," The supernova candidate identified in the HUDF region is described by, and this work makes use of the spectra that were serendipitously obtained for hundreds of other targets in the $2.1\arcmin \times 2.1\arcmin$ field."889 In particular we focus on the 28 galaxies exhibiting aand eemission [Οπήlines in the observed grism wavelength range (at 19«z 2.4)., In particular we focus on the 28 galaxies exhibiting and emission lines in the observed grism wavelength range (at $1.3<z<2.4$ ).890" Like the study by(2010), the high spatial resolution of the HST/WFC3 similarly allows for studiesofspatialgradientsinemission-lineproperties."," Like the study by, the high spatial resolution of the /WFC3 similarly allows for studiesofspatialgradientsinemission-lineproperties."891"Unlike anintegralfieldunit spectrograph, however, the WFC3 grism has the unique ability to do this for hundreds of objectsin the field of","Unlike anintegralfieldunit spectrograph, however, the WFC3 grism has the unique ability to do this for hundreds of objectsin the field of"892are known to get hotter again (Baralle Ixolb. 2000) at short periods. so a confirmed secondary spectral tvpe would provide insight as to the state of nuclear evolution in the donor star of480.,"are known to get hotter again (Baraffe Kolb, 2000) at short periods, so a confirmed secondary spectral type would provide insight as to the state of nuclear evolution in the donor star of."893. Figure 4 shows that in any case that the donor. will currently. appear to. be close to the ZAAIS. and thus that the distance estimate derived. by AleClintock ct al (2000) on this basis is likely to be quite &ooc.," Figure 4 shows that in any case that the donor will currently appear to be close to the ZAMS, and thus that the distance estimate derived by McClintock et al (2000) on this basis is likely to be quite good."894 We have compared the UV spectra of anc J1859|226., We have compared the UV spectra of and J1859+226.895 The former shows strong evidence of CNO processing. which σιιν constrains the evolution of the system.," The former shows strong evidence of CNO processing, which tightly constrains the evolution of the system."896 must have first reached contac with the donor star having a significantly nuclearevolvec core. at à period where nuclear and angular momentunm Loss timescales were comparable.," must have first reached contact with the donor star having a significantly nuclear–evolved core, at a period where nuclear and angular momentum loss timescales were comparable."897 This in turn constrains the enc point of the earlier commonenvelope. phase: immediately after the commonenvelope phase the system. had. a wide enough separation that significant nuclear evolution coul occur before contact was achieved., This in turn constrains the end point of the earlier common–envelope phase: immediately after the common–envelope phase the system had a wide enough separation that significant nuclear evolution could occur before contact was achieved.898 In à future paper we wil investigate such evolutions systematically., In a future paper we will investigate such evolutions systematically.899 CALL and RIL gratefully acknowledge the superb support of Pony Roman. IWailash Sahu. and all involved in the implementation. of our time-critical observations.," CAH and RIH gratefully acknowledge the superb support of Tony Roman, Kailash Sahu, and all involved in the implementation of our time-critical observations."900 Support for proposals C:O-08245 and CGO-OSG47 was provided by NASA through a grant from the Space Telescope Science Institute. which is operated by the Association of Universities lor Research in. Astrononiv. 1nc.. under NASA contract NAS5S-26555.," Support for proposals GO-08245 and GO-08647 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555."901 Εμ work was supported. by the Leverhulme Trust b/00-L80/.4. Theoretical astrophysics research at Leicester is supported by a PPARC rolling grant., This work was supported by the Leverhulme Trust F/00-180/A. Theoretical astrophysics research at Leicester is supported by a PPARC rolling grant.902 We thank Christian Ixnigge for discussion about the nature of the 1425A feature. and an anonvimous referee for useful comments.," We thank Christian Knigge for discussion about the nature of the ${\rm 1425\AA}$ feature, and an anonymous referee for useful comments."903model light. curve.,model light curve.904 The times of observed first contact were TJD 2451959.83. 2452352.68. 2452383.69. and 2452662.83. while a fourth. contact was observed al ILJD. 2452228.95. and one niid-eclipse point could be determined at ILJD 2452600.96.," The times of observed first contact were HJD 2451959.83, 2452352.68, 2452383.69, and 2452662.83, while a fourth contact was observed at HJD 2452228.95, and one mid-eclipse point could be determined at HJD 2452600.96."905" This information was used in a sinmltaneous live-parameter [it to the combined dataset. where the parameters used were period P. epoch of primary eclipse 75. svstem velocity >. velocity semi-amplitude A4. ancl phase hall-width of primary eclipse 060,. assuming that the orbit has zero eccentricity, ("," This information was used in a simultaneous five-parameter fit to the combined dataset, where the parameters used were period $P$, epoch of primary eclipse $T_{0}$, system velocity $\gamma$ , velocity semi-amplitude $K_{1}$, and phase half-width of primary eclipse $\delta \phi_{p}$, assuming that the orbit has zero eccentricity. ("906Tests indicated that Chere was no measurable eccentricity.),Tests indicated that there was no measurable eccentricity.)907 The ephemeris lor primary. eclipse is The numbers in parentheses indicate the uncertainty in the last digits of Zi and P., The ephemeris for primary eclipse is The numbers in parentheses indicate the uncertainty in the last digits of $T_{0}$ and $P$.908 The period is consistent (as expected) with the value of Mathieu et al., The period is consistent (as expected) with the value of Mathieu et al.909 (ο within their quoted error., to within their quoted error.910 The velocity parameters also match the Mathieu οἱ al., The velocity parameters also match the Mathieu et al.911 measurements very well since the same radial velocity dala was used: 5=33.+£0.11 and vy=33.8£0.2J., measurements very well since the same radial velocity data was used: $\gamma = 33.7 \pm 0.1$ and $K_{1} = 33.8 \pm 0.2$.912. Finally. the fit constrains the width of primary eclipse to be o;—Ὁ=0.0318£0.0084.," Finally, the fit constrains the width of primary eclipse to be $\phi_{4} - \phi_{1} = 2 \delta913\phi_{p} = 0.0318 \pm 0.0084$."914 The reduced 4? for the overall fit was 1.32., The reduced $\chi^2$ for the overall fit was 1.32.915 Phased data for the phases of primary. and secondary eclipse are shown in Figs. 2.. 3..," Phased data for the phases of primary and secondary eclipse are shown in Figs. \ref{vprime}, \ref{iprime},"916 and 4.., and \ref{isec}.917 The curvature of the light curve at second and third contacts (entering and exiting total eclipse) indicates that the primary eclipse is indeed due (to a smaller star transiting across the [ace of a larger star., The curvature of the light curve at second and third contacts (entering and exiting total eclipse) indicates that the primary eclipse is indeed due to a smaller star transiting across the face of a larger star.918 The eclipse depths provide robust information about the flux ratios of the two stars (although this is affected by the third star contributing to the svstems light)., The eclipse depths provide robust information about the flux ratios of the two stars (although this is affected by the third star contributing to the system's light).919 The overall depth of the primary eclipse is approximately 0.086 mag in V. and 0.078 mag in J. consistent with eclipse bx a fant cool companion.," The overall depth of the primary eclipse is approximately 0.086 mag in $V$ and 0.078 mag in $I$ , consistent with eclipse by a faint cool companion."920 The secondary eclipse was not detected in V. but we did find evidence of a decrease in brightness in J on several nights.," The secondary eclipse was not detected in $V$, but we did find evidence of a decrease in brightness in $I$ on several nights."921 Data taken on (he night with best atmospheric conditions (Jan. 17/18. 2003) provided our cleanest measurement of the depth of the secondary. eclipse in J (0.0111x0.0011 mae) using the difference between (he average magnitudes out of eclipse and in total eclipse. (," Data taken on the night with best atmospheric conditions (Jan. 17/18, 2003) provided our cleanest measurement of the depth of the secondary eclipse in $I$ $0.0111 \pm 0.0011$ mag) using the difference between the average magnitudes out of eclipse and in total eclipse. ("922It appears that there was a slight zero-point differences between the (wo nights. so a single reference level in J was not use.,"It appears that there was a slight zero-point differences between the two nights, so a single reference level in $I$ was not used."923 This may have come about because the majority of our measurements in / were taken during niehts of eclipse.), This may have come about because the majority of our measurements in $I$ were taken during nights of eclipse.)924 We have a second measurementof the eclipse depth (0.010120.0013 mae) from Apr. 20/21. 2003.Combining these measurements. we have a final value 0.01072:0.0005 mag.," We have a second measurementof the eclipse depth $0.0101 \pm 0.0013$ mag) from Apr. 20/21, 2003.Combining these measurements, we have a final value $0.0107 \pm 0.0008$ mag."925of Lh<Lek). where L-Lp»0) aud LL(0) are the mininuni aud maxiuuni values of the fuuctiou L=Lira:Or).,"of $\tilde{L}_{-} < \tilde{L} < \tilde{L}_{+}$, where $\tilde{L}=\tilde{L}_{+} (>0)$ and $\tilde{L}=\tilde{L}_{-} (<0)$ are the minimum and maximum values of the function $\tilde{L}=\tilde{L}(r_{\rm A};\Omega_F)$."926" On the other haucd. if an area with &>0 exists between two light surfaces; we see two super-Alfvénnic regions separated by ""tvpe D forbidden regions. and obtain larger total aneular momentum MIID flows (E>L4 or|L| >|L.|)."," On the other hand, if an area with $k>0$ exists between two light surfaces, we see two super-Alfvénnic regions separated by “type B” forbidden regions, and obtain larger total angular momentum MHD flows $\tilde{L} > \tilde{L}_{+}$ or $|\tilde{L}| > |\tilde{L}_{-}|$ )."927 Thus. we can classify the forbidden regions by Qr and L as type L IL or IIE and type A or D. independently: hereafter. we will denote the typeof forbidden regious as. for example. type IA.," Thus, we can classify the forbidden regions by $\Omega_F$ and $\tilde L$ as type I, II or III and type A or B, independently; hereafter, we will denote the typeof forbidden regions as, for example, type IA."928" «45Y =2eg,andD 4,5 =Dugcurves are located in the: super-Alfvénnic regionH andm the sub-Alfvénunic region..The respectively."," The $u_p^2=u_{\rm FM}^2$ and $u_p^2=u_{\rm SM}^2$ curves are located in the super-Alfvénnic region and the sub-Alfvénnic region, respectively."929 Figure 2aa shows a case for strong maguctic fields satisfying (C's. Dyy<4.5 and Figure. :2bb shows a case for. weak magueticH fieldsd satisfeiugfd (Cz)4>uy.2," Figure \ref{fig:dd}a a shows a case for strong magnetic fields satisfying $(C_{\rm sw}^{2})_{\rm A} < u_{\rm A}^2$, and Figure \ref{fig:dd}b b shows a case for weak magnetic fields satisfying $(C_{\rm sw}^{2})_{\rm A} > u_{\rm A}^2$."930" Iu FigureH 42aa the u2.PH=URAL42 CURVEsqpev connectss to the Alfvénn""A point: marked by - (r=ry.uy2= X). while:in: Figure: κ2bb the uo2=αι eve connects to the Alfvénn point."," In Figure \ref{fig:dd}a a the $u_p^2=u_{\rm FM}^2$ curve connects to the Alfvénn point marked by ” $r=r_{\rm A}, u_p^2=u_{\rm A}^2$ ), whilein Figure \ref{fig:dd}b b the $u_p^2=u_{\rm SM}^2$ curve connects to the Alfvénn point."931 At the Alfvenn r=ry the value of the function f=f(uyira) is zero except at the Alfvénn pointA., At the Alfvénn $r=r_{\rm A}$ the value of the function $f=f(u_p; r_{\rm A})$ is zero except at the Alfvénn point.932" Then. ue=C2. is one of the solutions of D(uy:r)—0 Quarked by ""C in Fig. 2))."," Then, $u_p^2=C_{\rm sw}^2$ is one of the solutions of ${\cal D}(u_p; r_{\rm A})=0$ (marked by ” in Fig. \ref{fig:dd}) )."933 A similar situation at the (outer) Alfvénn point ciu be seen in the Newtonian case (sec (1989)))., A similar situation at the (outer) Alfvénn point can be seen in the Newtonian case (see \citet{Heyvaerts-Norman89}) ).934 We also plot a typical curve with Av=0 in Figure 3.., We also plot a typical curve with ${\cal N}=0$ in Figure \ref{fig:nn}.935 Crossing of the D=0 curves aud Av=0 curves iu the super- or sub-Alfvénnic region means the fast or slow magnetosonic point. respectively.," Crossing of the ${\cal D}=0$ curves and ${\cal N}=0$ curves in the super- or sub-Alfvénnic region means the fast or slow magnetosonic point, respectively."936 In the cold limit. between the Alfvén poiut aud the event horizon iu the super-AlfvGunic region. crossing of the Av=0 curve aud D=0 curve always exists regardless of the jj value (Paper I).," In the cold limit, between the Alfvénn point and the event horizon in the super-Alfvénnic region, crossing of the ${\cal N}=0$ curve and ${\cal D}=0$ curve always exists regardless of the $\eta$ value (Paper I)."937 However. in the case of (C2.)4>m we cannot find amy reason for crossing of these lines.," However, in the case of $(C_{\rm sw}^{2})_{\rm A}>u_{\rm A}^2$, we cannot find any reason for crossing of these lines."938 In fact. we find a restriction on the hot traus-fast MIID accretion by the thermal effects.," In fact, we find a restriction on the hot trans-fast MHD accretion by the thermal effects."939 In this case. the condition AY=D0 is not achieved between the inner Alfvénn radius aud the event horizon: that is. no plivsical traus-fast MOTD accretion solution exists.," In this case, the condition ${\cal N}={\cal D}=0$ is not achieved between the inner Alfvénn radius and the event horizon; that is, no physical trans-fast MHD accretion solution exists."940 When the thermal effects dominate over the magnetic effects; we cau find that the crossing of these lines is ouly available for smaller ||. while for larger |i] it becomes impossible to generate a plivsieal traus-fast MIID accretion solution (see below).," When the thermal effects dominate over the magnetic effects, we can find that the crossing of these lines is only available for smaller $|\eta|$, while for larger $|\eta|$ it becomes impossible to generate a physical trans-fast MHD accretion solution (see below)."941 Iu the cold limit. because the slow maguetosouic wave speed is zero. the N-type slowmagnetosonic point is located just on the maxis (u=0 line).which is just the separation point.," In the cold limit, because the slow magnetosonic wave speed is zero, the X-type slowmagnetosonic point is located just on the $r$ -axis $u^r=0$ line),which is just the separation point."942" When thermal effects are effective. we can see A-type slow magnuetosonic poiuts with a sub-slow maguetosonic region in the sub-Alfvéunic region of the ru"" plane."," When thermal effects are effective, we can see X-type slow magnetosonic points with a sub-slow magnetosonic region in the sub-Alfvénnic region of the $r$ $u^r$ plane."943" Now. we will discuss the condition for crossiues of the Ar.uy)—O0 aud Dir.u,)=0 curves."," Now, we will discuss the condition for crossings of the ${\cal N}(r,u_p)=0$ and ${\cal D}(r,u_p)=0$ curves."944" We use the indices ""E aud ""S to denote the quantities evaluated at the fast aud slow magnuetosonic points. respectively. and use the index “cr” to unite the quautities at these maenetosouic poiuts."," We use the indices “F” and “S” to denote the quantities evaluated at the fast and slow magnetosonic points, respectively, and use the index “cr” to unite the quantities at these magnetosonic points."945" In the following equations. to discuss MIID flows passing through the fast or slow maguetosouie point. we canreplace the subscript ""or by “FO or ""S."," In the following equations, to discuss MHD flows passing through the fast or slow magnetosonic point, we canreplace the subscript “cr” by “F” or “S”."946 From the coucdition D=0 at the fast aud slow maguetosonic poiuts. the poloidal velocity at these critical points wA=(rar) is written as and by use of the definition of Mach-uumuber (11)). the particle flux through a flux tube 5 is determined by where the critical Mach-uiuuber Ar=APPre:V) is obtained as a solution of A= 0. which is a cubic. equation. tn. » A7.," From the condition ${\cal D}=0$ at the fast and slow magnetosonic points, the poloidal velocity at these critical points $u_{\rm cr}^2\equiv u_p^2(r_{\rm cr}; \Psi)$ is written as and by use of the definition of Mach-number \ref{eq:Mach}) ), the particle flux through a flux tube $\eta$ is determined by where the critical Mach-number $M_{\rm cr}^2\equiv M^2(r_{\rm cr}; \Psi)$ is obtained as a solution of ${\cal N}=0$ , which is a cubic equation in $M^2$ ."947 Thus.: we cau express αν a fuuctiou: of: rq with: given: parameters Op. L. (aL)2 and WV.," Thus, we can express $\eta$ as a function of $r_{\rm cr}$ with given parameters $\Omega_F$ , $\tilde L$ $(a_{\rm sw}^2)_{\rm cr}$ and $\Psi$ ."948 The total enerev of the traus-fast (or trans-slow) ΑΠΟ flow is also evaluated at the fast (or slow), The total energy of the trans-fast (or trans-slow) MHD flow is also evaluated at the fast (or slow)949" normalizedto the samerms, but thespatial pattern was different haveevery simulationas by",In Figure \ref{fig10} we plot the energy spectra obtained from runs F and G. They are very similar to each other.950 the random amplitudes.for Inthe simulations determinedpresented here," Both the velocity and magnetic fields develop inertial ranges following power laws, and overlap each other."951" forcingis the same simulation, asit theis a exactlyFourier modefor[eq.each(1))). Assimplythe forcingsi"," For both runs the spectral index of the kinetic spectrum $\sim -0.5$ ) is much smaller than that of the magnetic energy $\sim -2.1$ ), that is steeper than kolmogorov $-5/3$ )."952"ngle the same each simulation the overlapis moreis evident, and formakes strongerthe claim "," Also the kinetic energy has a lower value than the magnetic energy, as already noticed for the integrated quantities (Figure \ref{fig1}) )."953Reynoldsthat total beyonddissipation is threshold.. independentWe of conjecturedthe this hypothesisnumber a independent, The energy that is injected into the system for unit time is the integrated Poynting flux where $\mathbf{u_{_\perp}^L}$ and $\mathbf{u_{_\perp}^0}$ are the imposed velocity patterns at the top and bottom planes.954" from the Reynolds number, where the turbulent transport exhibits ficiently high valueof the Reynolds number. This unfortunately thermodynamicaland"," For run G, we excite all wavenumbers $3 \le n_{_\perp} \le 4$, while for run F we as $\mathbf{u_{_\perp}^L} = - \mathbf{u_{_\perp}^0} = 955\sin \left( 8\pi x + 1 \right) \mathbf{\hat{e}_y}$ , we are injecting energy in the system only at $\mathbf{n_{in}} = 4 \cdot 2\pi\, \mathbf{\hat{e}_x}$, the wavenumber $4$ along $x$."956radiativeoutcome is independent ofthe Reynolds number.In fact howfield-linesare heatedstrongly," This can be noticed also in Figure \ref{fig10}, where the kinetic spectrum for run G at $n=3$ is higher than for run F, as part of the energy is injected also at $n=3$ in the vortical case."957 depends on the dynamics and properties around the single current sheet. These become, The lower level for the kinetic spectrum is due to the boundary conditions that roughly set the value or the velocity at the injection wavenumbers inside the volume.958 thinner and thinnerat higher Reynolds, In the simple linear case this is given by eq. \ref{eq:lin2}) ).959 numbersand theoverall dynamics more chaotic. Hence propertiesof the field-linesthat crossthe current sheets alongthe axial direction) and getso," In the shear case we would have $E_K(4)= 1/2 \cdot V \cdot \langle \mathbf{u^2} \rangle = 2.5$ $V=10$ is the volume) in the linear regime, and from Figure \ref{fig10} we notice that also in the nonlinear regime $E_K(4) \sim 2.5$."960 heated impulsively(elongated arealltobe explored. An o, On the other hand the magnetic field grows linearly in time [eq. \ref{eq:lin1}) )]961pen question is whether the dissipation is independent ofthe Reynoldsnumberalsoint, until a balance is reached between the energy flux that is injected at this scale and the flux of energy flowing towards smaller scales through a turbulent cascade.962"hesingle current sheets, ortheir number and properties changeto attain independence for", The magnetic energy spectra of the two simulations are slightly different at the large scales with $n_{_\perp} \le 5$.963 the total dissipation. Research inthisarea, The large scale dynamics is in fact slightly different in the two cases.964 is active (Loureiroetal.| 2001: andhas alreadyshown numbers reconnection departs the classic Sweet-Parker scaling, In the vortical case (run G) energy is injected in all modes with wavenumbers $3 \le n_{_\perp} \le 4$ thatthen cascades toward smaller scales.965sin the MHD regime. Furtherm," In the shear case (run F) energy is injected only at one wavenumber $\mathbf{n_{_\perp}} = (4, 0)$."966"ore fora plasma in coronal conditions kinetic effects cannot be excluded apriori, dissipa", We have already noticed in \ref{sec411} that although we continue shearing the footpoints of the field-lines with our 1D forcing [eq. \ref{eq:f0}) )]967tingenergy through particle acceleration.Also the highvalue of themagnetic Pr," in the nonlinear stage the orthogonal magnetic field is organized in magnetic islands (Figure \ref{fig3}) ), so that it is no longer a mapping of the boundary velocity."968"andtlnumber couldhavea bearing (Schekochihinet al.|2004).. Nonetheless the total 800 650μυ- | − 350r − 200 R=800 200 300 400 500 600 890 J+Q 650 - − | N 500 85ο R=400 | 200 650[- 500 R=200350 200 600 700 800t/t, 9001000Fic. 9.— Transition to turbulence, total"," Although energy is injected only in the wavenumber 4 along x, energy is then redistributed by the nonlinear terms also to modes with wavenumbers along y at the large scales, and a small inverse cascade is present as in run G. This is the basic mechanism by which magnetic islands are sustained throughout the simulation in the nonlinear stage."969" ohmic andviscous dissipation(displayed asafunction oftimeform simulations A,Band C simulations onimplementthe samescale for200,anbutequal different interval Reynoldsoftime).numbers, All the fromRe thesignal (19)."," In this paper we have investigated the dynamics of the Parker problem for the heating of coronal loops when the footpoints of the magnetic field-lines are stirred by a 1D shear velocity pattern at the photosphere-mimicking boundary, and compared these results with those previously obtained when a more complex ``vortex-like'' velocity pattern was imposed \citep{rved08}."970"iscompletelyup flatfollowing Reynolds exactlythe linear saturation 100, curveeq.Athigher Reynoldsnumbers,", This very simple forcing is ideal to investigate the origin of turbulence in coronal loops and the influence of the boundary velocity forcing on the dynamics of the system.971 smaller temporal structuresare present displayinga," We willalso compare our results with those of \cite{hp92} and of the more recent simulations of \cite{dka05,dlkn09}. ."972transitionto turbulence.," In summary, the main results presented in this paper are the following:"973are significant only for the arguments £1. one can extend the limits of integration over eto (xso).,"are significant only for the arguments $\xi\la 1$, one can extend the limits of integration over $\psi$ to $(-\infty,\infty)$."974 Furthermore. as these functions peak at high harmonics. s5. one can replace the summation over s by integration over jy.," Furthermore, as these functions peak at high harmonics, $ s\sim\gamma_0^3$, one can replace the summation over $ s$ by integration over $y$."975 Then the scattered power is written as where the superscripts of  denote the polarization of the incident waves. €=(y/2)(1 eye? and the synchrotron power reads Integrating Eqs. (7))-(8))," Then the scattered power is written as where the superscripts of $P$ denote the polarization of the incident waves, $\xi\equiv(y/2)(1+\psi^2)^{3/2}$ , and the synchrotron power reads Integrating Eqs. \ref{eq19}) \ref{eq20}) )"976 over the angular coordinate o with the help of the well-known integrals of the svnchrotron theory anc the analogous integrals (Al4)) and (ALS)) calculated in Appendix A. one can obtain the normalized spectral distributions where it is taken that I(pH|piedy=h(pes ," over the angular coordinate $\psi$ with the help of the well-known integrals of the synchrotron theory and the analogous integrals \ref{a14}) ) and \ref{a18}) ) calculated in Appendix A, one can obtain the normalized spectral distributions where it is taken that $\int_0^\infty(f^{AA}+f^{AB})\mathrm{d}y=\int_0^\infty(f^{BA}+f^{BB})\mathrm{d}y=\int_0^\infty(f^A_{\mathrm{syn}}+f^B_{\mathrm{syn}})\mathrm{d}y=1$ ."977Proceeding from the approximationo of the modified. Bessel function. at. small arguments. where E(j) is the geamma-function. one can find. the asvmptotie behaviour of the spectra at jj70: Note that the scattered radiation. has much. steeper spectra.," Proceeding from the approximation of the modified Bessel function at small arguments, where $\Gamma(\mu)$ is the gamma-function, one can find the asymptotic behaviour of the spectra at $y\to 0$: Note that the scattered radiation has much steeper spectra."978" Provided that gyl. bly)mVE2ygexp(gy) and the spectra crop exponentially,"," Provided that $y\gg 1$, $K_\mu(y)\approx\sqrt{\pi/2y}\exp(-y)$ and the spectra drop exponentially."979 The overall spectral distributions (9)) are plotted in Fig. 1.., The overall spectral distributions \ref{eq21}) ) are plotted in Fig. \ref{f1}.980 One can see that the power ofthe scattered. radiation peaks at markedly larger frequencies than the svynehrotron. power in. both cases. of the incident A- and. D-polarizations (peu:71.25 and 2.5. respectively. whereas the svnchrotron peak lies at ye0.3).," One can see that the power ofthe scattered radiation peaks at markedly larger frequencies than the synchrotron power in both cases of the incident A- and B-polarizations $y_{\mathrm{peak}}\approx 1.25$ and $2.5$, respectively, whereas the synchrotron peak lies at $y\approx 0.3$ )."981 Alaking use of the formula one can integrate the spectral distributions to obtain the total power in cach polarization: tt should. be noted. that. the. polarization states. of the scattered: radiation. in the cases of incident A- and D-polarizations are distinct ancl both diller. from. the svnchrotron case., Making use of the formula one can integrate the spectral distributions to obtain the total power in each polarization: It should be noted that the polarization states of the scattered radiation in the cases of incident A- and B-polarizations are distinct and both differ from the synchrotron case.982 Besides that. R=(eb!|pycpfpBEj ((xwap )6snt06/g57).," Besides that, $R\equiv(P^{AA}+P^{AB})/(P^{BA}+P^{BB})\sim (\Omega^2/\omega^2\eta^2)(\sin^2\theta/\eta^2\gamma^2)$ ."983 Although the quantity sin-6pa may be much less than unity. in our consideration /?x1. since only the leading terms in OFfui are retained.," Although the quantity $\sin^2\theta/\eta^2\gamma_\Vert^2\gamma_0^2$ may be much less than unity, in our consideration $R\gg 1$, since only the leading terms in $\Omega^2/\omega^2\eta^2$ are retained."984 Thus. the waves of the A-polarization are scattered. much. more cllicienth.," Thus, the waves of the A-polarization are scattered much more efficiently."985 Note also that. the linearization technique applied. for the derivation. of the scattering cross-section (2)) is valid only until the power scattered is less than the svnchrotron power of the particle (formoredetailsseePetrova 2008a).., Note also that the linearization technique applied for the derivation of the scattering cross-section \ref{eq14}) ) is valid only until the power scattered is less than the synchrotron power of the particle \citep[for more details see][]{p08a}. .986 The angular distributions can be obtained by integratingEqs. (7))-(8)), The angular distributions can be obtained by integratingEqs. \ref{eq19}) \ref{eq20}) )987 over y with the help of the integral, over $y$ with the help of the integral988level (Lictal. 200129).,level \cite{li1}) ).989 On the other haud. the similarity of the reddening values given by two independent methods lav mean that the estimated L(BW) is close to the real value.," On the other hand, the similarity of the reddening values given by two independent methods may mean that the estimated $E(B-V)$ is close to the real value."990 Adopting E(BV)20.05 imag. the total absorption in the B. V. R and I bands is Ap=0.21. Ay=0.16. Ap= 0.13. Ay=0.09 mag. respectively. using the ealactic reddening law given by Schlegeletal.," Adopting $E(B-V) = 0.05$ mag, the total absorption in the $B$, $V$ , $R$ and $I$ bands is $A_B = 0.21$, $A_V = 0.16$, $A_R = 0.13$ , $A_I = 0.09$ mag, respectively, using the galactic reddening law given by \cite{sfd}."9911998.. The huuinositv paramcter A=0.17 nuplies that SN 2001V is a super-huninous Type Ta SN. relative to the majority of such SNe.," The luminosity parameter $\Delta = -0.47$ implies that SN 2001V is a super-luminous Type Ia SN, relative to the majority of such SNe."992 Super-luninous SNe are often referred as SN 1991T-. or SN 1999aa-like eveuts (see Lietal.. 200153).," Super-luminous SNe are often referred as SN 1991T-, or SN 1999aa-like events (see \cite{li2}) )."993 The distinction )etwoeen different subtypes of SNe Ia is usually used on spectroscopic xoperties. es. the streneth of the trough at 6150A.," The distinction between different subtypes of SNe Ia is usually based on spectroscopic properties, e.g. the strength of the trough at 6150."994. Overluminous SNe Ia have weaker 6150 line. aud the lines are strone.," Overluminous SNe Ia have weaker 6150 line, and the lines are strong."995 Iu addition. SN. 1999aa-ike events usually show strong I EK lines. which are weals in SN 1991T-like SNe.," In addition, SN 1999aa-like events usually show strong H K lines, which are weak in SN 1991T-like SNe."996 These spectroscopici characteristics correlate with photometric propertics: the ight curves of SN 1991T-like SNe declines more slowly. and they are bIuer i asian than normal SNe Ia. Thus. overhuninous SNe may be recognizable from photometry. e.g. via the MLCS-nethod.," These spectroscopic characteristics correlate with photometric properties: the light curves of SN 1991T-like SNe declines more slowly, and they are bluer in maximum than normal SNe Ia. Thus, overluminous SNe may be recognizable from photometry, e.g. via the MLCS-method."997 We do not have spectroscopic data of SN 2001V at our disposal. but two spectra of SN 2001V. obtained arom naxinuun. are available in eraplical form from the CLA-website ?.," We do not have spectroscopic data of SN 2001V at our disposal, but two spectra of SN 2001V, obtained around maximum, are available in graphical form from the CfA-website ."998. As the referee of this paper. Dr. Weidong Li. yoluted out. these spectra are very simular to that of SN 1999aa: broad. but less prominent 6150 line. strong aud IT Is lines.," As the referee of this paper, Dr. Weidong Li, pointed out, these spectra are very similar to that of SN 1999aa: broad, but less prominent 6150 line, strong and H K lines."999 These spectral features ullv support our conclusion (based on photometry). tha SN 2001V is an overluninous SN Ta. Note. however. that it is not clear whether the Πσ]ο luninosity is necessarily connected with the spectroscopic peculiarities.," These spectral features fully support our conclusion (based on photometry), that SN 2001V is an overluminous SN Ia. Note, however, that it is not clear whether the higher luminosity is necessarily connected with the spectroscopic peculiarities."1000" There are examples. such as SN 100210 (Riessctal.. 1998)). hat were super-""unmous. but otherwise showed normal spectra around Πακλα,"," There are examples, such as SN 1992bc \cite{riess2}) ), that were super-luminous, but otherwise showed normal spectra around maximum."1001 Thus. the overbluuinositv of some Type Ia SNe Πο be due to e.g. statistical fluctuation of the ejected νὰ nass that »owers the light curve. rather than a difference in the explosion uechanisni or the plivsical state of the progenitor.," Thus, the overluminosity of some Type Ia SNe might be due to e.g. statistical fluctuation of the ejected $^{56}$ Ni mass that powers the light curve, rather than a difference in the explosion mechanism or the physical state of the progenitor."1002 Receutlv. Richardsouctal..2002 found that the maxi brghtuess Mp of SNe Ian has a Gaussian distribution with &=0.56 mag (corrected for the effect of extinction)., Recently \cite{rich} found that the maximum brightness $M_B$ of SNe Ia has a Gaussian distribution with $\sigma = 0.56$ mag (corrected for the effect of extinction).1003 From νο unpublishec photometry. recently AMaudeletal..2002 concluded. that SN. 2001V Was a “normal Type Ia event. with light aud. colour curves very similar to SN 1990N. On the other haud. they also determined the initial decline vate. aud found Aanqs(D)=0.99£0.05.," From yet unpublished photometry, recently \cite{mandel} concluded that SN 2001V was a “normal” Type Ia event, with light and colour curves very similar to SN 1990N. On the other hand, they also determined the initial decline rate, and found $\Delta m_{15}(B) = 0.99 \pm 0.05$."1004 This decline rate may suggest an overlumunous. rather than a “normal SN Ia (e.g. ILuuuvetal.. 1996)).," This decline rate may suggest an overluminous, rather than a “normal” SN Ia (e.g. \cite{hamuy2}) )."1005 Although our photometry las less accuracy aud phase coverage. we also attempted to estimate this parameter and found Aim5(B)—0.9x0.1.," Although our photometry has less accuracy and phase coverage, we also attempted to estimate this parameter and found $\Delta m_{15}(B) = 0.9 \pm 0.1$."1006" According to the correlation between Ai,;(B) aud A (ee. Riessetab.1998)). this is consistent with the A parameter given by the MLCSAanethod."," According to the correlation between $\Delta m_{15}(B)$ and $\Delta$ (e.g. \cite{riess2}) ), this is consistent with the $\Delta$ parameter given by the MLCS-method."1007 Furthermore. Fig.l shows the essential simuübuitv of the Πο curves of SN 2001V with that of SN 1991T ΑΗ)=0.91. Παινetal..1996)).," Furthermore, Fig.4 shows the essential similarity of the light curves of SN 2001V with that of SN 1991T $\Delta m_{15}(B) = 0.94$, \cite{hamuy2}) )."1008 Thus. all available data consistently support the conchision that SN 2001V was an intrinsically bright SN Ta. At maxinuun. if was brighter than the fiducial Type Ta SN by about 0.5 mae.," Thus, all available data consistently support the conclusion that SN 2001V was an intrinsically bright SN Ia. At maximum, it was brighter than the fiducial Type Ia SN by about 0.5 mag."1009 Adopting the piriuneters given by the MILCS-inethod. the inferred absolute imaguitudes of SN 2OOLV at maxima are The true distance modulus. py=231.36+0.114 mag. corresponds to 71.545 Alpe.," Adopting the parameters given by the MLCS-method, the inferred absolute magnitudes of SN 2001V at maximum are The true distance modulus, $\mu_0 = 34.36 \pm 0.14$ mag, corresponds to $74.5 \pm 5$ Mpc."1010 The uncertainty eiven here is the formal error of the fttius. aud does not imchide possible systematic effects. such as the zero-point of the SN distance scale.," The uncertainty given here is the formal error of the fitting, and does not include possible systematic effects, such as the zero-point of the SN distance scale."1011 The MLECS distance marginally agrees with the οποιατίς distance of NGC 3987 corrected for Virgodufall (67 Mpc. see Sect.1). the difference is about 1.5o.," The MLCS distance marginally agrees with the kinematic distance of NGC 3987 corrected for Virgo-infall (67 Mpc, see Sect.1), the difference is about $1.5 ~ \sigma$."1012 The Tull-Fisher distance (58 Mpc. Sect.1) is about 20 percent shorter.," The Tully-Fisher distance (58 Mpc, Sect.1) is about 20 percent shorter."1013 The TF distance modulus (ijtTF)= 33.82. Mouldetal. 1993)) can o brought into agreement with the MLCS distance byadding 0.51 mag to the previous one. in accord with he sugeestion by Slauks (Shauks. 1997)) formatchine the TF aud SN distance SCOlCS.," The TF distance modulus $\mu_0(TF) = 33.82$ , \cite{mould}) ) can be brought into agreement with the MLCS distance byadding 0.54 mag to the previous one, in accord with the suggestion by Shanks \cite{shanks}) ) formatching the TF and SN distance scales."1014 The results of this paper can be sumuuiarized as follows., The results of this paper can be summarized as follows.1015where (he coellicients C; εἰ=1.2.3) are defined by ((9)) and Cy<CoCy.,"where the coefficients $C_{\rm i}$ $i=1,2,3)$ are defined by \ref{eq:coef}) ) and $C_{\rm 1}<C_{\rm 2}<C_{\rm 3}$."1016 This result was already. usecl in our recent rate estimation lor DNS svstems to include the newly discovered pulsar. J0737-3039 (Bureay et 22003: Nalogera et 22004)).," This result was already used in our recent rate estimation for DNS systems to include the newly discovered pulsar, J0737-3039 (Burgay et \nocite{burgay03}; Kalogera et \nocite{k04}) )."1017" As before. the confidence limit and the lower and upper limits (R4, and Ry) of the coalescence rate estimates are defined in (hie same wav we described in paper I. i.e. and In Fig. 3.."," As before, the confidence limit and the lower and upper limits ${\cal R}_{\rm L}$ and ${\cal1018R}_{\rm U}$ ) of the coalescence rate estimates are defined in the same way we described in paper I, i.e. and In Fig. \ref{fig:prtot},"1019" we show the resulting PCR4,)) lor binaries along with the individual PDFs for each observed. coalescing binaries.", we show the resulting $P$ ) for binaries along with the individual PDFs for each observed coalescing binaries.1020 The figure shown here is obtained [rom our reference model (model 6 in paper I)., The figure shown here is obtained from our reference model (model 6 in paper I).1021" As we found for the DNS svstems in paper LI. PS, )) is highly peaked aud dominated by a single object."," As we found for the DNS systems in paper I, $P$ ) is highly peaked and dominated by a single object."1022 In this case. PSI. J1141—6545 dominates the results by virtue of its short observable lifetime (my. ~105 Myr).," In this case, PSR $-$ 6545 dominates the results by virtue of its short observable lifetime $\tau_{\rm life} \sim$ 105 Myr)."1023" This is in spite of the fact that the estimated total number of binaries similar to P5. JOTSL+1807 (Noss,c 2900) is the largest among the observed systems.", This is in spite of the fact that the estimated total number of binaries similar to PSR J0751+1807 $N_{\rm 0751}\simeq$ 2900) is the largest among the observed systems.1024 We summarize our results for different pulsar population models in Table 2.., We summarize our results for different pulsar population models in Table \ref{tab:results}.1025" The model parameters are identical to those described in paper I. We note however. following Ixalogera οἱ ((2004). that our reference model is now model 6 (Li,= 0.3 mJv kpc?) rather than model 1 (Linin= 1.0mJy kpc?)."," The model parameters are identical to those described in paper I. We note however, following Kalogera et (2004), that our reference model is now model 6 $L_{\rm min}=$ 0.3 mJy $^{2}$ ) rather than model 1 $L_{\rm min}=$ 1.0 mJy $^{2}$ )."1026 This choice reflects the recent discoveries of faint pulsar with 1400-MIIz radio luminosities below than 1.0 mJv kpc? (Camilo 2003)., This choice reflects the recent discoveries of faint pulsar with 1400-MHz radio luminosities below than 1.0 mJy $^{2}$ (Camilo \nocite{cam03} 2003).1027 The peak values of PUR 4) lie in the range between ~0.2—10 ! where the reference model shows a peak around 4 |., The peak values of $P$ ) lie in the range between $\sim0.2-10$ $^{-1}$ where the reference model shows a peak around 4 $^{-1}$.1028" For the reference model. the uncertainties in the rates. (defined by Riπι) are estimated to be ~ 6. 27 and 62 al6850...95%... and CL. respectively,"," For the reference model, the uncertainties in the rates, (defined by ${\cal R}_{\rm U}/{\cal R}_{\rm L}$ ) are estimated to be $\sim$ 6, 27 and 62 at, and CL, respectively."1029 Comparing this to results from(2004). we find that the uncertainties at different CL of the coalescence rate of binaries are (vpically larger by [actor of ~1.4 than Chose ol the DNS systems.," Comparing this to results from, we find that the uncertainties at different CL of the coalescence rate of binaries are typically larger by factor of $\sim$ 1.4 than those of the DNS systems."1030 This result is robust for all models we consider., This result is robust for all models we consider.1031If one specifies ορ down toa vas Vinin- then BP(y) is i of -Yn] by (8).,"If one specifies $G^{(i)}(\chi)$ down to a value $\chi_{\rm min}$ , then $B^{(i)}(\chi)$ is well-defined in the range $\bb{\chi_{\rm min},\chi_{\rm hor}}$ by )."1032""" Note that if we dropped the assumption a flat universe. would still be solvable. but analytical progress would be hampered."," Note that if we dropped the assumption of a flat universe, ) would still be solvable, but analytical progress would be hampered."1033 To i the solution of the homogeneous equation. obtained from (8) by pPOsetting gyGy)=0. we define where H(y) denotes the Heaviside step function.," To find the solution of the homogeneous equation, obtained from ) by setting $G^{(i)}(\chi) \equiv 0$, we define where $H(\chi)$ denotes the Heaviside step function."1034 Then (8) can be re-written asa cross-correlation. The introduction of the Heaviside functions in (12) was used to extend the integration to zero and infinity.," Then ) can be re-written as a cross-correlation, The introduction of the Heaviside functions in ) was used to extend the integration to zero and infinity."1035 If we denote Fourier transforms by a tilde. the convolution theorem vields Gi?bf.," If we denote Fourier transforms by a tilde, the convolution theorem yields $\tilde{G}^{(i)} = \tilde{b}\, \tilde{f}$."1036" From thisMM is it readily seen that for ο)=0 elutionit follows B""(y)=0 homocencomsin the interv: "," From thisequation is it readily seen that for $G^{(i)}(\chi) \equiv 0$ it follows $B^{(i)}(\chi) \equiv 0$ in the interval $\bb{\chi,\chi_{\rm hor}}$."1037the of the Volterra equation consists only of the trivial one and ap constitutes the full. unique solution of (8).," Hence the solution of the homogeneous Volterra equation consists only of the trivial one and ) constitutes the full, unique solution of )."1038" In summary Qmm a given G'(y) that fulfils the conditions imposed by ""(7) and (9). we can calculate the corresponding weight via (11) and use the result to construct transformed power spectra (6)."," In summary, for a given $G^{(i)}(\chi)$ that fulfils the conditions imposed by ) and ), we can calculate the corresponding weight function via ) and use the result to construct transformed power spectra )."1039 Note the analogy between (8) and the NM of the lensing efficiency , Note the analogy between ) and the definition of the lensing efficiency ).1040This cfticieneycan be interpreted as Gy) constructbeing a modified lensing whichis then used to an alternative lensing convergence with desired properties chosen via G(y).," This can be interpreted as $G^{(i)}(\chi)$ being a modified lensing efficiency, which is then used to construct an alternative lensing convergence with desired properties chosen via $G^{(i)}(\chi)$."1041 For details on this view see the motivation of the nulling technique given in(2008)., For details on this view see the motivation of the nulling technique given in.1042 Apart from the requirements formulated in Sect.2.2 to ensure a boosting of the GI signal with respect to cosmic shear. the choice of G'(y) is arbitrary.," Apart from the requirements formulated in $\,$ to ensure a boosting of the GI signal with respect to cosmic shear, the choice of $G^{(i)}(\chi)$ is arbitrary."1043 In the following we choose a specific parametrisation of G(y) which is convenient and intuitive. but not necessarily optimal.," In the following we choose a specific parametrisation of $G^{(i)}(\chi)$ which is convenient and intuitive, but not necessarily optimal."1044 Its base is a Gaussian that is peaked at y;. which fosters a strong contribution of GI correlations via the first term of (7).," Its base is a Gaussian that is peaked at $\chi_i$, which fosters a strong contribution of GI correlations via the first term of )."1045 Some additional flexibility is needed at y.<y;. allowing for sign changes of G'(y) to downweight the lensing signal.," Some additional flexibility is needed at $\chi < \chi_i$, allowing for sign changes of $G^{(i)}(\chi)$ to downweight the lensing signal."1046 We define where N. c. b. se[-and γι are free parameters.," We define where ${\cal N}$, $\sigma$, $b$, and $\chi_{\rm m}$ are free parameters."1047 All four parameters depend on the choice of galaxy sample 7. but we do not specify this dependence for reasons of better readability.," All four parameters depend on the choice of galaxy sample $i$, but we do not specify this dependence for reasons of better readability."1048 The. first derivative of G'(y) with respect to comoving distance reads From this result and ο...by means of (11) one readily obtains the weight function ni normalisation of Gy) is related to the one of B(y) via 8). but κ.”is otherwise irrelevant to the problem.," The first derivative of $G^{(i)}(\chi)$ with respect to comoving distance reads From this result and by means of ) one readily obtains the weight function The normalisation of $G^{(i)}(\chi)$ is related to the one of $B^{(i)}(\chi)$ via ), but is otherwise irrelevant to the problem."1049 We fix N by Note that since AN depends on the other free parameters. e.g. cr. à consistent normalisation is actually important when studying Gy)v) as à function of these parameters. as we will do in Sects.5 and6.," We fix ${\cal N}$ by requiring Note that since ${\cal N}$ depends on the other free parameters, e.g. $\sigma$, a consistent normalisation is actually important when studying $G^{(i)}(\chi)$ as a function of these parameters, as we will do in $\,$ and."1050 Two of the remaining three free parameters of 14) will now be used to boost (7) and suppress (9)., Two of the remaining three free parameters of ) will now be used to boost ) and suppress ).1051" First. we demand that (14) is peaked at y;. Le. 9G""=0."," First, we demand that ) is peaked at $\chi_i$, i.e. $\partial G^{(i)}/ \partial \chi\, |_{\chi_i} = 0$."1052 Using (15). we obtain The second condition should render the integral in (9) close to zero.," Using ), we obtain The second condition should render the integral in ) close to zero."1053 While it is possible to numerically determine for instance the parameter 5 such that this condition is fulfilled for every angular frequency individually. we prefer to proceed in à way that does not rely on a model of cosmic shear power spectra at all.," While it is possible to numerically determine for instance the parameter $b$ such that this condition is fulfilled for every angular frequency individually, we prefer to proceed in a way that does not rely on a model of cosmic shear power spectra at all."1054 We note that if the width of the Gaussian o is relatively small. the support of the integral in (9) has a small range and hence P; can be well approximated as only varying slowly.," We note that if the width of the Gaussian $\sigma$ is relatively small, the support of the integral in ) has a small range and hence $P_\delta$ can be well approximated as only varying slowly."1055 The dependence on redshiftshould be roughly P(K.2)xDr Y2. where D(z) is the linear growth factor for which we assumed D(z)xxu as holds true in the matter-dominated epoch.," The dependence on redshiftshould be roughly $P_\delta(k,z) \propto D(z)^2 \propto (1+z)^{-2}$ , where $D(z)$ is the linear growth factor for which we assumed $D(z) \propto (1+z)^{-1}$ as holds true in the matter-dominated epoch."1056 Thisredshift dependence then cancels the (1+2° term in (9). S0 that we consider the condition," Thisredshift dependence then cancels the $(1+z)^2$ term in ), so that we consider the condition"1057The measured visibility data were reduced using spectral-line polarization calibration methods described by IXemball.Diamond.&Cotton(1995) and Nemball&Diamond(1997).. as implemented in a seni-automated pipeline using a modified version of the package maintained by the NRAQO.,"The measured visibility data were reduced using spectral-line polarization calibration methods described by \citet{kemball95} and \citet{kemball97}, as implemented in a semi-automated pipeline using a modified version of the package maintained by the NRAO."1058 These analvsis methods are optimized for the reduction of spectral-Hne polarization VLBI observations of the tvpe described here: in particular they make no implicit assumption that Stokes V.=0., These analysis methods are optimized for the reduction of spectral-line polarization VLBI observations of the type described here; in particular they make no implicit assumption that Stokes $V=0$.1059 The SiO molecule is non-paramagnetic. and (he mean degree of circular polarization in the SiO maser rotational (ransilious is small but not zero. my~1—3% (Barvainisοἱal.1987:Kemball&Diamond1997).," The SiO molecule is non-paramagnetic, and the mean degree of circular polarization in the SiO maser rotational transitions is small but not zero, $m_c \sim 1-3\%$ \citep{barvainis87,kemball97}."1060. In the data reduction method emploved here. all antenna-based group delay. Bringe-rate. and phase calibration. including final phase self-calibration. was performed relative to a relerence antenna in a reference receptor polarization.," In the data reduction method employed here, all antenna-based group delay, fringe-rate, and phase calibration, including final phase self-calibration, was performed relative to a reference antenna in a reference receptor polarization."1061 This calibration was translerred to the orthogonal receptor polarization by solving for all relevant phase and group delay offsets using continuum calibrator observations., This calibration was transferred to the orthogonal receptor polarization by solving for all relevant phase and group delay offsets using continuum calibrator observations.1062 This generalized reduction method retains positional coincidence between Stokes J and V images. while making no implicit assumption that Stokes V is identically zero (Ixemball.Diamond.&Cotton1995).," This generalized reduction method retains positional coincidence between Stokes $I$ and $V$ images, while making no implicit assumption that Stokes $V$ is identically zero \citep{kemball95}."1063. Amplitude calibration was performed with (he same goal of preserving the low Stokes V. signature., Amplitude calibration was performed with the same goal of preserving the low Stokes $V$ signature.1064 Each circular receptor polarization was calibrated independently using the method of Reidefαἱ.(1980) to fit (he autocorrelation spectra in each receptor polarization to a template reference spectrum in that polarization., Each circular receptor polarization was calibrated independently using the method of \citet{reid80} to fit the autocorrelation spectra in each receptor polarization to a template reference spectrum in that polarization.1065 The template spectra in each receptor polarization were calibrated on an absolute scale using svsten temperature measurements reported during (he observations and known point-source sensitivities and gain curves published for the VLBA antennas., The template spectra in each receptor polarization were calibrated on an absolute scale using system temperature measurements reported during the observations and known point-source sensitivities and gain curves published for the VLBA antennas.1066 A final sinele differential polarization gain correction was determined by cross-fitüng the spectra between receptor polarization at the template scan to measure a relative scale factor., A final single differential polarization gain correction was determined by cross-fitting the spectra between receptor polarization at the template scan to measure a relative scale factor.1067 For the low integrated i. known for SiO masers. this approximation is warranted for (he integrated autocorrelation spectrum it would not be appropriate for individual cross-power spectra. for exaniple. as some SIO maser components can be substantially cireularly polarized (IxemballDiamond 1997).," For the low integrated $m_c$ known for SiO masers, this approximation is warranted for the integrated autocorrelation spectrum; it would not be appropriate for individual cross-power spectra, for example, as some SiO maser components can be substantially circularly polarized \citep{kemball97}."1068. This final differential polarization gain correction adjusts for errors in the reported system temperatures and point source sensiüvilies. as used in (he a priori absolute calibration of the template spectrum in each receptor polarization.," This final differential polarization gain correction adjusts for errors in the reported system temperatures and point source sensitivities, as used in the a priori absolute calibration of the template spectrum in each receptor polarization."1069 We estimate these uncertainties very approximately as for the VLBA at this frequeney., We estimate these uncertainties very approximately as for the VLBA at this frequency.1070. We do nol correct [or atmospheric opacity al the pointing position and time of observation of the template spectrum for the data reported here., We do not correct for atmospheric opacity at the pointing position and time of observation of the template spectrum for the data reported here.1071 ILowever. (his has no polarization dependence. and accordingly does not affect our measurement of linear or circular polarization percentage or orientation: it only introduces à modest uncertainty in our absolute [lux density scale.," However, this has no polarization dependence, and accordingly does not affect our measurement of linear or circular polarization percentage or orientation; it only introduces a modest uncertainty in our absolute flux density scale."1072 This uncertainty is mütigated bv the fact that the template spectrum is chosen for its, This uncertainty is mitigated by the fact that the template spectrum is chosen for its1073We uote that the ispersious for the two COuponeuts are still execsssive for a Richuess 0 chster.,We note that the dispersions for the two components are still excessive for a Richness 0 cluster.1074 Ou the other lane. the presence of X-ray Cluission at the observed evel is consistent with a R= 1 or 2 cluster (?.Figure9).. which leuds suyport to the high veloci vodispersious found for tlre| two coniponeuts," On the other hand, the presence of X-ray emission at the observed level is consistent with a $R =$ 1 or 2 cluster \citep[][Figure 9]{led03}, which lends support to the high velocity dispersions found for the two components."1075 Furhermore. such a large vaue of Ly is also consisteat with a cluster merecr along the line of sielt.," Furthermore, such a large value of $L_{\rm{x}}$ is also consistent with a cluster merger along the line of sight."1076 In any case. the redshifts of both compoucuts are wel outside the kinematic core of the IIRS.," In any case, the redshifts of both components are well outside the kinematic core of the HRS."1077 Although we add no τιew observations in this cluster. a compilation of 1L previously published ealaxy redshifts provides more established kinematic properties.," Although we add no new observations in this cluster, a compilation of 14 previously published galaxy redshifts provides more established kinematic properties."1078 The ESO Nearby Abell Cluster Survey (ENACS.7?) focused on rch clusters with R col.," The ESO Nearby Abell Cluster Survey \citep[ENACS,][]{kat98}1079 focused on rich clusters with R $\geqslant$ 1."1080" The periphery of Abell 3112 (031799τσαμα.R=2.οἱ22.500iu7) overlaps with A3LO9, providing us with 9 redshifts from the ENACS data."," The periphery of Abell 3112 \citep[03\h\ 17\fm 9 $-$44\degr\ 14\farcm 0, R $=$ 2, $cz =1081 $ 22,500 in][]{maz96} overlaps with A3109, providing us with 9 redshifts from the ENACS data."1082" The assmued BCC in A3LO9, 2NMASXN. | 1351169. 6;= 15.60. has a published redshift of 18.59] citepiuur95.. which isiiconsistent with the published value for the cluster (27.581 inu SBR99. sce their note)."," The assumed BCG in A3109, 2MASX $-$ 4351169, $b_{\rm{J}} =$ 15.60, has a published redshift of 18,594 \\citep{mur95}, which is inconsistent with the published value for the cluster (27,581 in SR99, see their note)."1083 By mcorporaine al ealaxy redshifts withiu the xcscribed radius. the biweieht estinator selects 11 cluster menivers with the following kinematic Xxypertics: ez= 18.95) aand στ 850.," By incorporating all galaxy redshifts within the prescribed radius, the biweight estimator selects 11 cluster members with the following kinematic properties: $\overline{cz} =$ 18,950 and $\sigma =$ 850."1084 Reducing tfjo radial exteut O 13’ and thereby exeποιο 2 pro)osed ΠΟΙΟΥΣ. we obtain a slightlv decreased dispersion: ez= 15e.850 tand o= 700.," Reducing the radial extent to $'$ and thereby excluding 2 proposed members, we obtain a slightly decreased dispersion: $\overline{cz} =$ 18,850 and $\sigma =$ 700."1085. Even though he* dispersion real1» greater han the ~ LOO Laeadd for R = 0 clusters that we obtained earlier. he| archived redshift information establishes a reliable. cluster location (1.6.. mean redshift) aud aces A3109 within the TRS.," Even though the dispersion remains greater than the $\sim$ 400 mean for R $=$ 0 clusters that we obtained earlier, the archived redshift information establishes a reliable cluster location (i.e., mean redshift) and places A3109 within the HRS."1086 The 0. 5 clustcv.s A120. for which we have obtained 5 ealaxy redshifts. is the nearest cluster to the published spatial center of the IRS (2)..," The 0, 5 cluster, A3120, for which we have obtained 5 galaxy redshifts, is the nearest cluster to the published spatial center of the HRS \citep{zuc93}."1087 Its published redshift of 20.700 ((SR99) is also close to the 719.900 nuneau redshift of the URS ).," Its published redshift of 20,700 (SR99) is also close to the $\sim$ 19,900 mean redshift of the HRS )."1088 While À3120 does not mect the specific clustcY criteria for the APAICC. it does contain the brigit galaxy. 2ATASN 5119357 (by= 15.9)) with a previously published redshift of 21.010 citeplucs3..," While A3120 does not meet the specific cluster criteria for the APMCC, it does contain the bright galaxy, 2MASX $-$ 5119357 $b_{\rm{J}} =$ 15.91), with a previously published redshift of 21,040 \\citep{luc83}."1089 The biweight estimator routiie accepts all observed galaxies. aud we derive the ollowiug cluster properties: cz= 20.525lo omg= 1100i.," The biweight estimator routine accepts all observed galaxies, and we derive the following cluster properties: $\overline{cz} =$ 20,525, $\sigma1090=$ 1400."1091. While the mean derive velocity is in accord with the published value. he large dispersion ids clearly inconsistent with an 0 cluster.," While the mean derived velocity is in accord with the published value, the large dispersion is clearly inconsistent with an 0 cluster."1092 Furthermore. the five galaxies with redshift information show no discernible spatial or kinematic segregation. as one müeht exect with a cluster.," Furthermore, the five galaxies with redshift information show no discernible spatial or kinematic segregation, as one might expect with a cluster."1093 Hence there is reason to suspect ha A3120 is not a cluster but the projection1 of many iuter-cluster galaxies near the center of he IIRS., Hence there is reason to suspect that A3120 is not a cluster but the projection of many inter-cluster galaxies near the center of the HRS.1094" Ou the other hand. ? fud X-rav cussion a a level of L,=2.22ς10P eres 1. ceutered on 2NASN. 5119357. aud proose tha he X-rays are enuütted by a ""fossil group” (Seo heir Figure 20)."," On the other hand, \citet{rom00} find X-ray emission at a level of $L_{\rm{x}} = 2.22\times\ 10^{43}\, $ ergs $^{-1}$, centered on 2MASX $-$ 5119357, and propose that the X-rays are emitted by a “fossil group” (see their Figure 20)."1095 These groups form as a resit of uultiple mergers within the group or a cluster hat lead to a single dominant eiaut cllipica surrounded by aji Naayv halo (27).," These groups form as a result of multiple mergers within the group or a cluster that lead to a single dominant giant elliptical surrounded by an X-ray halo \citep{pon94,jon03}."1096 However. he A-rav position also coincides wiha raclio source Toni the Syvduev University Molouglo Slav Survey (SUMSS). SUMSS. 511935. witji a flux density of 19.0 τιν (?)..," However, the X-ray position also coincides with a radio source from the Sydney University Molonglo Sky Survey (SUMSS), SUMSS $-$ 511935, with a flux density of 49.0 mJy \citep{mau03}."1097 Considering the wide range of X-ray luuinosities in active ealactic nuclei (AGN). it is conceivable that sone (or: ul) of the ο endssion Is a result of the ACN. rather thu the fossil halo.," Considering the wide range of X-ray luminosities in active galactic nuclei (AGN), it is conceivable that some (or all) of the X-ray emission is a result of the AGN, rather than the fossil halo."1098" Because the eaaxvs redshift is taken from the lierature aud no optical ""pectruni is available. we couclude that the situation iu A3120 is not solude with the cureit observational data."," Because the galaxy's redshift is taken from the literature and no optical spectrum is available, we conclude that the situation in A3120 is not soluble with the current observational data."1099 In Table 2 we give the formal nica Lire«luft (location). uncertaiutv. and dispersion (scale) as deduced. from the biweight estinator analysis.," In Table \ref{tb2} we give the formal mean redshift (location), uncertainty, and dispersion (scale) as deduced from the biweight estimator analysis."1100" Ilowever. since we believe that the iuost likely value of the actial cluster redshift is tliat of the (preuned) BCC 2MASN. 5119357 (ο:= 21010 13) we adopt this value for the mean redshift of &3120 in Table 3 (noted by the ""1 in coluuu 7)."," However, since we believe that the most likely value of the actual cluster redshift is that of the (presumed) BCG 2MASX $-$ 5119357 $cz =$ 21,040 ), we adopt this value for the mean redshift of A3120 in Table \ref{tb3} (noted by the “1” in column 7)."1101 Fortunately. the difference in redshift between 20.700 iin Table 2 aud 21.010 iu Table 3 is within the biweiglit uncertainty.," Fortunately, the difference in redshift between 20,700 in Table \ref{tb2} and 21,040 in Table \ref{tb3}1102 is within the biweight uncertainty."1103Motivated by (he common occurrence of spherical. or almost spherical. faint halos around inner axisvimnetric regions of elliptical PNs (Corradi et 22003: Balick et al.,"Motivated by the common occurrence of spherical, or almost spherical, faint halos around inner axisymmetric regions of elliptical PNs (Corradi et 2003; Balick et al."1104 1992). I explore another possible mechanism (hat max influence (he rapid change in the mass loss geometry and rate of stars evolving near the AGB tip.," 1992), I explore another possible mechanism that may influence the rapid change in the mass loss geometry and rate of stars evolving near the AGB tip."1105 This mechanism is based on the steep change in the behavior of the opacity of solar composition gas al a temperature of 2900Ix (Sec., This mechanism is based on the steep change in the behavior of the opacity of solar composition gas at a temperature of $\sim 2900 \K$ (Sec.1106 2). and it may coexist with. and increase the efficiency of. the other (wo mechanisms mentioned above.," 2), and it may coexist with, and increase the efficiency of, the other two mechanisms mentioned above."1107 The mechanism may operate in AGB stars having an oxvgen (o carbon abundance ralio of —LI., The mechanism may operate in AGB stars having an oxygen to carbon abundance ratio of $~\gtrsim 1.1$.1108 It is not important in AGB stars with a carbon to oxvgen abundance ralio of =0.95. whose opacity behaves differently (Marigo 2002. 2003).," It is not important in AGB stars with a carbon to oxygen abundance ratio of $~\gtrsim 0.95$, whose opacity behaves differently (Marigo 2002, 2003)."1109 Many of the relevant PNs discussed here have indeed =1.5. e.g..6826.. (Quigley Druhweiler 1995: Guerrero Manchado 1999).το. and (Perinotto Denvenuti 1981).," Many of the relevant PNs discussed here have indeed $~\gtrsim 1.5$, e.g., (Quigley Bruhweiler 1995; Guerrero Manchado 1999), and (Perinotto Benvenuti 1981)."1110 In Section 3 I discuss possible implications of the proposed mechanism., In Section 3 I discuss possible implications of the proposed mechanism.1111 A short summary is in Section 4., A short summary is in Section 4.1112" The photospheric density is given bv. (IXippenhahn Weigert 1990) where M. and L are the stellar mass and Iuminosity. 7, is the photospheric (effective) temperature. Ay is (he Doltzimann constant. and & is the opacity."," The photospheric density is given by (Kippenhahn Weigert 1990) where $M_\ast$ and $L$ are the stellar mass and luminosity, $T_p$ is the photospheric (effective) temperature, $k_B$ is the Boltzmann constant, and $\kappa$ is the opacity."1113 To incorporate both low and high temperatures. I scale (he mean mass per particle by samy—2x107!e. and use il throughout the paper unless otherwise mentioned explicitly.," To incorporate both low and high temperatures, I scale the mean mass per particle by $\mu m_H =2 \times 10^{-24} \g$, and use it throughout the paper unless otherwise mentioned explicitly."1114 Substituting (vpical values for upper AGB stars in the last equation. and expressing the radius in terms of the Iuminosity and temperature. eive The averagec» densitv in the envelope is meaningfulex as longe as the envelope mass is Moy20.0LM..," Substituting typical values for upper AGB stars in the last equation, and expressing the radius in terms of the luminosity and temperature, give The average density in the envelope is meaningful as long as the envelope mass is $M_{\rm env} \gtrsim 0.01 M_\odot$."1115 At lower envelope mass most of the mass is concentrated near the core., At lower envelope mass most of the mass is concentrated near the core.1116 The average envelope density is, The average envelope density is1117for nearby SDSS galaxies which has an intrinsic scatter of roughly 0.071 dex,for nearby SDSS galaxies which has an intrinsic scatter of roughly $0.071$ dex.1118" For galaxies at higher redshifts, we add an (Gallazzievolution 2006)..correction to the above relation by interpolating its measured deviations to higher redshifts"," For galaxies at higher redshifts, we add an evolution correction to the above relation by interpolating its measured deviations to higher redshifts."1119" For a late-type galaxy, the velocity dispersion of its bulge3).. (if any) can also be estimated from equation (7)) after replacing M, there by M, as bulges appear to follow the same Faber-Jackson relationbulge, as faint ellipticals2007)."," For a late-type galaxy, the velocity dispersion of its bulge (if any) can also be estimated from equation \ref{eq:vsig}) ) after replacing $M_*$ there by $M\bulge$, as bulges appear to follow the same Faber-Jackson relation as faint ellipticals."1120. We summarize MCthe procedures to generate dAGNs in our Monte-Carlo simulations as follows., We summarize the procedures to generate dAGNs in our Monte-Carlo simulations as follows.1121" In order to compare with the results given by systematic surveys by using double-peaked narrow lines we only count(e.g., the number of those simulated dAGNs2011), with two components having a separation within the range from 0.5kpc to 10kpc and comparable luminosities, i.e., the luminosity ratio of the two components is within a factor of 4 here."," In order to compare with the results given by systematic surveys by using double-peaked narrow lines, we only count the number of those simulated dAGNs with two components having a separation within the range from $0.5\kpc$ to $10\kpc$ and comparable luminosities, i.e., the luminosity ratio of the two components is within a factor of 4 here."1122" And we then calculate their luminosity function and projected separation distribution, etc.,"," And we then calculate their luminosity function and projected separation distribution, etc.,"1123 as illustrated in the following section., as illustrated in the following section.1124" Figure 1 shows the [OIII] LF of the bright components of the simulated dAGNs that could be selected through double-peaked narrow lines and long-dashed lines) at redshifts z—0.1 and 0.3, respectively."," Figure \ref{fig:f1} shows the [OIII] LF of the bright components of the simulated dAGNs that could be selected through double-peaked narrow lines (solid and long-dashed lines) at redshifts $z=0.1$ and $0.3$, respectively."1125(solid These simulated dAGNS are selected through similar thresholds as that in for double-peaked narrow line dAGNs (see Section , These simulated dAGNs are selected through similar thresholds as that in for double-peaked narrow line dAGNs (see Section \ref{subsec:vsep}) ).1126"And the threshold on the separation for the nuclear activity??)). to be triggered, Dc;=Kry,;, is set to have K—1.25 (which is the reference value, see also Figure where i—1,2 represent the two components of a merging2)), pair and {σεj."," And the threshold on the separation for the nuclear activity to be triggered, $D_{{\rm c},i}= Kr_{{\rm h},j}$, is set to have $K=1.25$ (which is the reference value, see also Figure \ref{fig:f2}) ), where $i=1,2$ represent the two components of a merging pair and $i\ne j$."1127 Note that the LF of the faint components of dAGNS is only slightly smaller than that for the bright components., Note that the LF of the faint components of dAGNs is only slightly smaller than that for the bright components.1128 The observed [ΟΠΠ LFs, The observed [OIII] LFs1129momentum transport to large radii of the galaxy by spiral arm formation.,momentum transport to large radii of the galaxy by spiral arm formation.1130 Phe mean circular velocity (second row. left) is 210 km s+ ab large radii. and crops to zero towards 1e centre (see also Fig. 4)).," The mean circular velocity (second row, left) is 210 km $^{-1}$ at large radii, and drops to zero towards the centre (see also Fig. \ref{vrot}) )."1131 Phe toroidal magnetic field xttom left) is wound up by differential rotation. leading o à structure of altering positive and negative magnetic field Pvalues from centre to the edee of the galaxy.," The toroidal magnetic field (bottom left) is wound up by differential rotation, leading to a structure of altering positive and negative magnetic field values from centre to the edge of the galaxy."1132 Consequently je derivatives with respect to s (right panel) are smaller iun the radial derivatives (middle panel). mirroring the pproximate axial svmmetry.," Consequently the derivatives with respect to $\varphi$ (right panel) are smaller than the radial derivatives (middle panel), mirroring the approximate axial symmetry."1133 However. since the terms of 1e induction equation depend always on a product between a cerivative and a velocity or magnetic field component. one cannot a priori neglect the terms depending on azimuthal derivatives.," However, since the terms of the induction equation depend always on a product between a derivative and a velocity or magnetic field component, one cannot a priori neglect the terms depending on azimuthal derivatives."1134 In order to quantify the inlluence of the dilferent ternis 1-10 during the simulation we calculated. their values in cylindrical bins within the disc (5 to 15 kpe) and their mean value at dilferent. times., In order to quantify the influence of the different terms 1-10 during the simulation we calculated their values in cylindrical bins within the disc (5 to 15 kpc) and their mean value at different times.1135 We have taken the negative values of each. term in case of negative magnetic field. to distinguish between amplifving and attenuating terms., We have taken the negative values of each term in case of negative magnetic field to distinguish between amplifying and attenuating terms.1136 The result of this calculation is shown in Fig. 18.., The result of this calculation is shown in Fig. \ref{IndEqsAna}.1137 Phe upper plot shows the temporal evolution of the terms responsible for amplification/attenuation of the radial magnetic field (terms 1 to 5) and the lower of the toroidal magnetic field (terms 6 to 10)., The upper plot shows the temporal evolution of the terms responsible for amplification/attenuation of the radial magnetic field (terms 1 to 5) and the lower of the toroidal magnetic field (terms 6 to 10).1138 Positive values imply amplification. ancl negative attenuation of the corresponding B-component.," Positive values imply amplification, and negative attenuation of the corresponding $\textbf{B}$ -component."1139 The axisvmmoetrie terms are shown in red., The non-axisymmetric terms are shown in red.1140 Looking at Fig. 1δ..," Looking at Fig. \ref{IndEqsAna},"1141 the most important term for the evolution. of⋅ the radial: magnetic ⋠⋅field is⋠ term 5. 1.6.. =DB:29.," the most important term for the evolution of the radial magnetic field is term 5, i.e. $-\frac{v_\varphi}{r}\frac{\partial B_r}{\partial \varphi}$."1142" Since the toroidal velocity dominates the velocitw field. this term is most important although OB,choo is comparatively small."," Since the toroidal velocity dominates the velocity field, this term is most important although $\frac{\partial B_r}{\partial \varphi}$ is comparatively small."1143 Phis can be seen following the evolution of the circular velocity and the racial magnetic Ποιά more closely: The radial magnetic field is strongest where the circular velocity has its highest. value. with a delay of roughly 40 Myr.," This can be seen following the evolution of the circular velocity and the radial magnetic field more closely: The radial magnetic field is strongest where the circular velocity has its highest value, with a delay of roughly $40$ Myr."1144 All other terms lie in the same range and therefore compete with each other., All other terms lie in the same range and therefore compete with each other.1145 Since their values are positive as well as negative. one should. not expect a significant. amplification on their account.," Since their values are positive as well as negative, one should not expect a significant amplification on their account."1146 This analysis shows. that even. small deviations," This analysis shows, that even small deviations"1147respectively. there is no guarantee thatb(A) will be a constant.,"respectively, there is no guarantee that$b(k)$ will be a constant."1148" The best we can hope for is that there will be a ""linear response’ limit. in which b(/:) tends to a constant 5j, on large scales."," The best we can hope for is that there will be a `linear response' limit, in which $b(k)$ tends to a constant $b_{\rm lin}$ on large scales."1149 Although it is easy to invent artificial models in which this is not true. the concept of linear bias does hold for many bias models — and in particular or the most detailed attempts to include all the physics of galaxy ormation (e.g. Benson et al.," Although it is easy to invent artificial models in which this is not true, the concept of linear bias does hold for many bias models – and in particular for the most detailed attempts to include all the physics of galaxy formation (e.g. Benson et al."1150 2000)., 2000).1151 Sucrsimulations ean also give a realistic idea of the scales on which the linear-bias assumption breaks down. and we assume for the purposes of this paper tha inear bias is true (or that small deviations from scale-independence can be corrected for).," Such simulations can also give a realistic idea of the scales on which the linear-bias assumption breaks down, and we assume for the purposes of this paper that linear bias is true (or that small deviations from scale-independence can be corrected for)."1152" Nevertheless. even in the linear-bias limit. bias can complicate the analysis of LSS data. because the value of bi, will be different for different classes of galaxy."," Nevertheless, even in the linear-bias limit, bias can complicate the analysis of LSS data, because the value of $b_{\rm lin}$ will be different for different classes of galaxy."1153 The purpose of his paper is to investigate the extent to which this can affect the recovered power spectrum shape., The purpose of this paper is to investigate the extent to which this can affect the recovered power spectrum shape.1154 The fact that galaxies selected in different ways have differen clustering properties has been known for some time (e.g. Davis Geller 1976: Peacock Dodds 1994: Seaborne et al., The fact that galaxies selected in different ways have different clustering properties has been known for some time (e.g. Davis Geller 1976; Peacock Dodds 1994; Seaborne et al.1155 1999)., 1999).1156 For the 2dFGRS galaxies. although the average bias is close to unity (Lahav et al.," For the 2dFGRS galaxies, although the average bias is close to unity (Lahav et al."1157 2002: Verde et al., 2002; Verde et al.1158 2002). the bias is dependent on galaxy uminosity (Norberg et al.," 2002), the bias is dependent on galaxy luminosity (Norberg et al."1159 2001: 2002: Zehavi et al., 2001; 2002; Zehavi et al.1160" 2002 find a very similar dependence for SDSS galaxies). with = 0.85 + 0.15 Ly— where the bias b(L) is assumed to be a simple function of galaxy luminosity and £, is defined such that 19.7 (Norberg et al."," 2002 find a very similar dependence for SDSS galaxies), with = 0.85 + 0.15 , where the bias $b(L)$ is assumed to be a simple function of galaxy luminosity and $L_*$ is defined such that $M_{b_{\rm J}}-5\log_{10}h=-19.7$ (Norberg et al."1161 2001)., 2001).1162 In a magnitude limited survey. galaxies of different luminosity are probed at different radii: at high redshift. galaxies more luminous than average (and with lower number density) dominate the sample. while at low redshift galaxies less luminous than average (and with higher number density) dominate.," In a magnitude limited survey, galaxies of different luminosity are probed at different radii: at high redshift, galaxies more luminous than average (and with lower number density) dominate the sample, while at low redshift galaxies less luminous than average (and with higher number density) dominate."1163 As a consequence. the power spectrum at large scales is measured preferentially from galaxies more luminous than average. and on small scales from galaxies less luminous than average.," As a consequence, the power spectrum at large scales is measured preferentially from galaxies more luminous than average, and on small scales from galaxies less luminous than average."1164 Without correction. luminosity-dependent bias would therefore distort the shape of the recovered galaxy power spectrum from that of the matter power spectrum (see Tegmark et al.," Without correction, luminosity-dependent bias would therefore distort the shape of the recovered galaxy power spectrum from that of the matter power spectrum (see Tegmark et al."1165 2003)., 2003).1166 In this paper we consider how best to estimate the shape of the underlying matter power spectrum given a sample of galaxies tha have a clustering amplitude dependent on galaxy properties., In this paper we consider how best to estimate the shape of the underlying matter power spectrum given a sample of galaxies that have a clustering amplitude dependent on galaxy properties.1167" Specifieully. in Section 2. we consider a set of galaxies with a simple luminosity-dependent bias such that. on the scales of interest £2,(4)=DPGL,Ck)."," Specifically, in Section \ref{sec:lumbias} we consider a set of galaxies with a simple luminosity-dependent bias such that, on the scales of interest $P_g(k)=b^2(L) P_m(k)$."1168 For generality. the expected bias need not be simply a function of luminosity: all that is required is that the bias can be predicted from some combination of the properties of each galaxy.," For generality, the expected bias need not be simply a function of luminosity; all that is required is that the bias can be predicted from some combination of the properties of each galaxy."1169 The results of this paper are therefore relevant to more general problems where we have a mixed set of galaxies tracing the same density field., The results of this paper are therefore relevant to more general problems where we have a mixed set of galaxies tracing the same density field.1170 For instance the method would be applicable to type-dependent clustering or a survey covering a large redshift range where the linear evolution of the matter power spectrum and evolution in the bias of the objects selected Were important., For instance the method would be applicable to type-dependent clustering or a survey covering a large redshift range where the linear evolution of the matter power spectrum and evolution in the bias of the objects selected were important.1171 Previous studies have already extended the calculation of optimal weights presented by FKP., Previous studies have already extended the calculation of optimal weights presented by FKP.1172 Hamilton (1997) considered he effect of the window function which the FKP method assumes Ὁ be negligible., Hamilton (1997) considered the effect of the window function which the FKP method assumes to be negligible.1173 More recently. Yamamoto (2003) attempted to derive optimal weights including the effect of both redshift-space distortions and the light-cone effect. which. as we will illustrate ater. has a similar net effect as luminosity dependent bias.," More recently, Yamamoto (2003) attempted to derive optimal weights including the effect of both redshift-space distortions and the light-cone effect, which, as we will illustrate later, has a similar net effect as luminosity dependent bias."1174 In this xiper. the work of FKP is extended in a different context to the work of Yamamoto (2003). and we consider the systematic effect of luminosity-dependent bias on the recovered power in addition © providing optimal weights.," In this paper, the work of FKP is extended in a different context to the work of Yamamoto (2003), and we consider the systematic effect of luminosity-dependent bias on the recovered power in addition to providing optimal weights."1175 Interestingly. our derived optimal weights. following an independent calculation. differ from those of Yamamoto (2003) and a comparison is given in Section 5..," Interestingly, our derived optimal weights, following an independent calculation, differ from those of Yamamoto (2003) and a comparison is given in Section \ref{sec:discussion}."1176 The layout of this paper is as follows., The layout of this paper is as follows.1177 First. in Section 2.1 we present a generalization of the power spectrum analysis method introduced by Feldman. Kaiser Peacock (1994: FKP). extended tocorrect for galaxy luminosity dependent bias.," First, in Section \ref{sec:fkp_intro} we present a generalization of the power spectrum analysis method introduced by Feldman, Kaiser Peacock (1994: FKP), extended to correct for galaxy luminosity dependent bias."1178 We then follow the FKP derivation leading to revised optimal weights in Section 2.3.. in the limit of a large survey volume.," We then follow the FKP derivation leading to revised optimal weights in Section \ref{sec:optimise}, in the limit of a large survey volume."1179 The method and weights are tested in Section 3. using simple mock catalogues with a window function similar to that of the 2dFGRS. and the relevance for the analysis of POI is considered in Section 4..," The method and weights are tested in Section \ref{sec:mocks}1180 using simple mock catalogues with a window function similar to that of the 2dFGRS, and the relevance for the analysis of P01 is considered in Section \ref{sec:2dFGRS}."1181 We conclude in Section 5.., We conclude in Section \ref{sec:discussion}.1182 In this Section we extend the method of FKP to cover a sample of galaxies with different large-scale biases., In this Section we extend the method of FKP to cover a sample of galaxies with different large-scale biases.1183 In order to make the description transparent. we adopt the notation of ΕΚΡ. and refer extensively to this paper.," In order to make the description transparent, we adopt the notation of FKP, and refer extensively to this paper."1184 In particular. we adopt the Fourier transform convention of FKP. equivalent to that of Peebles (1980) with V=I.," In particular, we adopt the Fourier transform convention of FKP, equivalent to that of Peebles (1980) with $V=1$."1185 Let us consider a set of galaxies of luminosity £ forming a Poisson sampling of a linearly biased density tield ΠΟ” Liwatn., Let us consider a set of galaxies of luminosity $L$ forming a Poisson sampling of a linearly biased density field 1 + ) = ).1186 Here b(r.L) is the linear bias of galaxies of luminosity L at position r.," Here $b(\r,L)$ is the linear bias of galaxies of luminosity $L$ at position $\r$."1187 We have generalized the idea of bias being a function of L only to allow for e.g. slow evolution of 6(L) within the survey volume., We have generalized the idea of bias being a function of $L$ only to allow for e.g. slow evolution of $b(L)$ within the survey volume.1188 The probability that volume element OV contains a galaxy of luminosity £ is given by Probt(V. L)= 6Vnttr L)o((n))]. where n(r.L) is the mean expected number density of galaxies at r with luminosity £L.," The probability that volume element $\delta V$ contains a galaxy of luminosity $L$ is given by V,L) = V )], where $\bar{n}(\r,L)$ is the mean expected number density of galaxies at $\r$ with luminosity $L$."1189 The power spectrum and correlation function form a Fourier pair with £(7)£(r)(rtr!| r).and Ξ Ρικ) -yer.," The power spectrum and correlation function form a Fourier pair with $\xi(\r)=\xi(r)=\llangle1190\delta(\r')\delta(\r'+\r)\rrangle$ , and ) = P(k) =."1191 Here and hereafter £?(4°) denotes the power spectrum of the underlying matter fluctuation field 9., Here and hereafter $P(k)$ denotes the power spectrum of the underlying matter fluctuation field $\delta$ .1192 If. rather than consideringthe bias of each galaxy. we had instead considered the ratio of the bias to that of a particular galaxy type. then we simply have to redetine," If, rather than consideringthe bias of each galaxy, we had instead considered the ratio of the bias to that of a particular galaxy type, then we simply have to redefine"1193ouler gap does not exist (cf.,outer gap does not exist (cf.1194 Eq., Eq.1195 9 and Table 1)., 9 and Table 1).1196 IF (he outer gap indeed exists in MSPs of Globular clusters. CR must contribute to GeV eanmma-rays and hence the contribution bv the IC component is only partial.," If the outer gap indeed exists in MSPs of Globular clusters, CR must contribute to GeV gamma-rays and hence the contribution by the IC component is only partial."1197 The predicted diffuse radio flux for optical above is asstuned all observed GeV gamma-rays result from IC., The predicted diffuse radio flux for optical above is assumed all observed GeV gamma-rays result from IC.1198 I this is not the case then the reduction of the diffuse radio flux should be prorata., If this is not the case then the reduction of the diffuse radio flux should be prorata.1199 On the other hand. for the other soft photon fields (i.e. I. and relie photons). the IC: model-predicted flux densiües appear to be more consistent with this limit.," On the other hand, for the other soft photon fields (i.e. IR and relic photons), the IC model-predicted flux densities appear to be more consistent with this limit."1200 At 1 Gllz. the IC moclel-predicted values for all the soft photon fields in our consideration are lar below the observed upper bound at 1.4 GllIz (Reich et al.," At 1 GHz, the IC model-predicted values for all the soft photon fields in our consideration are far below the observed upper bound at 1.4 GHz (Reich et al."

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