A method is presented for finding anisotropic distribution functions for stellar systems with known, spherically symmetric, densities, which depends only on the two classical integrals of the energy and the magnitude of the angular momentum. It requires the density to be expressed as a sum of products of functions of the potential and of the radial coordinate. The solution corresponding to this type of density is in turn a sum of products of functions of the energy and of the magnitude of the angular momentum. The products of the density and its radial and transverse velocity dispersions can be also expressed as a sum of products of functions of the potential and of the radial coordinate. Several examples are given, including some of new anisotropic distribution functions. This device can be extended further to the related problem of finding two-integral distribution functions for axisymmetric galaxies.
We add to the lore of spherical, stellar-system models a two-parameter family with an anisotropic velocity dispersion, and a central point mass (``black hole''). The ratio of the tangential to radial dispersions, is constant--and constitutes the first parameter--while each decreases with radius as r^{-1/2}. The second parameter is the ratio of the central point mass to the total mass. The Jeans equation is solved to give the density law in closed form: rho\propto (r/r0)^{-c}/[1+(r/r0)^{3-c}]^2, where r0 is an arbitrary scale factor. The two parameters enter the density law only through their c…
Spherically symmetric expansionfree distributions are systematically studied. The whole set of field equations and junction conditions are presented for a general distribution of dissipative anisotropic fluid (principal stresses unequal), and the expansionfree condition is integrated. In order to understand the physical meaning of expansionfree motion, two different definitions for the radial velocity of a fluid element are discussed. It is shown that the appearance of a cavity is inevitable in the expansionfree evolution. The nondissipative case is considered in detail and the Skripkin model …
In this talk we briefly review the inverse Compton (IC) scattering of nuclear photons in the lobes of radio galaxies and quasars. We concentrate on the possibility to test this model with the Chandra observatory and to constrain the electron energy distribution by measuring the X-ray fluxes produced by this effect. We also discuss the evidence for IC scattering of nuclear photons in the powerful radio galaxies.
We examine a possible connection between the anisotropic distribution of satellite galaxies around giant spiral galaxies and the evolution of satellite systems. The observed polar anisotropy (Zaritsky et al.1997) is either imprinted by initial conditions or develops from an initially symmetric distribution. We attempt to discriminate between these two possibilities by exploring the implications of the latter one. From the observed distribution of satellite galaxies relative to the primary galaxy's disk, we derive constrains on the orbital inclinations of the current satellite population. Using…
A family of potential--density pairs has been found for spherical halos and bulges of galaxies in the Newtonian limit of scalar--tensor theories of gravity. The scalar field is described by a Klein--Gordon equation with a source that is coupled to the standard Poisson equation of Newtonian gravity. The net gravitational force is given by two contributions: the standard Newtonian potential plus a term stemming from massive scalar fields. General solutions have been found for spherical systems. In particular, we compute potential--density pairs of spherical galactic systems, and some other astro…
In this paper we investigate the gravothermal instability of spherical stellar systems endowed with a radially anisotropic velocity distribution. We focus our attention on the effects of anisotropy on the conditions for the onset of the instability and in particular we study the dependence of the spatial structure of critical models on the amount of anisotropy present in a system. The investigation has been carried out by the method of linear series which has already been used in the past to study the gravothermal instability of isotropic systems. We consider models described by King, Wilson a…
The full set of equations governing the evolution of self--gravitating spherically symmetric dissipative fluids with anisotropic stresses is deployed and used to carry out a general study on the behaviour of such systems, in the context of general relativity. Emphasis is given to the link between the Weyl tensor, the shear tensor, the anisotropy of the pressure and the density inhomogeneity. In particular we provide the general, necessary and sufficient, condition for the vanishing of the spatial gradients of energy density, which in turn suggests a possible definition of a gravitational arrow…
If a magnetic field is frozen into a plasma that undergoes spherical compression then the magnetic field B varies with the plasma density ρaccording to B \propto ρ^{2/3}. In the gravitational collapse of cosmological density perturbations, however, quasi-spherical evolution is very unlikely. In anisotropic collapses the magnetic field can be a much steeper function of gas density than in the isotropic case. We investigate the distribution of amplifications in realistic gravitational collapses from Gaussian initial fluctuations using the Zel'dovich approximation. Representing our results using …
We study the effects of anisotropic thermal conduction on magnetized spherical accretion flows using global axisymmetric MHD simulations. In low collisionality plasmas, the Bondi spherical accretion solution is unstable to the magnetothermal instability (MTI). The MTI grows rapidly at large radii where the inflow is subsonic. For a weak initial field, the MTI saturates by creating a primarily radial magnetic field, i.e., by aligning the field lines with the background temperature gradient. The saturation is quasilinear in the sense that the magnetic field is amplified by a factor of $\sim 10-3…
We performe N-body simulations of encounters between spherical systems surrounded by a spherical halo. Following a preceding paper with a similar aim, the initial systems include a spherical Jaffe model for the luminous matter and a Hernquist model for the halo. The merger remnants from this sample are mainly slowly rotating, prolate spheroids with a radially anisotropic velocity distribution. The results are compared with real-life ellipticals and with the models without halo in paper I. We argue that elliptical galaxies with evidence of dark matter could be formed in the field via a merger o…
We identify satellites of isolated galaxies in SDSS and examine their angular distribution. Using mock catalogues generated from cosmological N-body simulations, we demonstrate that the selection criteria used to select isolated galaxies and their satellites must be very strict in order to correctly identify systems in which the primary galaxy dominates its environment. The criteria used in many previous studies instead select predominantly group members. We refine a set of selection criteria for which the group contamination is estimated to be less than 7% and present a catalogue of the resul…
We have developed an analytical model to describe the evolution of anisotropic galactic outflows. With it, we investigate the impact of varying opening angle on galaxy formation and the evolution of the IGM. We have implemented this model in a Monte Carlo algorithm to simulate galaxy formation and outflows in a cosmological context. Using this algorithm, we have simulated the evolution of a comoving volume of size [12h^(-1)Mpc]^3 in the LCDM universe. Starting from a Gaussian density field at redshift z=24, we follow the formation of ~20,000 galaxies, and simulate the galactic outflows produce…
We present a method to investigate the radial stability of a spherical anisotropic system that hosts a central supermassive black hole (SBH). Such systems have never been tested before for stability, although high anisotropies have been considered in the dynamical models that were used to estimate the masses of the central putative supermassive black holes. A family of analytical anisotropic spherical Hernquist models with and without a black hole were investigated by means of N-body simulations. A clear trend emerges that the supermassive black hole has a significant effect on the overall sta…
We study a phenomenological model for the continuum emission of Seyfert galaxies. In this quasi-spherical accretion scenario, the central X-ray source is constituted by a hot spherical plasma region surrounded by spherically distributed cold dense clouds. The cold material is radiatively coupled with the hot thermal plasma. Assuming energy balance, we compute the hard X-ray spectral slope Gamma and reflection amplitude R. This simple model enables to reproduce both the range of observed hard X-ray spectral slopes, and reflection amplitude R. It also predicts a correlation between R and Gamma w…
We develop a self-consistent model of Seyfert galaxies continuum emission. High energy emission is produced by Inverse Compton process on soft photons emitted as thermal radiation by the accretion disk. Thermal emission is, at turn, entirely due to reprocessing of the impinging high energy photons. The high energy source is assumed to be an optically thin plasma of highly relativistic leptons ($e^+-e^-$), at rest at a given height on the disk axis. This warm source could be the result of a strong schock between an abortive jet coming from the disk and the interstellar medium. Such a geometry i…
It has long been realized that dark matter halos formed in cosmological N-body simulations are characterized by density profiles rho(r) that, when suitably scaled, have similar shapes. Additionally, combining the density and velocity dispersion profiles sigma(r), each of which have decidedly nonpower-law shapes, leads to quantity rho/(sigma^3) that is a power-law in radius over 3 orders of magnitude in radius. Halos' velocity anisotropy profiles beta(r) vary from isotropic near the centers of halos to quite radially anisotropic near the virial radius. Finally, there appears to be a nearly line…
The distribution of satellite galaxies relative to isolated host galaxies in the Sloan Digital Sky Survey (SDSS) is investigated. Host-satellite systems are selected using three different methods, yielding samples of ~3300, ~1600, and \~950 satellites. In the plane of the sky, the distributions of all three samples show highly significant deviations from circular symmetry (> 99.99%, > 99.99%, and 99.79% confidence levels, respectively), and the degree of anisotropy is a strong function of the projected radius, r_p, at which the satellites are found. For r_p < 100 kpc, the SDSS satellites are a…
We report here on a survey of N-body simulations of encounters between spherical galaxies. Initial systems are isotropic Jaffe models. Different sets of mass ratios, impact parameters and orbital energies are studied. Both merger remnants and systems perturbed after a non-merging encounter are analysed and compared to real-life elliptical galaxies. The properties of merger remnants show a large variety. Merger remnants resulting from head-on encounters are mainly non-rotating prolate spheroids. Merger remnants from models with angular momentum different from zero are triaxial or mildly oblate …
We calculate the reflection component predicted by the anisotropic illumination model of Henri & Petrucci 1997. This component appears to be more important than for isotropic models. The overall X/gamma spectrum is found to be strongly angle-dependent. When the accretion disc is seen with a nearly edge-on orientation the reflection hump is weak, while a face-on viewing angle leads to a proeminent reflection hump with an equivalent reflection coefficient R close to 50. Such reflection dominated Seyfert 1s galaxies are not observed. By fitting observed X/gamma spectra, we derive inclination angl…
We present the results of spectropolarimetry of a sample of 7 powerful radio galaxies and 2 quasars with $0.07<z<0.35$ obtained to detect possible anisotropies in the [OIII] line emission, which could explain the higher [OIII] luminosity of quasars than that of radio galaxies within the framework of the Unified Model of radio-loud AGN. We detect polarized [OIII] in 4 radio galaxies, consistent with the possibility that a considerable fraction ($\sim 20%$) of the observed [OIII] emission is scattered in a similar way to the hidden nuclear continuum. However, small but detectable rotation betwee…
We consider the sample of weakly active galaxies situated in 'Local Universe' collected in the paper of Pellegrini (2005) with inferred accretion efficiencies from $10^{-2}$ to $10^{-7}$. We apply a model of spherically symmetrical Bondi accretion for given parameters ($M_{BH}$,$T_{\infty}$,$ρ_{\infty}$,) taken from observation. We calculate spectra emitted by the gas accreting onto its central objects using Monte Carlo method including synchrotron and bremsstrahlung photons as seed photons. We compare our results with observed nuclear X-ray luminosities $L_{X,nuc}$ (0.3-10 keV) of the sample.…
The problem of the anisotropic Inverse Compton scattering between a monochromatic photon beam and relativistic electrons is revisited and formally solved without approximations. Solutions are given for the single scattering with an electron beam and with a population of electrons isotropically distributed, under the assumption that the energy distribution of the relativistic particles follows a simple power law as it is the case in many astrophysical applications. Both the Thomson approximation and the Klein-Nishina regime are considered for the scattering of an unpolarized photon beam. The eq…
We investigate dynamical response on size and velocity dispersion to mass loss by supernovae in formation of two-component spherical galaxies composed of baryon and dark matter. Three-dimensional deprojected de Vaucouleurs-like and exponential-like profiles for baryon, embedded in truncated singular isothermal and homogeneous profiles for dark matter, are considered. As a more realistic case, we also consider a dark matter profile proposed by Navarro, Frenk & White. For simplicity we assume that dark matter distribution is not affected by mass loss and that the change of baryonic matter distri…
The spherical gravitational collapse and virialization of arbitrary density fluctuations in an expanding universe is studied. In the context of the standard cosmological model and the peak $ansatz$, disk galaxies are supposed to be the product of "extended" gravitational collapses of regions surrounding local-maxima of the density fluctuation field. The substructure over the main profile (merging) is considered as a second-order phenomenon. The range and distribution of possible mass growth histories or accretion regimes for a given present-day mass are estimated and used as the initial condit…
We present a simple and efficient anisotropic generalization of the semi-isotropic (two-integral) axisymmetric Jeans formalism which is used to model the stellar kinematics of galaxies. The following is assumed: (i) a constant mass-to-light ratio M/L and (ii) a velocity ellipsoid that is aligned with cylindrical coordinates (R,z) and characterized by the classic anisotropy parameter beta_z=1-sigma_z^2/sigma_R^2. Our simple models are fit to SAURON integral-field observations of the stellar kinematics for a set of fast-rotator early-type galaxies. With only two free parameters (beta_z and the i…
By considering that the distribution of measured light along any galactocentric radius of an elliptical galaxy can be well represented by a R^{1/n} Sersic law, we propose in this paper a ``discrete ordenate'' method, which, for any value of n, allows an explicit expression for the luminous density, rho(r), to be found that can be numerically evaluated to any required precision. Once we have this semi-analytical expression for the spatial density, rho(r), the mass distribution, M(r), the potential, phi(r), and the velocity dispersions, sigma_s^2(r), in the space and in the observational plane, …
We present cross sections and reaction rates for merging to occur during encounters of equal-mass spherical galaxies. As an application, we determine the rate of galaxy merging in clusters of galaxies. We present results for two types of Plummer models (a full and a truncated one), two King models and the Hernquist model. Cross sections are determined on the basis of a large number ($\sim 500$) of simulations of galaxy encounters, using the 10-Gigaflops GRAPE 3A special-purpose computer. We characterize the overall merger rate of galaxies in a galaxy cluster by a single number, derived from ou…
We present a new model of accretion disk where the disk luminosity is entirely due to the reprocessing of hard radiation impinging on the disk. The hard radiation itself is emitted by a hot point source above the disk, that could be physically realized by a strong shock terminating an aborted jet. This hot source contains ultra-relativistic leptons scattering the disk soft photons by Inverse Compton (IC) process. Using simple formula to describe the IC process in an anisotropic photon field, we derive a self-consistent solution in the Newtonian geometry, where the angular distribution of soft …
We present new analytical distribution functions for anisotropic spherical galaxies. They have the density profiles of the gamma-models, which allow a wide range of central density slopes, and are widely used to fit elliptical galaxies and the bulges of spiral galaxies. Most of our models belong to two two-parameter families. One of these parameters is the slope gamma of the central density cusp. The other allows a wide range of varying radial and tangential anisotropies, at either small or large radii. We give analytical formulas for their distribution functions, velocity dispersions, and the…
We investigate the locations of the satellites of relatively isolated host galaxies in the Sloan Digital Sky Survey and the Millennium Run simulation. Provided we use two distinct prescriptions to embed luminous galaxies within the simulated dark matter halos (ellipticals share the shapes of their halos, while disks have angular momenta that are aligned with the net angular momenta of their halos), we find a fair agreement between observation and theory. Averaged over scales r_p \le 500 kpc, the satellites of red, high-mass hosts with low star formation rates are found preferentially near the …
We study the large-scale anisotropic two-point correlation function using 46,760 luminous red galaxies at redshifts 0.16 -- 0.47 from the Sloan Digital Sky Survey. We measure the correlation function as a function of separations parallel and perpendicular to the line-of-sight in order to take account of anisotropy of the large-scale structure in redshift space. We find a slight signal of baryonic features in the anisotropic correlation function, i.e., a ``baryon ridge'' which corresponds to a baryon acoustic peak in the spherically averaged correlation function which has already been reported …
We present a family of spherical models for elliptical galaxies and bulges consisting of a stellar component and a central black hole. All models in this family share the same stellar density profile, which has a steep central cusp. The gravitational potential of each models is a linear combination of the potential generated selfconsistently by the stars and the potential of a central black hole. The relative importance of these two contributions is a free parameter in the models. Assuming an isotropic dynamical structure, almost all kinematical properties of these models can be calculated ana…
We study a spherically symmetric fluctuation of scalar dark matter in the cosmos and show that it could be the dark matter in galaxies, provided that the scalar field has an exponential potential whose overall sign is negative and whose exponent is constrained observationally by the rotation velocities of galaxies. The local space-time of the fluctuation contains a three dimensional space-like hypersurface with surplus of angle.
We investigate the stability of self-gravitating spherically symmetric anisotropic spheres under radial perturbations. We consider both the Newtonian and the full general-relativistic perturbation treatment. In the general-relativistic case, we extend the variational formalism for spheres with isotropic pressure developed by Chandrasekhar. We find that, in general, when the tangential pressure is greater than the radial pressure, the stability of the anisotropic sphere is enhanced when compared to isotropic configurations. In particular, anisotropic spheres are found to be stable for smaller v…
