Sharif Digital Repository

A set of bi-orthogonal potential-density basis functions is introduced to model the density and its associated gravitational field of three dimensional stellar systems. Radial components of our basis functions are weighted integral forms of spherical Bessel functions. We discuss on the properties of our basis functions and demonstrate their shapes for the latitudinal Fourier number l = 2. © 2008 Copyright International Astronomical Union 2008  

As an alternative to dark matter models, Modified Gravity (MOG) theory is a covariant modification of Einstein gravity. The theory introduces two additional scalar fields and one vector field. The aim is to explain the dynamics of astronomical systems based only on their baryonic matter. The effect of the vector field in the theory resembles a Lorentz force where each particle has a charge proportional to its inertial mass. The weak field approximation of MOG is derived by perturbing the metric and the fields around Minkowski space-time. We obtain an effective gravitational potential which yields the Newtonian attractive force plus a repulsive Yukawa force. This potential, in addition to the... 

We apply the weak field approximation limit of the covariant scalar-tensor-vector gravity theory, so-called MOdified gravity (MOG), to the dynamics of clusters of galaxies by using only baryonic matter. The MOG effective gravitational potential in the weak field approximation is composed of an attractive Newtonian term and a repulsive Yukawa term with two parameters α and μ. The numerical values of these parameters have been obtained by fitting the predicted rotation curves of galaxies to observational data, yielding the best-fitting result: α =8.89±0.34 and μ = 0.042 ± 0.004 kpc-1. We extend the observational test of this theory to clusters of galaxies, using data for the ionized gas and... 

We study the linear perturbations of collisionless near-Keplerian discs. Such systems are models for debris discs around stars and the stellar discs surrounding supermassive black holes at the centres of galaxies. Using a finite-element method, we solve the linearized collisionless Boltzmann equation and Poisson's equation for a wide range of disc masses and rms orbital eccentricities to obtain the eigenfrequencies and shapes of normal modes. We find that these discs can support large-scale 'slow' modes, in which the frequency is proportional to the disc mass. Slow modes are present for arbitrarily small disc mass so long as the self-gravity of the disc is the dominant source of apsidal... 

We describe a new finite element method (FEM) to construct continuous equilibrium distribution functions (DFs) of stellar systems. The method is a generalization of Schwarzschild's orbit superposition method from the space of discrete functions to continuous ones. In contrast to Schwarzschild's method, FEM produces a continuous DF and satisfies the intra-element continuity and Jeans equations. The method employs two finite element meshes, one in configuration space and one in action space. The DF is represented by its values at the nodes of the action-space mesh and by interpolating functions inside the elements. The Galerkin projection of all equations that involve the DF leads to a linear... 

I formulate a general finite element method (FEM) for self-gravitating stellar systems. I split the configuration space to finite elements, and express the potential and density functions over each element in terms of their nodal values and suitable interpolating functions. General expressions are then introduced for the Hamiltonian and phase-space distribution functions of the stars that visit a given element. Using the weighted residual form of Poisson's equation, I derive the Galerkin projection of the perturbed collisionless Boltzmann equation, and assemble the global evolutionary equations of nodal distribution functions. The FEM is highly adaptable to all kinds of potential and density... 

We use the weighted integral form of spherical Bessel functions and introduce a new analytical set of complete and biorthogonal potential-density basis functions. The potential and density functions of the new set have finite central values and they fall off, respectively, similar to r-(1+ l) and r-(4+ l) at large radii, where l is the latitudinal quantum number of spherical harmonics. The lowest order term associated with l = 0 is the perfect sphere of de Zeeuw. Our basis functions are intrinsically suitable for the modelling of three-dimensional, soft-centred stellar systems and they complement the basis sets of Clutton-Brock, Hernquist & Ostriker and Zhao. We test the performance of our... 

I utilize the Petrov-Galerkin formulation and develop a new method for solving the unsteady collisionless Boltzmann equation in both the linear and nonlinear regimes. In the first-order approximation, the method reduces to a linear eigen-value problem which is solved using standard numerical methods. I apply the method to the dynamics of a model stellar disk which is embedded in the field of a soft-centered logarithmic potential. The outcome is the full spectrum of eigen-frequencies and their conjugate normal modes for prescribed azimuthal wavenumbers. The results show that the fundamental bar mode is isolated in the frequency space, while spiral modes belong to discrete families that... 

In this article, we have investigated the possibility to distinguish between different galactic models through microlensing parallax studies. We show that a systematic search for parallax effects can be done using the currently running alert systems and complementary photometric telescopes, to distinguish between different lens distance distributions. We have considered two galactic dark compact object distributions, with total optical depths corresponding to the EROS current upper limits. These models correspond to two extreme hypotheses on a three component galactic structure made of a thin disk, a thick disk, and a spherically symmetric halo. Our study shows that for sub-solar mass... 

We present the study of a large sample of early-type dwarf galaxies in the Coma cluster observed with DEIMOS on the Keck II to determine their internal velocity dispersion. We focus on a subsample of 41 member dwarf elliptical galaxies for which the velocity dispersion can be reliably measured, 26 of which were studied for the first time. The magnitude range of our sample is -21 < M R < -15mag. This paper (Paper I) focuses on the measurement of the velocity dispersion and their error estimates. The measurements were performed using penalized pixel fitting (ppxf) and using the calcium triplet absorption lines. We use Monte Carlo bootstrapping to study various sources of uncertainty in our... 

We present a study of the Fundamental Plane (FP) for a sample of 71 dwarf galaxies in the core of the Coma cluster in the magnitude range -21 < M I < -15. Taking advantage of the high-resolution DEIMOS spectrograph on Keck II for measuring the internal velocity dispersion of galaxies and high-resolution imaging of the Hubble Space Telescope (HST)/ACS, which allows an accurate surface brightness modelling, we extend the FP of galaxies to luminosities of ~1 mag fainter than all the previous studies of the FP in the Coma cluster. We find that the scatter about the FP depends on the faint-end luminosity cut-off, such that the scatter increases for fainter galaxies. The residual from the FP... 

Aims. EROS (Expérience de Recherche d'Objets Sombres) has searched for microlensing toward four directions in the Galactic plane away from the Galactic center. The interpretation of the catalog optical depth is complicated by the spread of the source distance distribution. We compare the EROS microlensing observations with Galactic models (including the Besançon model), tuned to fit the EROS source catalogs, and take into account all observational data such as the microlensing optical depth, the Einstein crossing durations, and the color and magnitude distributions of the catalogued stars. Methods. We simulated EROS-like source catalogs using the HIgh-Precision PARallax COllecting Satellite...