On gravitating stellar systems I. formulation using distribution function method

Abstract

An interesting work on self-gravitating gaseous disks has con- cerned the behaviour of the precursor of massive central dark object that might be the energy source existing at centers of galaxies and powering quasars. With this view, we present a model of self gravitating gas flattened in a disk. We make the following assumptions: (i) the interaction force between individual pairs of particles is negligibly small, (ii) the distribution function f in phase space satisfies collision-free Boltzmann equation and (iii) the system is conser- vative. We set up a third order linear differential equation satisfied by the disk for axisymmetric case. We obtain a particular solution for the disk in steady state. We derive the expression for gravitational potential W and surface mass density sigma of the disk. We also calculate the velocity profiles