Gravitational Instability of the Isothermal Sphere

Abstract

A generic problem related to the establishment of thermodynamic equilibrium can be stated as follows: Consider a large number (N) of particles, interacting through a two-body potential U(x-y) and confined in a region of volume V. We start off the particles with a generic set of initial positions and velocities and let them interact (“collide”) with each other as well as with the boundary of the volume V. We are interested in the very late time behaviour of such a system. In particular, we are often interested in the kind of equilibrium configuration to which such a system might evolve into at sufficiently late times.