Statistical mechanics of unbound two-dimensional self-gravitating systems

Abstract

We study, using both theory and molecular dynamics simulations, the\nrelaxation dynamics of a microcanonical two dimensional self-gravitating\nsystem. After a sufficiently large time, a gravitational cluster of N particles\nrelaxes to the Maxwell-Boltzmann distribution. The time to reach the\nthermodynamic equilibrium, however, scales with the number of particles. In the\nthermodynamic limit, $N\\to\\infty$ at fixed total mass, equilibrium state is\nnever reached and the system becomes trapped in a non-ergodic stationary state.\nAn analytical theory is presented which allows us to quantitatively described\nthis final stationary state, without any adjustable parameters.\n