Equipartition and Mass Segregation in a One-Dimensional Self-Gravitating System

Abstract

The one-dimensional self-gravitating system (OGS) has been used as a simple model to study relaxation in N-body gravitational systems for several decades. In the OGS the gravitational field is uniform, and therefore simple algebraic equations which can be easily and rapidly solved on a computer govern the motion of the particles. Current computer technology allows for very long time dynamical simulations of reasonably large systems with little loss of numerical accuracy. Because the phase space of the OGS is compact, these systems do not suffer from some of the difficulties encountered in three dimensions (e.g., singularities, evaporation). However, a consequence of this is a somewhat tenuous connection with real galactic systems. Computer simulations of the OGS show that they tend to progress through various quasiequilibrium states as they evolve from arbitrary initial conditions. These quasiequilibrium states often last for very long times, and are approximately stationary. Fluctuations caused by changes in the mean field potential within the initial nonstationary distribution rapidly decay and the system reaches a state of microscopic relaxation, distinguished from the longer macroscopic time scale for relaxation to thermal equilibrium. Early predictions and dynamical simulations put thermal equilibrium on a time scale proportional to N 2 tc, where N is the number of particles and tc is the typical time for a particle to traverse the system [1,2]. Later work tended to refute these earlier claims by showing that the system was still far from equilibrium after 2N 2 tc [3,4].