Distribution of Forces in Gravitationally Clustered System

We have studied the distribution of forces in gravitational systems through numerical experiments. Data were taken from an N-body simulation in an expanding universe. Before clustering, the distribution of random forces was represented as a Holtsmark distribution; the nearest-neighbor distribution is also shown as a comparison. The analytical and simulation distributions are in good agreement. When clustering becomes strong, the simulation result showed that the contribution of the forces acting on each galaxy, which is generated from all other galaxies, is almost entirely due to the gravitational attraction of its nearest neighbor. This implies that nearest-neighbor galactic encounters may play the main role in the dynamics of galaxy clustering.