Distribution of Stochastic Forces in Gratationally Clustered System of Galaxies

We study the distribution of stochastic forces in gravitational clustered systems through numerical simulations. Data are taken from N-body simulation in an expanding universe. Before clustering, distribution of random forces is represented as a Holtsmark distribution, and nearest neighbor distribution is also shown as a comparison. The analytical and numerical results are in good agreement. When clustering becomes strong, the simulation results showed that the contribution of stochastic forces acting on each galaxy is almost entirely due to the gravitational attraction of its nearest neighbor galaxy. We conclude that nearest neighbor galactic encounters may play the main role in the dynamics of galaxy clustering. If so, this may have two implications. First, in a gravitationally clustered system such as clustered of galaxies, each encounter can be treated as a two-body encounter representing the perturber galaxy and its nearest neighbor galaxy. Second, the using of large softening parameter in the collisionless N-body simulation method may not be well suited to study the dynamics of galaxy clustering, in which the gravitational attraction of the nearest neighbor galaxies play the main role, because the forces from the nearest neighbors may be neglected.