Orbital deflections in N-body systems

Abstract

Two types of orbital deflection in N-body systems with a softened field - two-body relaxation and orbital divergence - are discussed. Two-body relaxation is studied using tree code N-body simulations of King models with N ranging from 100 to 400,000, and a softening length ranging from 0.0002 to 0.075 in units of the half-mass radius. The relaxation time depends linearly on N for a fixed softening length. The energy evolution of particles is a pure random walk or diffusion process as shown by the constant rate of change of the squared energy fluctuation, and the particles' energy power spectrum follows a power law with a spectral index of -2. The diffusion time is nearly equal to the relaxation time.