PNNL

Abstract

The halo-mediated inverse mass cascade is a key feature of the intermediate statistically steady state for self-gravitating collisionless flow (SG-CFD). How inverse mass cascade maximizes the system entropy and develops the associated limiting distributions while system evolves toward the final equilibrium are fundamental questions to answer. We present a new statistical mechanics theory concerning the limiting distributions of particle velocity, speed, and energy for self-gravitating systems involving a power-law long-range interaction with arbitrary exponent n. For systems with long-range interactions, sub-systems (halos and halo groups) are required to spontaneously form to maximize the system entropy. While particle velocities in each sub-system is still Gaussian, the limiting distribution of entire system can be non-Gaussian. The virial equilibrium is assumed to be valid for local mechanical equilibrium. The limiting particle velocity, speed, and energy distributions are analytically derived by applying a maximum entropy principle for global system. Halo mass function is not required in this formulation and can be treated as a direct result of entropy maximization. The predicted particle velocity distribution involves a shape parameter a that is dependent on the exponent n.