Relaxation of spherical systems with long-range interactions: a numerical investigation

TL;DR

This paper investigates how the relaxation process in spherical systems with long-range interactions varies with the force law exponent, revealing that smaller exponents lead to longer virialization and phase-mixing times, with implications for alternative gravity theories.

Contribution

It introduces a numerical model for spherical shells with 1/r^alpha interactions, exploring how relaxation times depend on the force law exponent, extending understanding beyond classical Newtonian gravity.

Findings

Relaxation times increase as the force law exponent alpha decreases.

Virialization and phase-mixing times are dependent on alpha.

Longer relaxation times are observed for smaller alpha, similar to modified gravity scenarios.

Abstract

The process of relaxation of a system of particles interacting with long-range forces is relevant to many areas of Physics. For obvious reasons, in Stellar Dynamics much attention has been paid to the case of 1/r^2 force law. However, recently the interest in alternative gravities emerged, and significant differences with respect to Newtonian gravity have been found in relaxation phenomena. Here we begin to explore this matter further, by using a numerical model of spherical shells interacting with an 1/r^alpha force law obeying the superposition principle. We find that the virialization and phase-mixing times depend on the exponent alpha, with small values of alpha corresponding to longer relaxation times, similarly to what happens when comparing for N-body simulations in classical gravity and in Modified Newtonian Dynamics.