Statistical mechanics of collisionless orbits. I. Origin of central cusps in dark-matter halos

TL;DR

This paper develops a new statistical mechanical theory for collisionless self-gravitating systems, explaining the origin of central density cusps in dark-matter halos through a modified energy distribution model called DARKexp.

Contribution

It introduces a novel approach by computing microstates in energy space and properly handling low occupation numbers, leading to a predictive model for dark-matter halo density profiles.

Findings

Predicts a differential energy distribution N(E) ~ [exp(phi_0 - E) - 1]

Shows that systems have central density cusps rho(r) ~ r^-1

Provides a statistical mechanical basis for simulated dark-matter halo structures

Abstract

We present an equilibrium statistical mechanical theory of collisionless self-gravitational systems with isotropic velocity distributions. Compared to existing standard theories, we introduce two changes: (1) the number of possible microstates is computed in energy (orbit) space rather than phase space and (2) low occupation numbers are treated more appropriately than using Stirling's approximation. Combined, the two modifications predict that the relaxed parts of collisionless self-gravitating systems, such as dark-matter halos, have a differential energy distribution N(E) ~ [exp(phi_0 - E) - 1], dubbed "DARKexp". Such systems have central power-law density cusps rho(r) ~ r^-1, which suggests a statistical mechanical origin of cusps in simulated dark-matter halos.