Statistical mechanics of collisionless orbits. III. Comparison with N-body simulations

TL;DR

This paper compares the DARKexp energy distribution model, derived from statistical mechanics, with N-body simulation results of dark matter halos, finding a good match and supporting the maximum entropy principle in such systems.

Contribution

It demonstrates that DARKexp models accurately reproduce N-body simulation energy distributions, suggesting maximum entropy principles explain dark matter halo equilibria.

Findings

DARKexp N(E) with pprox 4-5 fits simulation data well.

Anisotropic velocity distributions do not significantly alter density and energy profiles.

Statistical mechanics can potentially explain the final states of dark matter halos.

Abstract

We compare the DARKexp differential energy distribution, N(E) \propto \exp(\phi_0-E)-1, obtained from statistical mechanical considerations, to the results of N-body simulations of dark matter halos. We first demonstrate that if DARKexp halos had anisotropic velocity distributions similar to those of N-body simulated halos, their density and energy distributions could not be distinguished from those of isotropic DARKexp halos. We next carry out the comparison in two ways, using (1) the actual energy distribution extracted from simulations, and (2) N-body fitting formula for the density distribution as well as N(E) computed from the density using the isotropic Eddington formula. Both the methods independently agree that DARKexp N(E) with \phi_0\approx 4-5 is an excellent match to N-body N(E). Our results suggest (but do not prove) that statistical mechanical principles of maximum entropy can be used to explain the equilibrated final product of N-body simulations.