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

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

2010-10-01

arxiv.org/abs/1010.0265v1

Astrophys.J. 722 (2010) 851-855

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

6 pages, 2 figures

Scientific paper

10.1088/0004-637X/722/1/851

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.

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