Density Profiles of Collisionless Equilibria. I. Spherical Isotropic Systems

Details Density Profiles of Collisionless Equilibria. I. Spherical Isotropic Systems Density Profiles of Collisionless Equilibria. I. Spherical Isotropic Systems

2005-10-11

arxiv.org/abs/astro-ph/0510332v2

Astrophys.J.643:797-803,2006

Astronomy and Astrophysics

Astrophysics

21 pages, 8 fig. (2 new), accepted by ApJ, a PDF version with full resolution figures can be found at http://www.astro.umn.e

Scientific paper

10.1086/503025

We investigate the connection between collisionless equilibria and the phase-space relation between density $\rho$ and velocity dispersion $\sigma$ found in simulations of dark matter halo formation, $F=\psd \propto r^{-\alpha}$. Understanding this relation will shed light on the physics relevant to collisionless collapse and on the subsequent structures formed. We show that empirical density profiles that provide good fits to N-body halos also happen to have nearly scale-free \psd distributions when in equilibrium. We have also done a preliminary investigation of variables other than $r$ that may match or supercede the correlation with $F$. In the same vein, we show that $\rho/\sigma^m$, where $m=3$ is the most appropriate combination to use in discussions of the power-law relationship. Since the mechanical equilibrium condition that characterizes the final systems does not by itself lead to power-law $F$ distributions, our findings prompt us to posit that dynamical collapse processes (such as violent relaxation) are responsible for the radial power-law nature of the \psd distributions of virialized systems.

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