The velocity anisotropy—density slope relation
Abstract
One can solve the Jeans equation analytically for equilibrated dark matter structures once two pieces of input from numerical simulations have been obtained. These inputs are (1) a connection between phase-space density and radius, and (2) a connection between velocity anisotropy and density slope, the α β relation. The first (phase-space density versus radius) has already been analysed through several different simulations, however the second (α β relation) has not been quantified yet. We perform a large set of numerical experiments in order to quantify the slope and zero-point of the α β relation. We find a strong indication that the relation is indeed an attractor. When combined with the assumption of phase-space being a power-law in radius, this allows us to conclude that equilibrated dark matter structures indeed have zero central velocity anisotropy β0 ap 0, a central density slope of α0 ap -0.8, and outer anisotropy of \beta_\infty \approx 0.5 .
- Publication:
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Journal of Cosmology and Astroparticle Physics
- Pub Date:
- May 2006
- DOI:
- 10.1088/1475-7516/2006/05/014
- arXiv:
- arXiv:astro-ph/0510656
- Bibcode:
- 2006JCAP...05..014H
- Keywords:
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- Astrophysics
- E-Print:
- 15 pages, 7 figures