Power-laws and Non-Power-laws in Dark Matter Halos

Abstract

Simulated dark matter profiles are often modelled as a `NFW' density profile rather than a single power law. Recently, attention has turned to the rather rigorous power-law behaviour exhibited by the `pseudo phase-space density' of the dark matter halo, which is defined dimensionally in terms of the local density and velocity dispersion of the dark matter particles. The non-power-law behaviour of the density profile is generally taken to exclude simple scale-free, in-fall models; however the power-law behaviour of the `pseudo-density' is a counter indication. We argue in this paper that both behaviours may be at least qualitatively understood in terms of a dynamically evolving self-similarity, rather than the form for self-similar infall that is fixed by cosmological initial conditions. The evolution is likely due to collective relaxation such as that provided by the radial-orbit instability on large scales. We deduce, from a distribution function given by first order coarse-graining, both the NFW-type density profile and the power-law pseudo-density profile. The results are not greatly sensitive to variation about 3 in the power of the velocity dispersion used in the definition of the phase space pseudo-density. We suggest that the power 2 may create the more physical quantity, whose deviations from a power-law are a diagnostic of incomplete relaxation.

arXiv comment31 pages, 4 figures

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• Dark Matter Accretion into Supermassive Black Holes
• Black Holes and Galactic Density Cusps : From Black Hole to Bulge
• Black holes and Galactic density cusps -- I. Radial orbit cusps and bulges
• Nature and Nurture in Dark Matter Halos
• Power law pseudo phase-space density profiles of dark matter halos: fluke of physics?
• Extremal noncommutative black holes as dark matter furnaces