Is the Radial Profile of the Phase-Space Density of Dark Matter Halos a Power-Law?

TL;DR

This paper uses the Jeans equation to analyze the radial profiles of dark matter halos, showing that the power-law behavior of rho/sigma3 is only valid over limited scales and cannot hold at all radii, challenging previous assumptions.

Contribution

It demonstrates that the pseudo-phase-space density profile is only approximately a power law within current simulation resolutions and cannot be universally true at all scales.

Findings

rho/sigma3 is a power law only over limited radii

Deviations from power-law occur below current simulation resolution

Enforcing specific density-velocity relations does not produce Einasto profiles

Abstract

The latest cosmological N-body simulations find two intriguing properties for dark matter haloes: (1) their radial density profile, rho, is better fit by a form that flattens to a constant at the halo center (the Einasto profile) than the widely-used NFW form; (2) the radial profile of the pseudo-phase-space density, rho/sigma3, on the other hand, continues to be well fit by a power law, as seen in earlier lower-resolution simulations. In this paper we use the Jeans equation to argue that (1) and (2) cannot both be true at all radii. We examine the implied radial dependence of rho/sigma3 over 12 orders of magnitude in radius by solving the Jeans equation for a broad range of input rho and velocity anisotropy beta. Independent of beta, we find that rho/sigma3 is approximately a power law only over the limited range of halo radius resolvable by current simulations (down to ~0.1% of the virial radius), and rho/sigma3 deviates significantly from a power-law below this scale for both the Einasto and NFW rho. The same conclusion also applies to a more general density-velocity relation rho/sigma_D^epsilon. Conversely, when we enforce rho/sigma^3 r^{-eta} as an input, none of the physically allowed rho (occurring for the narrow range 1.8<eta<1.9444) follows the Einasto form. We expect the next generation simulations with better spatial resolution to settle the debate: either the Einasto profile will continue to hold and rho/sigma3 will deviate from a power law, or rho/sigma3 will continue as a power law and rho will deviate from its current parameterizations.