Phase-Space Density Profiles in Scale-Free Cosmologies

Abstract

We use a set of high-resolution simulations of scale-free Einstein-de Sitter cosmologies to investigate the logarithmic slope of the phase-space density profile $Q(r)=\rho (r)/{\sigma }^3(r)$ of dark matter (DM) haloes. The initial conditions for the simulations are determined by a power law power spectrum of the form $P(k)\propto k^n$. We compute the Q(r) profiles using the radial, tangential and full velocity dispersion, and the velocity anisotropy parameter, $\beta (r)$. We express Q(r) as a single power-law $Q(r)\propto r^{\alpha }$ and derive a median slope $\alpha$ in each simulation and for each definition of Q. Our main findings are: 1. The various Q(r) profiles follow a power law to a good approximation. 2. The slopes depend on the concentration parameter c of the DM haloes, where for $c\gtrsim 10$ the slopes steepen with rising concentration and for $c\lesssim 10$ the trend flattens and even turns around. 3. The asymptotic value of $\beta$ as $r\to R_{\mathrm{vir}}$ increases with the value of c. 4. In accordance with Zait et al. 2007 ${\alpha }_{\mathrm{rad}}$ becomes more negative as the asymptotic value of $\beta$ at the virial radius increases. 5. This introduces a weak dependence of the $Q(r)$ slopes on the slope of the power spectrum.

7 pages, 4 figures. Accepted for publication in MNRAS

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• Might we eventually understand the origin of the dark matter velocity anisotropy?
• An attractor for dark matter structures
• Evolution of Dark Matter Phase-Space Density Distributions in Equal-Mass Halo Mergers
• On the Apparent Power Law in CDM Halo Pseudo Phase Space Density Profiles
• Power law pseudo phase-space density profiles of dark matter halos: fluke of physics?
• Structural and dynamical modeling of WINGS clusters. III. The pseudo phase-space density profile