Phase-Space Density Profiles in Scale-Free Cosmologies
  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. 
Steffen R. Knollmann, Alexander Knebe, Yehuda Hoffman