Secondary Infall and the Pseudo-Phase-Space Density Profiles of Cold Dark Matter Halos

TL;DR

This study uses N-body simulations to analyze the phase-space density profiles of cold dark matter halos, revealing a power-law behavior in the inner regions and deviations near the virial radius consistent with secondary infall models.

Contribution

It extends previous work by examining local and ellipsoidal radius-based phase-space density profiles, showing their agreement with secondary infall predictions and highlighting limitations of power-law assumptions.

Findings

Q profiles follow a power law near the center

Deviations from power law occur near the virial radius

Results agree with Bertschinger's secondary-infall model

Abstract

We use N-body simulations to investigate the radial dependence of the density and velocity dispersion in cold dark matter (CDM) halos. In particular, we explore how closely Q rho/sigma^3, a surrogate measure of the phase-space density, follows a power-law in radius. Our study extends earlier work by considering, in addition to spherically-averaged profiles, local Q-estimates for individual particles, Q_i; profiles based on the ellipsoidal radius dictated by the triaxial structure of the halo, Q_i(r'); and by carefully removing substructures in order to focus on the profile of the smooth halo, Q^s. The resulting Q_i^s(r') profiles follow closely a power law near the center, but show a clear upturn from this trend near the virial radius, r_{200}. The location and magnitude of the deviations are in excellent agreement with the predictions from Bertschinger's spherical secondary-infall similarity solution. In this model, Q \propto r^{-1.875} in the inner, virialized regions, but departures from a power-law occur near r_{200} because of the proximity of this radius to the location of the first shell crossing - the shock radius in the case of a collisional fluid. Particles there have not yet fully virialized, and so Q departs from the inner power-law profile. Our results imply that the power-law nature of $Q$ profiles only applies to the inner regions and cannot be used to predict accurately the structure of CDM halos beyond their characteristic scale radius.