Velocity Structure of Self-Similar Spherically Collapsed Halos

TL;DR

This paper develops an analytical model of halo velocity profiles considering tidal torques, comparing results with N-body simulations to understand the internal dynamics of self-similar spherically collapsed halos.

Contribution

It introduces a generalized self-similar infall model including tidal torques and analytically and numerically studies velocity anisotropy and phase-space density profiles.

Findings

Anisotropy profile asymptotes to a constant at small radii.

Pseudo-phase-space density is universal on intermediate and large scales.

Small-scale asymptotic slope depends on halo mass and tidal torques.

Abstract

Using a generalized self-similar secondary infall model, which accounts for tidal torques acting on the halo, we analyze the velocity profiles of halos in order to gain intuition for N-body simulation results. We analytically calculate the asymptotic behavior of the internal radial and tangential kinetic energy profiles in different radial regimes. We then numerically compute the velocity anisotropy and pseudo-phase-space density profiles and compare them to recent N-body simulations. For cosmological initial conditions, we find both numerically and analytically that the anisotropy profile asymptotes at small radii to a constant set by model parameters. It rises on intermediate scales as the velocity dispersion becomes more radially dominated and then drops off at radii larger than the virial radius where the radial velocity dispersion vanishes in our model. The pseudo-phase-space density is universal on intermediate and large scales. However, its asymptotic slope on small scales depends on the halo mass and on how mass shells are torqued after turnaround. The results largely confirm N-body simulations but show some differences that are likely due to our assumption of a one-dimensional phase space manifold.