Velocity Structure of Self-Similar Spherically Collapsed Halos
  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.
