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