A Simple Model for the Density Profiles of Isolated Dark Matter Halos
  We explore the possibility that the density profiles of elliptical galaxies
and cold dark matter (CDM) halos found in cosmological simulations can be
understood in terms of the same physical process, collisionless gravitational
collapse. To investigate this, we study a simplified model, the collapse of a
perfectly cold Plummer sphere. First, we examine an N-body simulation of this
model with particles constrained to purely radial orbits. This results in a
final state characterized by a profile slightly steeper than \rho \propto
r^{-2} at small radii and behaving as \rho \propto r^{-4} at large radii, which
can be understood in terms of simple analytic arguments. Next, we repeat our
simulation without the restriction of radial orbits. This results in a
shallower inner density profile, like those found in elliptical galaxies and
CDM halos. We attribute this change to the radial orbit instability (ROI) and
propose a form of the distribution function (DF) motivated by a physical
picture of collapse. As evidence of the link between our model and CDM halos,
we find that our collapse simulation has a final state with pseudo-phase-space
density which scales roughly as \rho/\sigma^3 \propto r^{-1.875}, like that
observed in CDM halos from cosmological simulations (Navarro et al. 2010). The
velocity anisotropy profile is also qualitatively similar to that found near
the centers of these halos. We argue that the discrepancy at large radii (where
CDM halos scale as \rho \propto r^{-3}) is due to the presence of the
cosmological background or continued infall. This leads us to predict that the
outer CDM halo density profile is not "universal," but instead depends on
cosmological environment (be it an underdense void or overdense region).
