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).