Density Profiles of Dark Halos from their Mass Accretion Histories

We use the universal mass accretion history recently reported for simulations of halo formation in the cold dark matter model (CDM) to analyze the formation and growth of a single halo. We derive the time-dependent density profile three different ways, based upon three approximations of successively greater realism: equilibrium, radial orbits, and a fluid approximation. For the equilibrium model, the density profile is well-fit by either an NFW or Moore profile over a limited range of radii and scale factors. For the radial orbit model, we find profiles which are generally steeper than the NFW profile, with an inner logarithmic slope approaching -2, consistent with a purely radial collisionless system. In the fluid approximation, we find good agreement with the NFW and Moore profiles for radii resolved by N-body simulations (r/r_200 > 0.01), and an evolution of concentration parameter nearly identical to that found in N-body simulations. The evolving structure of cosmological halos is therefore best understood as the effect of a time-varying rate of mass infall on a smoothly distributed, isotropic, collisionless fluid.