The origin of cold dark matter halo density profiles

N-body simulations predict that CDM halo-assembly occurs in two phases: a rapid accretion phase dominated by major mergers and a slow accretion phase characterised by a gentle addition of mass to the outer halo. We demonstrate that this two-phase accretion leads to CDM halos of the NFW form. During the fast accretion phase fluctuations in the gravitational potential effectively isotropise the velocities of CDM particles and we show that this leads to an inner profile ρ(r) ∝ r-1. Slow accretion onto an established potential well leads to an outer profile with ρ(r) ∝ r-3. Using a simple analytic model that captures much of the important physics we show that the inner r-1 profile of CDM halos is a natural result of hierarchical mass assembly with a initial phase of rapid accretion.