The origin of cold dark matter halo density profiles

N -body simulations predict that CDM halo-assembly occurs in two phases: 1) a rapid accretion phase dominated by major mergers with a rapidly deepening potential well; and 2) a slow accretion phase characterised by a gentle addition of mass to the outer halo with little change in the inner potential well. We demonstrate, using onedimensional simulations, that this two-phase accretion leads to CDM halos of the NFW form and provides physical insight into the properties of the mass accretion history that influence the final profile. 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. Slow accretion onto an established potential well leads to an outer profile with ρ(r) ∝ r. The concentration of a halo is determined by the fraction of mass that is accreted during the fast accretion phase. Using an ensemble of realistic mass accretion histories, we show that the model predictions of the dependence of halo concentration on halo formation time, and hence the dependence of halo concentration on halo mass, and the distribution of halo concentrations all match those found in cosmological N -body simulations. Using a simple analytic model that captures much of the important physics we show that the inner r profile of CDM halos is a natural result of hierarchical mass assembly with a initial phase of rapid accretion. Our results also suggest that violent relaxation plays a minor role in structuring CDM halos.