On the physical origin of dark matter density profiles

The radial mass distribution of dark matter haloes is investigated within the framework of the spherical infall model. We present a new formulation of spherical collapse including non-radial motions, and compare the analytical profiles with a set of high-resolution N-body simulations ranging from galactic to cluster scales. We argue that the dark matter density profile is entirely determined by the initial conditions, which are described by only two parameters: the height of the primordial peak and the smoothing scale. These are physically meaningful quantities in our model, related to the mass and formation time of the halo. Angular momentum is dominated by velocity dispersion, and it is responsible for the shape of the density profile near the centre. The phase-space density of our simulated haloes is well described by a power-law profile, rho/sigma(3) = 10(1.46+/-0.04) (rho(c)/v(vir)(3)) (r/r(vir))(-1.90+/-0.05). Setting the eccentricity of particle orbits according to the numerical results, our model is able to reproduce the mass distribution of individual haloes within 20 per cent accuracy.