Mass growth and density profiles of dark matter haloes in hierarchical clustering

We develop a model for the growth of dark matter haloes and use it to study their evolved density profiles. In this model, haloes are spherical and form by quiescent accretion of matter in clumps, which are called satellites. The halo mass as a function of redshift is given by the mass of the most massive progenitor, and is determined from Monte Carlo realizations of the merger-history tree. Inside the halo, satellites move under the action of the gravitational force of the halo and a dynamical friction drag force. The associated equation of motion is solved numerically. The energy lost to dynamical friction is transferred to the halo in the form of kinetic energy. As satellites sink into the halo, they continually lose matter as a result of tidal stripping. The stripped matter moves inside the halo free of dynamical friction. The evolved density profiles are steeper than those obtained by assuming that, once they have been accreted on to the parent halo, satellites remain at a fixed distance from the halo centre. We find that the final density profile depends mainly on the rate of infall of matter on to the halo. This, in turn, depends on the initial fluctuation field as well as on cosmology. For mass scales where the effective spectral index of the initial density field is less than -1, the model predicts a profile that can only be approximately matched by the one-parameter family of curves suggested by Navarro, Frenk and White. For scale-free power spectra with initial slope n, the density profile, within about 1 per cent of the virial radius, is rho proportional to r(-beta), with 3(3 + n)/(5 + n) less than or equal to beta less than or equal to 3(3 + n)/(4 + n).