The universal mass accretion history of cold dark matter haloes

We use the extended Press-Schechter formalism to investigate the rate at which cold dark matter haloes accrete mass. We discuss the shortcomings of previous methods that have been used to compute the mass accretion histories of dark matter haloes, and present an improved method based on the N-branch merger tree algorithm of Somerville & Kolatt. We show that this method no longer suffers from inconsistencies in halo formation times, and compare its predictions with high-resolution N-body simulations. Although the overall agreement is reasonable, there are slight inconsistencies which are most easily interpreted as a reflection of ellipsoidal collapse (as opposed to spherical collapse assumed in the Press-Schechter formalism). We show that the average mass accretion histories follow a simple, universal profile, and we present a simple recipe for computing the two scale-parameters which is applicable to a wide range of halo masses and cosmologies. Together with the universal profiles for the density and angular momentum distributions of cold dark matter haloes, these universal mass accretion histories provide a simple but accurate framework for modelling the structure and formation of dark matter haloes. In particular, they can be used as a backbone for modelling various aspects of galaxy formation where one is not interested in the detailed effects of merging. As an example we use the universal mass accretion history to compute the rate at which dark matter haloes accrete mass, which we compare with the cosmic star formation history of the Universe.