The accretion history of dark matter haloes - III. A physical model for the concentration-mass relation

Abstract

We present a semi-analytic, physically motivated model for dark matter halo concentration as a function of halo mass and redshift. The semi-analytic model combines an analytic model for the halo mass accretion history (MAH), based on extended Press-Schechter (EPS) theory, with an empirical relation between concentration and formation time obtained through fits to the results of numerical simulations. Because the semi-analytic model is based on EPS theory, it can be applied to wide ranges in mass, redshift and cosmology. The resulting concentration- mass (c-M) relations are found to agree with the simulations, and because the model applies only to relaxed haloes, they do not exhibit the uptur..