An Accurate Physical Model for Halo Concentrations

The relation between halo mass, M, and concentration, c, is a critical component in our understanding of the structure of dark matter halos. While numerous models for this relation have been proposed, almost none of them attempt to derive the evolution of the relation analytically. We build on previous efforts to model the c-M relation as a function of physical parameters such as the peak height,nu, and the effective power spectrum slope, n(eff), which capture the dependence of c on halo mass, redshift, and cosmology. We present three major improvements over previous models. First, we derive an analytical expression for the c-M relation that is valid under the assumption of pseudo-evolution, i.e., assuming that the density profiles of halos are static in physical coordinates while the definition of their boundary evolves. We find that this ansatz is highly successful in describing the evolution of the low-mass end of the c-M relation. Second, we employ a new physical variable, the effective exponent of linear growth, alpha(eff), to parameterize deviations from an Einstein-de Sitter expansion history. Third, we combine an updated definition of n(eff) with the additional dependence on alpha(eff) and propose a phenomenological extension of our analytical framework to include all halo masses. This semianalytical model matches simulated concentrations in both scale-free models and Lambda CDM to 5% accuracy with very few exceptions and differs significantly from all previously proposed models. We present a publicly available code to compute the predictions of our model in the python toolkit COLOSSUS, including updated parameters for the model of Diemer and Kravtsov.