A Random Walk Model for Dark Matter Halo Concentrations

We describe an algorithm for predicting the concentrations of dark matter halos via a random walk in energy space. Given a full merger tree for a halo, the total internal energy of each halo in that tree is determined by summing the internal and orbital energies of progenitor halos. For halos described by single-parameter density profiles (such as the NFW profile) the energy can be directly mapped to a scale radius, and so to a concentration. We show that this model can accurately reproduce the mean of the concentration mass relation measured in N-body simulations, and reproduces more of the scatter in that relation than previous models. However, our model underpredicts the kurtosis of the distribution of N-body concentrations. We test this model by examining both the autocorrelation of scale radii across time, and the correlations between halo concentration and spin, and comparing to results measured from cosmological N-body simulations. In both cases we find that our model closely matches the N-body results. Our model is implemented within the open source Galacticus toolkit.