A Random Walk Model for Dark Matter Halo Concentrations

Abstract

For idealized (spherical, smooth) dark matter halos described by single-parameter density profiles (such as the Navarro–Frenk–White profile), there exists a one-to-one mapping between the energy of the halo and the scale radius of its density profile. The energy therefore uniquely determines the concentration parameter of such halos. We exploit this fact to predict the concentrations of dark matter halos via a random walk in halo 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. We show that, when calibrated, 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. We further test this model by examining both the autocorrelation of scale radii across time and the correlations between halo concentration and spin, and comparing them 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.