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 halos, they do not exhibit the upturn at high masses or high redshifts found by some recent works. We predict a change of slope in the z ∼ 0 c − M relation at a mass scale of 10 11 M ⊙ . We find that this is due to the change in the functional form of the halo MAH, which goes from being dominated by an exponential (for high-mass halos) to a power-law (for low-mass halos). During the latter phase, the core radius remains approximately constant, and the concentration grows due to the drop of the background density. We also analyse how the c − M relation predicted by this work affects the power produced by dark matter annihilation, finding that at z = 0 the power is two orders of magnitude lower than that obtained from extrapolating best-fitting c − M relations. We provide fits to the c − M relations as well as numerical routines to compute concentrations and MAHs †.

The mass–concentration–redshift relation of cold and warm dark matter haloes

“…Ludlow et al 2012;Correa et al 2015c;Klypin et al 2016, for discussions). A full assessment will likely require a detailed study of the perils and virtues of a variety of different equilibrium benchmarks, which we defer to future work.…”

A unified model for the spatial and mass distribution of subhaloes

“…For the median mass-concentration relation, we consider two z = 0 models from the literature. One is a power-law fit from Macciò, Dutton & van den Bosch (2008) for virialized haloes, and the other is a physical model from Ludlow et al (2014) that calculates concentration from the mass accretion history (see also Macciò et al 2008;Zhao et al 2009;Prada et al 2012;Correa et al 2015, for some similar models). In both models, we adopt the same cosmology as that of our simulations.…”

Exponentially growing bubbles around early supermassive black holes

“…The vertical dotted lines are as in Fig. 2. concentration-mass relation derived by Correa et al (2015) (see their Eq.20). For the massive halos in the redshift range z=6-12.5 considered here, the concentration parameter is nearly constant, c ∼ 2.8.…”