Concentrations of Dark Halos from Their Assembly Histories

We study the relation between the density profiles of dark matter halos and their mass assembly histories, using a statistical sample of halos in a high-resolution N-body simulation of the LCDM cosmology. For each halo at z=0, we identify its merger-history tree, and determine concentration parameters cᵥir for all progenitors, thus providing a structural merger tree for each halo. We fit the mass accretion histories by a universal function with one parameter, the formation epoch ac, defined when the log mass accretion rate dlogM/dloga falls below a critical value S (e. g. , S=2). We find that late forming galaxies tend to be less concentrated, such that cᵥir ``observed'' at any epoch aₒ is strongly correlated with ac via cᵥir=c₁*aₒ/ac. Scatter about this relation is mostly due to measurement errors in cᵥ and ac, implying that the actual spread in cᵥir for halos of a given mass can be mostly attributed to scatter in ac. We demonstrate that this relation can also be used to predict the mass and redshift dependence of cᵥ, and the scatter about the median cᵥir (M, z), using accretion histories derived from the Extended Press-Schechter (EPS) formalism, after adjusting for a constant offset between the formation times as predicted by EPS and as measured in the simulations. This should provide a useful new ingredient for semi-analytic models of galaxy formation. The correlation found between halo concentration and mass accretion rate suggests a physical interpretation: for high mass infall rates the central density is related to the background density; when the mass infall rate slows, the central density stays approximately constant and the halo concentration just grows as Rᵥir.