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 LambdaCDM cosmology. For each halo at z = 0, we identify its merger history tree and determine concentration parameters c(vir) 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 a(c), defined when the log mass accretion rate d log M\d log a falls below a critical value S. We find that late-forming galaxies tend to be less concentrated, such that c(vir) observed at any epoch a(o) is strongly correlated with a(c) via c(vir) = c(1) a(o)/a(c). Scatter about this relation is mostly due to measurement errors in c vir and ac, implying that the actual spread in c vir 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 c(vir) and the scatter about the median c(vir) (M, z) using accretion histories derived from the extended Press-Schechter (EPS) formalism, after adjusting for a constant off set between the formation times as predicted by EPS and as measured in the simulations; this new ingredient can thus be easily incorporated into semianalytic 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 R-vir. Because of the direct connection between halo concentration and velocity rotation curves and because of probable connections between halo mass assembly history and star formation history, the tight correlation between these properties provides an essential new ingredient for galaxy formation modeling.