Concentrations of Dark Halos from Their Assembly Histories

TLDR

The study investigates how dark matter halo density profiles relate to their mass assembly histories using a large statistical sample from a high‑resolution ΛCDM N‑body simulation. The authors construct structural merger trees for each halo, fit their mass accretion histories with a universal function defined by a formation epoch ac, and relate halo concentration to ac via \(c_{\rm vir}=c_{1}a_{\rm o}/a_{\rm c}\). They find a tight, physically motivated correlation between halo concentration and formation epoch, with scatter mainly from measurement errors, enabling predictions of concentration evolution and providing a key ingredient for galaxy formation models.

Abstract

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 ΛCDM 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 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 cvir "observed" at any epoch ao is strongly correlated with ac via cvir = c1ao/ac. Scatter about this relation is mostly due to measurement errors in cvir 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 cvir 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 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 Rvir. 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.