The physical origin of the universal accretion history of dark matter halos

Camila Correa, Stuart Wyithe, Joop Schaye, Alan Duffy

Published 2014-09-18Version 1

Understanding the universal accretion history of dark matter halos is the first step towards determining the origin of their universal structure. In this work, we begin by using the extended Press-Schechter (EPS) formalism to show that the halo mass accretion history is determined by the growth rate of initial density perturbations, and that it follows the expression M(z)=M0(1+z)^{af(M0)}e^{-f(M0)z}, where M0=M(z=0), a depends on cosmology and f(M0) depends only on the matter power spectrum. We then explore the relation between the structure of the inner dark matter halo and halo mass history using a suite of cosmological, hydrodynamical simulations. We confirm that the formation time, defined as the time when the virial mass of the main progenitor equals the mass enclosed within the scale radius, correlates strongly with concentration. We provide a fitting formula for the relation between concentration and formation time, from which we show analytically that the scatter in formation time determines the scatter in concentration. Based on our analytic and numerical work, we conclude that the concentration is determined by the halo mass history, and show by simple modeling that one can be determined from the other. Since halo concentrations are characterized by their mass histories, and the latter are described by the initial density perturbations and the growth rate, we have therefore established the physical link between halo concentrations and the initial density perturbation field. Finally, we model the halo mass history as M(z)=M0(1+z)^{alpha}e^{beta z} and find a direct correlation between the parameters alpha, beta and concentration. We provide fitting formulas for the halo mass history and accretion rate as a function of halo mass, and demonstrate how halo mass history changes according to the adopted mass definition and cosmology.