Understanding the universal accretion history of dark matter haloes is the first step towards determining the origin of their structure. Previous studies have quantified halo mass accretion histories using catalogues of halos from numerical simulations, in this work (Correa C. A., Wyithe J. S. B., Schaye J., Duffy A. R., 2015a, MNRAS, 450, 1514) we take a different approach. We use the extended Press Schechter formalism to interpret the complex numerical results and to unravel the physics behind halo mass growth.

We show that the halo mass history is well described by an exponential function of redshift in the high-redshift regime. However, in the low-redshift regime the mass history follows a power law because the growth of density perturbations is halted in the dark energy dominated era due to the accelerated expansion of the Universe. We provide an analytic model that depends on cosmology and on the linear matter power spectrum. We compare our model in the figure below with the latest empirical models for the mass accretion history in the literature and find very good agreement.

The figure shows the analytic model presented in this work (turquoise solid lines), the median mass history obtained from the Bolshoi simulation and merger trees from van den Bosch et al. (2014) (purple dashed lines) and the best-fit relations from the Millennium simulation from McBride et al. (2009) (dark blue dot dashed lines). We provide numerical routines for the analytic model online (available at https://bitbucket.org/astroduff/commah).

In a companion paper, Correa et al. (2015b), we explore the relation between the structure of the inner dark matter halo and halo mass history using a suite of cosmological simulations.