The accretion history of dark matter halos II: The connections with the
  mass power spectrum and the density profile
  We explore the relation between the structure and mass accretion histories of
dark matter halos using a suite of cosmological 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 semi-analytic model for halo mass
history that combines analytic relations with fits to simulations. This model
has the functional form, $M(z) = M_{0}(1+z)^{\alpha}e^{\beta z}$, where the
parameters $\alpha$ and $\beta$ are directly correlated with concentration. We
then combine this model for the halo mass history with the analytic relations
between $\alpha$, $\beta$ and the linear power spectrum derived by Correa et
al. (2014) to establish the physical link between halo concentration and the
initial density perturbation field. Finally, we provide fitting formulas for
the halo mass history as well as numerical routines, we derive the accretion
rate as a function of halo mass, and we demonstrate how the halo mass history
depends on cosmology and the adopted definition of halo mass.
