The accretion history of dark matter halos II: The connections with the mass power spectrum and the density profile

TL;DR

This paper investigates the relationship between dark matter halo structure, their mass accretion histories, and the initial density perturbations using simulations and semi-analytic models, revealing how formation time and concentration are interconnected.

Contribution

It introduces a semi-analytic model linking halo mass history with concentration and initial density fluctuations, and provides fitting formulas and routines for these relations.

Findings

Formation time correlates strongly with halo concentration.

The model $M(z) = M_{0}(1+z)^{\alpha}e^{eta z}$ effectively describes halo mass history.

Halo accretion rates depend on cosmology and mass definitions.

Abstract

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.