The Merger Rates and Mass Assembly Histories of Dark Matter Haloes in the Two Millennium Simulations

TL;DR

This study uses the Millennium simulations to analyze dark matter halo merger rates and mass assembly histories across a wide range of masses, redshifts, and progenitor ratios, updating existing models with new fitting formulas.

Contribution

It provides new, comprehensive fitting formulas for halo merger rates and mass growth, extending previous analyses to higher redshifts and lower progenitor mass ratios.

Findings

Merger rate per unit redshift is nearly independent of redshift up to z~15.

Mass dependence of merger rate is weak, proportional to M0^0.13.

Mean mass growth rate increases with halo mass and redshift, fitting well with the simulated data.

Abstract

We construct merger trees of dark matter haloes and quantify their merger rates and mass growth rates using the joint dataset from the Millennium and Millennium-II simulations. The finer resolution of the Millennium-II Simulation has allowed us to extend our earlier analysis of halo merger statistics to an unprecedentedly wide range of descendant halo mass (10^10 < M0 < 10^15 Msun), progenitor mass ratio (10^-5 < xi < 1), and redshift (0 < z < 15). We update our earlier fitting form for the mean merger rate per halo as a function of M_0, xi, and z. The overall behavior of this quantity is unchanged: the rate per unit redshift is nearly independent of z out to z~15; the dependence on halo mass is weak (M0^0.13); and it is nearly a power law in the progenitor mass ratio (xi^-2). We also present a simple and accurate fitting formula for the mean mass growth rate of haloes as a function of mass and redshift. This mean rate is 46 Msun/yr for 10^12 Msun haloes at z=0, and it increases with mass as M^{1.1} and with redshift as (1+z)^2.5 (for z > 1). When the fit for the mean mass growth rate is integrated over a halo's history, we find excellent match to the mean mass assembly histories of the simulated haloes. By combining merger rates and mass assembly histories, we present results for the number of mergers over a halo's history and the statistics of the redshift of the last major merger.