paper

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

arXiv:1001.2304 · doi:10.1111/j.1365-2966.2010.16859.x

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.

12 pages, 9 figures, accepted in MNRAS

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