Get access

The merger rates and mass assembly histories of dark matter haloes in the two Millennium simulations


E-mail: (OF); (C-PM)


We construct merger trees of dark matter haloes and quantify their merger rates and mass growth rates using the joint data set 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 (1010M0≲ 1015 M), progenitor mass ratio (10−5≲ξ≤ 1) and redshift (0 ≤z≲ 15). We update our earlier fitting form for the mean merger rate per halo as a function of M0,  ξ and z. The overall behaviour 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 (∝M0.130); and it is nearly a power law in the progenitor mass ratio (∝ξ−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 M yr−1 for 1012 M haloes at z= 0, and it increases with mass as M1.1 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.