The Nearly Universal Merger Rate of Dark Matter Haloes in Lambda-CDM Cosmology

Understand

We construct merger trees from the largest database of dark matter haloes to date provided by the Millennium simulation to quantify the merger rates of haloes over a broad range of descendant halo mass (1e12 < M0 < 1e15 Msun), progenitor mass ratio (1e-3 < xi < 1), and redshift (0 < z < 6).

• We find the mean merger rate per halo, B/n, to have very simple dependence on M0, xi, and z, and propose a universal fitting form for B/n that is accurate to 10-20%.
• Overall, B/n depends very weakly on the halo mass (proportional to M0^0.08) and scales as a power law in the progenitor mass ratio (proportional to xi^-2) for minor mergers (xi < 0.1) with a mild upturn for major mergers.
• As a function of time, we find the merger rate per Gyr to evolve as (1+z)^n with n=2-2.3, while the rate per unit redshift is nearly independent of z.