Environmental dependence of dark matter halo growth – I. Halo merger rates

In an earlier paper, we quantified the mean merger rate of dark matter haloes as a function of redshift z , descendant halo mass M ₀, and progenitor halo mass ratio ξ using the Millennium simulation of the Λ cold dark matter cosmology. Here, we broaden that study and investigate the dependence of the merger rate of haloes on their surrounding environment. A number of local mass overdensity variables, both including and excluding the halo mass itself, are tested as measures of a halo's environment. The simple functional dependence on   z , M ₀  , and ξ of the merger rate found in our earlier work, is largely preserved in different environments, but we find that the overall amplitude of the merger rate has a strong positive correlation with the environmental densities. For galaxy-mass haloes, we find mergers to occur ～2.5 times more frequently in the densest regions than in voids at both   z = 0  and higher redshifts. Higher mass haloes show similar trends. We present a fitting form for this environmental dependence that is a function of both mass and local density and valid out to   z = 2  . The amplitude of the progenitor (or conditional) mass function shows a similar correlation with local overdensity, suggesting that the extended Press–Schechter model for halo growth needs to be modified to incorporate environmental effects.