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 it function Of redshift z, descendant halo mass M-0, and progenitor halo mass ratio xi using the Millennium simulation of the A cold dark matter cosmology. Here, we broaden that study and investigate file 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 xi 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 file environmental densities. For galaxy-mass haloes, we find mergers to occur similar to 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.