Dark matter halo growth - II. Diffuse accretion and its environmental dependence

Dark matter haloes in Lambda CDM simulations grow by mergers with other haloes as well as accretion of 'diffuse' non-halo material. We quantify the mass growth rates via these two processes, (M) over dot(mer) and (M) over dot(dif), and their respective dependence on the local halo environment using the similar to 500 000 haloes of mass similar to 10(12) to 10(15) M(circle dot) in the Millennium simulation. Adopting a local mass density parameter as a measure of halo environment, we find the two rates to show strong but opposite environmental dependence, with mergers playing an increasingly important role for halo growths in overdense regions while diffuse accretion dominating the growth in the voids. For galaxy-scale haloes, these two opposite correlations largely cancel out, but a weak environmental dependence remains that results in a slightly lower mean total growth rate, and hence an earlier mean formation redshift, for haloes in denser environments. The mean formation redshift of cluster-mass haloes, on the other hand, shows no correlation with halo environment. The origin of the positive correlation of (M) over dot(mer) with local density can be traced to the surrounding mass reservoir outside the virial radii of the haloes, where more than 80 per cent of the mass is in the form of resolved haloes for haloes residing in densest regions, while this fraction drops to similar to 20 per cent in the voids. The negative correlation of (M) over dot(dif) with local density, however, is not explained by the available diffuse mass in the reservoir outside of haloes, which is in fact larger in denser regions. The non-halo component may therefore be partially composed of truly diffuse dark matter particles that are dynamically hotter due to tidal stripping and are accreted at a suppressed rate in denser regions. We also discuss the implications of these results for how to modify the analytic extended Press-Schechter model of halo growths, which in its original form does not predict environmental dependence.