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, dM_mer/dt and dM_dif/dt, and their
dependence on halo environment using the ~500,000 haloes in the Millennium
simulation. Adopting a local mass density parameter as a measure of halo
environment, we find the two rates show strong but opposite environmental
dependence, with mergers playing an increasingly important role for halo
growths in overdense regions and diffuse accretion dominating growth in voids.
This behaviour is independent of the mass cuts used to define haloes vs
non-haloes. 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 regions. The mean formation redshift of the
~5000 cluster-mass haloes, on the other hand, appears to have no correlation
with halo environment. The origin of the positive correlation of dM_mer/dt with
local density can be traced to the surrounding mass reservoir outside the
haloes, where more progenitor haloes are available in denser regions. The
negative correlation of dM_dif/dt with density, however, is not explained by
the available diffuse mass in the reservoir, which is in fact larger in denser
regions. The non-halo component may therefore be partially comprised of truly
diffuse dark matter particles that are dynamically hotter and are accreted at a
suppressed rate in denser regions. We also discuss the implications of these
results for how to modify the Extended Press-Schechter model of halo growth,
which in its original form does not predict environmental dependence.
