  We present a new analytic tool for the study of cosmic structure formation, a
double distribution of the number density of dark matter halos with respect to
both halo mass and local over- (or under-) density. The double distribution
provides a statistical treatment of the properties of matter surrounding
collapsed objects, and can be used to provide analytical insight into
environmental effects on hierarchical structure formation. We apply this new
tool to the case of cosmic accretion shocks. We investigate and quantify the
effect of environmental factors on the statistical properties of these shocks.
For this purpose, we explore two different models. The first control model uses
a Press-Schechter mass function to describe the population of collapsed
structures, and assumes that all objects accrete gas of the same density and
temperature. The second model treats the accreted material as a
multi-temperature, multi-density medium with densities and temperatures derived
from the double distribution. We find that the shock environment significantly
alters the physical impact of cosmic accretion shocks on the intergalactic
medium, as well as the cosmic history of their properties.
