An Analytic Model of Environmental Effects on Cosmic Structure Formation and an Application to Cosmic Accretion Shocks

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.