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

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