The Statistics of Density Peaks and the Column Density Distribution of the Lyα Forest

Abstract

We develop a method to calculate the column density distribution of the Ly alpha forest for column densities in the range 1012.5--1014.5 cm-2. The Zeldovich approximation, with appropriate smoothing, is used to compute the density and peculiar velocity fields. The effect of the latter on absorption profiles is discussed, and it is shown to have little effect on the column density distribution. An approximation is introduced in which the column density distribution is related to a statistic of density peaks (involving its height and first and second derivatives along the line of sight) in real space. We show that the slope of the column density distribution is determined by the temperature-density relation, as well as the power spectrum, on scales 2 h Mpc-1