The Column Density Distribution of the Lyman-Alpha Forest: A Measure of Small Scale Power

Absorption lines in the Lyman-alpha forest can be thought of as peaks in neutral hydrogen density along lines of sight. The column density distribution (the number density of absorption lines as a function of column density) is then a statistic of density peaks, which contains information about the underlying power spectrum. In particular, we show that the slope of the distribution provides a measure of power on scales smaller than those probed by studies of present-day large scale structure.