The b distribution of the Lyα forest:: Probing cosmology and the intergalactic medium

We investigate a method for determining the temperature-density relation of the intergalactic medium (IGM) at z similar to 2-4 using quasar absorption-line systems. Using a simple model combined with numerical simulations, we show that there is a lower cutoff in the distribution of column density (N-H iota) and line width (b parameter). The location of this cutoff can be used to determine the temperature-density relation (under certain conditions). We describe and test an algorithm to do this. The method works as long as the amplitude of fluctuations on these scales (similar to 100 kpc) is sufficiently large. Models with less power can mimic higher temperatures. A preliminary application is made to data from two quasar lines of sight, and we determine an upper limit to the temperature of the IGM. Finally, we examine the full distribution of b parameters and show that this is completely specified by just two: the temperature of the gas and the amplitude of the power spectrum. Using the temperature upper limit measured with the N-H iota-b cutoff method, we derive an upper limit to the amplitude of the power spectrum. The limiting uncertainty in this work appears to come from the nonunique nature of Voigt-profile fitting.