The b Distribution of the Lya Forest: Probing Cosmology and the Intergalactic Medium

We investigate a method to determine the temperature-density relation of the intergalactic medium (IGM) at z~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 (NHI) 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 (~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 parameters: the temperature of the gas and the amplitude of the power spectrum. Using the temperature upper limit measured with the NHI-b cutoff method, we derive an upper limit to the amplitude of the power spectrum.