Measuring the temperature of the intergalactic medium

Numerical simulations indicate that the smooth, photoionized intergalactic medium (IGM) responsible for the low column density Lyman-alpha forest follows a well defined temperature-density relation. We show that such an equation of state results in a cutoff in the distribution of line widths (b-parameters) as a function of column density (N) for the low column density absorption lines. This explains the existence of the lower envelope which is clearly seen in scatter plots of the b(N)-distribution in observed QSO spectra. The intercept and slope of this cutoff can be used to measure the equation of state of the IGM. Measuring the evolution of the equation of state with redshift will allow us to put tight constraints on the reionization history of the universe.