Measuring the equation of state of the intergalactic medium

Abstract

(Abridged) Numerical simulations indicate that the intergalactic medium (IGM) responsible for the low column density Lyman-alpha forest follows a well defined temperature-density relation. We demonstrate 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. We show that the parameters of the cutoff in the b(N)-distribution are strongly correlated with the parameters of the underlying equation of state. We use simulations to determine these relations, which can then be applied to the observed cutoff in the b(N)-distribution to measure the equation of state of the IGM. Using Monte Carlo simulations of Keck spectra at z=3, we show that determining the slope of the equation of state will be difficult, but that the amplitude can be determined to within ten per cent, even from a single QSO spectrum. Measuring the evolution of the equation of state with redshift will allow us to put tight constraints on the reionization history of the universe.