Measuring the equation of state of the intergalactic medium

Numerical simulations indicate that the smooth, photoionized intergalactic medium (IGM) responsible for the low column density Ly alpha forest follows a well-defined temperature-density relation, which is well described by a power law T = T-0(rho/<(rho)over bar>)(gamma-1). We demonstrate that such an equation of state results in a power-law cut-off in the distribution of linewidths (b-parameters) as a function of column density (N) for the low column density (N less than or similar to 10(14.5) cm(-2)) absorption lines. This explains the existence of the lower envelope that is clearly seen in scatter plots of the b(N) distribution in observed QSO spectra. Even a strict power-law equation of state will not result in an absolute cut-off because of line blending and contamination by unidentified metal lines. We develop an algorithm to determine the cut-off, which is insensitive to these narrow lines. We show that the parameters of the cut-off 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 cut-off in the b(N) distribution to measure the equation of state of the IGM. We show that systematics that change the b(N) distribution, such as cosmology (for a fixed equation of state), peculiar velocities, the intensity of the ionizing background radiation and variations in the signal-to-noise ratio, do not affect the measured cut-off. We argue that physical processes that have not been incorporated in the simulations, e.g. feedback from star formation, are unlikely to affect the results. 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 10 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.