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 Lyα forest follows a well defined temperature-density relation, which is well described by a power-law T = T0(ρ/ρ̄)γ−1. We demonstrate that such an equation of state results in a power-law cutoff in the distribution of line widths (b-parameters) as a function of column density (N) for the low column density (N10 cm−2) 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. Even a strict power-law equation of state will not result in an absolute cutoff because of line blending and contamination by unidentified metal lines. We develop an algorithm to determine the cutoff, which is insensitive to these narrow lines. 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. We show that systematics which 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 cutoff. 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 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.