Compton heating of the intergalactic medium by the hard X-ray background

High-resolution hydrodynamics simulations of the Ly alpha forest in cold da rk matter dominated cosmologies appear to predict line widths that are subs tantially narrower than those observed. Here we point out that Compton heat ing of the intergalactic gas by the hard X-ray background (XRB), an effect neglected in all previous investigations, may help to resolve this discrepa ncy. The rate of gain in thermal energy by Compton scattering will dominate over the energy input from hydrogen photoionization if the XRB energy dens ity is similar to 0.2 x/[epsilon] times higher than the energy density of t he UV background at a given epoch, where x is the hydrogen neutral fraction in units of 10(-6) and [epsilon] is the mean X-ray photon energy in units of m(e)c(2). The numerical integration of the time-dependent rate equations shows that the intergalactic medium approaches a temperature of about 1.5 x 10(4) K at z > 3 in popular models for the redshift evolution of the extr agalactic background radiation. The importance of Compton heating can be te sted experimentally by measuring the Ly alpha line width distribution as a function of redshift, thus the Ly alpha forest may provide a useful probe o f the evolution of the XRB at high redshifts.