The evolution of the effective equation of state of the intergalactic medium

We develop a method to extract the effective equation of state of the intergalactic medium from the Doppler (b) parameter distribution of the low-density Ly alpha forest. We test the method on numerical simulations and then apply it to published observations of the Ly alpha forest at redshifts z similar or equal to 0-4. We find that the effective equation of state is close to isothermal at redshift z similar to 3, indicating that a second reheating of the intergalactic medium took place at z similar to 3. This reheating can plausibly be identified with the reionization of He II observed to occur at z similar to 3.