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 Lyman-alpha forest. We test the method on numerical simulations and then apply it to published observations of the Lyman-alpha forest at redshifts z from 0 to 4. We find that the effective equation of state is close to isothermal at redshift z=3, indicating that a second reheating of the IGM took place at z=3. This reheating can plausibly be identified with the reionization of HeII observed to occur at z about 3.