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We develop a method to extract the "effective equation of state" of theintergalactic medium from the doppler b parameter distribution of thelow-density Lyman-alpha forest. We test the method on numerical simulations andthen apply it to published observations of the Lyman-alpha forest at redshiftsz from 0 to 4. We find that the effective equation of state is close toisothermal at redshift z=3, indicating that a second reheating of the IGM tookplace at z=3. This reheating can plausibly be identified with the reionizationof HeII observed to occur at z about 3.Comment: Revised version accepted for publication in ApJ. Vol. 534 May 1, 2000  (in press); 32 pages, 13 figures, 7 table

The Evolution of the Effective Equation of State of the Intergalactic Medium