The Temperature-Density Relation of the Intergalactic Medium After Hydrogen Reionization

We use an analytic model to study how inhomogeneous hydrogen reionization affects the temperature distribution of the intergalactic medium (IGM). During this process, the residual energy of each ionizing photon is deposited in the IGM as heat, increasing its temperature to 20,000-30,000 K; subsequent expansion of the Universe then cools the gas. Because reionization most likely proceeds from high to low densities, underdense voids are ionized last, have less time to cool, and are (on average) warmer than mean-density gas immediately after reionization is complete (an "inverted" equation of state). From this initial configuration, the low-density gas cools quickly and eventually returns to a more normal equation of state. The rapidly evolving temperature introduces systematic uncertainties in measurements of the ionizing background at z~6. For example, late reionization implies rapid cooling, so that the ionizing background would have to evolve even more rapidly at z ~5-6 than typically claimed. This degeneracy is difficult to disentangle, because the Lyman-alpha forest probes only a narrow range in densities (over which the gas is nearly isothermal). However, higher Lyman-series transitions probe wider density ranges, sampling different effective temperatures, and offer a new way to measure the IGM equation of state that should work where nearly saturated absorption precludes other methods. This will help to separate evolution in temperature from that in the ionizing background. While more detailed study with hydrodynamic simulations is needed, we show that such measurements could potentially distinguish early and late reionization using only a handful of lines of sight.