The thermal memory of reionization history

The recent measurement by WMAP of a large electron-scattering optical depth tau(e) = 0.17 +/- 0.04 is consistent with a simple model of reionization in which the intergalactic medium (IGM) is ionized at redshift z similar to 15 and remains highly ionized thereafter. Here we show that existing measurements of the IGM temperature from the Lyalpha forest at z similar to 2-4 rule out this vanilla model. Under reasonable assumptions about the ionizing spectrum, as long as the universe is reionized before z = 10 and remains highly ionized thereafter, the IGM reaches an asymptotic thermal state that is too cold compared to observations. To simultaneously satisfy the cosmic microwave background and Lyalpha forest constraints, the reionization history must be complex: reionization begins early at z e 15, but there must have been significant (order-of-unity) changes in fractions of neutral hydrogen and/or helium at 6 < z < 10 and/or singly ionized helium at 4 < z < 10. We describe a physically motivated reionization model that satisfies all current observations. We also explore the impact of a stochastic reionization history and show that a late epoch of (He II --> He III) reionization induces a significant scatter in the IGM temperature, but the scatter diminishes with time quickly. Finally, we provide an analytic formula for the thermal asymptote and discuss possible additional heating mechanisms that might evade our constraints.