The Thermal Memory of Reionization History

The recent measurement by {\it WMAP} of a large electron scattering optical depth $\tau_e = 0.17 \pm 0.04$ is consistent with a simple model of reionization in which the intergalactic medium (IGM) was ionized at redshift $z \sim 15$, and has remained highly ionized ever since. Here, we show that existing measurements of the IGM temperature from the Lyman-alpha forest at $z \sim 2 - 4$ rule out this ``vanilla'' model. Under reasonable assumptions about the ionizing spectrum, as long as the universe was reionized before $z = 10$ {\it and has remained highly ionized since}, the IGM reaches an asymptotic thermal state which is too cold compared to observations. To simultaneously satisfy the CMB and forest constraints, the reionization history is likely complex: reionization begins early at $z \gsim 15$, but there must have been significant (order 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 (HeII$\rightarrow$HeIII) reionization induces a significant scatter in the IGM temperature, which diminishes with time quickly nonetheless. Finally, we provide an analytic formula for the thermal asymptote, and discuss possible additional heating mechanisms that might evade our constraints.