Is double reionization physically plausible?

Recent observations of z similar to 6 quasars and the cosmic microwave background imply a complex history of cosmic reionization. Such a history requires some form of feedback to extend reionization over a long time interval, but the nature of the feedback and how rapidly it operates remain highly uncertain. Here we focus on one aspect of this complexity: which physical processes can cause the global ionized fraction to evolve nonmonotonically with cosmic time? We consider a range of mechanisms and conclude that double reionization is much less likely than a long, but still monotonic, ionization history. We first examine how galactic winds affect the transition from metal-free to normal star formation. Because the transition is actually spatially inhomogeneous and temporally extended, this mechanism cannot be responsible for double reionization, given plausible parameters for the winds. We next consider photoheating, which causes the cosmological Jeans mass to increase in ionized regions and hence suppresses galaxy formation there. In this case, double reionization requires that small halos form stars efficiently, that the suppression from photoheating is strong relative to current expectations, and that ionizing photons are preferentially produced outside previously ionized regions. Finally, we consider H-2 photodissociation, in which the buildup of a soft ultraviolet background suppresses star formation in small halos. This can in principle cause the ionized fraction to temporarily decrease, but only during the earliest stages of reionization. Finally, we briefly consider the effects of some of these feedback mechanisms on the topology of reionization.