Feedback from clustered sources during reionization

The reionization history of the intergalactic medium at high redshift (z greater than or similar to 6) was likely strongly shaped by several global feedback processes. Because the earliest ionizing sources formed at the locations of the rare density peaks, their spatial distribution was strongly clustered. Here we demonstrate that this clustering significantly boosts the impact of feedback processes operating at high redshift. We build a semianalytical model to include feedback and clustering simultaneously and apply this model to the suppression of star formation in minihalos due to photoionization. The model is built on the excursion-set-based formalism of Furlanetto, Zaldarriaga, and Hernquist, which incorporates the clustering of ionizing sources and which we here extend to include the suppression of star formation in minihalos. We find that clustering increases the mean H II bubble size by a factor of several, and it dramatically increases the fraction of minihalos that are suppressed by a factor of up to similar to 60 relative to a randomly distributed population. This enhanced suppression can significantly reduce the electron-scattering optical depth tau, as required by the 3 year data from the Wilkinson Microwave Anisotropy Probe. We argue that source clustering is likely to similarly boost the importance of a variety of other feedback mechanisms.