We consider the degree to which 21 cm tomography of the high-redshift universe can distinguish different ionization histories. Using a new analytic model for the size distribution of H II regions that associates these ionized bubbles with large-scale galaxy overdensities, we compute the angular power spectrum and other statistical properties of the 21 cm brightness temperature during reionization. We show that the H II regions imprint features on the power spectrum that allow us to separate histories with discrete bubbles from those with partial uniform ionization (by, for example, X-rays). We also show that "double reionization" scenarios will modify the morphology of the bubbles in ways that depend on the mechanism through which the first generation of sources shuts off. If, for example, the transition occurs globally at a fixed redshift, the first generation imprints a persistent feature on the 21 cm power spectrum. Finally, we compare our model to one in which voids are ionized first. While the power spectra of these two models are qualitatively similar, we show that the underlying distributions of neutral hydrogen differ dramatically and suggest that other statistical tests can distinguish them. The next generation of low-frequency radio telescopes will have the sensitivity to distinguish all of these models and strongly constrain the history and morphology of reionization.
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