Measuring the History of Cosmic Reionization using the 21-cm Difference PDF

During cosmic reionization, the 21-cm brightness fluctuations were highly non-Gaussian, and complementary statistics can be extracted from the distribution of pixel brightness temperatures that are not derivable from the 21-cm power spectrum. One such statistic is the 21-cm difference PDF, the probability distribution function of the difference in the 21-cm brightness temperatures between two points, as a function of the distance between the points. Guided by 21-cm difference PDFs extracted from simulations, we perform a maximum likelihood analysis on mock observational data, and analyze the ability of present and future low-frequency radio array experiments to estimate the shape of the 21-cm difference PDF, and measure the history of cosmic reionization. We find that one-year data with an experiment such as the Murchison Wide-field Array should suffice for probing large scales during the mid-to-late stages of reionization, while a second-generation experiment should yield detailed measurements over a wide range of scales during most of the reionization era.