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A new generation of radio telescopes are currently being built with the goal of tracing the cosmic distribution of atomic hydrogen at redshifts 6–15 through its 21‐cm line. The observations will probe the large‐scale brightness fluctuations sourced by ionization fluctuations during cosmic reionization. Since detailed maps will be difficult to extract due to noise and foreground emission, efforts have focused on a statistical detection of the 21‐cm fluctuations. During cosmic reionization, these fluctuations are highly non‐Gaussian and thus more information can be extracted than just the one‐dimensional function that is usually considered, i.e. the correlation function. We calculate a two‐dimensional function that if measured observationally would allow a more thorough investigation of the properties of the underlying ionizing sources. This function is the probability distribution function (PDF) of the difference in the 21‐cm brightness temperature between two points, as a function of the separation between the points. While the standard correlation function is determined by a complicated mixture of contributions from density and ionization fluctuations, we show that the difference PDF holds the key to separately measuring the statistical properties of the ionized regions.

The difference PDF of 21‐cm fluctuations: a powerful statistical tool for probing cosmic reionization