Barkana, RennanLoeb, Abraham2019-09-272008Barkana, Rennan, and Abraham Loeb. 2008. “The Difference PDF of 21-Cm Fluctuations: A Powerful Statistical Tool for Probing Cosmic Reionization.” Monthly Notices of the Royal Astronomical Society 384 (3): 1069–79. https://doi.org/10.1111/j.1365-2966.2007.12729.x.0035-87111365-2966http://nrs.harvard.edu/urn-3:HUL.InstRepos:41417394A 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.en-USJournal Article2019-09-2710.1111/j.1365-2966.2007.12729.x