Statistics of 21-cm Fluctuations in Cosmic Reionization Simulations:
  PDFs and Difference PDFs
  In the coming decade, low-frequency radio arrays will begin to probe the
epoch of reionization via the redshifted 21-cm hydrogen line. Successful
interpretation of these observations will require effective statistical
techniques for analyzing the data. Due to the difficulty of these measurements,
it is important to develop techniques beyond the standard power spectrum
analysis in order to offer independent confirmation of the reionization
history, probe different aspects of the topology of reionization, and have
different systematic errors. In order to assess the promise of probability
distribution functions (PDFs) as statistical analysis tools in 21-cm cosmology,
we first measure the 21-cm brightness temperature (one-point) PDFs in six
different reionization simulations. We then parametrize their most distinct
features by fitting them to a simple model. Using the same simulations, we also
present the first measurements of difference PDFs in simulations of
reionization. We find that while these statistics probe the properties of the
ionizing sources, they are relatively independent of small-scale, sub-grid
astrophysics. We discuss the additional information that the difference PDF can
provide on top of the power spectrum and the one-point PDF.
