Position-dependent power spectra of the 21-cm signal from the epoch of reionization

The 21-cm signal from the epoch of reionization is non-Gaussian. Current radio telescopes are focused on detecting the 21-cm power spectrum, but in the future the Square Kilometre Array is anticipated to provide a first measurement of the bispectrum. Previous studies have shown that the position-dependent power spectrum is a simple and efficient way to probe the squeezed-limit bispectrum. In this approach, the survey is divided into subvolumes and the correlation between the local power spectrum and the corresponding mean density of the subvolume is computed. This correlation is equivalent to an integral of the bispectrum in the squeezed limit, but is much simpler to implement than the usual bispectrum estimators. It also has a clear physical interpretation: it describes how the small-scale power spectrum of tracers such as galaxies and the 21-cm signal respond to a large-scale environment. Reionization naturally couples large and small scales as ionizing radiation produced by galactic sources can travel up to tens of Megaparsecs through the intergalactic medium during this process. Here we apply the position-dependent power spectrum approach to fluctuations in the 21-cm background from reionization. We show that this statistic has a distinctive evolution in time that can be understood with a simple analytic model. We also show that the statistic can easily distinguish between simple inside-out and outside-in models of reionization. The position-dependent power spectrum is thus a promising method to validate the reionization signal and to extract higher-order information on this process.