Probing non-Gaussian features in the HI distribution at the epoch of re-ionization

The H-I distribution at the epoch of re-ionization (EOR) is largely determined by the sizes and distribution of the ionized regions. In the scenario where the ionized regions have comoving sizes of the order of a few Mpc, the large-scale statistical properties of the H-I distribution are dominated by the Poisson noise of the discrete ionized regions and it is highly non-Gaussian. We investigate the possibility of probing re-ionization by studying these non-Gaussian features using future radio-interferometric observations of redshifted 21-cm H-I radiation. We develop a formalism relating correlations between the visibilities measured at three different baselines and frequencies to the bispectrum of H-I fluctuations. For visibilities at the same frequency, this signal is found to be of the same order as the two visibility correlation, which probes the H-I power spectrum. For visibilities at different frequencies, we find that the correlations decay within a frequency difference of similar to 1 MHz. This implies that it is, in principle, straightforward to extract this H-I signal from various contaminants, which are believed to have a continuum spectrum and are expected to be correlated even at large frequency separations.