The impact of non-Gaussianity on the error covariance for observations of the Epoch of Reionization 21-cm power spectrum

Recent simulations show the Epoch of Reionization (EoR) 21-cm signalto be inherently non-Gaussian whereby the error covariance matrix of the 21-cm power spectrum (PS) contains a trispectrum contribution that would be absent if the signal were Gaussian. Using the binned power spectrum and trispectrum from simulations, here we present a methodology for incorporating these with the baseline distribution and system noise to make error predictions for observations with any radio-interferometric array. Here we consider the upcoming SKA-Low. Non-Gaussianity enhances the errors introducing a positive deviation Delta relative to the Gaussian predictions. Delta increases with observation time t(obs) and saturates as the errors approach the cosmic variance. Considering t(obs)= 1024 hours where a 5 sigma detection is possible at all redshifts 7 <= z <= 13, in the absence of foregrounds we find that the deviations are important at small k where we have at for some of the redshifts and also at intermediate where we have at z= 7. Non-Gaussianity also introduces correlations between the errors in different k bins, and we find both correlations and anticorrelations with the correlation coefficient value spanning -0.4 <= r(ij)<= 0.8. Incorporating the foreground wedge, Delta continues to be important () at z= 7. We conclude that non-Gaussianity makes a significant contribution to the errors and this is important in the context of the future instruments that aim to achieve high-sensitivity measurements of the EoR 21-cm PS.