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

Abstract

Recent simulations show the Epoch of Reionization (EoR) 21-cm signal to be inherently non-Gaussian whereby the error covariance matrix Cij 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 Δ relative to the Gaussian predictions. Δ increases with observation time tobs and saturates as the errors approach the cosmic variance. Considering tobs = 1024 hours where a 5σ 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 Δ∼40−100 per cent at k∼0.04Mpc−1 for some of the redshifts and also at intermediate k(∼0.4Mpc−1) where we have Δ∼200 per cent 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 ≤ rij ≤ 0.8. Incorporating the foreground wedge, Δ continues to be important (⁠>50 per cent⁠) 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.