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 |$\boldsymbol{\sf C}_{ij}$| 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 |$\Delta \sim 40\!-\!100 {{\ \rm per\ cent}}$| at |$k \sim 0.04 \,\rm Mpc^{-1}$| for some of the redshifts and also at intermediate |$k \, (\sim 0.4 \,\rm Mpc^{-1})$| where we have |$\Delta \sim 200 {{\ \rm per\ cent}}$| 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 (⁠|$\gt 50 {{\ \rm per\ cent}}$|⁠) 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.