The impact of non-Gaussianity on the error covariance for observations of the Epoch of Reionization 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 ${\mathbf{C}}_{ij}$ 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 $\Delta$ relative to the Gaussian predictions. $\Delta$ increases with observation time $t_{\mathrm{obs}}$ and saturates as the errors approach the cosmic variance. Considering $t_{\mathrm{obs}}=1024$ hours where a $5\sigma$ detection is possible at all redshifts $7\le z\le 13$, in the absence of foregrounds we find that the deviations are important at small $k$ where we have $\Delta \sim 40-100\%$ at $k\sim 0.04{\mathrm{Mpc}}^{-1}$ for some of the redshifts and also at intermediate $k(\sim 0.4{\mathrm{Mpc}}^{-1})$ where we have $\Delta \sim 200\%$ 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 $-0.4\le r_{ij}\le 0.8$. Incorporating the foreground wedge, $\Delta$ continues to be important ($>50\%$) 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.

15 pages, 10 figures, Accepted for publication in MNRAS

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