Statistics of the epoch of reionization (EoR) 21-cm signal – II. The evolution of the power-spectrum error-covariance

Abstract

The epoch of reionization (EoR) 21-cm signal is expected to become highly non-Gaussian as reionization progresses. This severely affects the error-covariance of the EoR 21-cm power spectrum that is important for predicting the prospects of a detection with ongoing and future experiments. Most earlier works have assumed that the EoR 21-cm signal is a Gaussian random field where (1) the error-variance depends only on the power spectrum and the number of Fourier modes in the particular k bin, and (2) the errors in the different k bins are uncorrelated. Here, we use an ensemble of simulated 21-cm maps to analyse the error-covariance at various stages of reionization. We find that even at the very early stages of reionization (⁠| $\bar{x}_{\rm H\,{\small \small {I}}}\sim 0.9$ |⁠), the error-variance significantly exceeds the Gaussian predictions at small length-scales (k > 0.5 Mpc−1) while they are consistent at larger scales. The errors in most k bins (both large and small scales) are however found to be correlated. Considering the later stages (⁠| $\bar{x}_{\rm H\,{\small \small {I}}}=0.15$ |⁠), the error-variance shows an excess in all k bins within k ≥ 0.1 Mpc−1, and it is around 200 times larger than the Gaussian prediction at k ∼ 1 Mpc−1. The errors in the different k bins are all also highly correlated, barring the two smallest k bins that are anti-correlated with the other bins. Our results imply that the predictions for different 21-cm experiments based on the Gaussian assumption underestimate the errors, and it is necessary to incorporate the non-Gaussianity for more realistic predictions.