Statistics of the epoch of reionization 21-cm signal – I. Power spectrum error-covariance

Abstract

The non-Gaussian nature of the epoch of reionization (EoR) 21-cm signal has a significant impact on the error variance of its power spectrum P(k). We have used a large ensemble of seminumerical simulations and an analytical model to estimate the effect of this non-Gaussianity on the entire error-covariance matrix Cij. Our analytical model shows that Cij has contributions from two sources. One is the usual variance for a Gaussian random field which scales inversely of the number of modes that goes into the estimation of P(k). The other is the trispectrum of the signal. Using the simulated 21-cm Signal Ensemble, an ensemble of the Randomized Signal and Ensembles of Gaussian Random Ensembles we have quantified the effect of the trispectrum on the error variance Cii. We find that its relative contribution is comparable to or larger than that of the Gaussian term for the k range 0.3 ≤ k ≤ 1.0 Mpc−1, and can be even ∼200 times larger at k ∼ 5 Mpc−1. We also establish that the off-diagonal terms of Cij have statistically significant non-zero values which arise purely from the trispectrum. This further signifies that the error in different k modes are not independent. We find a strong correlation between the errors at large k values (≥0.5 Mpc−1), and a weak correlation between the smallest and largest k values. There is also a small anticorrelation between the errors in the smallest and intermediate k values. These results are relevant for the k range that will be probed by the current and upcoming EoR 21-cm experiments.