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

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 C-ij. Our analytical model shows that C-ij 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 C-ii. We find that its relative contribution is comparable to or larger than that of the Gaussian term for the k range 0.3 = k <= 1.0Mpc-1, and can be even similar to 200 times larger at k similar to 5Mpc(-1). We also establish that the off-diagonal terms of C-ij 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 (>= 0.5Mpc(-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.