Statistics of the epoch of reionization (EoR) 21-cm signal -- II. The
  evolution of the power spectrum error-covariance
  The 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 which 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 analyze the
error-covariance at various stages of reionization. We find that even at the
very early stages of reionization ($\bar{x}_{\rm HI} \sim 0.9 $) the error
variance significantly exceeds the Gaussian predictions at small length-scales
($k > 0.5 \,{\rm 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 ($\bar{x}_{\rm HI} = 0.15$), the error
variance shows an excess in all $k$ bins within $k \ge 0.1 \, {\rm Mpc}^{-1}$,
and it is around $200$ times larger than the Gaussian prediction at $k \sim 1
\, {\rm Mpc}^{-1}$. The errors in the different $k$ bins are all also highly
correlated, barring the two smallest $k$ bins which 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.
