The effect of non-Gaussianity on error predictions for the Epoch of
  Reionization (EoR) 21-cm power spectrum
  The Epoch of Reionization (EoR) 21-cm signal is expected to become
increasingly non-Gaussian as reionization proceeds. We have used semi-numerical
simulations to study how this affects the error predictions for the EoR 21-cm
power spectrum. We expect $SNR=\sqrt{N_k}$ for a Gaussian random field where
$N_k$ is the number of Fourier modes in each $k$ bin. We find that
non-Gaussianity is important at high $SNR$ where it imposes an upper limit
$[SNR]_l$. For a fixed volume $V$, it is not possible to achieve $SNR >
[SNR]_l$ even if $N_k$ is increased. The value of $[SNR]_l$ falls as
reionization proceeds, dropping from $\sim 500$ at $\bar{x}_{HI} = 0.8-0.9$ to
$\sim 10$ at $\bar{x}_{HI} = 0.15 $ for a $[150.08\, {\rm Mpc}]^3$ simulation.
We show that it is possible to interpret $[SNR]_l$ in terms of the trispectrum,
and we expect $[SNR]_l \propto \sqrt{V}$ if the volume is increased. For $SNR
\ll [SNR]_l$ we find $SNR = \sqrt{N_k}/A $ with $A \sim 0.95 - 1.75$, roughly
consistent with the Gaussian prediction. We present a fitting formula for the
$SNR$ as a function of $N_k$, with two parameters $A$ and $[SNR]_l$ that have
to be determined using simulations. Our results are relevant for predicting the
sensitivity of different instruments to measure the EoR 21-cm power spectrum,
which till date have been largely based on the Gaussian assumption.
