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 seminumerical simulations to study how this affects the error predictions for the EoR 21-cm power spectrum. We expect SNR=√{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 ∼500 at bar{x}_{H I} = 0.8-0.9 to ∼10 at bar{x}_{H I} = 0.15 for a [150.08 Mpc]³ simulation. We show that it is possible to interpret [SNR]_l in terms of the trispectrum, and we expect [SNR]_l ∝ √{V} if the volume is increased. For SNR ≪ [SNR]_l we find SNR= √{N_k}/A with A ∼ 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.