The effect of non-Gaussianity on error predictions for the Epoch of Reionization (EoR) 21-cm power spectrum

Abstract

Abstract 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 ${\rm SNR}=\sqrt{N_k}$ for a Gaussian random field where Nk 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 Nk is increased. The value of [SNR]l falls as reionization proceeds, dropping from ∼500 at $\bar{x}_{{\rm H\,{\small {i}}}}= 0.8{\rm -}0.9$ to ∼10 at $\bar{x}_{{\rm H\,{\small {i}}}}= 0.15$ 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 $[{\rm SNR}]_l \propto \sqrt{V}$ if the volume is increased. For SNR ≪ [SNR]l we find ${\rm SNR}= \sqrt{N_k}/A$ with A ∼ 0.95–1.75, roughly consistent with the Gaussian prediction. We present a fitting formula for the SNR as a function of Nk, 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.