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

Abstract

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 $[150.08\mathrm{Mpc}{]}^3$ 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.

Accepted for publication in MNRAS Letters. The definitive version is available at http://mnrasl.oxfordjournals.org/content/449/1/L41

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