Statistics of the epoch of reionization (EoR) 21-cm signal -- II. The evolution of the power spectrum error-covariance

Abstract

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 (${\bar{x}}_{\mathrm{HI}}\sim 0.9$) the error variance significantly exceeds the Gaussian predictions at small length-scales ($k>0.5{\mathrm{Mpc}}^{-1}$) 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 (${\bar{x}}_{\mathrm{HI}}=0.15$), the error variance shows an excess in all $k$ bins within $k\ge 0.1{\mathrm{Mpc}}^{-1}$, and it is around $200$ times larger than the Gaussian prediction at $k\sim 1{\mathrm{Mpc}}^{-1}$. 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.

Published in Monthly Notices of the Royal Astronomical Society (MNRAS). Available at "this URL http://dx.doi.org/10.1093/mnras/stw2599"

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