Statistics of the epoch of reionization 21-cm signal - I. Power spectrum error-covariance

Abstract

The non-Gaussian nature of the epoch of reionization (EoR) 21-cm signal has a significant impact on the error variance of its power spectrum $P(\text{k})$. We have used a large ensemble of semi-numerical simulations and an analytical model to estimate the effect of this non-Gaussianity on the entire error-covariance matrix ${\mathcal{C}}_{ij}$. Our analytical model shows that ${\mathcal{C}}_{ij}$ has contributions from two sources. One is the usual variance for a Gaussian random field which scales inversely of the number of modes that goes into the estimation of $P(\text{k})$. The other is the trispectrum of the signal. Using the simulated 21-cm signal ensemble, an ensemble of the randomized signal and ensembles of Gaussian random ensembles we have quantified the effect of the trispectrum on the error variance ${\mathcal{C}}_{ij}$. We find that its relative contribution is comparable to or larger than that of the Gaussian term for the $k$ range $0.3\le k\le 1.0{\mathrm{Mpc}}^{-1}$, and can be even $\sim 200$ times larger at $k\sim 5{\mathrm{Mpc}}^{-1}$. We also establish that the off-diagonal terms of ${\mathcal{C}}_{ij}$ have statistically significant non-zero values which arise purely from the trispectrum. This further signifies that the error in different $k$ modes are not independent. We find a strong correlation between the errors at large $k$ values ($\ge 0.5{\mathrm{Mpc}}^{-1}$), and a weak correlation between the smallest and largest $k$ values. There is also a small anti-correlation between the errors in the smallest and intermediate $k$ values. These results are relevant for the $k$ range that will be probed by the current and upcoming EoR 21-cm experiments.

Published in Monthly Notices of the Royal Astronomical Society (MNRAS)

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