Abstract The radio interferometric closure phases can be a valuable tool for studying cosmological HI from the early Universe. Closure phases have the advantage of being immune to element-based gains and associated calibration errors. Thus, calibration and errors therein, which are often sources of systematics limiting standard visibility-based approaches, can be avoided altogether in closure phase analysis. In this work, we present the first results of the closure phase power spectrum of HI 21-cm fluctuations using the Murchison Widefield Array (MWA), with $\sim12$ h of MWA phase II observations centred around redshift, $z\approx 6.79$ , during the Epoch of Reionisation. On analysing three redundant classes of baselines – 14, 24, and 28 m equilateral triads, our estimates of the $2\sigma$ (95% confidence interval) 21-cm power spectra are $\lesssim(184)^2 pseudo\,\mathrm{mK}^2$ at ${k}_{||} = 0.36 pseudo\ h \mathrm{Mpc}^{-1}$ in the EoR1 field for the 14 m baseline triads, and $\lesssim(188)^2 pseudo\,\mathrm{mK}^2$ at $k_{||} = 0.18 \,pseudo\ h \mathrm{Mpc}^{-1}$ in the EoR0 field for the 24 m baseline triads. The ‘pseudo’ units denote that the length scale and brightness temperature should be interpreted as close approximations. Our best estimates are still 3-4 orders high compared to the fiducial 21-cm power spectrum; however, our approach provides promising estimates of the power spectra even with a small amount of data. These data-limited estimates can be further improved if more datasets are included into the analysis. The evidence for excess noise has a possible origin in baseline-dependent systematics in the MWA data that will require careful baseline-based strategies to mitigate, even in standard visibility-based approaches.
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