Constraining the 21 cm brightness temperature of the IGM at z = 6.6 around LAEs with the murchison widefield array

The locations of Ly-$\alpha$ emitting galaxies (LAEs) at the end of the Epoch of Reionisation (EoR) are expected to correlate with regions of ionised hydrogen, traced by the redshifted 21~cm hyperfine line. Mapping the neutral hydrogen around regions with detected and localised LAEs offers an avenue to constrain the brightness temperature of the Universe within the EoR by providing an expectation for the spatial distribution of the gas, thereby providing prior information unavailable to power spectrum measurements. We use a test set of 12 hours of observations from the Murchison Widefield Array (MWA) in extended array configuration, to constrain the neutral hydrogen signature of 58 LAEs, detected with the Subaru Hypersuprime Cam in the \textit{Silverrush} survey, centred on $z$=6.58. We assume that detectable emitters reside in the centre of ionised HII bubbles during the end of reionization, and predict the redshifted neutral hydrogen signal corresponding to the remaining neutral regions using a set of different ionised bubble radii. A prewhitening matched filter detector is introduced to assess detectability. We demonstrate the ability to detect, or place limits upon, the amplitude of brightness temperature fluctuations, and the characteristic HII bubble size. With our limited data, we constrain the brightness temperature of neutral hydrogen to $\Delta{\rm T}_B<$30 mK ($<$200 mK) at 95% (99%) confidence for lognormally-distributed bubbles of radii, $R_B =$ 15$\pm$2$h^{-1}$cMpc.