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The 21 cm transition from neutral Hydrogen promises to be the best observational probe of the Epoch of Reionisation (EoR). This has led to the construction of low-frequency radio interferometric arrays, such as the Hydrogen Epoch of Reionization Array (HERA), aimed at systematically mapping this emission for the first time. Precision calibration, however, is a requirement in 21 cm radio observations. Due to the spatial compactness of HERA, the array is prone to the effects of mutual coupling, which inevitably lead to non-smooth calibration errors that contaminate the data. When unsmooth gains are used in calibration, intrinsically spectrally-smooth foreground emission begins to contaminate the data in a way that can prohibit a clean detection of the cosmological EoR signal. In this paper, we show that the effects of mutual coupling on calibration quality can be reduced by applying custom time-domain filters to the data prior to calibration. We find that more robust calibration solutions are derived when filtering in this way, which reduces the observed foreground power leakage. Specifically, we find a reduction of foreground power leakage by 2 orders of magnitude at k=0.5.

Interferometric experiments designed to detect the highly redshifted 21-cm signal from neutral hydrogen are producing increasingly stringent constraints on the 21-cm power spectrum, but some k-modes remain systematics-dominated. Mutual coupling is a major systematic that must be overcome in order to detect the 21-cm signal, and simulations that reproduce effects seen in the data can guide strategies for mitigating mutual coupling. In this paper, we analyse 12 nights of data from the Hydrogen Epoch of Reionization Array and compare the data against simulations that include a computationally efficient and physically motivated semi-analytic treatment of mutual coupling. We find that simulated coupling features qualitatively agree with coupling features in the data; however, coupling features in the data are brighter than the simulated features, indicating the presence of additional coupling mechanisms not captured by our model. We explore the use of fringe-rate filters as mutual coupling mitigation tools and use our simulations to investigate the effects of mutual coupling on a simulated cosmological 21-cm power spectrum in a "worst case" scenario where the foregrounds are particularly bright. We find that mutual coupling contaminates a large portion of the "EoR Window", and the contamination is several orders-of-magnitude larger than our simulated cosmic signal across a wide range of cosmological Fourier modes. While our fiducial fringe-rate filtering strategy reduces mutual coupling by roughly a factor of 100 in power, a non-negligible amount of coupling cannot be excised with fringe-rate filters, so more sophisticated mitigation strategies are required., Comment: 19 pages, 12 figures, submitted to MNRAS

Current attempts to measure the 21cm Power Spectrum of neutral hydrogen during the Epoch of Reionization are limited by systematics which produce measured upper limits above both the thermal noise and the expected cosmological signal. These systematics arise from a combination of observational, instrumental, and analysis effects. In order to further understand and mitigate these effects, it is instructive to explore different aspects of existing datasets. One such aspect is the choice of observing field. To date, MWA EoR observations have largely focused on the EoR0 field. In this work, we present a new detailed analysis of the EoR1 field. The EoR1 field is one of the coldest regions of the Southern radio sky, but contains the very bright radio galaxy Fornax-A. The presence of this bright extended source in the primary beam of the interferometer makes the calibration and analysis of EoR1 particularly challenging. We demonstrate the effectiveness of a recently developed shapelet model of Fornax-A in improving the results from this field. We also describe and apply a series of data quality metrics which identify and remove systematically contaminated data. With substantially improved source models, upgraded analysis algorithms and enhanced data quality metrics, we determine EoR power spectrum upper limits based on analysis of the best $\sim$14-hours data observed during 2015 and 2014 at redshifts 6.5, 6.8 and 7.1, with the lowest $2\sigma$ upper limit at z=6.5 of $\Delta^2 \leq (73.78 ~\mathrm{mK)^2}$ at $k=0.13~\mathrm{h~ Mpc^{-1}}$, improving on previous EoR1 measurement results., Comment: 18 pages, 17 figures, Accepted for publication in MNRAS

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., Comment: 9 pages, 6 figures, accepted for publication in MNRAS

Observations in the lowest MWA band between $75-100$ MHz have the potential to constrain the distribution of neutral hydrogen in the intergalactic medium at redshift $\sim 13-17$. Using 15 hours of MWA data, we analyse systematics in this band such as radio-frequency interference (RFI), ionospheric and wide field effects. By updating the position of point sources, we mitigate the direction independent calibration error due to ionospheric offsets. Our calibration strategy is optimized for the lowest frequency bands by reducing the number of direction dependent calibrators and taking into account radio sources within a wider field of view. We remove data polluted by systematics based on the RFI occupancy and ionospheric conditions, finally selecting 5.5 hours of the cleanest data. Using these data, we obtain two sigma upper limits on the 21 cm power spectrum in the range of $0.1\lessapprox k \lessapprox 1 ~\rm ~h~Mpc^{-1}$ and at $z$=14.2, 15.2 and 16.5, with the lowest limit being $6.3\times 10^6 ~\rm mK^2$ at $\rm k=0.14 \rm ~h~Mpc^{-1}$ and at $z=15.2$ with a possibility of a few \% of signal loss due to direction independent calibration., Comment: 17 pages, 18 figures, accepted to MNRAS

We compute the spherically-averaged power spectrum from four seasons of data obtained for the Epoch of Reionisation (EoR) project observed with the Murchison Widefield Array (MWA). We measure the EoR power spectrum over $k= 0.07-3.0~h$Mpc$^{-1}$ at redshifts $z=6.5-8.7$. The largest aggregation of 110 hours on EoR0 high-band (3,340 observations), yields a lowest measurement of (43~mK)$^2$ = 1.8$\times$10$^3$ mK$^2$ at $k$=0.14~$h$Mpc$^{-1}$ and $z=6.5$ (2$\sigma$ thermal noise plus sample variance). Using the Real-Time System to calibrate and the CHIPS pipeline to estimate power spectra, we select the best observations from the central five pointings within the 2013--2016 observing seasons, observing three independent fields and in two frequency bands. This yields 13,591 2-minute snapshots (453 hours), based on a quality assurance metric that measures ionospheric activity. We perform another cut to remove poorly-calibrated data, based on power in the foreground-dominated and EoR-dominated regions of the two-dimensional power spectrum, reducing the set to 12,569 observations (419 hours). These data are processed in groups of 20 observations, to retain the capacity to identify poor data, and used to analyse the evolution and structure of the data over field, frequency, and data quality. We subsequently choose the cleanest 8,935 observations (298 hours of data) to form integrated power spectra over the different fields, pointings and redshift ranges., Comment: 19 pages, 29 figures, accepted for publication in Monthly Notices of the Royal Astronomical Society

The compact configuration of Phase II of the Murchison Widefield Array (MWA) consists of both a redundant subarray and pseudo-random baselines, offering unique opportunities to perform sky-model and redundant interferometric calibration. The highly redundant hexagonal cores give improved power spectrum sensitivity. In this paper, we present the analysis of nearly 40 hours of data targeting one of the MWA's EoR fields observed in 2016. We use both improved analysis techniques presented in Barry et al. (2019) as well as several additional techniques developed for this work, including data quality control methods and interferometric calibration approaches. We show the EoR power spectrum limits at redshift 6.5, 6.8 and 7.1 based on our deep analysis on this 40-hour data set. These limits span a range in $k$ space of $0.18$ $h$ $\mathrm{Mpc^{-1}}$ $

Measurements of 21 cm Epoch of Reionization (EoR) structure are subject to systematics originating from both the analysis and the observation conditions. Using 2013 data from the Murchison Widefield Array (MWA), we show the importance of mitigating both sources of contamination. A direct comparison between results from Beardsley et al. 2016 and our updated analysis demonstrates new precision techniques, lowering analysis systematics by a factor of 2.8 in power. We then further lower systematics by excising observations contaminated by ultra-faint RFI, reducing by an additional factor of 3.8 in power for the zenith pointing. With this enhanced analysis precision and newly developed RFI mitigation, we calculate a noise-dominated upper limit on the EoR structure of $\Delta^2 \leq 3.9 \times 10^3$ mK$^2$ at $k=0.20$ $\textit{h}$ Mpc$^{-1}$ and $z=7$ using 21 hr of data, improving previous MWA limits by almost an order of magnitude., Comment: 21 pages, 10 figures, published in ApJ, updated title and text

We apply two methods to estimate the 21~cm bispectrum from data taken within the Epoch of Reionisation (EoR) project of the Murchison Widefield Array (MWA). Using data acquired with the Phase II compact array allows a direct bispectrum estimate to be undertaken on the multiple redundantly-spaced triangles of antenna tiles, as well as an estimate based on data gridded to the $uv$-plane. The direct and gridded bispectrum estimators are applied to 21 hours of high-band (167--197~MHz; $z$=6.2--7.5) data from the 2016 and 2017 observing seasons. Analytic predictions for the bispectrum bias and variance for point source foregrounds are derived. We compare the output of these approaches, the foreground contribution to the signal, and future prospects for measuring the bispectra with redundant and non-redundant arrays. We find that some triangle configurations yield bispectrum estimates that are consistent with the expected noise level after 10 hours, while equilateral configurations are strongly foreground-dominated. Careful choice of triangle configurations may be made to reduce foreground bias that hinders power spectrum estimators, and the 21~cm bispectrum may be accessible in less time than the 21~cm power spectrum for some wave modes, with detections in hundreds of hours., Comment: 19 pages, 10 figures, accepted for publication in PASA

We explore methods for robust estimation of the 21 cm signal from the Epoch of Reionisation (EoR). A Kernel Density Estimator (KDE) is introduced for measuring the spatial temperature fluctuation power spectrum from the EoR. The KDE estimates the underlying probability distribution function of fluctuations as a function of spatial scale, and contains different systematic biases and errors to the typical approach to estimating the fluctuation power spectrum. Extraction of histograms of visibilities allows moments analysis to be used to discriminate foregrounds from 21 cm signal and thermal noise. We use the information available in the histograms, along with the statistical dis-similarity of foregrounds from two independent observing fields, to robustly separate foregrounds from cosmological signal, while making no assumptions about the Gaussianity of the signal. Using two independent observing fields to robustly discriminate signal from foregrounds is crucial for the analysis presented in this paper. We apply the techniques to 13 hours of Murchison Widefield Array (MWA) EoR data over two observing fields. We compare the output to that obtained with a comparative power spectrum estimation method, and demonstrate the reduced foreground contamination using this approach. Using the second moment obtained directly from the KDE distribution functions yields a factor of 2-3 improvement in power for k < 0.3hMpc^{-1} compared with a matched delay space power estimator, while weighting data by additional statistics does not offer significant improvement beyond that available for thermal noise-only weights., Comment: 19 pages, 18 figures, accepted for publication in MNRAS