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Precise instrumental calibration is of crucial importance to 21-cm cosmology experiments. The Murchison Widefield Array's (MWA) Phase II compact configuration offers us opportunities for both redundant calibration and sky-based calibration algorithms; using the two in tandem is a potential approach to mitigate calibration errors caused by inaccurate sky models. The MWA Epoch of Reionization (EoR) experiment targets three patches of the sky (dubbed EoR0, EoR1, and EoR2) with deep observations. Previous work in Li et al. (2018) and (2019) studied the effect of tandem calibration on the EoR0 field and found that it yielded no significant improvement in the power spectrum (PS) over sky-based calibration alone. In this work, we apply similar techniques to the EoR1 field and find a distinct result: The improvements in the PS from tandem calibration are significant. To understand this result, we analyse both the calibration solutions themselves and the effects on the PS over three nights of EoR1 observations. We conclude that the presence of the bright radio galaxy Fornax A in EoR1 degrades the performance of sky-based calibration, which in turn enables redundant calibration to have a larger impact. These results suggest that redundant calibration can indeed mitigate some level of model incompleteness error.

To make a power spectrum (PS) detection of the 21-cm signal from the Epoch of Reionisation (EoR), one must avoid/subtract bright foreground sources. Sources such as Fornax A present a modelling challenge due to spatial structures spanning from arc seconds up to a degree. We compare modelling with multi-scale (MS) CLEAN components to 'shapelets', an alternative set of basis functions. We introduce a new image-based shapelet modelling package, SHAMFI. We also introduce a new CUDA simulation code (WODEN) to generate point source, Gaussian, and shapelet components into visibilities. We test performance by modelling a simulation of Fornax A, peeling the model from simulated visibilities, and producing a residual PS. We find the shapelet method consistently subtracts large-angular-scale emission well, even when the angular resolution of the data is changed. We find that when increasing the angular resolution of the data, the MS CLEAN model worsens at large angular scales. When testing on real Murchison Widefield Array data, the expected improvement is not seen in real data because of the other dominating systematics still present. Through further simulation, we find the expected differences to be lower than obtainable through current processing pipelines. We conclude shapelets are worthwhile for subtracting extended galaxies, and may prove essential for an EoR detection in the future, once other systematics have been addressed.

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 h 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 h, 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.

© 2019 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society. We explore methods for robust estimation of the 21 cm signal from the Epoch of Reionization (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 h of Murchison Widefield Array 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 < 0.3 h Mpc-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.

Structure imprinted in foreground extragalactic point sources by ionospheric refraction has the potential to contaminate Epoch of Reionization (EoR) power spectra of the 21 cm emission line of neutral hydrogen. The alteration of the spatial and spectral structure of foreground measurements due to total electron content gradients in the ionosphere creates a departure from the expected sky signal. We present a general framework for understanding the signatures of ionospheric behavior in the 2D neutral hydrogen power spectrum measured by a low-frequency radio interferometer. Two primary classes of ionospheric behavior are considered, corresponding to dominant modes observed in Murchison Widefield Array (MWA) EoR data, namely, anisotropic structured wave behavior and isotropic turbulence. Analytic predictions for power spectrum bias due to this contamination are computed and compared with simulations. We then apply the ionospheric metric described in Jordan et al. to study the impact of ionospheric structure on MWA data, by dividing MWA EoR data sets into classes with good and poor ionospheric conditions, using sets of matched 30-minute observations from 2014 September. The results are compared with the analytic and simulated predictions, demonstrating the observed bias in the power spectrum when the ionosphere is active (displays coherent structures or isotropic turbulence). The analysis demonstrates that unless ionospheric activity can be quantified and corrected, active data should not be included in EoR analysis in order to avoid systematic biases in cosmological power spectra. When data are corrected with a model formed from the calibration information, bias reduces below the expected 21 cm signal level. Data are considered "quiet" when the median measured source position offsets are less than 10farcs–15farcs.

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We present the 21 cm power spectrum analysis approach of the Murchison Widefield Array Epoch of Reionization project. In this paper, we compare the outputs of multiple pipelines for the purpose of validating statistical limits cosmological hydrogen at redshifts between 6 and 12. Multiple independent data calibration and reduction pipelines are used to make power spectrum limits on a fiducial night of data. Comparing the outputs of imaging and power spectrum stages highlights differences in calibration, foreground subtraction, and power spectrum calculation. The power spectra found using these different methods span a space defined by the various tradeoffs between speed, accuracy, and systematic control. Lessons learned from comparing the pipelines range from the algorithmic to the prosaically mundane; all demonstrate the many pitfalls of neglecting reproducibility. We briefly discuss the way these different methods attempt to handle the question of evaluating a significant detection in the presence of foregrounds., National Science Foundation (U.S.) (award AST-1109257), National Science Foundation (U.S.). Astronomy and Astrophysics Postdoctoral Fellowship (award AST 1109257), Australian Research Council (DECRA Award DEI140100316), National Science Foundation (U.S.) (grant AST-1410484), National Science Foundation (U.S.) (grant AST-0821321), National Science Foundation (U.S.) (grant AST-0457585), National Science Foundation (U.S.) (grant PHYS-0835713), National Science Foundation (U.S.) (grant CAREER-0847753), National Science Foundation (U.S.) (grant AST-0908884), Australian Research Council (LIEF grant LE0775621), Australian Research Council (LIEF grant LE0882938), Smithsonian Astrophysical Observatory, Massachusetts Institute of Technology. School of Science, Raman Research Institute, Australian National University, Victoria University of Wellington, New Zealand. Ministry of Economic Development (grant MED-E1799), IBM Research (Shared University Research Grant)