Patterns of primary beam non-redundancy in close-packed 21 cm array observations

Abstract

Radio interferometer arrays such as HERA consist of many close-packed dishes arranged in a regular pattern, giving rise to a large number of `redundant' baselines with the same length and orientation. Since identical baselines should see an identical sky signal, this provides a way of finding a relative gain/bandpass calibration without needing an explicit sky model. In reality, there are many reasons why baselines will not be exactly identical, giving rise to a host of effects that spoil the redundancy of the array and induce spurious structure in the calibration solutions if not accounted for. In this paper, we seek to build an understanding of how differences in the primary beam response between antennas affect redundantly-calibrated interferometric visibilities and their resulting frequency (delay-space) power spectra. We use simulations to study several generic types of primary beam variation, including differences in the width of the main lobe, the angular and frequency structure of the sidelobes, and the beam ellipticity and orientation. For all of these types, we find that additional temporal structure is induced in the gain solutions, particularly when bright point sources pass through the beam. In comparison, only a low level of additional spectral structure is induced. The temporal structure modulates the cosmological 21cm power spectrum, but only at the level of a few percent in our simulations. We also investigate the possibility of signal loss due to decoherence effects when non-redundant visibilities are averaged together, finding that the decoherence is worst when bright point sources pass through the beam, and that its magnitude varies significantly between baseline groups and types of primary beam variation. Redundant calibration absorbs some of the decoherence effect however, reducing its impact compared to if the visibilities were perfectly calibrated.

22 pages, 19 figures, accepted for publication in MNRAS

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• Statistical recovery of 21cm visibilities and their power spectra with Gaussian constrained realisations and Gibbs sampling
• The Impact of Beam Variations on Power Spectrum Estimation for 21-cm Cosmology I: Simulations of Foreground Contamination for HERA
• Methods of Error Estimation for Delay Power Spectra in $21\text{cm}$ Cosmology
• On the use of temporal filtering for mitigating galactic synchrotron calibration bias in 21 cm reionization observations
• A Bayesian approach to high fidelity interferometric calibration II: demonstration with simulated data
• Probing early universe through redshifted 21-cm signal: Modelling and observational challenges
• SKA-Low Intensity Mapping Pathfinder Updates: Deeper 21 cm Power Spectrum Limits from Improved Analysis Frameworks
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• Sensitivity of Bayesian 21 cm power spectrum estimation to foreground model errors
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• Field-level Reconstruction from Foreground-Contaminated 21-cm Maps
• Simulations of primary beam effects on the cosmic bispectrum phase observed with the Hydrogen Epoch of Reionization Array
• The impact of lunar topography on the 21-cm power spectrum for grid-based arrays : Insights for the Dark-ages EXplorer (DEX)
• A Bayesian approach to high fidelity interferometric calibration I: mathematical formalism
• Clustering redshifts with the 21cm-galaxy cross-bispectrum
• Generalized Redundant Calibration of Radio Interferometers