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.

Simulations of primary beam effects on the cosmic bispectrum phase observed with the Hydrogen Epoch of Reionization Array

“…In field 2 and 3 where there are bright emissions on the sidelobe, the non-redundancy proves to be higher, with a non-redundancy value of ∼ 6% and ∼ 7% respectively, qualitatively previous works (e.g., Choudhuri et al 2021) have also shown similar results. These values are also well within the 10% non-redundancy estimated by previous studies (e.g., Dillon et al 2020).…”

“…In summary, our simulations show that, in the presence of bright emissions on the sidelobes, we may expect the power to leak at high 𝑘 values, and the power leakage increases with brightness of sources on the sidelobes. Indeed, previous work by Choudhuri et al (2021) shows similar results, as well as analysis of HERA data (e.g., Kern et al 2020;Dillon et al 2020). In addition, our simulations also show that the presence of bright sources on the main lobe mitigates the power leakage by dominating the overall closure spectra.…”

“…Variations of primary beams across the array invalidates the assumption of redundancy (i.e., that baselines with the same length and orientation measure exactly the same signal from the sky) which is the core of the HERA calibration strategy (Dillon et al 2020). Several authors have empirically simulated the impact that deviations from redundancy have on the calibration and proposed possible mitigation schemes (Ewall-Wice et al 2017;Joseph et al 2018;Orosz et al 2019;Choudhuri et al 2021). It has been established that variations from redundancy due to enhanced structure in primary beams couples foreground structure observed through sidelobes into spectral structure in calibration solutions (Orosz et al 2019;Kern et al 2020;Choudhuri et al 2021).…”

“…Several authors have empirically simulated the impact that deviations from redundancy have on the calibration and proposed possible mitigation schemes (Ewall-Wice et al 2017;Joseph et al 2018;Orosz et al 2019;Choudhuri et al 2021). It has been established that variations from redundancy due to enhanced structure in primary beams couples foreground structure observed through sidelobes into spectral structure in calibration solutions (Orosz et al 2019;Kern et al 2020;Choudhuri et al 2021).…”

Precision Calibration of Radio Interferometers for 21 cm Cosmology with No Redundancy and Little Knowledge of Antenna Beams and the Radio Sky

“…), positional errors, and over-the-air mutual coupling between antennas (Fagnoni et al 2021;Josaitis et al in preparation.). Joseph et al (2018) demonstrate that small errors in antenna positions lead to significant biases in redundant calibration solutions and Orosz et al (2019) find that gain solution errors arising from expected levels of non-redundancy introduce foreground contamination can exceed 21 cm fluctuations by orders of magnitude while Choudhuri et al (2021) determined that these errors also cause mild decoherence in the 21 cm fluctuations themselves. The equations in redundant calibration still admit frequency dependent degeneracies which must still be solved for by referencing back to a sky-model and the associated errors can be amplified by redundant antenna arrangements (Byrne et al 2019).…”