Redundant-baseline calibration of the hydrogen epoch of reionization array

Abstract

In 21 cm cosmology, precision calibration is key to the separation of the neutral hydrogen signal from very bright but spectrally-smooth astrophysical foregrounds. The Hydrogen Epoch of Reionization Array (HERA), an interferometer specialized for 21 cm cosmology and now under construction in South Africa, was designed to be largely calibrated using the self-consistency of repeated measurements of the same interferometric modes. This technique, known as redundant-baseline calibration resolves most of the internal degrees of freedom in the calibration problem. It assumes, however, on antenna elements with identical primary beams placed precisely on a redundant grid. In this work, we review the detailed implementation of the algorithms enabling redundant-baseline calibration and report results with HERA data. We quantify the effects of real-world non-redundancy and how they compare to the idealized scenario in which redundant measurements differ only in their noise realizations. Finally, we study how non-redundancy can produce spurious temporal structure in our calibration solutions—both in data and in simulations—and present strategies for mitigating that structure.

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.…”

“…Closure phase quantities, however, are affected by directiondependent effects such as varying antenna primary beams due to mutual coupling induced by a very compact configuration (e.g., Fagnoni et al 2021;Josaitis et al 2021). 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).…”

Array Element Coupling in Radio Interferometry I: A Semi-Analytic Approach

“…First-order coupling makes baselines which were otherwise redundant no longer have identical sky responses. For redundantly-configured arrays such as HERA to achieve the measurement sensitivity required to make interferometric measurements of the EoR (the principal scientific goal of the experiment) in any practical duration of observation time, it is imperative, according to analyses such as those presented in Dillon et al (2020), that visibilities from redundant baselines be able to be redundantly averaged -for at least some subset of fringe and delay space. It is beyond the scope of this paper to further address the challenge of nonredundancy caused by array element coupling, but a follow-up study could investigate filtering strategies whereby first-order visibilities of redundant baselines may continue to be identical in certain subsets of fringe and delay space, at least to the level of EoR sensitivity.…”

Developing a Real-Time Processing System for HERA

“…Furthermore, there are several steps that are effectively prerequisite for a subsequent step. For example, an initial calibration solution is determined using a redundant calibration technique [4], after which a sky-referenced calibration is performed [5]. The redundant calibration must be performed before the absolute calibration, though only for each data file specifically.…”