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ABSTRACT In a companion paper, we presented bayescal, a mathematical formalism for mitigating sky-model incompleteness in interferometric calibration. In this paper, we demonstrate the use of bayescal to calibrate the degenerate gain parameters of full-Stokes simulated observations with a HERA-like hexagonal close-packed redundant array, for three assumed levels of completeness of the a priori known component of the calibration sky model. We compare the bayescal calibration solutions to those recovered by calibrating the degenerate gain parameters with only the a priori known component of the calibration sky model both with and without imposing physically motivated priors on the gain amplitude solutions and for two choices of baseline length range over which to calibrate. We find that bayescal provides calibration solutions with up to 4 orders of magnitude lower power in spurious gain amplitude fluctuations than the calibration solutions derived for the same data set with the alternate approaches, and between ∼107 and ∼1010 times smaller than in the mean degenerate gain amplitude, on the full range of spectral scales accessible in the data. Additionally, we find that in the scenarios modelled only bayescal has sufficiently high fidelity calibration solutions for unbiased recovery of the 21-cm power spectrum on large spectral scales (k∥ ≲ 0.15 hMpc−1). In all other cases, in the completeness regimes studied, those scales are contaminated. 

ABSTRACT High-fidelity radio interferometric data calibration that minimizes spurious spectral structure in the calibrated data is essential in astrophysical applications, such as 21 cm cosmology, which rely on knowledge of the relative spectral smoothness of distinct astrophysical emission components to extract the signal of interest. Existing approaches to radio interferometric calibration have been shown to impart spurious spectral structure to the calibrated data if the sky model used to calibrate the data is incomplete. In this paper, we introduce BayesCal: a novel solution to the sky-model incompleteness problem in interferometric calibration, designed to enable high-fidelity data calibration. The BayesCal data model supplements the a priori known component of the forward model of the sky with a statistical model for the missing and uncertain flux contribution to the data, constrained by a prior on the power in the model. We demonstrate how the parameters of this model can be marginalized out analytically, reducing the dimensionality of the parameter space to be sampled from and allowing one to sample directly from the posterior probability distribution of the calibration parameters. Additionally, we show how physically motivated priors derived from theoretical and measurement-based constraints on the spectral smoothness of the instrumental gains can be used to constrain the calibration solutions. In a companion paper, we apply this algorithm to simulated observations with a HERA-like array and demonstrate that it enables up to four orders of magnitude suppression of power in spurious spectral fluctuations relative to standard calibration approaches.