A Bayesian approach to high fidelity interferometric calibration II: demonstration with simulated data

TL;DR

This paper demonstrates that BayesCal, a Bayesian calibration method, significantly reduces calibration errors in simulated interferometric data, enabling more accurate recovery of the 21 cm power spectrum compared to traditional approaches.

Contribution

The paper introduces and validates BayesCal for high-fidelity interferometric calibration, showing its superior performance in reducing spurious gain fluctuations and improving spectral fidelity.

Findings

BayesCal achieves up to four orders of magnitude lower gain fluctuation power.

It provides unbiased 21 cm power spectrum recovery on large spectral scales.

Traditional methods are less effective in suppressing calibration errors.

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 four 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 $\sim10^7$ and $\sim10^{10}$ 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 ($k_\parallel \lesssim 0.15~h\mathrm{Mpc}^{-1}$). In all other cases, in the completeness regimes studied, those scales are contaminated.