Bayesian data analysis for sky-averaged 21-cm experiments with contamination from linearly polarized foregrounds

ABSTRACT The precise measurement of the sky-averaged H i signal against the radio background is the goal of global 21-cm cosmology. This measurement has the potential to unravel the underlying physics of cosmic structure formation and evolution during the Cosmic Dawn and the Epoch of Reionization. It is, however, hindered by various non-smooth, frequency-dependent effects, whose structures resemble those of the signal. One such effect is the leakage of polarized foregrounds into the measured intensity signal: polarized foreground emission undergoes Faraday rotation as it passes through the magnetic fields of the interstellar medium, imprinting a chromatic structure which complicates the extraction of the cosmological H i absorption feature. We investigate the effect of polarized Galactic foregrounds on extracting the global 21-cm signal from simulated data using REACH’s data analysis pipeline; the Radio Experiment for the Analysis of Cosmic Hydrogen (REACH) is an experiment designed to detect the sky-averaged 21-cm signal using physically informed models. Using the REACH pipeline, we successfully recover injected global 21-cm signals with an amplitude of approximately 0.16 K, centred between 80 and 120 MHz, achieving a low root-mean-square error (less than 30 per cent of the injected signal strength). This includes scenarios with simulated polarized Galactic diffuse emissions and polarized point source emissions, provided the overall polarization fraction is below ${\sim} 3~{{\ \rm per\ cent}}$. The linear mixing of contamination, caused by the superposition of multiple patches with varying strengths of Faraday rotation, produces patterns that are more distinct from the global signal. This distinction makes global signal recovery easier compared to contamination resulting from a single, slow oscillation pattern.