On the contamination of the global 21~cm signal from polarized foregrounds

Global (i.e. sky-averaged) $21$~cm signal experiments can measure the evolution of the universe from the Cosmic Dawn to the Epoch of Reionization. These measurements are challenged by the presence of bright foreground emission that can be separated from the cosmological signal if its spectrum is smooth. This assumption fails in the case of single polarization antennas as they measure linearly polarized foreground emission - which is inevitably Faraday rotated through the interstellar medium. We investigate the impact of Galactic polarized foregrounds on the extraction of the global 21~cm signal through realistic sky and dipole simulations both in a low frequency band from $50$ to $100$~MHz, where a 21~cm absorption profile is expected, and in a higher frequency band ($100-200$~MHz). We find that the presence of a polarized contaminant with complex frequency structure can bias the amplitude and the shape of the reconstructed signal parameters in both bands. We investigate if polarized foregrounds can explain the unexpected $21$~cm Cosmic Dawn signal recently reported by the EDGES collaboration. We find that unaccounted polarized foreground contamination can produce an enhanced and distorted $21$~cm absorption trough similar to the anomalous profile reported by Bowman et al. (2018), and whose amplitude is in mild tension with the assumed input Gaussian profile (at $\sim 1.5 \sigma$ level). Moreover, we note that, under the hypothesis of contamination from polarized foreground, the amplitude of the reconstructed EDGES signal can be overestimated by around $30\%$, mitigating the requirement for an explanation based on exotic physics.