Detectability of Galactic Faraday Rotation in Multi-wavelength CMB Observations: A Cross-Correlation Analysis of CMB and Radio Maps

We introduce a new cross-correlation method to detect and verify the astrophysical origin of Faraday Rotation (FR) in multiwavelength surveys. FR is well studied in radio astronomy from radio point sources but the $\lambda^{2}$ suppression of FR makes detecting and accounting for this effect difficult at millimeter and sub-millimeter wavelengths. Therefore statistical methods are used to attempt to detect FR in the cosmic microwave background (CMB). Most estimators of the FR power spectrum rely on single frequency data. In contrast, we investigate the correlation of polarized CMB maps with FR measure maps from radio point sources. We show a factor of $\sim30$ increase in sensitivity over single frequency estimators and predict detections exceeding $10\sigma$ significance for a CMB-S4 like experiment. Improvements in observations of FR from current and future radio polarization surveys will greatly increase the usefulness of this method.