The Role of Faraday Rotation in the Polarization of the X-Rays from Magnetically Powered Black Hole Coronas

Abstract Magnetic reconnection is one of the prime candidate mechanisms that may energize the plasma emitting the strongly polarized X-ray emission from black hole X-ray binaries (BHXRBs) in their hard states. The mechanism requires strong magnetic fields in the upstream plasma entering the reconnection layer, and weaker, but still substantial, magnetic fields in the downstream regions. In this Letter, we estimate the coronal magnetic fields for three different magnetic energy dissipation mechanisms: plasmoid-dominated magnetic reconnection, fast collisionless reconnection, and magnetic field relaxation. We show that the lack of strong Faraday depolarization constrains viable models and can be used to benchmark numerical accretion flow models. We conclude by discussing the difficulties of disentangling the various effects that can depolarize the signals from BHXRBs at low energies. We furthermore emphasize that Faraday rotation is unlikely to play a role in the polarization of the coronal X-ray emission of active galactic nuclei.