Polarization from magnetized accretion discs: II. The effects of   absorption opacity on Faraday rotation
  Equipartition magnetic fields can dramatically affect the polarization of radiation emerging from accretion disk atmospheres in active galactic nuclei. We extend our previous work on this subject by exploring the interaction between Faraday rotation and absorption opacity in local, plane-parallel atmospheres with parameters appropriate for accretion discs. Faraday rotation in pure scattering atmospheres acts to depolarize the radiation field by rotating the polarization planes of photons after last scattering. Absorption opacity in an unmagnetized atmosphere can increase or decrease the polarization compared to the pure scattering case, depending on the thermal source function gradient. Combining both Faraday rotation and absorption opacity, we find the following results. If absorption opacity is much larger than scattering opacity throughout the atmosphere, then Faraday rotation generally has only a small effect on the emerging polarization because of the small electron column density along a photon mean free path. However, if the absorption opacity is not too large and it acts alone to increase the polarization, then the effects of Faraday rotation can be enhanced over those in a pure scattering atmosphere. Finally, while Faraday rotation often depolarizes the radiation field, it can in some cases increase the polarization when the thermal source function does not rise too steeply with optical depth. We confirm the correctness of the Silant'ev (1979) analytic calculation of the high magnetic field limit of the pure scattering atmosphere, which we incorrectly disputed in our previous paper. 
Eric Agol (1), Omer Blaes (1) and Cristian Ionescu-Zanetti (2) ((1)   University of California at Santa Barbara, (2) Univers...