Polarization from a Strongly Magnetized Accretion Disks: Asymptotic Wavelength Behaviour

We calculate the polarization of radiation from thick accretion disks with vertically averaged global magnetic field. The polarization arises as a result of the radiation scattering by free electrons in magnetized plasma of a disk. We consider as a basic effect the Faraday rotation of polarization plane along the photon propagation in a magnetized disk. The various models of optically thick accretion disk with a vertically averaged magnetic field are considered. The main goal of this paper is to obtain simple asymptotic formulae for the polarization of radiation when the Faraday rotation angle >> 1 at the Thomson optical length ~1. The results of our calculation allows us to estimate the magnetic field magnitude near the marginally stable orbit region of a black hole via the data of polarimetric observations including the expected future X-ray polarimetric observations. The wavelength dependence of polarization is strongly dependent on various models of an accretion disks and thus allows to choose a real model from the polarization data.