The Black Hole Mass and Magnetic Field Correlation in AGN: Testing by Optical Polarimetry

We consider the integral light polarization from optically thick accretion disks. Basic mechanism is the multiple light scattering on free electrons (Milne's problem) in magnetized atmosphere. The Faraday rotation of the polarization plane changes both the value of integral polarization degree $p$ and the position angle $\chi$. Besides, the characteristic spectra of these values appear. We are testing the known relation between magnetic field of black hole at the horizon $B_{BH}$ and its mass $M_{BH}$, and the usual power-law distribution inside the accretion disk. The formulae for $p(\lambda)$ and $\chi(\lambda)$ depend on a number of parameters describing the particular dependence of magnetic field in accretion disk (the index of power-law distribution, the spin of the black hole, etc.). Comparison of our theoretical values of $p$ and $\chi$ with observed polarization can help us to choice more realistic values of parameters if the accretion disk mechanism gives the main contribution to the observed integral polarization. The main content is connected with estimation of validity of the relation between $B_{BH}$ and $M_{BH}$. We found for the AGN NGC 4258 that such procedure does not confirm the mentioned correlation between magnetic field and mass of black hole.