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.
