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We have developed the method that allows us to estimate the magnetic field strength at the horizon of a supermassive black hole (SMBH) through the observed polarization of optical emission of the accreting disk surrounding SMBH. The known asymptotic formulae for the Stokes parameters of outgoing radiation are azimuthal averaged, which corresponds to an observation of the disk as a whole. We consider two models of the embedding 3D-magnetic field, the regular field, and the regular field with an additional chaotic (turbulent) component. It is shown that the second model is preferable for estimating the magnetic field in NGC 4258. For estimations we used the standard accretion disk model assuming that the same power-law dependence of the magnetic field follows from the range of the optical emission down to the horizon. The observed optical polarization from NGC 4258 allowed us to find the values 10 3 −10 4 Gauss at the horizon, depending on the particular choice of the model parameters. We also discuss the wavelength dependencies of the light polarization, and possibly applying them for a more realistic choice of accretion disk parameters.

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We estimated the magnetic field strength at the horizon radius of black holes, that is derived by the magnetic coupling process and depended on the black hole mass M BH and the accretion rate Ṁ . Our estimation is based on the use of the fundamental variability plane for stellar mass black holes, AGNs and QSOs. The typical values of magnetic field strength on the black hole horizon are appeared at the level of B BH ∼ 10 8 G for stellar mass black holes and B BH ∼ 10 4 G for the supermassive black holes. We have obtained the relation p l ∼ ν −1/2 b between the intrinsic polarization of the accretion disk radiation and the characteristic frequency of the black hole X-ray variability.

We present estimates of magnetic field in a number of AGNs from the Spectropolarimetric atlas of Smith, Young & Robinson (2002) from the observed degrees of linear polarization and the positional angles of spectral lines (Hα) (broad line regions of AGNs) and nearby continuum. The observed degree of polarization is lower than the Milne value in a nonmagnetized atmosphere. We hypothesize that the polarized radiation escapes from optically thick magnetized accretion discs and is weakened by the Faraday rotation effect. The Faraday rotation depolarization effect is able to explain both the value of the polarization and the position angle. We estimate the required magnetic field in the broad line region by using simple asymptotic analytical formulas for Milne's problem in magnetized atmosphere, which take into account the last scattering of radiation before escaping from the accretion disc. The polarization of a broad spectral line escaping from disc is described by the same mechanism. The characteristic features of polarization of a broad line is the minimum of the degree of polarization in the center of the line and continuous rotation of the position angle from one wing to another. These effects can be explained by existence of clouds in the left (keplerian velocity is directed to an observer) and the right (keplerian velocity is directed from an observer) parts of the orbit in a rotating keplerian magnetized accretion disc. The base of explanation is existence of azimuthal magnetic field in the orbit. The existence of normal component of magnetic field (usually weak) makes the picture of polarization asymmetric. The existence of clouds in left and right parts of the orbit with different emissions also give the contribution in asymmetry effect. Assuming a power-law dependence of the magnetic field inside the disc, we obtain the estimate of the magnetic field strength at first stable orbit near the central supermassive black hole (SMBH) for a number of AGNs from the mentioned Spectropolarimetric atlas.