N. A. Silant'ev

Magnetic fields of AGNs and standard accretion disk model: testing by optical polarimetry

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 NGC4258. 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.

The appearance of polarization in radiation from hot stars due to the faraday rotation effect as a possible method of determining stellar magnetic fields

The effect of Faraday rotation is shown to lead to the appearance of linear polarization of stellar radiation scattered in an optically-thin circumstellar electron-magnetized shell, even in the case when the shell is spherical. The spectral dependence of the polarization degree is evaluated for scattering in (i) a spherically-symmetric magnetized shell with a power-law radial dependence of the electron density, and (ii) a non-spherical ellipsoidal uniform envelope. The position of maximum in the polarization spectrum permits us to determine the magnetic field magnitude on a star surface. If the rotational and magnetic axes do not coincide, the periodic variability of the polarization will be observed with the period of stellar rotation. Some Be-stars, such as γCas, 48 Lib, EW Lac, πAqr, HD 45677, X Per, are proposed as candidates to be investigated for magnetic fields, as well as some stars of the T Tau-type. This method may be also applied to supernovae shells.

Photon polarization and frequency change in multiple scattering

Abstract Maxwells equations were used to derive a system of equations for the Stokes parameters and for the intensity of multiply-scattered radiation in a medium, taking into consideration the change of the photon frequency. The coefficients of the equations are expressed in terms of the quantum-mechanical scattering amplitudes. There was obtained an analytical solution of the equations for the multiple Compton and Rayleigh scattering of photons and for the multiple scattering of photons by a free-oriented system in a thick slab, as well as a stationary and a nonstationary solution for a point source in an infinite medium.

A polarimetric method for measuring black hole masses in Active Galactic Nuclei

The structure of the broad emission line region (BLR) in active galactic nuclei (AGN) remains unclear. We test in this paper a flattened configuration model for BLR. The virial theorem, by taking into account the disc shape of BLR, allows us to get a direct connection between the mass of a supermassive black hole (SMBH) and the inclination angle of the accretion flow. The inclination angle itself is derived from the spectropolarimetric data on broad emission lines using the theory for the generation of polarized radiation developed by Sobolev and Chandrasekhar. As the result, the new estimates of SMBH masses in AGN with measured polarization of BLR are presented. It is crucial that the polarimetric data allow also to determine the value of the virial coefficient that is essential for determining SMBH masses.

Polarization of radiation of point-like source reflected from turbulent magnetized atmosphere

We consider the multiple scattering of the light from a point-like source located above the semi-infinite electron, turbulent, and magnetized atmospheres. The frozen magnetic field has both the regular B0 and stochastic B components (B = B0 + B). The stochastic Faraday rotations due to fluctuations Bdecrease the intensity of each separate polarized beam (the extinction factor is proportional to λ 4 � B � 2 � ). This decrease at large λ dominates the usual decrease (∝λ 2 B0 cos Θ0) caused by summing beams with very different Faradays rotation angles. This effect changes the spectrum of polarization degree as compared with what is influenced by the regular magnetic field. We calculated the integral (observed) polarization of the reflected radiation with the inclusion of unpolarized radiation going directly from the point-like source. We present the observed polarization for various degrees of true absorption of the radiation into the atmosphere and the values of magnetic energy fluctuations. The spectra of polarization in the optical (λ = 0-1 µm), infrared (λ = 1-5 µm), and X-ray (E = 1-50 keV) regions of the wavelengths are presented. We discuss the possibility of estimating parameters of magnetic field fluctuations from the observation of the spectra of polarization in AGNs with the X-ray excesses and in the turbulent accretion disk in NGC 4258.

Solution of the Milne Problem for a Magnetized Atmosphere

The Milne problem is solved numerically for a magnetized semi-infinite electron atmosphere in the case where the magnetic field is directed along the normal to the medium. The calculated angular distribution, degree of linear polarization, and positional angle of inclination of the plane of polarization of the emerging radiation are given in tables for a number of values of the Faraday rotation parameter and for degrees of intrinsic optical absorption, q=0, 0.2, and 0.4. It is assumed that the magnetic field B≤106 G, so that scattering in the optical range is purely Thomson scattering.

New mechanism of radiation polarization in type 1 Seyfert active galactic nuclei

In most of Seyfert-1 active galactic nucei (AGN) the optical linear continuum polarization degree is usually small (less than 1%) and the polarization position angle is nearly parallel to the AGN radio-axis. However, there are many types-1 AGNs with unexplained intermediate values for both positional angles and polarization degrees. Our explanation of polarization degree and positional angle of Seyfert-1 AGNs focuses on the reflection of non-polarized radiation from sub-parsec jets in optically thick accretion discs. The presence of a magnetic field surrounding the scattering media will induce Faraday rotation of the polarization plane that may explain the intermediate values of positional angles if there is a magnetic field component normal to the accretion disc. The Faraday rotation depolarization effect in disc diminishes the competition between polarization of the reflected radiation with the parallel component of polarization and the perpendicular polarization from internal radiation of disc (the Milne problem) in favor of polarization of reflected radiation. This effect allows us to explain the observed polarization of Seyfert-1 AGN radiation even though the jet optical luminosity is much lower than the luminosity of disc. We present the calculation of polarization degrees for a number of Seyfert-1 AGNs.

Magnetic fields of active galactic nuclei and quasars: Redshift dependence

The observed reduction in the fraction of quasars with polarized radiation as the redshift increases is explained by an increase in the magnetic-field strength in accretion disks at high z. The emerging Faraday rotation causes the radiation to be depolarized. This mechanism allows the magnetic fields in accretion disks to be estimated at several hundred gauss. We give simple asymptotic formulas that describe the Faraday depolarization in optically thick accretion disks.