N. A. Silant’ev

Magnetic fields of active galactic nuclei and quasars with regions of polarized broad Hα lines

Estimates of magnetic fields for a number of active galactic nuclei are presented. These estimates are based on the observed polarization degrees and position angles of broad Hα lines and in the nearby continuum and on asymptotic analytical formulas for the Stokes parameters of the radiation emerging from a magnetized accretion disk (the Milne problem in a magnetized atmosphere). The characteristic observed feature of the wavelength dependence of the polarization degree inside the line—a minimum at the center and a fast increase of the position angle from one wing to another—can be explained by the superposition of resonance emission from two or more clouds located in the right (Keplerian velocity directed away from the observer) and left (Keplerian velocity directed toward the observer) parts of the orbit in the rotating magnetized accretion disk. The main component in our mechanism is the azimuthal magnetic field in the disk. The presence of a magnetic field perpendicular to the disk plane (which is usually weaker than the azimuthal field) results in the asymmetry of the distribution of the polarization degree and position angle inside the line. The inferred magnetic field strengths at the galactocentric distances where broad lines are emitted can be used to estimate the magnetic fields in the region of the centermost stable orbit and at the horizon of the central black hole, using the power-law dependence of the magnetic field strength corresponding to the standard model of the accretion disk.

Polarimetric differences between Schwarzschild and Kerr black holes in active galactic nuclei

If the linear polarization of the optical emission of active galactic nuclei (AGNs) arises in magnetized accretion disk (the Milne problem), the degree of polarization should depend strongly on the spin of the central black hole. For the same black hole luminosities and masses, the polarization is substantially higher for rotating Kerr than for non-rotating Schwarzschild black holes. Statistically, this means that the majority of AGNs displaying appreciable linear polarization should have Kerr black holes. The spin dependence of the polarization is due to the fact that the radius of the innermost stable circular orbit risco depends on the spin—this radius is three gravitational radii for a Schwarzschild black hole, and a factor of six smaller for a rapidly rotating black hole. This means that the magnetic field in the region of emergence of the optical emission, which decreases with distance from risco, is higher for a non-rotating than for a rapidly rotating black hole. This higher magnetic field gives rise to strong Faraday depolarization, explaining the effect considered here.

Polarization of radiation in turbulent magnetized atmospheres

Multiple scattering of radiation in a semi-infinite electron atmosphere in the absence of true absorption (the Milne problem) is considered. The electron plasma is assumed to be turbulent, i.e., the magnetic field B has a regular B0 and a stochastic B′ component (B = B0 + B′). Faraday rotation of the plane of polarization (s8 λ2B0 cos gJ) due to the field B0 depolarizes the outcoming radiation due to the superposition of rays with different polarization-angle rotations, corresponding to different paths traveled before they left the atmosphere. Stochastic Faraday rotation due to isotropic fluctuations, B′, efficiently decreases the amplitude of the polarization of each individual beam as it travels through the turbulent atmosphere. This effect is proportional to λ4 〈(B′)2〉, and becomes the dominant factor at large λ. We use the Ambartsumian-Chandrasekhar invariance principle, which results in six nonlinear equations (for the field B0 perpendicular to the surface of the medium). We also compute the degree of polarization for the cases B0 = 0, B′ ≠ 0, and B′ = 0, B0 ≠ 0, and for a number of versions of the general case, B0 ≠ 0, B′ ≠ 0. The spectra of the degree of polarization (for the case B0 = 0) are presented for optical (λ = 0 − 1 μm), infrared (λ = 1−5 μm), and X-ray (1–50 keV) wavelengths.

Polarization of radiation from a strongly magnetized accretion disk: The asymptotic spectral distribution

We calculate the polarization of the radiation from an optically thick accretion disk with a vertical averaged magnetic field. The polarization arises from the scattering of light by free electrons in a magnetized disk plasma. The Faraday rotation of the polarization plane during the propagation of a photon in a medium with a magnetic field is considered as the main effect. We discuss various models of optically thick accretion disks with a vertical averaged magnetic field. Our main goal is to derive simple asymptotic formulas for the polarization of radiation in the case where the Faraday rotation angle Ψ ≫ 1 at the Thomson optical depth τ = 1. The results of our calculations allow the magnetic field strength in the region of the marginally stable orbit near a black hole to be estimated from polarimetric observations, including X-ray observations expected in the future. Since the polarization spectrum of the radiation strongly depends on the accretion disk model, a realistic physical model of the accretion disk can be determined from data on the polarization of its radiation.

Depolarization of multiple scattered light in atmospheres due to anisotropy of small grains and molecules. II. The problems with sources

In the previous paper we considered two classic problems—the diffuse reflection of the light beam from semi-infinite atmosphere, and the Milne problem. For both problems we used the technique of invariance principle. In this paper we consider the solution of the problem when in semi-infinite atmosphere the sources of unpolarized radiation exist. It is assumed that the atmosphere is non-conservative and consists of freely oriented anisotropic grains and molecules and free electrons. Here we use the technique of the resolvent matrices. The consideration is restricted to derivation of simple formulas for the intensity and linear polarization of radiation emerging from semi-infinite atmosphere. These formulas can be used for interpretation of observational data. We consider only continuum radiation.

Magnetic fields and quasi-periodic oscillations of black hole radiation

Various relations are found between the key parameters of black holes and active galactic nuclei. Some have a statistical property, others follow from the theoretical consideration of the evolution of these objects. In this paper we use a recently discovered empirical relation between the characteristic frequency of quasi-periodic oscillations of radiation νbr of black holes, their masses and matter accretion rates to determine the magnetic field strength BH at the black hole event horizon. Since the characteristic frequency can be determined from observations, the use of a new relation for the estimations of magnetic field BH can yield more definite results, since we are decreasing the number of the unknown or poorly-determined parameters of objects (it especially concerns the accretion rate Ṁ). The typical values which we have found are BH ≃ 108G for the stellar mass black holes, and BH ≃ 104G for the supermassive black holes. Besides, we demonstrate that if the linear polarization of an object is caused by the radiation of a magnetized accretion disk, then the degree of observable polarization is p ∼ νbr−1/2.

Polarization effects in the radiation of magnetized envelopes and extended accretion structures

We have calculated the degree and position angle of the polarization of radiation scattered in a magnetized, optically thin or optically thick envelope around a central source, taking into account Faraday rotation of the plane of polarization during the propagation of the scattered radiation and the finite size of the radiation source. The wavelength dependence of the degree of polarization can be used to estimate the magnetic field of the source (a star, the region around a neutron star, or a black hole), and we have used our calculations to estimate the magnetic fields in a number of individual objects: several hot O and Wolf-Rayet stars, compact objects in X-ray close binaries with black holes (SS 433, Cyg X-1), and supernovae. The spectrum of the linear polarization can be used to determine the magnetic field in the vicinity of a central supermassive black hole, where the polarized optical radiation is generated. In a real physical model, this value can be extrapolated to the region of the last stable orbit. In the future, the proposed technique will make it possible to directly estimate the magnetic field in the region of the last stable orbit of a supermassive black hole using X-ray polarimetry.

Depolarization of multiple scattered light in atmospheres due to anisotropy of small grains and molecules

Freely oriented small anisotropic grains and molecules depolarize radiation both in single scattering and in the process of multiple scattering. Especially large depolarization occurs for resonant scattering corresponding to the electron transitions between the energy levels with very different quantum numbers. The existence of light absorption also changes essentially the angular distribution and polarization of radiation, outgoing from an atmosphere. In the present paper we consider these effects in detail both for continuum radiation and for resonant lines. Because the term describing the depolarization deals with isotropic radiation, we consider the axially symmetric part of radiation. We derived the formulas for observed intensity and polarization using the invariance-principles both for continuum and resonant scattering. We confine ourselves to two problems—the diffuse reflection of the light beam from semi-infinite atmosphere, and the Milne problem.

Wavelength dependence of the polarization of radiation from an accretion disk: Testing accretion disk models

We show that a fundamental choice between various models of an accretion disk around a black hole can be made based on the spectral wavelength distribution of the polarization. This conclusion is based on the possibility of comparing the observed spectral distribution of the polarization with its theoretical values obtained in various accretion disk models. The expected power-law wavelength (frequency) dependences of the polarization for various accretion disk models known in the literature are presented in the table.

A nonlinear theory of turbulent diffusion

It is shown that the well-known conservation laws for magnetic helicity and passive-scalar fluctuation intensity in the case of negligible molecular diffusion require that the hierarchy of nonlinear equations for the averaged Green function and the hierarchy of Bethe-Salpeter-type equations for fluctuation intensity be treated in a mutually consistent manner. These hierarchies are obtained to the sixth order in turbulent velocity correlators. Asymptotic formulas describing the evolution of scalar fluctuations and magnetic field are presented. A number of new effects are revealed that strongly affect diffusion, but are beyond the scope of the frequently used model of a delta-correlated turbulent field.