Possible mechanisms for the polarization of the radiation of Active Galactic Nuclei and quasars

Two mechanisms for the formation of polarized radiation in Active Galactic Nuclei and quasars are considered-synchrotron radiation from a jet and the emergence of radiation from a magnetized, optically thick accretion disk (the Milne problem in a magnetized atmosphere). These mechanisms are applied to the polarization of objects studied in [1]. We have shown that the polarization of some sources cannot be explained as synchrotron radiation. The second mechanism is more general and, in principle, can be applied to the polarized radiation of all the sources in [1].     

Linear polarization of the radiation from active galactic nuclei and the redshift dependence of their main parameters

We consider the observed continuum linear polarization of extragalactic objects with various redshifts z, most of which have degrees of polarization p ≤ 10%. We propose that this polarization is due to multiple scattering of the radiation in magnetized accretion disks around the Active Galactic Nuclei (AGN; the Milne problem in an optically thick atmosphere). The structure of the accretion disks and the polarization of the emergent radiation depend on the main parameters of the AGN—the mass of the central body M _BH , accretion rate $ \dot M $ \dot M , magnetic field at the black-hole event horizon B _H , angular momentum a _*, and the explicit form of the magnetic-field distribution in the accretion disk. Theoretical expressions for the degree of polarization are averaged over all angles of the disks to the line of sight, and the resulting formula compared with the mean observed polarizations in redshift intervals Δz = 0.25. The dependence of the observed degree of polarization and the main parameters on the redshift z is derived. The degrees of polarization of 305 objects from the catalog of Hutsemekers et al. with redshifts from zero to z = 2.25 are used for the analysis.     

Polarization in resonance lines: Diffuse reflection

The linear polarization of resonance radiation diffusely reflected from a semi-infinite atmosphere is analyzed, including a full account of the azimuthal dependence. The radiating atom is assumed to have two levels and the radiation to be fully redistributed in frequency. A new approach to the transformation of the equations of polarized radiative transport is proposed based on factorization of the full (3×3) Rayleigh phase matrix. The emergent radiation field is expressed in terms of a matrix analog for the Chandrasekhar H function. The polarization properties of radiation at the frequencies of resonance lines diffusely reflected from a scattering atmosphere are discussed. The degree of polarization of the reflected radiation can be very high.     

Solution of the radiative-transfer equations with an azimuth-averaged Hanle phase matrix

The system of radiative-transfer equations for polarized radiation is solved analytically using an azimuth-averaged Hanle phase matrix. A Milne-Eddington model with a constant ratio of the line and continuum absorption coefficients and a linear dependence of the source function on optical depth is adopted for the atmosphere. The vector magnetic field is taken to be constant with optical depth. The dependence of the linear polarization obtained during observations at the solar limb on the magnitude and inclination of the magnetic field to the normal of the atmosphere is presented as an illustration of the theoretical computations. The measured polarization corresponds to two magnetic-field values and several possible field inclinations. The measured polarization is directly proportional to the quantum coefficient W ₂ determining the resonance polarization in lines.     

The hanle effect in a turbulent magnetic field

Exact analytical expressions for the scattering phase matrix are presented for various models of a turbulent magnetic field having a symmetry axis in the solar atmosphere. The polarization of the scattered radiation in the plane of the scattering is shown to be virtually independent of the predominant direction of the turbulent magnetic field. The Hanle effect does not operate in a longitudinal magnetic field normal to the surface of the atmosphere, since the phase matrix has the form of a resonance phase matrix with zero magnetic field.     

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 r _isco 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 r _isco , 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.     

A magnetized disk around an O star: Polarization of the OH maser emission

W75N is one of the first OH masers in which 100% linear polarization has been observed in several spots. Two spots contain Zeeman pairs, corresponding to magnetic fields of 5.2 and 7.7 mG. Another Zeeman pair consisting of two linearly polarized components was tentatively detected in one spot. The linearly polarized spots are σ components for the case when the magnetic field is perpendicular to the line of sight. For these spots, the magnetic field is perpendicular to the plane of the circumstellar disk, though a correction for Galactic Faraday rotation may considerably modify this conclusion.     

Scattering of cyclotron radiation in a moving plasma

We consider the scattering of cyclotron radiation in a plasma moving along a homogeneous magnetic field. The equation of radiation transfer in a co-moving frame is derived and two limiting cases are pointed out. In the first case of a “small” velocity gradient, the total Doppler frequency shift due to variations in the plasma velocity over the flow is much smaller than the width of the line. The second, opposite, case of a “large” velocity gradient is analogous to the Sobolev approximation in the theory of moving stellar envelopes. The solution of the transfer equation for a wind-type flow illuminated by radiation of a given intensity is obtained in the latter case, when the influence of the plasma motion on cyclotron scattering is most important. It is shown that cyclotron scattering in a moving plasma differs from the known (and qualitatively similar) problems of resonance scattering in moving stellar envelopes and cyclotron scattering in a motionless plasma permeated by an inhomogeneous magnetic field. In particular, a symmetric absorption band with residual intensity proportional to the velocity gradient appears in the spectrum of the outgoing radiation, while in these two other problems, the depth of the corresponding spectral features cannot exceed half the continuum level. Detailed qualitative analysis reveals that this difference is due to the particular form of the frequency redistribution for cyclotron scattering.     

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 B ₀ and a stochastic B′ component (B = B ₀ + B′). Faraday rotation of the plane of polarization (s8 λ² B ₀ cos gJ) due to the field B ₀ 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 B ₀ perpendicular to the surface of the medium). We also compute the degree of polarization for the cases B ₀ = 0, B′ ≠ 0, and B′ = 0, B ₀ ≠ 0, and for a number of versions of the general case, B ₀ ≠ 0, B′ ≠ 0. The spectra of the degree of polarization (for the case B ₀ = 0) are presented for optical (λ = 0 ? 1 μm), infrared (λ = 1?5 μm), and X-ray (1–50 keV) wavelengths.     

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.     

Spectropolarimetric Observations of Magnetic White Dwarfs with the SAO 6-m Telescope

The results of spectropolarimetric observations of a number of magnetic white dwarfs obtained on the 6-m optical telescope of the Special Astrophysical Observatory are presented. The observations were carried out using the SCORPIO focal aperture-ratio reducer in a spectropolarimetric regime. Two characteristic dependences of the degree of polarization on the wavelength are observed. For one group of objects, the degree of linear polarization grows with wavelength, suggesting that the alignment of atoms and molecules in Rydberg states in the atmosphere of the white dwarf due to the action of its magnetic field influences scattering processes. The second group of objects displays an increase in the degrees of both linear and circular polarization with wavelength, providing evidence for the presence of protoplanetary disks around these magnetic white dwarfs, in which the alignment of circumstellar grains leads to the observed behavior.     

Curvature radiation for intermediate pitch angles

The radiation by a charged particle in a non-uniform magnetic field is analyzed when the particle’s trajectory forms a curved spiral. The case when the pitch angle is less than the inverse of the Lorentz factor is considered. It is shown that the spectral angular distribution of the radiation consists of two parts that are substantially separated in frequency. One of these components represents curvature radiation, which is primarily linearly polarized, while the other possesses the typical properties of undulatory radiation, with a high degree of circular polarization. The derived formulas can be used to analyze the radiation of pulsars.     

The phase matrix for scattering in a weak magnetic field. The Hanle effect

A new formulation for the phase matrix for the scattering of radiation in a weak magnetic field is presented. The phase matrix is represented as a product of individual matrices that depend on the angle of incidence and the scattering angle. It is shown that the Hanle effect is absent in observations of scattered light in the solar atmosphere when the magnetic field is perpendicular to the atmosphere. In strong magnetic fields, the phase matrix depends only on the direction of the magnetic field relative to the basic coordinate system.     

A point source of radiation in the early Universe: Solution in a one-dimensional approximation

The radiation field of a point source with a specified power in the early Universe acting for a specified time in the radiation-dominated epoch after the annihilation of electron-positron pairs is considered. A three-component model for this period is adopted. The equations of radiative transfer for the source are formulated, taking into account polarization arising during scattering of the radiation by free electrons. Analytical, numerical, and asymptotic solutions of the transfer equation are obtained for a flat model in a one-dimensional approximation, which describe the evolution of the intensity and flux of scattered radiation of the source in periods close to the onset of its action. Intervals of redshift corresponding to these periods are estimated. The behavior of the linear polarization near the source is traced. It is shown that the source radiation can be comparable to the thermal background only if the source energy is very high or we consider regions in its immediate vicinity. More optimistic estimates will require that we take into account the decrease in the degree of ionization of matter in the epoch of recombination.     

Scattering of elastic wave by a partially sealed cylindrical shell embedded in poroelastic medium

Scattering of an elastic wave by a cylindrical shell embedded in poroelastic medium is investigated theoretically with the assumption that the shell material is also a porous elastic medium. The porous medium is modellized via Biot's theory and the scattering by cylindrical shell is expressed by the definition of scattering matrix. The normal mode expansion technique is employed for analysing the scattering field, and the asymptotic solutions of displacements, stresses and pore pressure are derived. Two limiting cases‐scattering by a poroelastic cylinder in Biot medium and a elastic cylindrical shell in elastic medium are obtained from the general solutions. The dispersion curves of displacement amplitude at the interface of shell and medium is compared with the case of elastic shell. The scattering amplitude associated with the fast, slow and transverse waves are identified by numerical simulation. Furthermore, the influence of the poroelastic property of shell material on scattering amplitude is analysed. Copyright © 2005 John Wiley & Sons, Ltd.     

The possible escape of electron cyclotron maser radiation from hot stellar coronas through a window of transparency

The main argument against the idea that the intense radio emission observed from active regions on the Sun and flare stars is electron-cyclotron maser (ECM) radiation is that such radiation should be strongly absorbed in higher-lying layers where the condition for the cyclotron resonance at harmonics of the electron gyrofrequency is fulfilled. Cyclotron absorption lowers the efficiency of ECM radiation virtually to zero for a broad range of angles between the direction of propagation of the radiation and the magnetic field. Less severe absorption is possible only in narrow angular “windows” along (for ordinary and extraordinary waves) and perpendicular to (for ordinary waves) the magnetic field. However, the ECM radiation that is generated does not fall into these windows of transparency due to the kinematic conditions corresponding to coronal magnetic traps. We investigate the efficiency of induced scattering of ECM radiation on ions in the equilibrium plasma in the source. Under certain conditions, induced scattering leads to the formation of a condensate of ECM radiation with the direction of its wave vectors approximately along the magnetic field, enabling the escape of the radiation through windows of transparency. The most favorable conditions for this phenomenon are realized for ordinary waves. We estimate the optical depths of the sources of the ECM radiation to the scattering and the angular width of the condensate for ordinary and extraordinary waves for the cases of the flare radio emission of the star AD Leo and the sources of type I noise storms in the solar corona. In both cases, the polarization of the emergent radiation should correspond to the ordinary wave.     

The photopolarimetric activity and circumstellar environment of the T Tauri star CO Ori

We present the results of simultaneous UBVRI photometry and polarimetry of the classical T Tauri star CO Ori carried out at the Crimean Astrophysical Observatory during the 18 years between 1986 and 2004. We show that the variations of linear polarization accompanying the star’s brightness variations follow the law characteristic of UX Ori stars. This suggests that the brightness variations of the star are mainly due to changes of the circumstellar extinction due to non-uniform structure of the circumstellar environment, and to an “optimal” orientation of the circumstellar gas and dust disk relative to the observer, whose line of sight crosses the gas and dust atmosphere of the disk. We determine the star’s intrinsic polarization due to scattering of light in the circumstellar disk. The polarization position angle indicates the orientation of the disk’s symmetry axis in the plane of the sky. Our analysis of an archival light curve for CO Ori confirms the existence of a many-year cycle of photometric activity, suspected by us earlier. The refined period of this cycle is 12.4 years. The existence of such activity cycles of UX Ori stars testifies to considerable deviations of their circumstellar disks from axial symmetry, a reflection of either stellar binarity or the commencement of the process of planetary formation.     

Polarization observations of the OH maser W75N on the Nançay radio telescope

Results of observations of the OH maser in W75N at 18 cm are reported. The observations were obtained on the radio telescope of the Nancay Radio Astronomy Observatory (France) from October 2007 to April 2009. The profiles of the Stokes parameters I, Q, U, and V in the 1665 and 1667 MHz OH lines have been measured. A technique taking into account instrumental polarization has been developed and applied. The emission in the OH lines is strongly polarized both linearly and circularly. The degree of polarization of some emission features reaches almost 100%. There were two flares of the maser emission in 2008–2009. During a flare at a radial velocity of +5.5 km/s, a Zeeman pattern was detected in the 1667 MHz line. The measured intensity of the line-of-sight component of the magnetic field was −1.1 mG, which corresponds to the field being directed away from the observer. The maser flares and the associated enhancement of the magnetic field could be associated with the compression of gas at a shock front.     

The effect of acoustic waves on spectral-line profiles in the solar atmosphere: Observations and theory

The fine structure of the FeI λ 532.4185-nm line of neutral iron is studied with high spatial (0.5″) and temporal (9.3 s) resolution using observations of a quiet region at the center of the solar disk. The character of the line asymmetry depends strongly on the nature of the velocity field, i.e., on whether it is due to convective or wave motions. The magnitude of the asymmetry due to acoustic waves is comparable to that due to convective motions. The propagation of acoustic waves in moving granules and intergranular lanes is studied by solving a system of hydrodynamical equations in a three-dimensional model for the solar atmosphere. The temporal variations in the bisector of the line synthesized in a non-LTE approximation agree well with the observational data.     

地下线状长导体对激发极化场的影响——以胶东地区为例

线状长导体,如金属管道、裸金属线、光缆等,其直径相对于埋深虽然很小,但受到激发时,能够产生很大的极化场,生产实践中对极化率的影响很大。该文主要研究了中梯和联剖2种装置下地下线状长导体的异常特征,分析了异常产生的原因,并提出了辨别这种干扰因素的方法。