Radiative transfer in scattering stochastic atmospheres

Many stars, active galactic nuclei, accretion discs etc. are affected by the stochastic variations of temperature, turbulent gas motions, magnetic fields, number densities of atoms and dust grains. These stochastic variations influence on the extinction factors, Doppler widths of lines and so on. The presence of many reasons for fluctuations gives rise to Gaussian distribution of fluctuations. The usual models leave out of account the fluctuations. In many cases the consideration of fluctuations improves the coincidence of theoretical values with the observed data. The objective of this paper is the investigation of the influence of the number density fluctuations on the form of radiative transfer equations. We consider non-magnetized atmosphere in continuum.Comment: 11 pages. Has been accepted for publication in Astrophysics and Space Scienc

Intensity and polarization of radiation reflected from accretion disc

We consider the reflection of non-polarized radiation from the point-like sources above the accretion discs both the optically thick and optically thin. We investigate the dependence of the polarization of reflected radiation on the aperture angle of incident radiation. The aperture angle is determined by the radius of accretion disc and the height of the source above the disc. For optically thick accretion discs we show that, if the aperture angle is smaller 70 grad, then the wave electric field oscillations of reflected radiation are parallel to the accretion disc plane. For aperture angle greater than 70 grad the electric field oscillations are parallel to the plane "normal to accretion disc - the line of sight". The latter also holds for reflection from the optically thin accretion disc independent of the aperture angle value.Comment: 11 pages, 4 figures.This is a pre-print of an article published in Astrophysics and Space Scienc

Sco X-1 and Cyg X-1: Determination of Strength and Structure of Magnetic Field in the Nearest Environment of Accreting Compact Stars

We estimated the magnetic field strength of compact stars in X-ray binaries Sco X-1 and Cyg X-1, via various methods of determination of magnetic fields. For Sco X-1 we used three independent methods. One of them is based on the correct account of the Faraday rotation of polarization plane in the process of electron scattering of X-rays from accreting neutron stars. Numerical calculations are made with use of first X-rays polarimetric data presented by Long et al. (1979). Other original method of determing the magnetic field developed by Titarchuk at al. (2001) is based on observed quasi-periodic oscillations (QPO) frequencies in X-ray binaries that can be considered as magnetoacoustic oscillations of boundary layer near a neutron star. The optical polarimetric data obtained in 70-th have been also used for estimation of magnetic field of the neutron star in Sco X-1 and of nearest environment around the black hole in Cyg X-1.Comment: 10 page

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 are exist. Here we used the technique of the Green matrices. We consider only continuum radiation.Comment: 9 pages. In submission to Astrophysics and Space Scienc

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.Comment: 18 pages, 2 table

Influence of temperature fluctuations on continuum spectra of cosmic objects

The presence of convective and turbulent motions, and the evolution of magnetic fields give rise to existence of temperature fluctuations in stellar atmospheres, active galactic nuclei and other cosmic objects. We observe the time and surface averaged radiation fluxes from these objects. These fluxes depend on both the mean temperature and averaged temperature fluctuations. The usual photosphere models do not take into account the temperature fluctuations and use only the distribution of the mean temperature into surface layers of stars. We investigate how the temperature fluctuations change the spectra in continuum assuming that the degree of fluctuations (the ratio of mean temperature fluctuation to the mean temperature) is small. We suggest the procedure of calculation of continuum spectra, which takes into account the temperature fluctuations. As a first step one uses the usual model of a photosphere without fluctuations. The observed spectrum is presented as a part depending on mean temperature and the additional part proportional to quadratic value of fluctuation degree. It is shown that for some forms of absorption factor the additional part in Wien's region of spectrum can be evaluated directly from observed spectrum. This part depends on the first and second wavelength derivatives, which can be calculated numerically from the observed spectrum. Our estimates show that the temperature dependence of absorption factors is very important by calculation of continuum spectra corrections. As the examples we present the estimates for a few stars from Pulkovo spectrophotometric catalog and for the Sun. The influence of temperature fluctuations on color indices of observed cosmic objects is also investigated.Comment: 22 pages, 5 tables. Accepted for publication in Astrophysics & Space Scienc

Magnetic Fields of Black Holes and the Variability Plane

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 $\dot{M}$. 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 $B_{BH}\sim 10^8$G for stellar mass black holes and $B_{BH}\sim 10^4$G for the supermassive black holes. We have obtained the relation $p_l\sim \nu^{-1/2}_b$ between the intrinsic polarization of the accretion disk radiation and the characteristic frequency of the black hole X-ray variability.Comment: 4 page

Intrinsic Origin Of Extreme-Scale Rotation Of Quasar Polarization Vectors

Extreme-scale alignment of quasar optical polarization vectors at cosmological scales ($z\le 2$) is also characterized by the rotation of mean position angle $\chi$ with $\Delta \chi \approx 30^{\circ}$ per 1 Gpc. For observing interval of $z$ the total rotation angle acquires the value $\sim 90^{\circ}$. We suggest the possible explanation of the half of this rotation as a consequence of physical transformation of initially vertical magnetic field ${\bf B}_{\|}$, directed along the normal ${\bf N}$ to the surface of accretion disk, into the horizontal (perpendicular to ${\bf N}$) one. We found asymptotical analytical expressions for axially averaged polarization degree $p$ and mean position angle $\chi$ for various types of magnetized accretion disks. We found also that during the evolution can be realized the case $B_{\bot}\approx B_{\|}$ where position angle $\chi$ rotates from $45^{\circ}$ to zero. This rotation may occur during fairly great cosmological time (corresponding to $\Delta z\sim 1-2$). The part of rotation $\sim \Delta \chi \approx 45^{\circ}$ can be explained by a mechanism of alignment of polarization vectors, say distribution of the part of quasars as a spiral in the cosmic space with slow variation of rotation axis of corresponding accretion disks. Both mechanisms are mutually related one with another.Comment: 7 page

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.Comment: 7 page

New mechanism of radiation polarization in Seyfert-1 AGNs

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.Comment: 10 pages, 4 figure