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

Magnetic fields of active galaxy nuclei and cosmological models

We present the review of various methods of detection of magnetic field strengths in the nearest regions of the active galaxy nuclei (AGN) which are the high energetic machines. Original spectropolarimetric method developed in the Pulkovo Observatory allows us to determine the magnitude and geometry of the magnetic field in the region of the optical and more hard electromagnetic radiation. The results of theoretical calculations are compared to the results of spectropolarimetric observations of AGN. We used the method of determining magnetic fields through the spectrum synchrotron radiation in the region of synchrotron self-absorption. As the magnitude of magnetic field of the extragalactic source depends very strongly on the angular size of extragalactic source and therefore on the photometric distance the calculated magnetic field magnitudes depends very strongly on the definite cosmological model. This result allows us to present the new method for determination of the most important cosmological parameters including dark matter and dark energy parameters.Comment: 8 pages, 7 figure

Magnetic Fields of Nearby Active Galactic Nuclei and Correlation of the Highest-Energy Cosmic Rays with their Positions

The correlation between the pointing direction of ultra high energy cosmic rays and AGN observed by the Pierre Auger Collaboration is explained in the framework of acceleration process in AGN. This acceleration process is produced by a rotating accretion disk around a black hole that is frozen-in magnetic field. In a result the accretion disk is acting as a induction accelerator of cosmic rays. We estimate the resulting magnetic field in the framework of the magnetic coupling process. The results of our calculations allow to make the conclusion that the Flat Spectrum Radio Quasars appear the effective cosmic accelerators. We estimate also the attenuation of highest-energy cosmic rays in a result of their interaction with ambient radiation field.Comment: 5 page

Photon-Axion-Like Particle Coupling Constant and Cosmological Observations

We estimated the photon-pseudoscalar particle mixing constant from the effect of cosmological alignment and cosmological rotation of polarization plane of distant QSOs. This effect is explained in terms of birefringent phenomenon due to photon-pseudoscalar (axion-like) particle mixing in a cosmic magnetic field. On the contrary, one can estimate the strength of the cosmic magnetic field using the constraints on the photon-axion-like particle coupling constant from the CAST experiment and from SNe Ia dimming effect. In a result, the lower limit on the intergalactic ($z\approx 1\div 2$) magnetic field appears at the level of about $4\times 10^{-10}\div 10^{-11}$ G.Comment: 8 page

Synchrotron Self-Absorption Process in GRBs and the Isotropic Energy - Peak Energy Fundamental Relation

The existence of strong correlation between the peak luminosity (and/or bolometric energetics) of Gamma Ray Bursts (GRB) is one of the most intrigue problem of GRB physics. This correlation is not yet understood. Here we demonstrate that this correlation can be explained in framework of synchrotron self-absorption (SSA) mechanism of GRB prompt emission. We estimate the magnetic field strength of the central engine at the level $B\sim 10^{14} (10^3/\Gamma)^3 (1+z)^2$, where $\Gamma$ is the Lorentz factor of fireball.Comment: 5 page

Conductance matrix of multi terminal semiconductor devices with edge channels

This paper presents a method for determining the conductance matrix of multi terminal semiconductor structures with edge channels. This method appears to be applied within frameworks of the ordinary Landauer - uttiker formalism for the carrier transport analysis in the regime of both the quantum Hall Effect and the quantum spin Hall Effect. The proposed method proves to take into account principally the contribution of the probes resistance in the formation of the matrix conductance elements. Finally, the possibilities of the practical application of this method to develop new versions of analog cryptographic devices are discussed.Comment: 28 pages, 4 figures, Language - Russia

Supernova 2014J at maximum light

We present UBVRI photometry of the supernova 2014J in M82, obtained in the period from January 24 until March 3, 2014, as well as two spectra, taken on February 4 and March 5. We derive dates and magnitudes of maximum light in the UBVRI bands, the light curve parameters Delta m(15) and expansion velocities of the prominent absorption lines. We discuss colour evolution, extinction and maximum luminosity of SN 2014J.Comment: 10 pages, 4 figures, submitted to Contrib. Astron. Obs. Skalnate Ples

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

A Hilbert Lemniscate Theorem in C^2

For a regular, compact, polynomially convex circled set K in C^2, we construct a sequence of pairs {P_n,Q_n} of homogeneous polynomials in two variables with deg P_n = deg Q_n = n such that the sets K_n: = {(z,w) \in C^2 : |P_n(z,w)| \leq 1, |Q_n(z,w)| \leq 1} approximate K and the normalized counting measures {\mu_n} associated to the finite set {P_n = Q_n = 1} converge to the pluripotential-theoretic Monge-Ampere measure for K. The key ingredient is an approximation theorem for subharmonic functions of logarithmic growth in one complex variable