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2021, The Astrophysical Journal
Accurate radiative transfer coefficients (emissivities, absorptivities, and rotativities) are needed for modeling radiation from relativistically hot, magnetized plasmas such as those found in Event Horizon Telescope sources. Here we review, update, and correct earlier work on radiative transfer coefficients. We also describe an improved method for numerically evaluating rotativities and provide convenient fitting formulae for the relativistic κ distribution of electron energies. Here α S and ρ S are absorption and Faraday mixing coefficients, respectively, in the Stokes basis. We use a Cartesian coordinate system in the calculation of the transfer coefficients. We setẑ parallel to the magnetic field B. The observer angle θ is the angle between B and the photon wavevector k which we choose to lie in the x − z plane. Note that we have chosen a coordinate system (in the plasma rest frame) such that all Stokes U coefficients are zero.
The Astrophysical Journal, 1996
Monthly Notices of the Royal Astronomical Society, 2013
The polarization transfer coefficients of a relativistic magnetized plasma are derived. These results apply to any momentum distribution function of the particles, isotropic or anisotropic. Particles interact with the radiation either in a non-resonant mode when the frequency of the radiation exceeds their characteristic synchrotron emission frequency, or quasi-resonantly otherwise. These two classes of particles contribute differently to the polarization transfer coefficients. For a given frequency, this dichotomy corresponds to a regime change in the dependence of the transfer coefficients on the parameters of the particle's population, since these parameters control the relative weight of the contribution of each class of particles. Our results apply to either regimes as well as the intermediate one. The derivation of the transfer coefficients involves an exact expression of the conductivity tensor of the relativistic magnetized plasma that has not been used hitherto in this context. Suitable expansions valid at frequencies much larger than the cyclotron frequency allow us to analytically perform the summation over all resonances at high harmonics of the relativistic gyrofrequency. The transfer coefficients are represented in the form of two-variable integrals that can be conveniently computed for any set of parameters by using Olver's expansion of high-order Bessel functions. We particularize our results to a number of distribution functions, isotropic, thermal or power-law, with different multipolar anisotropies of low order, or strongly beamed. Specifically, earlier exact results for thermal distributions are recovered. For isotropic distributions, the Faraday coefficients are expressed in the form of a one-variable quadrature over energy, for which we provide the kernels in the high-frequency limit and in the asymptotic low-frequency limit. An interpolation formula extending over the full energy range is proposed for these kernels. A similar reduction to a one-variable quadrature over energy is derived at high frequency for a large class of anisotropic distribution functions that may form a basis on which any smoothly anisotropic distribution could be expanded.
Australian Journal of Physics, 1992
Approximate analytic expressions are derived for the linear response 4-tensor of a strongly magnestised, mildly relativistic electron plasma. The results are obtained within the framework of quantum plasma dynamics, thus the response contains relativistic and quantum effects that are essential in a super-strong magnetic field. The response is obtained in terms of relativistic plasma dispersion functions known as Shkarofsky functions. These functions allow the wave properties of the plasma to be studied without resorting to complicated numerical schemes. The response derived is valid for radiation with frequency up to about the cyclotron frequency and is of use in the theory of spectra formation in X-ray pulsars. In addition, a simple graphical technique is introduced that allows one to visually locate the roots of the resonant denominator occurring in the response, as well as determine the conditions under which both roots are valid and contribute to absorption.
Radiophysics and Quantum Electronics, 2006
Linear conversion of the ordinary wave to the extraordinary wave and then to the Bernstein wave (O-X-B conversion) in a tokamak plasma is considered in the generalized geometric-optical approximation taking into account the relativistic effects in a dielectric permitivity tensor. Using the T-10 tokamak as an example, it is shown that even for a relatively low plasma temperature (about 1 keV at the plasma-column center) relativistic effects exert a notable influence on the cyclotron absorption of Bernstein waves. Power deposition profiles for O-X-B plasma heating are determined. The emission of spontaneously excited Bernstein waves resulting from the B-X-O conversion are considered. . 617 plasma density. As the region with a certain plasma density is reached, the X wave turns back (is reflected) and propagates in the reverse direction (of decreasing plasma density) up to the upper-hybrid resonance region where ω = ω uh ≈ ω 2 pe + ω 2 ce . In this region, secondary conversion of the X wave to an electron Bernstein wave (B mode) occurs. Upon conversion to the B wave, the radiation freely propagates toward the magnetic-field increase, including the supercritical plasma region (ω pe > ω), and reaches the EC resonance region where the radiation absorption and plasma heating take place. The optimal angle of electromagneticradiation input for actual setups can be searched with the use of codes for geometric-optical calculation of the ray trajectories modified in a certain way for taking into account the linear wave conversion effect. This scheme of plasma heating was implemented experimentally, in particular, using such large setups as W7-AS , MAST [2,, and, recently, TCV .
2008
The electromagnetic processes of Compton scattering and photon splitting/merging are investigated in the presence of strongly magnetized electron-positron plasma. The influence of these processes on the radiation transfer in the astrophysical environment is studied. In particular, the contribution of the processes under consideration in coefficients of the transfer equation is calculated. We show the importance of photon splitting/merging contribution and taking into account of photon dispersion and wave function renormalization in strong magnetic field and plasma.
Physics of Plasmas, 2012
The Astrophysical Journal, 2007
We show that there is no universal law describing how the spectra and luminosity of synchrotron and inverse Compton radiation from relativistic jets change with increasing observation angle. Instead, the physics of particle acceleration leaves pronounced imprints in the observed spectra and allows for a freedom in numerous modifications of them. The impact of these effects is the largest for high-energy radiation and depends on the details of particle acceleration mechanism(s), what can be used to discriminate between different models. Generally, the beam patterns of relativistic jets in GeV-TeV spectral domain are much wider than the inverse Lorentz factor. The off-axis emission in this energy range appear to be brighter, have much harder spectra and a much higher cut-off frequency compared to the values derived from Doppler boosting considerations alone.
The goal of the series of studies in this thesis is to understand the black hole accretion process and predict its observational properties. The highly non-linear process involves a turbulent magnetized plasma in a general relativistic regime, thus making it hard to study analytically. We use numerical simulations, specifically general relativistic magnetohydrodynamics (GRMHD), to construct a realistic dynamical and radiation model of accretion disks. Our simulations are for black holes in low luminous regimes that probably possesses a hot and thick accretion disk. Flows in this regime are called radiatively inefficient accretion flows (RIAF). The most plausible mechanism for transporting angular momentum is turbulence induced by magnetorotational instability (MRI). The RIAF model has been used to model the supermassive black hole at the center of our Milky Way galaxy, Sagittarius A* (Sgr A*). Owing to its proximity, rich observational data of Sgr A* is available to compare with the simulation results. We focus mainly on four topics. First, we analyse numerical convergence of 3D GRMHD global disk simulations. Convergence is one of the essential factors in deciding quantitative outcomes of the simulations. We analyzed dimensionless shell-averaged quantities such as plasma β, the azimuthal correlation length (angle) of fluid variables, and spectra of the source for four different resolutions. We found that all the variables converged with the highest resolution (384x384x256 in radial, poloidal, and azimuthal directions) except the magnetic field correlation length. It probably requires another factor of 2 in resolution to achieve convergence. Second, we studied the effect of equation of state on dynamics of GRMHD simulation and radiative transfer. Temperature of RIAF gas is high, and all the electrons are relativistic, but not the ions. In addition, the dynamical time scale of the accretion disk is shorter than the collisional time scale of electrons and ions, which makes the gas have two temperatures. We assumed that the temperature ratio of the ions and electrons T p /T e is constant and constructed a new Synge-type equation of state that takes the effect of two temperature fluid as well as variable adiabatic index caused by the non-relativistic to relativistic transition of the particles into account. We found that the effect of the Synge-type equation of state on In finishing this thesis, I received tremendous amount of help and support from many people. First, I would like to give the greatest appreciation to Professor Charles Gammie for being my advisor. I am very honored to be a student of the most intelligent person I have ever met and supervised under his deepest knowledge and insight. My appreciation to his kindness and patience in often slow progress of my research and countless grammatical mistakes and wording problems in my papers can not be expressed in any words. I am truly fortunate that I met Professor You-Hua Chu, whom I appreciate for introducing me to Professor Charles Gammie six years ago. It was absolutely impossible to complete this thesis without his great advise and guidance.
Initially optically thick (with τ = 3ṡ107) spherically symmetric outflow consisting of electron-positron pairs and photons is considered. We do not assume thermal equilibrium, and include the two-body processes that occur in such plasma: Möller and Bhabha scattering of pairs, Compton scattering, two-photon pair annihilation, two-photon pair production, together with their radiative three-body variants: bremsstrahlung, double Compton scattering, and three-photon pair annihilation, with their inverse processes. We solve numerically the relativistic Boltzmann equations in spherically symmetric case for distribution functions of pairs and photons. Three epochs are considered in details: a) the thermalization, which brings initially nonequilibrium plasma to thermal equilibrium; b) the self-accelerated expansion, which we find in agreement with previous hydrodynamic studies and c) decoupling of photons from the expanding electron-positron plasma. Photon spectra are computed, and appear to...
Universe
Strong γ-ray outbursts have been observed to emanate from PKS 1502+106, followed by highly variable fluxes in radio, visual, ultraviolet and X-ray bands. Numerical simulations have been conducted to relate the observations to potential theoretical models. The plasma attributes, such as mass density, plasma flow velocity and energy density, cannot be directly observed. However, the Stokes parameters of synchrotron radiation from the plasma can be measured to deduce the plasma attributes. Many studies have been conducted on synchrotron radiation intensity, with only a few on the rotation measure (RM) related to Faraday rotation. In this work, overpressured relativistic magnetized axisymmetric jets are simulated to acquire the synchrotron radiation maps, incorporating Faraday rotation, of the widely discussed jet, PKS 1502+106. The intensity maps and RM maps of the PKS 1502+106 are simulated under practical constraints, and compared with the available observation data to explore specif...
Physics of Fluids B: Plasma Physics, 1993
A theoretical analysis developed in a companion paper to treat the early-time evolution of plasmas moving across a background magnetic field is applied to the modeling of lowbeta, barium chemical releases in the magnetosphere. The results indicate that radiation damping plays an important role in defining the plasma cloud evolution, causing a rapid decay of the polarization field and a loss of plasma kinetic energy and momentum on time scales comparable to several ion gyroperiods. The radiation spectrum consists of a burst of chirped, high-frequency (in the range of the cloud plasma frequencies) waves, followed by a pulse of whistler waves, and subsequently by ion cyclotron emission. Scaling laws are derived for the plasma momentum and energy loss rates and predictions for the braking time, the amplitude and spectrum of the radiation field, and the total radiated power are presented for conditions relevant to the recent Combined Release and Radiation Effects Satellite (CRRES) experiments [
Australian Journal of Physics, 1992
Approximate analytic expressions are derived for the linear response 4-tensor of a strongly magnestised, mildly relativistic electron plasma. The results are obtained within the framework of quantum plasma dynamics, thus the response contains relativistic and quantum effects that are essential in a super-strong magnetic field. The response is obtained in terms of relativistic plasma dispersion functions known as Shkarofsky functions. These functions allow the wave properties of the plasma to be studied without resorting to complicated numerical schemes. The response derived is valid for radiation with frequency up to about the cyclotron frequency and is of use in the theory of spectra formation in X-ray pulsars. In addition, a simple graphical technique is introduced that allows one to visually locate the roots of the resonant denominator occurring in the response, as well as determine the conditions under which both roots are valid and contribute to absorption.
Monthly Notices of the Royal Astronomical Society, 2016
We find the forms of the transfer equations for polarized cyclotron radiation in the atmospheres of compact stars, which are simple enough to allow practical implementation and still preserve all important physical effects. We take into account a frequency redistribution of radiation within the cyclotron line as well as the relativistic and quantum-electrodynamic effects. Our analysis is valid for the magnetic fields up to 10 13 G and for temperatures well below 500 keV. We present and compare two forms of the radiation transfer equations. The first form, for the intensities of ordinary and extraordinary modes, is applicable for the compact stars with a moderate magnetic field strength up to 10 11 G for typical neutron star and up to 10 9 G for magnetic white dwarfs. The second form, for the Stokes parameters, is more complex, but applicable even if a linear mode coupling takes place somewhere in the scattering-dominated atmosphere. Analysing dispersion properties of a magnetized plasma in the latter case, we describe a range of parameters where the linear mode coupling is possible and essential.
The Astrophysical Journal
Pulsar radio emission is not well understood because of a lack of knowledge about the emission geometry and the plasma process involved. We develop a mechanism for pulsar radio emission that takes into account the detailed viewing geometry of pulsars and the dipolar magnetic field configuration. Using a suitably chosen geometry and plasma parameters, we derive analytical expressions for the Stokes parameters of the radiation field in the frame centered on the neutron star. We have simulated pulse profiles based on our analytical formulation. It seems that we can explain the enhanced radiation and most of the diverse polarization properties of radio pulsars. We have estimated the brightness temperature, which seems to agree with the observations. The polarization angle predicted by the model is in good agreement with the rotating vector model.
Physics of Atomic Nuclei, 2009
The photon-scattering process γe ± → γe ± is considered in strongly magnetized matter at arbitrary values of temperature and an arbitrary chemical potential. Simple expressions for the absorption coefficients in a strongly magnetized plasma are obtained in two limiting cases, that of a rarefied chargesymmetric plasma and that of a degenerate plasma. Astrophysical applications of the results obtained here are discussed.
Australian Journal of Physics
The purpose of this paper is to clarify the flux conservation, magnetohydrodynamic and force-free approximations, for plasmas whose component species may be relativistically streaming, by paying particular attention to the conditions for their validity and to their interrelationships. All three approximations involve consideration of inertial effects, either in the generalized Ohm law or in the equation of motion of the plasma as a whole. All three imply that the electric field component parallel to the magnetic field is small. The significance of the approximations for pulsar magnetospheric theory is commented on.
Physical Review E, 2020
The propagation of a relativistic electron-positron beam in a magnetized electron-ion plasma is studied, focusing on the polarization of the radiation generated in this case. Special emphasis is laid on investigating the polarization of the generated radiation for a range of beam-plasma parameters, transverse and longitudinal beam sizes, and the external magnetic fields. Our results not only help in understanding the high degrees of circular polarization observed in gamma-rays bursts but they also help in distinguishing the different modes associated with the filamentation dynamics of the pair-beam in laboratory astrophysics experiments.
Nonlinear Processes in Geophysics, 2014
Propagation of large-amplitude waves in plasmas is subject to several sources of nonlinearity due to relativistic effects, either when particle quiver velocities in the wave field are large, or when thermal velocities are large due to relativistic temperatures. Wave propagation in these conditions has been studied for decades, due to its interest in several contexts such as pulsar emission models, laser-plasma interaction, and extragalactic jets.
The Astrophysical Journal, 2020
The Event Horizon Telescope (EHT) Collaboration has recently produced the first resolved images of the central supermassive black hole in the giant elliptical galaxy M87. Here we report on tests of the consistency and accuracy of the general relativistic radiative transfer codes used within the collaboration to model M87 * and Sgr A *. We compare and evaluate (1) deflection angles for equatorial null geodesics in a Kerr spacetime; (2) images calculated from a series of simple, parameterized matter distributions in the Kerr metric using simplified emissivities and absorptivities; (3) for a subset of codes, images calculated from general relativistic magnetohydrodynamics simulations using different realistic synchrotron emissivities and absorptivities; (4) observables for the 2017 configuration of EHT, including visibility amplitudes and closure phases. The error in total flux is of order 1% when the codes are run with production numerical parameters. The dominant source of discrepancies for small camera distances is the location and detailed setup of the software "camera" that each code uses to produce synthetic images. We find that when numerical parameters are suitably chosen and the camera is sufficiently far away the images converge and that for given transfer coefficients, numerical uncertainties are unlikely to limit parameter estimation for the current generation of EHT observations. The purpose of this paper is to describe a verification and comparison of EHT radiative transfer codes. It is not to verify EHT models more generally.
Physical Review D, 1975
By an explicit analytic solution it is shown how, in the accretion of apoloidally magnetized plasma into a Kerr black hole, a torque is exerted on the infalling gas, implying the extraction of rotational energy from the black hole. The torque arises from the twisting of magnetic field lines by the frame-dragging effect. It is also shown how, under suitable conditions, a sizable charge separation can be found in the magnetosphere of accreting black holes and hence an electric charge is expected to be induced on the black hole.
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