Polarized Anisotropic Synchrotron Emission and Absorption and Its Application to Black Hole Imaging

Abstract

Low-collisionality plasma in a magnetic field generically develops anisotropy in its distribution function with respect to the magnetic field direction. Motivated by the application to radiation from accretion flows and jets, we explore the effect of temperature anisotropy on synchrotron emission. We derive analytically and provide numerical fits for the polarized synchrotron emission and absorption coefficients for a relativistic bi-Maxwellian plasma (we do not consider Faraday conversion/rotation). Temperature anisotropy can significantly change how the synchrotron emission and absorption coefficients depend on observing angle with respect to the magnetic field. The emitted linear polarization fraction does not depend strongly on anisotropy, while the emitted circular polarization does. We apply our results to black hole imaging of Sgr A* and M87* by ray tracing a GRMHD simulation and assuming that the plasma temperature anisotropy is set by the thresholds of kinetic-scale anisotropy-driven instabilities. We find that the azimuthal asymmetry of the 230 GHz images can change by up to a factor of 3, accentuating (T ⊥ > T ∥) or counteracting (T ⊥ < T ∥) the image asymmetry produced by Doppler beaming. This can change the physical inferences from observations relative to models with an isotropic distribution function, e.g., by allowing for larger inclination between the line of sight and spin direction in Sgr A*. The observed image diameter and the size of the black hole shadow can also vary significantly due to plasma temperature anisotropy. We describe how the anisotropy of the plasma can affect future multifrequency and photon ring observations. We also calculate kinetic anisotropy-driven instabilities (mirror, whistler, and firehose) for relativistically hot plasmas.

Stochastic Averaging of Radiative Transfer Coefficients for Relativistic Electrons

“…The applications presented in this work stochastically average over a thermal distribution, and are therefore trivially applicable only to isotropic distributions. It would be interesting to generalize to anisotropic distributions (e.g., Galishnikova et al 2023).…”

“…Calculation of synchrotron transfer coefficients from f is notoriously difficult (Schwinger 1949). Methods for numerically evaluating coefficients for isotropic distribution functions now exist (Marszewski et al 2021), or even some coefficients for anisotropic distribution function (Verscharen et al 2018;Galishnikova et al 2023). Although the direct numerical evaluation of coefficients is possible, direct evaluation is not practical in numerical radiative transfer calculations.…”

Electron Heating in the Transrelativistic Perpendicular Shocks of Tilted Accretion Flows

“…2 in panels (b) and (i) of Figures 1 and 2. As we further discuss below, the relaxation of ion velocity-space anisotropies can result in proton cyclotron modes and mirror modes (for a review of anisotropy instabilities in relativistic plasmas, see Galishnikova et al 2023). For the magnetic geometry employed in this paper, proton cyclotron waves would appear in B x and B z , and their wavevector is aligned with the mean field; in contrast, mirror modes appear in B x and B y , and their wavevector is oblique with respect to the mean field.…”