Stochastic Averaging of Radiative Transfer Coefficients for Relativistic Electrons

TL;DR

This paper introduces a stochastic averaging method to efficiently estimate radiative transfer coefficients for relativistic electrons, accounting for electron distribution functions and turbulence effects in astrophysical modeling.

Contribution

It presents a novel stochastic averaging technique that simplifies the calculation of transfer coefficients and assesses turbulence effects on emissivity in astrophysical contexts.

Findings

Turbulence slightly reduces emissivity in EHT source conditions.

The method enables efficient evaluation of emissivities for complex electron distributions.

Turbulence can significantly increase emissivity in infrared regimes.

Abstract

Synchrotron emissivities, absorptivities, and Faraday rotation and conversion coefficients are needed in modeling a variety of astrophysical sources, including Event Horizon Telescope (EHT) sources. We develop a method for estimating transfer coefficients that exploits their linear dependence on the electron distribution function, decomposing the distribution function into a sum of parts each of whose emissivity can be calculated easily. We refer to this procedure as stochastic averaging and apply it in two contexts. First, we use it to estimate the emissivity of an isotropic $\kappa$ distribution function with a high energy cutoff. The resulting coefficients can be evaluated efficiently enough to be used directly in ray-tracing calculations, and we provide an example calculation. Second, we use stochastic averaging to assess the effect of subgrid turbulence on the volume-averaged emissivity and along the way provide a prescription for a turbulent emissivity. We find that for parameters appropriate to EHT sources turbulence reduces the emissivity slightly. In the infrared turbulence can dramatically increase the emissivity.