Polarization transfer in relativistic magnetized plasmas

TL;DR

This paper derives comprehensive polarization transfer coefficients for relativistic magnetized plasmas, applicable to various particle distributions, using advanced analytical methods to facilitate calculations relevant to astrophysical plasma studies.

Contribution

It introduces a novel derivation of the conductivity tensor and analytical expressions for polarization transfer coefficients applicable to any particle distribution in relativistic plasmas.

Findings

Derived exact conductivity tensor for relativistic plasmas

Expressed transfer coefficients as integrals suitable for numerical computation

Provided simplified formulas for isotropic and anisotropic distributions

Abstract

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. 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 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 powerlaw, with different multipolar anisotropies of low order, or strongly beamed. 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. 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.