A FORMALISM FOR COVARIANT POLARIZED RADIATIVE TRANSPORT BY RAY TRACING

Abstract

We write down a covariant formalism for polarized radiative transfer appropriate for ray tracing through a turbulent plasma. The polarized radiation field is represented by the polarization tensor (coherency matrix) N{sup {alpha}{beta}} {identical_to} (a{sup {alpha}}{sub k} a*{sup {beta}}{sub k}), where a{sub k} is a Fourier coefficient for the vector potential. Using Maxwell's equations, the Liouville-Vlasov equation, and the WKB approximation, we show that the transport equation in vacuo is k{sup {mu}}{nabla}{sub {mu}} N{sup {alpha}{beta}} = 0. We show that this is equivalent to Broderick and Blandford's formalism based on invariant Stokes parameters and a rotation coefficient, and suggest a modification that may reduce truncation error in some situations. Finally, we write down several alternative approaches to integrating the transfer equation.