The radiative transfer equations for Compton scattering of polarized low frequency radiation on a hot electron gas

We deduce the equations that describe how polarized radiation is Comptonized by a hot electron gas. Low frequencies are considered, and the equations are expanded to second order in electron velocities. Induced scattering terms are included and a Maxwellian velocity distribution for the electrons is assumed. The special case of an axisymmetric radiation field is also considered, and the corresponding radiative transfer equations are found. Our results correct errors and misprints in previosly published transfer equations. The extension to a moving electron gas is made, and the radiative transfer equations are deduced to second order in gas velocity. We use the equations to study polarization in the Sunyaev-Zeldovich effect.