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 Comptonize d by a hot electron gas. Low frequencies are considered, and the equations are expanded to second order in electron velocities. Induced scattering ter ms are included and a Maxwellian velocity distribution for the electrons is assumed. The special case of an axisymmetric radiation field is also consi dered, and the corresponding radiative transfer equations are found. Our re sults correct errors and misprints in previously published transfer equatio ns. The extension to a moving electron gas is made, and the radiative trans fer equations are deduced to second order in gas velocity. We use the equat ions to study polarization in the Sunyaev-Zeldovich effect.