Improved Fokker-Planck Equation for Resonance-Line Scattering

A new Fokker-Planck equation is developed for treating resonance-line scattering, which is especially relevant to the treatment of Lya in the early universe. It is a "corrected" form of the equation of Rybicki & Dell'Antonio that now obeys detailed balance, so the approach to thermal equilibrium is properly described. The new equation takes into account the energy changes due to scattering off moving particles, the recoil term of Basko, and stimulated scattering. One result is a surprising unification of the equation for resonance-line scattering and the Kompaneets equation. An improved energy exchange formula due to resonance-line scattering is derived. This formula is compared to previous formulas of Madau and coworkers and Chen & Miralda-Escude.