Kompaneets equation

Summary

The Kompaneets equation describes how repeated Compton scattering by a hot thermal gas of electrons changes the spectrum of a photon gas. It is a nonlinear diffusion equation in photon energy, of Fokker–Planck type, for the photon occupation number. It holds when the electrons are non-relativistic and each scattering changes the photon energy only a little. It is the basic tool for the Comptonised spectra of X-ray sources and for the Sunyaev–Zeldovich effect.