Compton scattering of blackbody photons by relativistic electrons

We present simple and accurate analytical formulae for the rates of Compton scattering by relativistic electrons integrated over the energy distribution of blackbody seed photons. Both anisotropic scattering, in which blackbody photons arriving from one direction are scattered by an anisotropic electron distribution into another direction, and scattering of isotropic seed photons are considered. Compton scattering by relativistic electrons off blackbody photons from either stars or CMB takes place, in particular, in microquasars, colliding-wind binaries, supernova remnants, interstellar medium, and the vicinity of the Sun.