Simple analytical approximations for treatment of inverse Compton scattering of relativistic electrons in the black-body radiation field

Abstract: The inverse Compton (IC) scattering of relativistic electrons is one of the major gamma-ray production mechanisms in different environments. Often the target photons for the IC scattering are dominated by black (or grey) body radiation. In this case, the precise treatment of the characteristics of IC radiation requires numerical integrations over the Planckian distribution. Formally, analytical integrations are also possible but they result in series of several special functions; this limits the efficiency of usage of these expressions. The aim of this work is the derivation of approximate analytical presentations which would provide adequate accuracy for the calculations of the energy spectra of up-scattered radiation, the rate of electron energy losses, and the mean energy of emitted photons. Such formulae have been obtained by merging the analytical asymptotic limits. The coefficients in these expressions are calculated via the least square fitting of the results of numerical integrations. The simple analytical presentations, obtained for both the isotropic and anisotropic target radiation fields, provide adequate (as good as $1\%$) accuracy for broad astrophysical applications.