Approximation of the radiation power of electrons due to the inverse-Compton process in the black-body photon field (Research Note)

Aims. An approximation is presented for the inverse-Compton radiation power of electrons in the isotropic black-body photon field. Methods. This approximation allows calculation of the inverse-Compton emissivity as an integral over the energies of incident electrons rather than over the field photon energies. Such an approach allows for accurate modeling of IC emission of electrons with energy spectra different from power law, in tasks where essential CPU resources are needed. Results. The high accuracy of this approximation allows it to be used in a wide range of conditions, from Thomson to extreme Klein-Nishina limits, in different astrophysical objects. This approach also results in some new analytic expressions representing the known results in the Thomson limit.