SIMPLE ANALYTICAL APPROXIMATIONS FOR TREATMENT OF INVERSE COMPTON SCATTERING OF RELATIVISTIC ELECTRONS IN THE BLACKBODY RADIATION FIELD

Abstract

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