On the spectral shape of radiation due to Inverse Compton Scattering close to the maximum cut-off

The spectral shape of radiation due to Inverse Compton Scattering is analyzed, in the Thomson and the Klein-Nishina regime, for electron distributions with exponential cut-off. We derive analytical, asymptotic expressions for the spectrum close to the maximum cut-off region. We consider monoenergetic, Planckian and Synchrotron photons as target photon fields. These approximations provide a direct link between the distribution of parent electrons and the up-scattered spectrum at the cut-off region.
Comment: 27 pages, 15 figures, accepted for publication in ApJ