Klein-Nishina steps in the energy spectrum of galactic cosmic-ray electrons

The full Klein-Nishina cross-section of the inverse Compton scattering interactions of electrons implies a significant reduction of the electron energy loss rate compared with the Thomson limit when the electron energy exceeds the critical Klein-Nishina energy EK=γKmec2=0.27m2ec4/(kBT), where T denotes the temperature of the photon graybody distribution. As a consequence, the total radiative energy loss rate of single electrons exhibits sudden drops in the overall γ-dot α γ2-dependence when the electron energy reaches the critical Klein-Nishina energy. The strength of the drop is proportional to the energy density of the photon radiation field. The diffuse galactic optical photon fields from stars of spectral type B and G-K lead to critical Klein-Nishina energies of 40 and 161 GeV, respectively. Associated with the drop in the loss rate are sudden increases (Klein-Nishina steps) in the equilibrium spectrum of cosmic-ray electrons. Because the radiative loss rate of electrons is the main ingredient in any transport model of high-energy cosmic-ray electrons, Klein-Nishina steps will modify any calculated electron equilibrium spectrum irrespective of the electron sources and the spatial transport mode. To delineate most clearly the consequences of the Klein-Nishina decreases in the radiative loss rate, we chose as an illustrative example the simplest realistic model for cosmic-ray electron dynamics in the galaxy, consisting of the competition of radiative losses and secondary production by inelastic hadron-hadron collisions. We demonstrate that the spectral structure in the FERMI and HESS data is well described and even the excess measured by ATIC might be explained by Klein-Nishina steps.