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 E_K=γ_Km_ec²=0.27m²_ec⁴/(k_BT), 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 -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.