THE INFLUENCE OF KLEIN–NISHINA STEPS ON THE SPATIAL DIFFUSION OF GALACTIC COSMIC-RAY ELECTRONS

Abstract

The full Klein–Nishina cross section for the inverse Compton scattering interactions of electrons implies a significant reduction of the electron energy loss rate compared to the Thomson limit when the electron energy exceeds the critical Klein–Nishina energy EK = 0.27m 2 c 4 /(kBT ), where T denotes the temperature of the photon graybody distribution. We investigate the influence of the Klein–Nishina reduction on the solution of the steady-state spatial diffusion transport equation for relativistic electrons. The modified electron spectrum at energies below 10 4 GeV, where only the Klein–Nishina modifications from interstellar optical target photons are relevant, are derived in terms of the Green’s function solution for one-, two-, and three-dimensional spatial diffusion. The modifications to the solutions of the one- and three-dimensional diffusion equations are calculated for a single point source of monoenergetic electrons. It is shown that significant enhancements in the local electron intensity occur at electron energies greater than the critical Klein–Nishina energy EK, and that the cosmic-ray electron anisotropy at the solar system resulting from a single steady point source exhibits a sharp drop near EK. These Klein–Nishina enhancements are potentially interesting for determining the contribution of point sources such as dark matter sources and/or electromagnetic particle accelerators (pulsars and micro-quasars) to the local electron intensity and the local positron fraction. Galactic relativistic electrons (positrons e + and negatrons e − ), no matter whether they result from dark matter decay or electromagnetic acceleration processes of cosmic rays, undergo severe inverse Compton energy-loss processes with ambient galactic photon target fields during their interstellar propagation from their sources to us. Using the full Klein–Nishina interaction cross section in the calculation of the inverse Compton energy-loss rate then 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 = γK mec 2 = 0.27m 2c 4 /(kBT ), where the radiation