On the Energy Spectra of GeV/TeV Cosmic Ray Leptons

Recent observations of cosmic ray electrons from several instruments have revealed various degrees of deviation in the measured electron energy distribution from a simple power-law, in a form of an excess around 0.1 to 1TeV energies. An even more prominent deviation and excess has been observed in the fraction of cosmic ray positrons around 10 and 100GeV energies. These observations have received considerable attention and many theoretical models have been proposed to explain them. The models rely on either dark matter annihilation/decay or specific nearby astrophysical sources, and involve several additional assumptions regarding the dark matter distribution or particle acceleration. In this paper we show that the observed excesses in the electron spectrum may be easily reproduced without invoking any unusual sources other than the general diffuse Galactic components of cosmic rays. The model presented here assumes a powerlaw injection of electrons (and protons) by supernova remnants, and evaluates their expected energy spectrum based on a simple kinetic equation describing the propagation of charged particles in the interstellar medium. The primary physical effect involved is the Klein-Nishina suppression of the electron cooling rate around TeV energies. With a very reasonable choice of the model parameters characterizing the local interstellar medium, we can reproduce the most recent observations by Fermi and HESS experiments. Interestingly, in our model the injection spectral index of cosmic ray electrons becomes comparable to, or even equal to that of cosmic ray protons. The Klein-Nishina effect may also affect the propagation of the secondary e pairs, and therefore modify the cosmic ray positron-to-electron ratio. We have explored this possibility by considering two mechanisms for production of e pairs within the Galaxy. The first is due to the decay of π’s produced by interaction of cosmic ray nuclei with ambient protons. The second source discussed here is due to the annihilation of the Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, Stanford, CA 94305, USA Astronomical Observatory of the Jagiellonian University, ul. Orla 171, 30-244 Kraków, Poland Departments of Physics and of Applied Physics, Stanford University, Stanford, CA 94305, USA