Cosmic ray electron spectrum due to the dispersion of injection spectrum

The cosmic-ray total electron spectrum （electrons plus positrons） has been measured precisely up to TeV energies, with more interesting features found. Exhaustive analyses of the electron spectrum strongly support a spectral hardening above 100 GeV, rather than a featureless single power-law, which is confirmed by the most recent observations. Meanwhile, the measurements of the DAMPE satellite have verified the presence of a knee-like structure around 1 TeV in the electron spectrum, resembling the cosmic-ray knee. In this paper, we establish a physical model in which the observed electron spectrum is composed of a superposition of CR sources with various spectral indices and high-energy cutoffs. The dispersion of the power index is assumed to be Gaussian, while the cutoff energy Ec follows a power-law distribution. These simple ideas can account naturally for both the hundred-GeV excess and the TeV spectral break.