Using a semianalytic model of nonlinear diffusive shock acceleration, we model the total spectrum of cosmic ray (CR) electrons accelerated by supernova remnants (SNRs). Because electrons experience synchrotron losses in the amplified magnetic fields characteristic of SNRs, they exhibit substantially steeper spectra than protons. In particular, we find that the difference between the electron and proton spectral index (power law slope) ranges from 0.1 to 0.4. Our findings must be reckoned with theories of Galactic CR transport, which often assume that electrons and protons are injected with the same slope, and may especially have implications for the observed “positron excess”.

• Received 17 May 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.071101