# On the Spectrum of Electrons Accelerated in Supernova Remnants

## TL;DR

This paper models the spectrum of cosmic ray electrons accelerated by supernova remnants, highlighting how synchrotron losses cause electrons to have steeper spectra than protons, impacting theories of Galactic cosmic ray transport.

## Contribution

It introduces a semi-analytic model accounting for synchrotron losses, revealing the spectral difference between electrons and protons in supernova remnants.

## Key findings

- Electrons have a steeper spectrum than protons by 0.1 to 0.4 in spectral index.
- The spectral difference affects models of Galactic cosmic ray transport.
- Implications for the observed positron excess in cosmic rays.

## Abstract

Using a semi-analytic model of non-linear diffusive shock acceleration, we model the 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."