Cosmic-ray electrons released by supernova remnants

Giovanni Morlino, Silvia Celli

Published 2021-06-11Version 1

The process that allows cosmic rays (CRs) to escape from their sources and be released into the Galaxy is still largely unknown. The comparison between CR electron and proton spectra measured at Earth suggests that electrons are released with a spectrum steeper than protons by $\Delta s_{\rm ep} \sim 0.3$ for energies above $\sim 10$ GeV and by $\Delta s_{\rm ep} \sim 1.2$ above $\sim 1$~TeV. Assuming that both species are accelerated at supernova remnant (SNR) shocks, we here explore two possible scenarios that can in principle justify steeper electron spectra: {\it i}) energy losses due to synchrotron radiation in an amplified magnetic field, and {\it ii}) time dependent acceleration efficiency. We account for magnetic field amplification (MFA) produced by either CR-induced instabilities or by magneto-hydrodynamics (MHD) instabilities using a parametric description. We show that both mechanisms are required to explain the electron spectrum. In particular synchrotron losses can produce a significant electron steepening only above $\sim 1$~TeV, while a time dependent acceleration can explain the spectrum at lower energies if the electron injection into diffusive shock acceleration (DSA) is inversely proportional to the shock speed. We discuss observational and theoretical evidences supporting such a behavior. In addition, we predict \gio{two additional spectral features: a spectral break below $\sim$ few GeV (as required by existing observations) due to the acceleration efficiency drop during the adiabatic phase and} a spectral hardening above $\sim 20$~TeV (where no data are available yet) resulting from electrons escaping from the shock precursor.