The `excess' of primary cosmic ray electrons

With the accurate cosmic ray (CR) electron and positron spectra (denoted as ${\mathrm{\Phi }}_{{\mathrm{e}}^{-}}$ and ${\mathrm{\Phi }}_{{\mathrm{e}}^{+}}$, respectively) measured by AMS-02 collaboration, the difference between the electron and positron fluxes (i.e., $\mathrm{\Delta }\mathrm{\Phi }={\mathrm{\Phi }}_{{\mathrm{e}}^{-}}-{\mathrm{\Phi }}_{{\mathrm{e}}^{+}}$), dominated by the propagated primary electrons, can be reliably inferred. In the standard model, the spectrum of propagated primary CR electrons at energies $\ge 30$ GeV softens with the increase of energy. The absence of any evidence for such a continuous spectral softening in $\mathrm{\Delta }\mathrm{\Phi }$ strongly suggests a significant excess' of primary CR electrons and at energies of $100-400$ GeV the identified excess component has a flux comparable to that of the observed positron excess. Middle-age but nearby’ supernova remnants (e.g., Monogem and Geminga) are favored sources for such an excess.