Multi-messenger constraints to the local emission of cosmic-ray electrons

The data on the inclusive flux of cosmic positrons and electrons ($e^++e^{-}$) have been recently collected from GeV to tens of TeV energies by several experiments with unprecedented precision. In addition, the Fermi-LAT Collaboration has provided a new energy spectrum for the upper bounds on the $e^++e^{-}$ dipole anisotropy. This observable can bring information on the emission from local Galactic sources, notably measured with high precision at radio frequencies. We develop a framework in which $e^-$ and $e^+$ measured at Earth from GeV up to tens of TeV energies have a composite origin. A dedicated analysis is deserved to Vela YZ and Cygnus Loop Supernova Remnants (SNRs), for which we consider two different models for the injection of $e^-$. We investigate the consistency of these models using the three physical observables: the radio flux from Vela YZ and Cygnus Loop at all the available frequencies, the $e^++e^-$ flux from five experiments from the GeV to tens of TeV energy, the $e^++e^-$ dipole anisotropy upper limits from 50 GeV to about 1 TeV. We find that the radio flux for these nearby SNRs strongly constraints the properties of the injection electron spectrum, partially compatible with the looser constraints derived from the $e^+ + e^-$ flux data. We also perform a multi-wavelength multi-messenger analysis by fitting simultaneously the radio flux on Vela YZ and Cygnus Loop and the $e^+ + e^-$ flux, and checking the outputs against the $e^+ + e^-$ dipole anisotropy data. Remarkably, we find a model which is compatible with all the $e^++e^-$ flux data, the radio data for Vela YZ and Cygnus Loop, and with the anisotropy upper bounds. We show the severe constraints imposed by the most recent data on the $e^+ + e^-$ dipole anisotropy.