Theoretical interpretation of Pass 8 Fermi-LAT $e^+ + e^-$ data

The flux of positrons and electrons ($e^+ + e^-$) has been measured by the $Fermi$ Large Area Telescope (LAT) in the energy range between 7 GeV and 2 TeV. We discuss a number of interpretations of Pass 8 $Fermi$-LAT $e^+ + e^-$ spectrum, combining electron and positron emission from supernova remnants (SNRs) and pulsar wind nebulae (PWNe), or produced by the collision of cosmic rays with the interstellar medium. We find that the $Fermi$-LAT spectrum is compatible with the sum of electrons from a smooth SNR population, positrons from cataloged PWNe, and a secondary component. If we include in our analysis constraints from AMS-02 positron spectrum, we obtain a slightly worse fit to the $e^+ + e^-$ $Fermi$-LAT spectrum, depending on the propagation model. As an additional scenario, we replace the smooth SNR component within 0.7 kpc with the { individual sources} found in Greens catalog of Galactic SNRs. We find that separate consideration of far and near sources helps to reproduce the $e^+ + e^-$ $Fermi$-LAT spectrum. However, we show that the fit degrades when the radio constraints on the positron emission from Vela SNR (which is the main contributor at high energies) are taken into account. We find that a break in the power-law injection spectrum at about 100 GeV can also reproduce the measured $e^+ + e^-$ spectrum} and, among the cosmic-ray propagation models that we consider, no reasonable break of the power-law dependence of the diffusion coefficient can modify the electron flux enough to reproduce the observed shape.