Galactic electrons and positrons at the Earth: new estimate of the primary and secondary fluxes

The so-called excess of cosmic ray (CR) positrons observed by the PAMELA satellite up to 100 GeV has opened windows for various interpretations involving standard astrophysics and/or a possible exotic contribution from dark matter annihilation or decay. The subsequent Fermi data on CR electrons plus positrons in the range 0.02-1 TeV, and HESS data above 1 TeV have provided additional information on the leptonic content of local Galactic CRs. In this paper, we wish to revisit the full predictions of the so-called "standard" CR lepton fluxes at the Earth of both secondary and primary origins, evaluate the theoretical uncertainties, and determine their level of consistency with respect to the available data. We find that the electron flux in the energy range 5-30 GeV is well reproduced from a smooth distant distribution of sources with index gamma 2.3-2.4, while local sources (supernova remnants and pulsars) dominate at higher energy. For positrons, local pulsars have important effect above 5-10 GeV. Uncertainties affecting the source modeling and propagation are degenerate and each translates into about one order of magnitude error in terms of local flux. The spectral shape at high energy is barely connected with the spectral indices of local sources, more with the hierarchy in their distance, age and power. Still, our global and self-consistent analysis can fairly explain all available data, without over-tuning the parameters. Our results show that though a standard paradigm of Galactic CRs is well established, we can hardly talk about any "standard model" of CR leptons, because of the very large theoretical uncertainties. Our analysis provides details on the impact of these uncertainties, thereby sketching a roadmap for further improvements.