Explaining the cosmic-ray e+/(e− + e+) and ratios using a steady-state injection model

We present a model of cosmic ray (CR) injection into the Galactic space based on recent γ-ray observations of supernova remnants (SNRs) and pulsar wind nebulae (PWNe) by the Fermi Large Area Telescope (Fermi) and imaging atmospheric Cherenkov telescopes (IACTs). Steady-state injection of nuclear particles and electrons (e−) from the Galactic ensemble of SNRs, and electrons and positrons (e+) from the Galactic ensemble of PWNe are assumed, with their injection spectra inferred under guidance of γ-ray observations and recent development of evolution and emission models. The ensembles of SNRs and PWNe are assumed to share the same spatial distributions. Assessment of possible secondary CR contribution from dense molecular clouds interacting with SNRs is also given. CR propagation in the interstellar space is handled by GALPROP. Different underlying source distribution models and Galaxy halo sizes are employed to estimate the systematic uncertainty of the model. We show that this observation-based model reproduces the positron fraction e+/(e− + e+) and antiproton-to-proton ratio ( p ¯ / p ) reported by PAMELA and other previous missions reasonably well, without calling for any speculative sources. A discrepancy remains, however, between the total e− + e+ spectrum measured by Fermi and our model below ∼20 GeV, for which the potential causes are discussed. Important quantities for Galactic CRs including their energy injection, average lifetime in the Galaxy, and mean gas density along their typical propagation path are also estimated.