The Contribution of Millisecond Pulsars to the Galactic Cosmic-Ray   Lepton Spectrum
  Pulsars are believed to be sources of relativistic electrons and positrons. The abundance of detections of gamma-ray millisecond pulsars by Fermi Large Area Telescope coupled with their light curve characteristics that imply copious pair production in their magnetospheres, motivated us to investigate this old pulsar population as a source of Galactic electrons and positrons and their contribution to the enhancement in cosmic-ray positron flux at GeV energies. We use a population synthesis code to predict the source properties (number, position, and power) of the present-day Galactic millisecond pulsars, taking into account the latest Fermi and radio observations to calibrate the model output. Next, we simulate pair cascade spectra from these pulsars using a model that invokes an offset-dipole magnetic field. We assume free escape of the pairs from the pulsar environment. We then compute the cumulative spectrum of transported electrons and positrons at Earth, following their diffusion and energy losses as they propagate through the Galaxy. Our results indicate that the predicted particle flux increases for non-zero offsets of the magnetic polar caps. Comparing our predicted spectrum and positron fraction to measurements by AMS-02, PAMELA, and Fermi, we find that millisecond pulsars are only modest contributors at a few tens of GeV, after which this leptonic spectral component cuts off. The positron fraction is therefore only slightly enhanced above 10 GeV relative to a background flux model. This implies that alternative sources such as young, nearby pulsars and supernova remnants should contribute additional primary positrons within the astrophysical scenario. 
C. Venter, A. Kopp, P.L. Gonthier, A.K. Harding, I. B\"usching
astro-ph.HE