Constraining the Milky Way's Pulsar Population with the Cosmic-Ray Positron Fraction

Observations of the TeV halos associated with nearby pulsars indicate that these objects inject significant fluxes of very high-energy electron-positrons pairs into the interstellar medium (ISM), thereby likely providing the dominant contribution to the cosmic-ray positron flux. In this paper, we use the cosmic-ray positron fraction as measured by the AMS-02 Collaboration to constrain the characteristics of the local pulsar population. For reasonable model parameters, we find that we can obtain good agreement with the measured positron fraction up to energies of $E_e \sim 300 \, {\rm GeV}$. At higher energies, the positron fraction is dominated by a small number of pulsars, making it difficult to reliably predict the shape of the expected positron fraction. The low-energy positron spectrum supports the conclusion that pulsars typically transfer approximately $\eta \sim 5-20\%$ of their total spindown power into the production of very high-energy electron-positron pairs, producing a spectrum of such particles with a hard spectral index, $\alpha \sim 1.5-1.7$. Such pulsars typically spindown on a timescale on the order of $\tau \sim 10^4 \, {\rm years}$. Our best fits were obtained for models in which the radio and gamma-ray beams from pulsars are detectable to 28% and 62% of surrounding observers, respectively.Comment: 15 pages, 6 figure