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.
