Features in the Spectrum of Cosmic-Ray Positrons from Pulsars

Pulsars have been invoked to explain the origin of recently observed high-energy Galactic cosmic-ray positrons. Since the positron propagation distance decreases with energy, the number of pulsars that can contribute to the observed positrons decreases from $O(10^3)$ for positron energies $E\gtrsim10$ GeV to only a few for $E \gtrsim 500$ GeV. Thus, if pulsars explain these positrons, the positron energy spectrum should become increasingly bumpy at higher energies. Here we present a power-spectrum analysis that can be applied to seek such spectral features in the energy spectrum for cosmic-ray positrons and for the energy spectrum of the combined electron/positron flux. We account for uncertainties in the pulsar distribution by generating hundreds of simulated spectra from pulsar distributions consistent with current observational constraints. Although the current AMS-02 data do not exhibit evidence for spectral features, we find that such features would be detectable in $\simeq 10\%$ of our simulations, with 20 years of AMS-02 data or three years of DAMPE measurements on the electron-plus-positron flux.