The cosmic-ray positron excess and its imprint in the Galactic gamma-ray sky

We study the origin of the positron excess observed in the local cosmic-ray spectrum at high energies, and relate it to the cosmic rays and gamma-ray emission across the entire Galaxy. In particular, we explore the hypothesis of a single, dominant source accountable for primary electron-positron pairs. Since we are agnostic about the physical nature of the underlying source population, we consider four simple models that are representative of young pulsars, old stars (as a tracer of millisecond pulsars), and annihilating dark matter particles. In the dark matter hypothesis, we consider both a cored and a cuspy model for the halo in the Milky Way. Then, we compare the associated gamma-ray sky maps with Fermi-LAT data. The aim of this work is not to derive constraints or upper limits for the different models considered, but rather to explore the possibility, as a proof of concept, of building a self-consistent model able to explain simultaneously the origin of all cosmic-ray species, including positrons, as well as the Galactic center GeV gamma-ray emission. We find that the emission arising from pulsar wind nebulae is fairly concentrated near the mid plane, and therefore additional cosmic-ray sources must be invoked to explain the emission at the center of the Galaxy. If the local positron excess were mainly due to millisecond pulsars, inverse Compton scattering by the particles injected in the Milky Way bulge would naturally account for a non-negligible fraction of the central gamma-ray emission. The case of annihilating dark matter is very sensitive to the precise shape of the dark matter profile. The results for a standard NFW cuspy profile are above the gamma-ray measurements by as much as a factor of 2 in some regions of the Galaxy, while the results for an isothermal, cored profile are still compatible with the data. However, the cross-sections exceed the current constraints.