Connecting the new H.E.S.S. diffuse emission at the Galactic center with the Fermi GeV excess: a combination of millisecond pulsars and heavy dark matter?

The H.E.S.S. collaboration has reported a high-energy spherically symmetric diffuse gamma-ray emission in the inner 50 pc of the Milky Way, up to ~ 50 TeV. Here we propose a leptonic model which provides an alternative to the hadronic scenario presented by the H.E.S.S. collaboration, and connects the newly reported TeV emission to the Fermi-LAT Galactic center GeV excess. Our model relies on a combination of inverse Compton emission from a population of millisecond pulsars---which can account for the GeV excess---and a supermassive black hole-induced spike of heavy (~ 60 TeV) dark matter particles annihilating into electrons with a sub-thermal cross-section. With an up-to-date interstellar radiation field, as well as a standard magnetic field and diffusion set-up, our model accounts for the spectral morphology of the detected emission. Moreover, we show that the dark matter induced emission reproduces the spatial morphology of the H.E.S.S. signal above ~ 10 TeV, while we obtain a slightly more extended component from pulsars at lower energies, which could be used as a prediction for future H.E.S.S. observations.