The possible gamma-ray excess in the inner Galaxy and the Galactic center (GC) suggested by Fermi-LAT observations has triggered a large number of studies. It has been interpreted as a variety of different phenomena such as a signal from WIMP dark matter annihilation, gamma-ray emission from a population of millisecond pulsars, or emission from cosmic rays injected in a sequence of burst-like events or continuously at the GC. We present the first comprehensive study of model systematics coming from the Galactic diffuse emission in the inner part of our Galaxy and their impact on the inferred properties of the excess emission at Galactic latitudes $2^\circ<|b|<20^\circ$ and 300 MeV to 500 GeV. We study both theoretical and empirical model systematics, which we deduce from a large range of Galactic diffuse emission models and a principal component analysis of residuals in numerous test regions along the Galactic plane. We show that the hypothesis of an extended spherical excess emission with a uniform energy spectrum is compatible with the Fermi-LAT data in our region of interest at $95\%$ CL. Assuming that this excess is the extended counterpart of the one seen in the inner few degrees of the Galaxy, we derive a lower limit of $10.0^\circ$ ($95\%$ CL) on its extension away from the GC. We show that, in light of the large correlated uncertainties that affect the subtraction of the Galactic diffuse emission in the relevant regions, the energy spectrum of the excess is equally compatible with both a simple broken power-law of break energy $2.1\pm0.2$ GeV, and with spectra predicted by the self-annihilation of dark matter, implying in the case of $\bar{b}b$ final states a dark matter mass of $49^{+6.4}_{-5.4}$ GeV.
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?
