Investigating the Fermi Large Area Telescope sensitivity of detecting the characteristics of the Galactic center excess

The center of the Milky Way is offering one of the most striking mystery in Astroparticle Physics. An excess of gamma rays (GCE) has been measured by several groups in the data collected by the Fermi Large Area Telescope (LAT) towards the Galactic center region. The spectrum and spatial morphology of the GCE have been claimed by some groups to be compatible with a signal from the Galactic halo of dark matter (DM). Instead, other analyses have demonstrated that the GCE properties, e.g., its energy spectrum, highly depend on the choice of the Galactic interstellar emission (IEM) model source catalogs and analysis techniques. In this paper we investigate the sensitivity of Fermi-LAT to detect the characteristics of the GCE. In particular we simulate the GCE as given by DM and we verify that, with a perfect knowledge of the background components, its energy spectrum, position, spatial morphology and symmetry is properly measured. We also inspect two more realist cases for which there are imperfections in the IEM model. In the first we have an un-modeled gamma-ray source, constituted by the low-latitude component of the Fermi bubbles. In the second we simulate the data with one IEM template and analyze the data with an other. We verify that a mismodeling of the IEM introduces a systematics of about 10-15% in the GCE energy spectrum between 1-10 GeV and about 5% in the value of the slope for a NFW DM density profile, which is used to fit the GCE spatial morphology. Finally, we show how the GCE would be detected in case of alternative processes such as gamma-ray emission from a bulge population of pulsars or from electrons and positrons or protons injected from the Galactic center. We demonstrate that for each of these cases there is a distinctive smoking gun signature that would help to identify the real mechanism behind the origin of the GCE.