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

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