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.
