Fermi-LAT Observations of High-Energy Gamma-Ray Emission Toward the Galactic Center

The Fermi Large Area Telescope (LAT) has provided the most detailed view to date of the emission towards the Galactic centre (GC) in high-energy gamma-rays. This paper describes the analysis of data taken during the first 62 months of the mission in the energy range 1-100 GeV from a $15^\circ \times 15^\circ$ region about the direction of the GC, and implications for the interstellar emissions produced by cosmic ray (CR) particles interacting with the gas and radiation fields in the inner Galaxy and for the point sources detected. Specialised interstellar emission models (IEMs) are constructed that enable separation of the gamma-ray emission from the inner $\sim 1$ kpc about the GC from the fore- and background emission from the Galaxy. Based on these models, the interstellar emission from CR electrons interacting with the interstellar radiation field via the inverse Compton (IC) process and CR nuclei inelastically scattering off the gas producing gamma-rays via $\pi^0$ decays from the inner $\sim 1$ kpc is determined. The IC contribution is found to be dominant in the region and strongly enhanced compared to previous studies. A catalog of point sources for the $15^\circ \times 15^\circ$ region is self-consistently constructed using these IEMs: the First Fermi-LAT Inner Galaxy point source Catalog (1FIG). After subtracting the interstellar emission and point-source contributions from the data a residual is found that is a sub-dominant fraction of the total flux. If spatial templates that peak toward the GC are used to model the positive residual and included in the total model for the $15^\circ \times 15^\circ$ region, the agreement with the data improves, but none of the additional templates account for all of the residual structure. The spectrum of the positive residual modelled with these templates has a strong dependence on the choice of IEM. [Abridged]