Improved modeling of the discrete component of the Galactic interstellar γ -ray emission and implications for the Fermi –LAT Galactic Center excess

The aim of this work is to improve models for the $\ensuremath{\gamma}$-ray discrete or small-scale structure related to ${\mathrm{H}}_{2}$ interstellar gas. Reliably identifying this contribution is important to disentangle $\ensuremath{\gamma}$-ray point sources from interstellar gas, and to better characterize extended $\ensuremath{\gamma}$-ray signals. Notably, the Fermi--LAT Galactic center (GC) excess, whose origin remains unclear, might be smooth or pointlike. If the data contain a pointlike contribution that is not adequately modeled, a smooth GC excess might be erroneously deemed to be pointlike. We improve models for the ${\mathrm{H}}_{2}$-related $\ensuremath{\gamma}$-ray discrete emission for a $50\ifmmode^\circ\else\textdegree\fi{}\ifmmode\times\else\texttimes\fi{}1\ifmmode^\circ\else\textdegree\fi{}$ region along the Galactic plane via ${\mathrm{H}}_{2}$ proxies better suited to trace these features. We find that these are likely to contribute significantly to the $\ensuremath{\gamma}$-ray Fermi--LAT data in this region, and the brightest ones are likely associated with detected Fermi--LAT sources, a compelling validation of this methodology. We discuss prospects to extend this methodology to other regions of the sky and implications for the characterization of the GC excess.