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 γ -ray discrete or small-scale structure related to H₂ interstellar gas. Reliably identifying this contribution is important to disentangle γ -ray point sources from interstellar gas, and to better characterize extended γ -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 H₂-related γ -ray discrete emission for a 50 °×1 ° region along the Galactic plane via H₂ proxies better suited to trace these features. We find that these are likely to contribute significantly to the γ -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.