We analyze about 12 years of Fermi-LAT data in the direction of the Andromeda galaxy (M31). We robustly characterize its spectral and morphological properties against systematic uncertainties related to the modeling of the Galactic diffuse emission. We perform this work by adapting and exploiting the potential of the skyFACT adaptive template fitting algorithm. We reconstruct the gamma-ray image of M31 in a template-independent way, and we show that flat spatial models are preferred by data, indicating an extension of the $gamma$-ray emission of about 0.3-0.4 degree for the bulge of M31. This study also suggests that a second component, extending to at least 1 degree, contributes to the observed total emission. We quantify systematic uncertainties related to mis-modeling of Galactic foreground emission at the level of 2.9%.
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