Dark Matter Interpretation of the Fermi-LAT Observations Toward the Outer Halo of M31

An excess $\gamma$-ray signal toward the outer halo of M31 has recently been reported. Although other explanations are plausible, the possibility that it arises from dark matter (DM) is valid. In this work we interpret the excess in the framework of DM annihilation, using as our representative case WIMP DM annihilating to bottom quarks, and we perform a detailed study of the systematic uncertainty in the $J$-factor for the M31 field. We find that the signal favors a DM particle with a mass of $\sim$46-73 GeV. While the mass is well constrained, the systematic uncertainty in the cross-section spans 2.5 orders of magnitude, ranging from $\sim$8$\times 10^{-27}-4 \times 10^{-24} \ \mathrm{cm^3 \ s^{-1}}$. This high uncertainty is due to two main factors, namely, an uncertainty in the substructure nature and geometry of the DM halos for both M31 and the Milky Way (MW), and correspondingly, an uncertainty in the contribution to the signal from the MW's DM halo along the line of sight. However, under the conditions that the minimum subhalo mass is $\lesssim 10^{-6} \ M_\odot$ and the actual contribution from the MW's DM halo along the line of sight is at least $\sim$30$\%$ of its total value, we show that there is a large overlap with the DM interpretations of both the Galactic center (GC) excess and the antiproton excess, while also being compatible with the limits for the MW dwarf spheroidals. More generally, we summarize the results from numerous complementary DM searches in the energy range 10 GeV $-$ 300 GeV corresponding to the GC excess and identify a region in parameter space that still remains viable for discovery of the DM particle.