Constraints on the dark matter annihilation from Fermi-LAT observation of M31

Gamma-ray is a good probe of dark matter (DM) particles in the Universe. We search for the DM annihilation signals in the direction of the Andromeda galaxy (M31) using 7.5 year Fermi-LAT pass 8 data. Similar to Pshirkov et al. (2016), we find that there is residual excess emission from the direction of M31 if only the galactic disk as traced by the far infrared emission is considered. Adding a point-like source will improve the fitting effectively, although additional slight improvements can be found if an extended component such as a uniform disk or two bubbles is added instead. Taking the far infrared disk plus a point source as the background model, we search for the DM annihilation signals in the data. We find that there is strong degeneracy between the emission from the galaxy and that from 10s GeV mass DM annihilation in the main halo with quark final state. However, the required DM annihilation cross section is about $10^{-25}-10^{-24}$ cm$^3$s$^{-1}$, orders of magnitude larger than the constraints from observations of dwarf spheroidal galaxies, indicating a non-DM origin of the emission. If DM subhalos are taken into account, the degeneracy is broken. When considering the enhancement from DM subhalos, the constraints on DM model parameters are comparable to (or slightly weaker than) those from the population of dwarf spheroidal galaxies. We also discuss the inverse Compton scattering component from DM annihilation induced electrons/positrons. For the first time we include an energy dependent template of the inverse Compton emission (i.e., a template cube) in the data analysis to take into account the effect of diffusion of charged particles. We find a significant improvement of the constraints in the high mass range of DM particles after considering the inverse Compton emission.