Could the Fermi Large Area Telescope detect gamma-rays from dark matter annihilation in the dwarf galaxies of the Local Group?

Context: The detection of γ-rays from dark matter (DM) annihilation is among the scientific goals of the Fermi Large Area Telescope (formerly known as GLAST) and Cherenkov telescopes. Aims: In this paper we investigate the chances of such a discovery, selecting some nearby dwarf spheroidal galaxies (dSph) as a target, and adopting the DM density profiles derived from both astronomical observations and N-body simulations. We also make use of recent studies about the presence of black holes and of a population of sub-subhalos inside the Local Group (LG) dwarfs to carry out boost factor studies. Methods: We study the detectability with the Fermi-LAT of the γ-ray flux from DM annihilation in four of the nearest and highly DM-dominated dSph galaxies of the LG, namely Draco, Ursa Minor, Carina, and Sextans, for which state-of-art DM density profiles were available. We assume the DM is made of weakly interacting massive particles such as the lightest supersymmetric particle and compute the expected γ-ray flux for estimations of the unknown underlying particle physics parameters. We then compute the boost factors due to the presence of DM clumps and of a central supermassive black hole. Finally, we compare our predictions with the Fermi-LAT sensitivity maps. Results: We find that the dSph galaxies shine above the Galactic smooth halo: e.g., the Galactic halo is brighter than the Draco dSph only for angles smaller than 2.3 degrees above the Galactic Center. We also find that the presence of a cusp or a constant density core in the DM mass density profile does not produce any relevant effects in the γ-ray flux due to the fortunate combination of the geometrical acceptance of the Fermi-LAT detector and the distance of the galaxies. Moreover, no significant enhancement is given by the presence of a central black hole or a population of sub-subhalos. Conclusions: We conclude that, even for the most optimistic scenario of particle physics, the γ-ray flux from DM annihilation in the dSph galaxies of the LG would be too low to be detected with the Fermi-LAT.