We analyze 2.8-yr data of 1-100 GeV photons for clusters of galaxies, collected with the Large Area Telescope onboard the Fermi satellite. By analyzing 49 nearby massive clusters located at high Galactic latitudes, we find no excess gamma-ray emission towards directions of the galaxy clusters. Using flux upper limits, we show that the Fornax cluster provides the most stringent constraints on the dark matter annihilation cross section. Stacking a large sample of nearby clusters does not help improve the limit for most dark matter models. This suggests that a detailed modeling of the Fornax cluster is important for setting robust limits on the dark matter annihilation cross section based on clusters. We therefore perform the detailed mass modeling and predict the expected dark matter annihilation signals from the Fornax cluster, by taking into account effects of dark matter contraction and substructures. By modeling the mass distribution of baryons (stars and gas) around a central bright elliptical galaxy, NGC 1399, and using a modified contraction model motivated by numerical simulations, we show that the dark matter contraction boosts the annihilation signatures by a factor of 4. For dark matter masses around 10 GeV, the upper limit obtained on the annihilation cross section times relative velocity is <sigma v> <~ (2-3)x10^{-25} cm^3 s^{-1}, which is within a factor of 10 from the value required to explain the dark matter relic density. This effect is more robust than the annihilation boost due to substructure, and it is more important unless the mass of the smallest subhalos is much smaller than that of the Sun.
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