The Fornax galaxy cluster was observed with the High Energy Stereoscopic System for a total live time of 14.5?hr, searching for very high energy (VHE; E 100GeV) γ-rays from dark matter (DM) annihilation. No significant signal was found in searches for point-like and extended emissions. Using several models of the DM density distribution, upper limits on the DM velocity-weighted annihilation cross-section σv as a function of the DM particle mass are derived. Constraints are derived for different DM particle models, such as those arising from Kaluza-Klein and supersymmetric models. Various annihilation final states are considered. Possible enhancements of the DM annihilation γ-ray flux, due to DM substructures of the DM host halo, or from the Sommerfeld effect, are studied. Additional γ-ray contributions from internal bremsstrahlung and inverse Compton radiation are also discussed. For a DM particle mass of 1?TeV, the exclusion limits at 95% of confidence level reach values of σv95% C.L. ~ 10–23?cm3 s–1, depending on the DM particle model and halo properties. Additional contribution from DM substructures can improve the upper limits on σv by more than two orders of magnitude. At masses around 4.5?TeV, the enhancement by substructures and the Sommerfeld resonance effect results in a velocity-weighted annihilation cross-section upper limit at the level of σv95% C.L. ~10–26?cm3 s–1.
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