The Sculptor and Carina Dwarf spheroidal galaxies were observed with the H.E.S.S. Cherenkov telescope array between January 2008 and December 2009. The data sets consist of a total of 11.8 and 14.8 hours of high quality data, respectively. No gamma-ray signal was detected at the nominal positions of these galaxies above 220 GeV and 320 GeV, respectively. Upper limits on the gamma-ray fluxes at 95% C.L. assuming two forms for the spectral energy distribution (a power law shape and one derived from dark matter annihilation) are obtained at the level of 10^-13 to 10^-12 cm^-2s^-1 in the TeV range. Constraints on the velocity weighted dark matter particle annihilation cross section for both Sculptor and Carina dwarf galaxies range from <sigma v> ~ 10^-21 cm^3s^-1 down to <sigma v> ~ 10^-22 cm^3s^-1 depending on the dark matter halo model used. Possible enhancements of the gamma-ray flux are studied: the Sommerfeld effect, which is found to exclude some dark matter particle masses, the internal Bremsstrahlung and clumps in the dark-matter halo distributions.
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