MAGIC upper limits on the VHE gamma-ray emission from the satellite galaxy Willman 1

We present the result of the observation of the ultra-faint dwarf galaxy Willman 1 performed with the 17 m MAGIC Cherenkov telescope during 15.5 hours between March and May 2008. No significant gamma-ray emission was found above 100 GeV. We derived upper limits of the order of $10^{-12}$ photons cm$^{-2}$ s$^{-1}$ on the integral flux above 100 GeV, which we compare with predictions from several of the established neutralino benchmark models in the mSUGRA parameter space. The neutralino annihilation spectra are defined after including the recently discovered contribution of internal bremsstrahlung from the virtual sparticles that mediate the annihilation. Flux boost factors of three orders of magnitude are required even in the most optimistic scenario to match our upper limits. However, uncertainties in the DM distribution (e.g., presence of substructure in the halo) may significantly reduce such boost estimates. Future observations will likely allow us to improve the derived upper limits probably by up to one order of magnitude so that - at least in some regions - the mSUGRA parameter space may be constrained.