Abstract
We present the result of the observation of the ultrafaint dwarf galaxy Willman 1 performed with the 17 m MAGIC telescope during 15.5 hr between March and May 2008. No significant $\gamma$-ray emission was found. We derived upper limits of the order of $10^{-12}$ ph 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 quantified 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 dark matter intrinsic and extrinsic properties (e.g., presence of substructures, Sommerfeld effect) may significantly reduce this gap.
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