The cosmic-ray positron excess from a local Dark Matter over-density

We show that the cosmic-ray positron excess measured by PAMELA and AMS could be induced by Dark Matter annihilations in a local over-density. In such a context leptophilic DM is not needed and good fits to positron data, in agreement with antiproton and gamma-ray measurements, are obtained for DM annihilations to $WW$, $hh$, $ZZ$, $ t \bar t$, $b \bar b$, $q\bar q$ channels. The classic Dark Matter candidates, such as the pure supersymmetric Wino with standard thermal annihilation cross-section, can fit the positron excess, without invoking any additional assumption on Dark Matter properties.