Local dark matter clumps and the positron excess

It has been proposed that the excess in cosmic ray positrons, at approximately 8GeV, observed on both flights of the HEAT balloon experiment may be associated with the annihilation of supersymmetric (SUSY) dark matter particles in the Milky Way halo. In this paper we show how the presence of local dark matter substructure could account for this excess. Specifically, we concentrate on dark matter clumps, with uniform density, located at distances much less than 1 kpc. We place limits on the clump mass and radius as well as the annihilation rate per particle, for a range of representative SUSY dark matter scenarios.