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Dark matter with Sommerfeld-enhanced annihilation has been proposed toexplain observed cosmic ray positron excesses in the 10 GeV to TeV energyrange. We show that the required enhancement implies thermal relic densitiesthat are too small to be all of dark matter. We also show that the dark matteris sufficiently self-interacting that observations of elliptical galactic darkmatter halos exclude large Sommerfeld enhancement for light force carriers.Resonant Sommerfeld enhancement does not modify these conclusions, and theastrophysical boosts required to resolve these discrepancies are disfavored,especially when significant self-interactions suppress halo substructure.

Halo Shape and Relic Density Exclusions of Sommerfeld-Enhanced Dark Matter Explanations of Cosmic Ray Excesses