Fermi constrains dark-matter origin of high-energy positron anomaly

Fermi measurements of the high-latitude γ-ray background strongly constrain a decaying-dark-matter origin for the 1-100GeV Galactic positron anomaly measured with PAMELA. Inverse Compton scattering of the microwave background by the emergent positrons produces a bump in the diffuse 100-200 MeV γ-ray background that would protrude from the observed background at these energies. The positrons are thus constrained to emerge from the decay process at a typical energy between ∼ 100GeV and ∼ 250GeV. By considering only γ-ray emission of the excess positrons and electrons, we derive a minimum diffuse γ-ray flux that, apart from the positron spectrum assumed, is independent of the actual decay modes. Any γ-rays produced directly by the dark-matter decay leads to an additional signal that makes the observational limits more severe. A similar constraint on the energy of emergent positrons from annihilation in dark-matter substructures is argued to exist, according to recent estimates of enhancement in low-mass dark-matter substructures, and improved simulations of such substructure will further sharpen this constraint.