Effective J -factors for Milky Way dwarf spheroidal galaxies with velocity-dependent annihilation

Abstract

We calculate the effective J -factors, which determine the strength of indirect detection signals from dark matter annihilation, for 25 dwarf spheroidal galaxies (dSphs). We consider several well-motivated assumptions for the relative velocity dependence of the dark matter annihilation cross section: σ_Av : s -wave (velocity independent), p -wave (σ_Av ∝v²), d -wave (σ_Av ∝v⁴), and Sommerfeld-enhancement in the Coulomb limit (σ_Av ∝1 /v ). As a result we provide the largest and most updated sample of J -factors for velocity-dependent annihilation models. For each scenario, we use Fermi-LAT gamma-ray data to constrain the annihilation cross section. Due to the assumptions made in our gamma-ray data analysis, our bounds are comparable to previous bounds on both the p -wave and Sommerfeld-enhanced cross sections using dSphs. Our bounds on the d -wave cross section are the first such bounds using indirect detection data.