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

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: σAv: s-wave (velocity independent), p-wave (σAv∝v²), d-wave (σAv∝v⁴), and Sommerfeld-enhancement in the Coulomb limit (σAv∝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.