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: $\sigma_A v$: $s$-wave (velocity independent), $p$-wave ($\sigma_A v \propto v^2$), $d$-wave ($\sigma_A v \propto v^4$), and Sommerfeld-enhancement in the Coulomb limit ($\sigma_A v \propto 1/v$). 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.