Constraining resonant dark matter self-interactions with strong gravitational lenses

We devise a method to constrain self-interacting dark matter (SIDM) from observations of quadruply imaged quasars, and apply it to five self-interaction potentials with a long-range dark force. We consider several SIDM models with an attractive potential that allows for the formation of quasibound states, giving rise to resonant features in the cross section localized at particular velocities below 50 km s^-1. We propose these resonances, which amplify or suppress the cross section amplitude by over an order of magnitude, accelerate or delay the onset of core collapse in low-mass dark matter halos, and derive constraints on the timescale for core collapse for the five interaction potentials we consider. Our data strongly disfavors scenarios in which a majority of halos core collapse, with the strongest constraints obtained for cross section strengths exceeding 100 cm^2 g^-1 at relative velocities below 30 km s^-1. This work opens a new avenue to explore the vast landscape of possible SIDM theories.