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 quasi-bound states, giving rise to resonant features in the cross section localized at particular velocities below $50 \ \rm{km} \ \rm{s^{-1}}$. 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 $100 \ \rm{cm^2} \rm{g}^{-1}$ at relative velocities below $30 \ \rm{km} \ \rm{s^{-1}}$. This work opens a new avenue to explore the vast landscape of possible SIDM theories.