%AGilman, Daniel [Department of Physics and Astronomy, University of California, Los Angeles, CA 90095, USA]%ABovy, Jo [Department of Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada]%ATreu, Tommaso [Department of Physics and Astronomy, University of California, Los Angeles, CA 90095, USA]%ANierenberg, Anna [Department of Physics, University of California Merced, 5200 North Lake Rd. Merced, CA 95343, USA]%ABirrer, Simon [Kavli Institute for Particle Astrophysics & Cosmology, Stanford University, P. O. Box 2450, Stanford, CA 94305, USA]%ABenson, Andrew [Carnegie Observatories, 813 Santa Barbara Street, Pasadena, CA 91101, USA]%ASameie, Omid [Department of Astronomy, The University of Texas at Austin, 2515 Speedway, Stop C1400, Austin, TX 78712 USA]%BJournal Name: Monthly Notices of the Royal Astronomical Society; Journal Volume: 507; Journal Issue: 2 %D2021%I %JJournal Name: Monthly Notices of the Royal Astronomical Society; Journal Volume: 507; Journal Issue: 2 %K %MOSTI ID: 10303234 %PMedium: X %TStrong lensing signatures of self-interacting dark matter in low-mass haloes %XABSTRACT Core formation and runaway core collapse in models with self-interacting dark matter (SIDM) significantly alter the central density profiles of collapsed haloes. Using a forward modelling inference framework with simulated data-sets, we demonstrate that flux ratios in quadruple image strong gravitational lenses can detect the unique structural properties of SIDM haloes, and statistically constrain the amplitude and velocity dependence of the interaction cross-section in haloes with masses between 106 and 1010 M⊙. Measurements on these scales probe self-interactions at velocities below $30 \ \rm {km} \ \rm {s^{-1}}$, a relatively unexplored regime of parameter space, complimenting constraints at higher velocities from galaxies and clusters. We cast constraints on the amplitude and velocity dependence of the interaction cross-section in terms of σ20, the cross-section amplitude at $20 \ \rm {km} \ \rm {s^{-1}}$. With 50 lenses, a sample size available in the near future, and flux ratios measured from spatially compact mid-IR emission around the background quasar, we forecast $\sigma _{20} \lt 11\rm {\small {--}}23 \ \rm {cm^2} \rm {g^{-1}}$ at $95 {{\ \rm per\ cent}}$ CI, depending on the amplitude of the subhalo mass function, and assuming cold dark matter (CDM). Alternatively, if $\sigma _{20} = 19.2 \ \rm {cm^2}\rm {g^{-1}}$ we can rule out CDM with a likelihood ratio of 20:1, assuming an amplitude of the subhalo mass function that results from doubly efficient tidal disruption in the Milky Way relative to massive elliptical galaxies. These results demonstrate that strong lensing of compact, unresolved sources can constrain SIDM structure on sub-galactic scales across cosmological distances, and the evolution of SIDM density profiles over several Gyr of cosmic time. %0Journal Article