Strong lensing signatures of self-interacting dark matter in low-mass haloes

Core formation and runaway core collapse in models with self-interacting dark matter (SIDM) significantly alter the central density profiles of collapsed halos. Using a forward modeling inference framework simulated datasets, we demonstrate that flux ratios quadruple image strong gravitational lenses can detect unique structural properties SIDM halos, statistically constrain amplitude velocity dependence interaction cross section halos masses between $10^6 - 10^{10} M_{\odot}$. Measurements on these scales probe self-interactions at velocities below $30 \ \rm{km} \rm{s^{-1}}$, relatively unexplored regime parameter space, complimenting constraints higher from galaxies clusters. We cast terms $\sigma_{20}$, $20 \rm{s^{-1}}$. With 50 lenses, sample size available near future, measured spatially compact mid-IR emission around background quasar, forecast $\sigma_{20} < 11-23 \rm{cm^2} \rm{g^{-1}}$ $95 \%$ CI, depending subhalo mass function, assuming cold (CDM). Alternatively, if = 19.2 \rm{cm^2}\rm{g^{-1}}$ rule out CDM likelihood ratio 20:1, an function results doubly-efficient tidal disruption Milky Way relative to massive elliptical galaxies. These lensing compact, unresolved sources structure sub-galactic across cosmological distances, evolution over several Gyr cosmic time.