We analyse strongly lensed images in 8 galaxy clusters to measure their dark matter density profiles in the radial region between 10 kpc and 150 kpc, and use this to constrain the self-interaction cross-section of dark matter (DM) particles. We infer the mass profiles of the central DM haloes, bright central galaxies, key member galaxies, and DM subhalos for the member galaxies for all 8 clusters using the QLenscode. The inferred DM halo surface densities are fit to a self-interacting dark matter (SIDM) model, which allows us to constrain the self-interaction cross-section over mass σ/m. When our full method is applied to mock data generated from two clusters in the Illustris-TNG simulation, we find results consistent with no dark matter self-interactions as expected. For the eight observed clusters with average relative velocities of $1458_{-81}^{+80}$ km/s, we infer $\sigma /m = 0.082_{-0.021}^{+0.027} \rm cm^2/g$ and $\sigma /m < 0.13~ \rm cm^2/g$ at the 95 per cent confidence level.

We analyze circular velocity profiles of seven ultradiffuse galaxies (UDGs) that are isolated and gas-rich. Assuming that the dark matter halos of these UDGs have a Navarro–Frenk–White (NFW) density profile or a Read density profile (which allows for constant-density cores), the inferred halo concentrations are systematically lower than the cosmological median, even as low as −0.6 dex (about 5σ away) in some cases. Alternatively, similar fits can be obtained with a density profile that scales roughly as 1/r 2 for radii larger than a few kiloparsecs. Both solutions require the radius where the halo circular velocity peaks ( R max ) to be much larger than the median expectation. Surprisingly, we find an overabundance of such large- R max halos in the IllustrisTNG dark-matter-only simulations compared to the Gaussian expectation. These halos form late and have higher spins compared to median halos of similar masses. The inner densities of the most extreme among these late-forming halos are higher than their NFW counterparts, leading to a ∼1/r 2 density profile. However, the two well-resolved UDGs in our sample strongly prefer lower dark matter densities in the center than the simulated ones. Comparing to IllustrisTNG hydrodynamical simulations, we also find a tension in getting both low enough circular velocities and high enough halo mass to accommodate the measurements. Our results indicate that the gas-rich UDGs present a significant challenge for galaxy formation models.