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We analyze strongly lensed images in 8 galaxy clusters to measure their darkmatter density profiles in the radial region between 10 kpc and 150 kpc, anduse this to constrain the self-interaction cross section of dark matter (DM)particles. We infer the mass profiles of the central DM halos, bright centralgalaxies, key member galaxies, and DM subhalos for the member galaxies for all8 clusters using the Qlens code. The inferred DM halo surface densities are fitto a self-interacting dark matter (SIDM) model, which allows us to constrainthe self-interaction cross section over mass $\sigma$/m. When our full methodis applied to mock data generated from two clusters in the Illustris-TNGsimulation, we find results consistent with no dark matter self-interactions asexpected. For the eight observed clusters with average relative velocities of$1458_{-81}^{+80}$ km/s, we infer $\sigma$/m = $0.082_{-0.021}^{+0.027}$cm$^2$/g and $\sigma$/m < 0.13 cm$^2$/g at the 95% confidence level.

A Stringent Upper Limit on Dark Matter Self-Interaction Cross Section from Cluster Strong Lensing