  We analyze strongly lensed images in 8 galaxy clusters to measure their dark
matter density profiles in the radial region between 10 kpc and 100 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 halos, bright central
galaxies, key member galaxies, and DM subhalos for the member galaxies for all
8 clusters using the QLens code. 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. 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 maximum circular velocities in the range of 1400
to 2000 km/s, we find that the upper limit for the self-interaction cross
section per unit mass of dark matter is 0.065 $cm^2/g$ at the 95% confidence
level.
