The Strongest Cluster Lenses: An Analysis of the Relation between Strong Gravitational Lensing Strength and the Physical Properties of Galaxy Clusters

Strong gravitational lensing provides unique opportunities to investigate the mass distribution at the cores of galaxy clusters and to study high-redshift galaxies. Using 110 strong-lensing models of 74 cluster fields from the Hubble Frontier Fields (HFF), Reionization Lensing Cluster Survey (RELICS), and Sloan Giant Arcs Survey (SGAS), we evaluate the lensing strength of each cluster (area with divide mu divide >= 3 for z ( s ) = 9, normalized to a lens redshift of z = 0.5). We assess how large-scale mass, projected inner-core mass, and the inner slope of the projected mass-density profile relate to lensing strength. While we do identify a possible trend between lensing strength and large-scale mass (Kendall tau = 0.26 and Spearman r = 0.36), we find that the inner slope (50 kpc <= r <= 200 kpc) of the projected mass-density profile has a higher probability of correlation with lensing strength and can set an upper bound on the possible lensing strength of a cluster (Kendall tau = 0.53 and Spearman r = 0.71). As anticipated, we find that the lensing strength correlates with the effective Einstein area and that a large ( greater than or similar to 30.'' 0) radial extent of lensing evidence is a strong indicator of a powerful lens. We attribute the spread in the relation to the complexity of individual lensing clusters, which is well captured by the lensing-strength estimator. These results can help us to more efficiently design future observations to use clusters as cosmic telescopes.