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

Abstract: Strong gravitational lensing provides unique opportunities to investigate the mass distribution at the cores of galaxy clusters and to study high redshift galaxies. Using $94$ strong lensing models of $74$ cluster fields from the \textit{Hubble} Frontier Fields (HFF), Reionization Lensing Cluster Survey (RELICS), and Sloan Giant Arcs Survey (SGAS), modeled with three parametric approaches, we evaluate the lensing strength of each cluster (area with $|\mu|\geq3$ for $z_s=9$). 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 not identify a strong correlation between lensing strength and large scale mass, we reveal that the inner slope ($50$ kpc~$\leq r \leq~200$ kpc) of the projected mass density profile is indicative of lensing strength and can set an upper bound on the possible lensing strength of a cluster. We find that the effective Einstein area correlates with lensing strength, and that a large ($\gtrsim 30^{''}0$) radial extent of lensing evidence is a strong indicator of a powerful lens. These results can help to more efficiently design future observations to maximize lensing strength.