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 $94$ 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.
