COOL-LAMPS. VII. Quantifying Strong-lens Scaling Relations with 177 Cluster-scale Strong Gravitational Lenses in DECaLS

We estimate the Einstein-radius-enclosed total mass for 177 cluster-scale strong gravitational lenses identified by the ChicagO Optically selected Lenses Located At the Margins of Public Surveys (COOL-LAMPS) collaboration with lens redshifts ranging from $0.2 \lessapprox z \lessapprox 1.0$ using the brightest-cluster-galaxy (BCG) redshift and an observable proxy for the Einstein radius. We constrain the Einstein-radius-enclosed luminosity and stellar mass by fitting parametric spectral energy distributions to aperture photometry from the Dark Energy Camera Legacy Survey in the $g$-, $r$-, and $z$-band Dark Energy Camera filters. We find that the BCG redshift, enclosed total mass, and enclosed luminosity are strongly correlated and well described by a planar relationship in 3D space. We find that the enclosed total mass and stellar mass are correlated with a logarithmic slope of $0.500^{+0.029}_{-0.031}$, and the enclosed total mass and stellar-to-total mass fraction are correlated with a logarithmic slope of $-0.495^{+0.032}_{-0.033}$. In tandem with the small radii within which these slopes are constrained, this may suggest invariance in baryon conversion efficiency and feedback strength as a function of cluster-centric radii in galaxy clusters. Additionally, the correlations described here should have utility in ranking strong-lensing candidates in upcoming imaging surveys -- such as Rubin/Legacy Survey of Space and Time -- in which an algorithmic treatment of strong lenses will be needed due to the sheer volume of data these surveys will produce.