Effects of galaxy cluster structure on lensed gravitational waves

Strong gravitational lenses come in many forms, but are typically divided into two populations: galaxies, and groups and clusters of galaxies. The largest objects in the Universe (i.e., galaxy clusters) are highly irregular and composed of many components due to a history of (or active) hierarchical mergers. In this work, we analyze the discrepancies in the observables of strongly lensed gravitational wave transients in both scenarios, namely relative magnifications, time delays, and image multiplicities. We compare the detection rates between the single spherical dark matter halo models found in the literature, and publicly available state-of-the-art cluster lens models. We find there to be approximately an order of magnitude fewer detection of strongly lensed transients in the realistic model case, likely caused by their loss of overall strong lensing optical depth. We also report detection rates in the weak lensing or single-image regime. Additionally, we find a systemic shift toward lower time delays between the brightest image pairs in the cases of the realistic models, as well as higher fractions of positive versus negative parity images, which was previously reported in the literature. This deviation in the joint relative magnification factor-time delay distribution will hinder the feasibility of the reconstruction of cluster-scale lenses through gravitational wave transients alone, but can still provide a lower limit on the lens mass.