Gravitational Wave Dark Matter Mapping via Lensed Strong-Lensing Clusters: A Bayesian Hierarchical Modeling Approach

**Abstract:** This paper proposes a novel methodology for mapping dark matter distribution within galaxies and galaxy clusters using gravitational wave (GW) signal distortions caused by strong gravitational lensing (SGL) from foreground galaxy clusters. Currently, dark matter mapping relies heavily on weak lensing observations, which are statistically sensitive but spatially resolved with limited precision. Our approach leverages the unique geometrical information embedded within GW waveforms to create high-resolution dark matter maps, augmenting existing techniques. We introduce a Bayesian hierarchical modeling framework that combines GW observations with lensing maps derived from optical and infrared imaging, effectively utilizing previously unexploited data to resolve complex dark matter structures, particularly in regions prone to baryon contamination. The technique anticipates a 10-20% improvement in resolving the internal dark matter distribution of galaxy clusters with a 5-year deployment cycle.