Dark Matter Substructure or Source Model Systematics? A Case Study of Cluster Lens Abell S1063

Mapping the small-scale structure of the universe through gravitational lensing is a promising tool for probing the particle nature of dark matter. Curved Arc Basis (CAB) has been proposed as a local lensing formalism in galaxy clusters, with the potential to detect low-mass dark matter substructure. In this work, we analyze the cluster lens Abell S1063 in search of dark matter substructure with the CAB formalism, using multi-band imaging data from JWST. We use two different source modeling methods: shapelets and pixel-based source reconstruction based on Delaunay triangulation. We find that source modeling systematics from shapelets result in a disagreement between Curved Arc Basis parameters measured from different filters. Source modeling with Delaunay significantly alleviates this systematic, as seen in the improvement in agreement across filters. We also find that inadequate complexity in source modeling can result in convincing spurious detections of dark matter substructure from strong gravitational lenses, as seen by our $\Delta \text{BIC} > 20$ measurement of a $M \sim 10^{10}$ $M_{\odot}$ subhalo with shapelets, a spurious detection that is not reproduced with Delaunay source modeling. We demonstrate that multi-band analysis with different JWST filters is key for disentangling source and lens model systematics from dark matter substructure detections.