Intracluster Light as a Probe for Dark Matter: Exploring SIDM and CDM with C-EAGLE Sims

We assess whether intracluster light (ICL) can serve as an observational discriminator of dark matter physics. The self-interacting dark matter (SIDM) model has gained increasing attention as a possible resolution to small-scale discrepancies between collisionless cold dark matter (CDM) simulations and observations, predicting distinct tidal interaction histories within galaxy clusters. We analyze Cluster-EAGLE zoom-in galaxy clusters re-simulated from identical initial conditions in both CDM and SIDM frameworks. The morphological similarity between dark matter and multiple baryonic tracers -- gas, all stars, galaxies, and the combined brightest cluster galaxy plus ICL (BCG+ICL) -- is quantified using the Weighted Overlap Coefficient, a contour-overlap statistic. We find that dark matter is traced most accurately by BCG+ICL, followed by gas, all stars, and galaxies. The BCG+ICL component remains a robust tracer even at high redshift, while gas initially traces dark matter poorly but improves over time, eventually approaching the performance of BCG+ICL. Notably, in the SIDM case the gas distribution more closely resembles dark matter than in CDM. This reflects the underlying physics: in CDM, collisionless dark matter behaves similarly to the collisionless BCG+ICL, whereas in SIDM, self-interactions introduce an effective collisionality, making dark matter evolve more like the gas component. We also find that dwarf and satellite galaxies are more sensitive to the underlying dark matter model, despite their poorer overall tracing performance. Our results demonstrate the potential of ICL as a novel observational probe of dark matter physics and provide a first step toward using diffuse cluster light to constrain the nature of dark matter.