Tracing Dark Matter in the Central Regions of Galaxy Clusters Using Galaxies, Gas, and Intracluster Light in TNG300: Connections to Cluster Dynamical State

Recent studies have highlighted the potential of intracluster light (ICL) as a dark matter tracer. Moreover, the ICL co-evolves with the brightest cluster galaxy (BCG) and the host cluster, making it a valuable tool for understanding cluster dynamics. In this study, we utilize 426 galaxy clusters (with total mass $M_{\rm tot}>10^{14} M_{\odot}$ at $z=0$) simulated in the cosmological hydrodynamical simulation Illustris TNG300 to compare the spatial distributions of dark matter, member galaxies, gas, and ICL and assess their effectiveness as dark matter tracers in the central regions of clusters at $R_{\rm vir}<0.3$. We apply the Weighted Overlap Coefficient (WOC), a methodology for quantifying the similarity of two-dimensional spatial distributions, to various components of the galaxy clusters at different dynamical stages. Our findings reveal that the spatial distributions of both ICL combined with the BCG and gas closely resemble the dark matter distribution, with higher fidelity observed in more relaxed galaxy clusters with earlier half-mass epochs. These results demonstrate that the BCG+ICL component serves as an effective tracer of dark matter, consistent with previous observational studies linking cluster light to mass. Moreover, the degree of spatial similarity between the BCG+ICL and dark matter distributions appears to reflect the dynamical state of the cluster.