Comparison of Spatial Distributions of Intracluster Light and Dark Matter

In a galaxy cluster, the relative spatial distributions of dark matter, member galaxies, gas, and intracluster light (ICL) may connote their mutual interactions over cluster evolution. However, it is challenging problem to provide quantitative measure for shape matching between two multi-dimensional scalar distributions. We present novel methodology, named {\em Weighted Overlap Coefficient (WOC)}, quantify similarity 2-dimensional compare WOC with standard method known as Modified Hausdorff Distance (MHD). find that our robust, performs well even existence multiple sub-structures. apply methodology search visible component whose distribution resembled matter. If such could be found trace matter high fidelity more relaxed clusters, then also used dynamical stage estimator cluster. six clusters at different stages simulated within GRT simulation, which an N-body simulation using replacement technique. Among various components (stellar particles, ICL), ICL+ brightest (BCG) most faithfully distribution. sample show stronger in ICL+BCG than dynamically young clusters. While MHD results weaker trend stages.