Comparison of Spatial Distributions of Intracluster Light and Dark Matter

Abstract

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