  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 evolution. However, it is a challenging problem
to provide a quantitative measure for the shape matching between two
multi-dimensional scalar distributions. We present a novel methodology, named
the {\em Weighted Overlap Coefficient (WOC)}, to quantify the similarity of
2-dimensional spatial distributions. We compare the WOC with a standard method
known as the Modified Hausdorff Distance (MHD). We find that our method is
robust, and performs well even with the existence of multiple sub-structures.
We apply our methodology to search for a visible component whose spatial
distribution resembled with 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 the 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 trace 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 MHD results show weaker trend
with the dynamical stages.

Astrophysics of Galaxies;Cosmology and Nongalactic Astrophysics;Instrumentation and Methods for Astrophysics