Comparison of spatial distributions of Intracluster light and Dark Matter

TL;DR

This paper introduces the Weighted Overlap Coefficient (WOC), a new method to quantitatively compare 2D spatial distributions in galaxy clusters, revealing that intracluster light plus BCG best traces dark matter, especially in relaxed clusters.

Contribution

The paper presents the WOC methodology for shape matching of scalar distributions and demonstrates its robustness and effectiveness over existing methods like MHD.

Findings

ICL+BCG component best traces dark matter distribution.

Relaxed clusters show higher similarity between dark matter and ICL+BCG.

WOC outperforms MHD in robustness and accuracy.

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 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.