[Paper Review] Dynamical Search for Substructures in Galaxy Clusters, A Hierarchical Clustering Method

A. Serna, D. Gerbal|arXiv (Cornell University)|Sep 15, 1995

Molecular spectroscopy and chirality3 citations

TL;DR

This paper introduces a dynamical hierarchical clustering method (h-method) that identifies substructures in galaxy clusters using relative binding energies from phase-space data. Applied to N-body simulations and two Abell clusters (ABCG151 and ABCG2670), it reveals stable substructures—ABCG151 splits into three subclusters, while ABCG2670 shows no subclustering but identifies a dense dynamical core—demonstrating robustness with both full and projected phase-space data.

ABSTRACT

We propose a new hierarchical method which uses dynamical arguments to find and describe substructures in galaxy clusters. This method (hereafter h--method or h--analysis) uses a hierarchical clustering analysis to determine the relationship between galaxies according to their relative binding energies. We have tested from N-body simulations, the two following features of the proposed method: 1) It extracts subgroups which are much more stable during the cluster evolution than those given by other techniques. 2) There exists a reasonable similarity between the structures found when only the coordinates ($x, y, v_z$) provided by "observations" are considered, and those found by using the six phase--space coordinates We have applied this method to two Abell clusters: ABCG151 and ABCG2670. Our results imply that ABCG151 is separated into two clusters, one of them is again divided into two subclusters. ABCG2670 has no subclustering. Our method allows however to extract the most bound galaxies in its dynamical core.

Motivation & Objective

• To develop a robust method for detecting substructures in galaxy clusters using dynamical information rather than spatial distribution alone.
• To address the instability of substructure detection in evolving clusters by incorporating binding energy as a clustering criterion.
• To test whether substructures identified using only projected coordinates (x, y, vz) resemble those found with full six-dimensional phase-space data.
• To apply the method to real Abell clusters and assess its ability to reveal dynamical substructure and core regions.

Proposed method

• The h-method performs hierarchical clustering based on relative binding energies between galaxy pairs, treating higher binding energy as stronger dynamical association.
• It uses a linkage criterion derived from gravitational binding energy to define galaxy groupings, favoring more tightly bound systems.
• The method is tested on N-body simulations to evaluate substructure stability over time.
• It compares results from full six-dimensional phase-space data (x, y, z, vx, vy, vz) with those from projected three-dimensional data (x, y, vz) to assess observational feasibility.
• Substructure identification is based on the hierarchical tree structure, where clusters are split at binding energy thresholds.
• The method identifies the most bound galaxies as forming a dynamical core, even in apparently smooth clusters.

Experimental results

Research questions

• RQ1 Can a hierarchical clustering method based on binding energy detect substructures in galaxy clusters more reliably than spatial-only methods?
• RQ2 How stable are the detected substructures over time in evolving N-body simulations?
• RQ3 To what extent do substructures identified using only projected phase-space coordinates (x, y, vz) match those found with full phase-space data?
• RQ4 Does the method successfully identify dynamical cores in clusters without clear subclustering?
• RQ5 How does the h-method perform when applied to real Abell clusters like ABCG151 and ABCG2670?

Key findings

• The h-method successfully identifies three distinct subclusters in ABCG151, with one of them further splitting into two, indicating a complex dynamical state.
• ABCG2670 shows no significant subclustering, but the method isolates a dense core of the most bound galaxies.
• Substructures detected via the h-method remain stable over time in N-body simulations, outperforming other techniques in stability.
• There is a reasonable agreement between substructures found using full phase-space data and those found using only projected coordinates (x, y, vz), supporting observational applicability.
• The method effectively identifies the dynamical core in clusters lacking obvious substructure, highlighting its sensitivity to dynamical binding.