New classification method for the dynamical state of galaxy clusters with a Gaussian mixture model

¹ Departamento de Fisica, Universidad Tecnica Federico Santa Maria, Avenida España, 1680 Valparaíso, Chile
² Millenium Nucleus for Galaxies (MINGAL)
³ Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea
⁴ School of Computer Science, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
⁵ Astronomy Program, Department of Physics and Astronomy, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, 08826, Republic of Korea
⁶ SNU Astronomy Research Center, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, 08826, Republic of Korea
⁷ University of Science and Technology (UST), Gajeong-ro, Daejeon 34113, Republic of Korea

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 5 September 2025
Accepted: 1 March 2026

Abstract

Context. Galaxy clusters are the largest gravitationally bound systems, and they continue their growth through mergers in a hierarchical ΛCDM Universe. Therefore, we can describe the merger stage of a cluster as the dynamical state of clusters. Previous studies have investigated this phenomenon, but several limitations remain, including reliance on dichotomous classifications, constraints on the number of indicators used, absence of reliability, and incompatibility of methods between observation and simulation studies.

Aims. To overcome the limitations, we developed an enhanced and observation-applicable cluster dynamical state classification method using the Bayesian classifier with the class-conditional distribution Gaussian mixture model using the N-cluster Run simulation data.

Methods. The Bayesian classifier was designed for two merger stages (merger and relaxed) as well as three merger stages (recent merger, ancient merger, and relaxed) to provide a more detailed interpretation of the merger processes. After the best classifier model was constructed, we applied it to the observation data to test its performance and usability.

Results. In the results, using a larger number of indicators yields better results, with their order of importance being: magnitude difference, center offset, sparsity, Kuiper V statistic, and mirror asymmetry. Additionally, our analyses show that a projected classifier (built on the 6D space, but evaluated on lower dimensional projections) consistently produces better outcomes than non-projected classifiers (i.e., classifiers built directly on the corresponding low dimensional spaces), which means limited observation data can be used to classify with enhanced performance. Furthermore, the new classification method outperforms our previous research.

Conclusions. This new method can suggest a way of overcoming previous limitations and provides new insights by providing the reliability of dynamical state classification results. We expect this enhanced method and its findings can be used in observational studies to better understand the evolution of galaxy clusters and the mass assembly history of the Universe.