New classification method for the dynamical state of galaxy clusters with a Gaussian mixture model
Galaxy clusters are the largest gravitationally bound systems, and they continue their growth through mergers in a hierarchical {\Lambda}CDM 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. To overcome this, we developed an enhanced and observation-applicable cluster dynamical state classification method using the Bayesian classifier with the class-conditional Gaussian mixture distribution model using the N-cluster Run simulation data. 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. 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. This new method can suggest a way of overcoming previous limitations and provides new insights by providing the reliability of dynamical state classification results.