2024ApJ...970..165K

During cluster assembly, a cluster's virialization process leaves behind signatures that can provide information on its dynamical state. However, no clear consensus yet exists on the best way to achieve this. Therefore, we attempt to derive improved recipes for classifying the dynamical states of clusters in observations using cosmological simulations. The cluster halo mass and their subhalos' mass are used to 10¹⁴M_⊙h^–1 and 10¹⁰M_⊙h^–1 to calculate five independent dynamical state indicators. We experiment with recipes by combining two to four indicators for detecting specific merger stages, like recent and ancient mergers. These recipes are made by plotting merging clusters and a control sample of relaxed clusters in multiple-indicator parameter space, then applying a rotation matrix method to derive the best way to separate mergers from the control sample. The success of the recipe is quantified using the success rate and overlap percentage of the merger and control histograms along the newly rotated x-axis. This provides us with recipes using different numbers of combined indicators and for different merger stages. Among the recipes, the stellar mass gap and center offset are the first and second most dominant of the indicators, and using more indicators improves the effectiveness of the recipe. When applied to observations, our results show good agreement with literature values of cluster dynamical states.