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Title: New observational recipes for measuring dynamical state of galaxy clusters

Abstract: During cluster assembly, the cluster’s virialization process is known to leave behind signatures that 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 state of clusters in observations using cosmological simulations. Cluster halos larger than 10^14M⊙/h and subhalos up to 10^10M⊙/h are used 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 indicators parameter space, and then applying the 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 the overlap percentage of the merger and control histograms along the rotated x-axis. This provides us with recipes for each number of combined indicators and each merger stage. 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. Our results show good agreement between observational data and simulations.

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