2026ApJ...997..221G

We present the results of our dynamical state proxy measurements performed on 28 strong lensing galaxy clusters from the Sloan Giant Arcs Survey. Using Chandra ACIS-I/S X-ray data supplemented with HST WFC3 imaging, we measure four morphological parameters: the concentration parameter (c), asymmetry parameter (A), centroid shift (log(w)), and the X-ray-BCG centroid separation (D [kpc]). Our goals are to (A) provide a robust classification of the dynamical state of the clusters in this strong lensing selected sample to enable studies that test various problems in cluster astrophysics and observational cosmology; (B) identify correlations, biases, or disagreements between different measurement proxies and cluster properties; and (C) measure the relaxation fraction (the fraction of clusters classified as relaxed based on X-ray morphology) and compare it to relaxation fractions from cluster samples selected using other methods. We combine the four morphological parameters into a single metric, the combined parameter M, which effectively separates the cluster sample into four dynamical state categories: relaxed, moderately relaxed, moderately disturbed, and disturbed. We find no significant trend in a cluster's dynamical state with its size, and only a weak, statistically limited dependence on mass and redshift. Based on our classification system, we find that $43{ \% }_{-9}^{+9}$ of the clusters are relaxed, which is consistent with relaxation fractions measured for other cluster samples selected on mass-observables. This implies a strong lensing selected sample of clusters is on average dynamically similar to clusters selected via different methods.