Exploiting Disequilibrium in the Abell 2146 Galaxy Clusters to Derive a Radial Mass Profile

We use 3-D K Means clustering to characterize the galaxy substructure of the Abell 2146 cluster of galaxies ( z = 0.2343). We find that the optimum model consists of 4 substructures. This approach objectively characterizes the cluster's substructure using projected position and velocity data for 67 galaxies within a 2.305 Mpc circular region centered on the cluster's optical center. Abell 2146 appears to be a cluster in the early stages of formation with 4 distinct substructures with velocity dispersions typical of galaxy groups or low mass subclusters. We utilize the disequilibrium that is so prevalent in galaxy clusters to construct a radial mass distribution. Substructures are assumed bound but not virialized. This method is in contrast to previous galaxy kinematical data analysis, which assumes that the galaxies satisfy the virial theorem. This assumption ignores the ubiquitous clumping of galaxies that characterizes nearly all galaxy clusters making the method of extremely limited use. The best fitting integrated radial mass profile derived from the substructure using our method is less concentrated than the well known NFW profile when normalized. The results are promising enough to extend this study to a sample of galaxy clusters.