Exploiting Machine Learning and Disequilibrium in Galaxy Clusters to Obtain a Mass Profile

We use 3D k -means clustering to characterize galaxy substructure in the A2146 cluster of galaxies ( z = 0.2343). This method 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. The optimal number of substructures is found to be four. Four distinct substructures with rms velocity typical of galaxy groups or low-mass subclusters, when compared to cosmological simulations of galaxy cluster formation, suggest that A2146 is in the early stages of formation. We utilize this disequilibrium, which is so prevalent in galaxy clusters at all redshifts, to construct a radial mass distribution. Substructures are bound but not virialized. This method is in contrast to previous kinematical analyses, which have assumed virialization, and ignored the ubiquitous clumping of galaxies. The best-fitting radial mass profile is much less centrally concentrated than the well-known Navarro–Frenk–White profile, indicating that the dark-matter-dominated mass distribution is flatter pre-equilibrium, becoming more centrally peaked in equilibrium through the merging of the substructure.