Establishing a Correlation between the Total Mass of Galaxy Clusters and the Black Hole Mass of Brightest Cluster Galaxies

Supermassive black holes (BHs) residing in the brightest cluster galaxies (BCGs) are over-massive relative to the stellar bulge mass or central stellar velocity dispersion of their host galaxies. The preferential location of these BHs at the bottom of a deep potential well suggests that they may undergo a different evolutionary path than BHs in satellite galaxies. Using a sample of galaxy clusters, we demonstrate that the total gravitating mass of galaxy clusters exhibits a tight correlation with the BH mass of the BCGs. We establish that this correlation is tighter than that between the stellar bulge mass and the BH mass of the BCGs. Our results suggest that the BH mass of BCGs may be set by physical processes that are governed by the properties of the host galaxy cluster, such as the inflow of cold gas onto the cluster center or a series of low angular momentum mergers.