Supermassive Black Holes (BHs) residing in brightest cluster galaxies (BCGs) are overly massive when considering the local relationships between the BH mass and stellar bulge mass or velocity dispersion. Due to the location of these BHs within the cluster, large-scale cluster processes may aid the growth of BHs in BCGs. In this work, we study a sample of 71 galaxy clusters to explore the relationship between the BH mass, stellar bulge mass of the BCG, and the total gravitating mass of the host clusters. Due to difficulties in obtaining dynamically measured BH masses in distant galaxies, we use the Fundamental Plane relationship of BHs to infer their masses. We utilize X-ray observations taken by $Chandra$ to measure the temperature of the intra-cluster medium (ICM), which is a proxy for the total mass of the cluster. We analyze the $rm M_{BH}-kT$ and $rm M_{BH}-M_{Bulge}$ relationships and establish the best-fitting power laws:$log_{10}(M_{rm BH} /10^9 M_{odot})=-0.35+2.08 log_{10}(kT / 1 rm keV)$ and $log_{10}(rm M_{BH}/10^9M_{odot})= -1.09+ 1.92 log_{10}(M_{rm bulge}/10^{11}M_{odot})$. Both relations are comparable with that established earlier for a sample of brightest group/cluster galaxies with dynamically measured BH masses. Although both the $rm M_{BH}-kT$ and the $rm M_{BH}-M_{Bulge}$ relationships exhibit large intrinsic scatter, based on Monte Carlo simulations we conclude that dominant fraction of the scatter originates from the Fundamental Plane relationship. We split the sample into cool core and non-cool core resembling clusters, but do not find statistically significant differences in the $rm M_{BH}-kT$ relation. We speculate that the overly massive BHs in BCGs may be due to frequent mergers and cool gas inflows onto the cluster center.
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