Expanding the Sample: The Relationship Between the Black Hole Mass of
  BCGs and the Total Mass of Galaxy Clusters
  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.
