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Supermassive black holes (BHs) residing in the brightest cluster galaxies areover-massive relative to the stellar bulge mass or central stellar velocitydispersion of their host galaxies. As BHs residing at the bottom of the galaxycluster's potential well may undergo physical processes that are driven by thelarge-scale characteristics of the galaxy clusters, it is possible that thegrowth of these BHs is (indirectly) governed by the properties of their hostclusters. In this work, we explore the connection between the mass of BHsresiding in the brightest group/cluster galaxies (BGGs/BCGs) and the virialtemperature, and hence total gravitating mass, of galaxy groups/clusters. Tothis end, we investigate a sample of 17 BGGs/BCGs with dynamical BH massmeasurements and utilize XMM-Newton X-ray observations to measure the virialtemperatures and infer the $M_{\rm 500}$ mass of the galaxy groups/clusters. Wefind that the $M_{\rm BH} - kT$ relation is significantly tighter and exhibitssmaller scatter than the $M_{\rm BH} - M_{\rm bulge}$ relations. Thebest-fitting power-law relations are $ \log_{10} (M_{\rm BH}/10^{9} \\rm{M_{\odot}}) = 0.20 + 1.74 \log_{10} (kT/1 \ \rm{keV}) $ and $ \log_{10}(M_{\rm BH}/10^{9} \ \rm{M_{\odot}}) = -0.80 + 1.72 \log_{10} (M_{\rmbulge}/10^{11} \ M_{\odot})$. Thus, the BH mass of BGGs/BCGs may be set byphysical processes that are governed by the properties of the host galaxygroup/cluster. These results are confronted with the Horizon-AGN simulation,which reproduces the observed relations well, albeit the simulated relationsexhibit notably smaller scatter.

Correlation Between the Total Gravitating Mass of Groups and Clusters and the Supermassive Black Hole Mass of Brightest Galaxies