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We present a study of relations between the masses of the centralsupermassive black holes (SMBHs) and the atmospheric gas temperatures andluminosities measured within a range of radii between $R_{\rm e}$ and 5$R_{\rme}$, for a sample of 47 early-type galaxies observed by the {\it Chandra X-rayObservatory}. We report the discovery of a tight correlation between theatmospheric temperatures of the brightest cluster/group galaxies (BCGs) andtheir central SMBH masses. Furthermore, our hydrostatic analysis reveals anapproximately linear correlation between the total masses of BCGs ($M_{\rmtot}$) and their central SMBH masses ($M_{\rm BH}$). State-of-the-artcosmological simulations show that the SMBH mass could be determined by thebinding energy of the halo through radiative feedback during the rapid blackhole growth by accretion, while for the most massive galaxies mergers are thechief channel of growth. In the scenario of a simultaneous growth of centralSMBHs and their host galaxies through mergers, the observed linear correlationcould be a natural consequence of the central limit theorem.

Correlations between supermassive black holes, hot atmospheres, and the total masses of early type galaxies