A possible relation between the masses of black holes in galactic nuclei and the parameters of the host galaxies

Data on about forty virialized galaxy clusters with bright central galaxies, for which both the galactic velocity dispersion (sigma(gal)) and the stellar velocity dispersion in the brightest galaxies (sigma(*)) are measured, have been used to obtain several approximate relations between sigma(gal), sigma(*), the absolute B magnitude of the brightest central galaxy M-B(BCG), and the mass of the central massive black hole M-BH: log sigma(*) = (0.12 +/- 0.14) log sigma(gal) + (2.1 +/- 0.4), log sigma(*) = -(0.15 +/- 0.02) M-B(BCG) + (0.85 +/- 0.5), log M-BH = 0.51 log sigma(gal) + 7.28. These relations can be used to derive crude estimates of M-BH in the nuclei of the brightest galaxies using the parameters of the both host galaxies and the host galaxy clusters. The last relation above confirms earlier suggestions of a quadratic relation between the masses of the coronas of the host systems and the masses their central objects: M-hg(halo) similar to M-cent(2) . The relations obtained are consistent with the common evolution of subsystems with different scales and masses formed in the process of hierarchical clustering.