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Thanks to the angular resolution of modern telescopes and kinematic models,the existence of supermassive black holes (SMBHs) in the inner part of galaxieshas been established on quite solid grounds. A possible correlation between themass of SMBHs and the evolutionary state of their host galaxies is expected.Based on the recent 2D decomposition of mid-infrared Spiter/IRAC images oflocal galaxies with M_bh measurements, we investigated various scaling laws,studying what the best predictor of the mass of the central SMBHs is. Wefocused on the M_bh-M_G sigma^2 law, the relation between the mass of SMBHs andthe kinetic energy of random motions of the corresponding host galaxies. Inorder to find the best fit for each of the scaling laws examined, we performeda least-squares regression of M_bh on x for the considered sample of galaxies,x being a whatever known parameter of the galaxy bulge. Our analysis shows thatM_bh-M_G sigma^2 law fits the examined experimental data successfully as muchas the other known scaling laws and shows a value of chi^2 better than theothers, a result which is consistent with previous determinations. This meansthat a combination of sigma and M_G could be necessary to drive thecorrelations between M_bh and other bulge properties. This issue has beeninvestigated by a careful analysis of the residuals of the various relations.In order to avoid rushed conclusions on galaxy activity and evolution, theindirect inferring of M_bh from the kinetic energy of random motions should beconsidered, especially when applied to higher redshift galaxies. This statementis suggested by a reanalysis of the SDSS data used to study the SMBH growth inthe nearby Universe. Adopting the M_bh-M_G sigma^2 relation instead of theM_bh-sigma, a radio-quiet/radio-loud dichotomy appears in the SMBH massdistribution of the corresponding SDSS early-type AGN galaxies.

The scaling relation between the mass of supermassive black holes and the kinetic energy of random motions of the host galaxies