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

Context. Thanks to the improved angular resolution of modern telescopes and kinematic models, the existence of supermassive black (SMBHs) in the inner part of galaxies, regardless their morphology and nuclear activity, has been established on quite solid A possible correlation between the mass of SMBHs (M-.) and the evolutionary state of their host galaxies is expected and is under a heated debate. Aims. Based on the recent 2D decomposition of 3.6 mu m Spitzer/IRAC images of local late-and early-type galaxies with M-. measurements, we investigated various scaling laws, studying what is the best predictor of the mass of the central black holes, that is the one the lowest value of intrinsic scatter. In particular, we focused on the M-.-M-G sigma(2) law, that is the relation between the mass of and the kinetic energy of random motions of the corresponding host galaxies, M-G is the mass and sigma the velocity dispersion the host galaxy (bulge). Methods. In order to find the best fit for each of the scaling laws examined, we performed a least-squares regression of M-. on x for considered sample of galaxies, x being a whatever known parameter of the galaxy bulge. For this purpose, we made use of both linear regression LINMIX_ERR and FITEXY methods. Results. Our analysis shows that M-.-M-G sigma(2) law fits the examined experimental data successfully as much as the other known scaling (all correlations have similar intrinsic scatters within the errors) and shows a value of chi(2) (estimated by FITEXY) better than the a result which is consistent with previous determinations at shorter wavelengths. This means that a combination of sigma and M-G (or R-e) could be necessary to drive the correlations between M-. and other bulge properties. This issue has been investigated by a although not fully conclusive, analysis of the residuals of the various relations. Conclusions. In order to avoid rushed conclusions on galaxy activity and evolution, the indirect inferring of the masses of the super-black holes from the kinetic energy of random motions via the M-.-M-G sigma(2) relation should be considered, especially when to higher redshift galaxies (z > 0.01). This statement is suggested by a reanalysis of Sloan Digital Sky Survey (SDSS) data to study the black hole growth in the nearby Universe. By adopting the M-.-M-G sigma(2) relation instead of the M-.-sigma relation, a quiet/radio-loud dichotomy appears in the SMBH mass distribution of the corresponding SDSS early-type AGN galaxies.