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We present a new determination of the slope and normalization of three popular scaling laws between the mass of supermassive black holes and stellar velocity dispersion, bulge mass and kinetic energy of the host galaxies. To this aim we have collected 72 objects taken from three different samples and we have used three fitting methods applying the statistical analysis also to the subset of early type galaxies and spirals separately. We find that the relation involving kinetic energy has a slightly better χ 2 and linear correlation coefficient than the other two laws. Furthermore, its Hertzsprung-Russell-like behavior is confirmed by the location of young and old galaxies in two different parts of the diagram. A test of its predictive power with the two giant galaxies NGC3842 and NGC4889 shows that the mass of the black hole inferred using the kinetic energy law is the closest to the experimental value. The subset of early type galaxies satisfies the theoretical models regarding the black hole mass vs stellar velocity dispersion relation, better than the full sample.

New calibration and some predictions of the scaling relations between the mass of supermassive black holes and the properties of the host galaxies