An experimental test of the relation M• ∝ Reσ3 and of the corresponding model to estimate the efficiency of a supermassive black hole

There are many correlations in literature that are useful to understand the link between the mass of a supermassive black hole with the properties of the galaxy that hosts it; among these, there is a fundamental relation, found by Feoli and Mancini, that binds the mass of the black hole M • to the effective radius R e and the stellar velocity dispersion σ. In this paper we have tested the existence of this correlation using experimental data extracted from a database of 230 galaxies published in 2016. In particular, we have studied the limits of the model that is valid in the approximation of low rotation velocity, showing that early-type galaxies satisfy the relation better than spiral galaxies. We have also obtained a slope and an intercept of the best fit line in agreement with the theoretical model. In the end, we have classified the supermassive black holes according to their efficiency.