Improved tests on the relationship between the kinetic energy of galaxies and the mass of their central black holes

We support, with new fitting instruments and the analysis of more recent experimental data, the proposal of a relationship between the mass of a Supermassive Black Hole (SMBH) and the kinetic energy of random motions in the host elliptical galaxy. The first results obtained in a previous paper with 13 elliptical galaxies are now confirmed by the new data and an enlarged sample. We find M-BH proportional to (M-G sigma(2)/c(2))(beta) with 0.8 <= beta <= 1 depending on the different fitting methods and samples used. The meaningful case beta = 1 is carefully analyzed. Furthermore, we test the robustness of our relationship, including in the sample also lenticular and spiral galaxies and we show that the result does not change. Finally, we find a stronger correlation between the mass of the galaxy and the corresponding velocity dispersion that allows us to connect our relationship to the M-BH proportional to sigma(proportional to) law. With respect to this law, our relationship has the advantage of having a smaller scatter.