The fundamental relation between supermassive black holes and their host galaxies

We study the correlations between supermassive black holes (BHs) and their host galaxies, using a sample of 83 BH masses collected from the most recent and reliable spatially resolved estimates available from the literature. We confirm the mono- and bivariate correlations between SMBHs and the bulges of their host galaxies, confirming that the correlation with the effective velocity dispersion is not significantly improved by higher dimensionality. Instead, pseudo-bulges do not seem to correlate with their SMBHs, probably because their secular evolution is often unable to trigger accretion onto the central BH. We then present a novel approach aimed at finding the fundamental relation between SMBHs and their host galaxies. For the first time, we analytically combine BH masses with the Fundamental Plane (FP), showing that MBH–σe appears to be the fundamental relation rather than a putative ‘BH Fundamental Plane’ of the kind MBH–σe–Re. These results can be explained by a picture which sees the MBH–σe relation as a natural outcome of the change in AGN feedback from momentum-driven to energy-driven. The other scaling relations are then established through the FP