The fundamental relation between supermassive black holes and their host galaxies

Abstract

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 M<SUB>BH</SUB>-σ<SUB>e</SUB> appears to be the fundamental relation rather than a putative `BH Fundamental Plane' of the kind M<SUB>BH</SUB>-σ<SUB>e</SUB>-R<SUB>e</SUB>. These results can be explained by a picture which sees the M<SUB>BH</SUB>-σ<SUB>e</SUB> 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.