Relation Between Globular Clusters and Supermassive Black Holes in Ellipticals as a Manifestation of the Black Hole Fundamental Plane

Abstract

We analyze the relation between the mass of the central supermassive black hole (M-BH) and the number of globular clusters (N-GC) in elliptical galaxies and bulges as a ramification of the black hole fundamental plane, the theoretically predicted and observed multi-variable correlation between M-BH and bulge binding energy. Although the tightness of the M-BH-N-GC correlation suggests an unlikely causal link between supermassive black holes and globular clusters (GCs), such a correspondence can exhibit small scatter even if the physical relationship is indirect. We show that the relatively small scatter of the M-BH-N-GC relation owes to the mutual residual correlation of M-BH and N-GC with stellar mass when the velocity dispersion is held fixed. Thus, present observations lend evidence for feedback-regulated models in which the bulge binding energy is most important; they do not necessarily imply any "special" connection between GCs and M-BH. This raises the question of why N-GC traces the formation of ellipticals and bulges sufficiently well to be correlated with binding energy.