2011ApJ...728L..24S

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_GCwith 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.