A black hole fundamental plane

We study observed correlations between supermassive black hole (BHs) and the properties of their host galaxies, and show that the observations define a BH "fundamental plane" (BHFP), of the form $\mbh∝σ^{3.0±0.3} \re^{0.43±0.19}$ or $\mbh∝\mstar^{0.54±0.17} σ^{2.2±0.5}$, analogous to the FP of elliptical galaxies. The BHFP is preferred over a simple relation between M_BH and any of σ, M_*, M_dyn, or R_e alone at > 3 σ (99.9%) significance. The existence of this BHFP has important implications for the formation of supermassive BHs and the masses of the very largest black holes, and immediately resolves several apparent conflicts between the BH masses expected and measured for outliers in both the M_BH − σ and M_BH − M_* relations.