An Observed Fundamental Plane Relation for Supermassive Black Holes

Abstract

We study observed correlations between super massive black hole (BHs) and the properties of their host galaxies and show that the observations define a BH ``fundamental plane'' (BHFP), of the form M-BH proportional to sigma(3.0 +/- 0.3) R-e(0.43 +/- 0.19) or M-BH proportional to M-(0.54 +/- 0.17 sigma 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 sigma, M-, M-dyn, or R-e alone at >3 sigma ( 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-sigma and M-BH-M-* relations.