A Fundamental Plane Relation for Black Hole Masses and Their Redshift Evolution

We study the relation between black hole (BH) mass and host galaxy properties in simulations of major galaxy mergers, including the effects of gas dissipation, cooling, star formation, and BH accretion and feedback. We show that the simulations predict the existence of a BH “fundamental plane” (BHFP), of the form MBH ∝ σ3.0 R0.5 e or MBH ∝ M0.64±0.1 ∗ σ1.7±0.2, analogous to the FP of elliptical galaxies. Comparing with existing BH mass measurements, the observed systems indeed follow an identical BHFP relation, favoring such a BHFP over a simple relation between MBH and any of σ, M∗, Mdyn, or Re alone at > 3σ (99.9%) significance. This can be roughly understood as a “tilted” intrinsic correlation between BH mass and spheroid binding energy, or the condition for feedback coupling to power a pressure-driven outflow. While changes in halo circular velocity, merger orbital parameters, progenitor disk redshifts and gas fractions, ISM gas pressurization, and other parameters can drive changes in e.g. σ at fixed M∗, and therefore changes in the MBH −σ or MBH −M∗ relations, the BHFP is robust. Given the empirical trend of decreasing Re at fixed M∗ at high redshift (i.e. increasingly deep potential wells), the BHFP predicts BHs will be more massive at fixed M∗, in good agreement with recent observations. This evolution in the structural properties of merger remnants, to smaller Re and larger σ (and therefore larger MBH, conserving the BHFP) at fixed M∗, is driven by the fact that disks (merger progenitors) have characteristically larger gas fractions at high redshifts. Adopting the observed evolution of disk gas fractions with redshift our simulations predict the observed trends in both Re(M∗) and MBH(M∗). The existence of this BHFP also has important implications for 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 MBH −σ and MBH −M∗ relations. Subject headings: quasars: general — galaxies: active — galaxies: evolution — cosmology: theory