A Theoretical Interpretation of the Black Hole Fundamental Plane

We examine the origin and evolution of correlations between properties ofsupermassive black holes (BHs) and their host galaxies using simulations ofmajor galaxy mergers, including the effects of gas dissipation, cooling, starformation, and BH accretion and feedback. We demonstrate that the simulationspredict the existence of a BH 'fundamental plane' (BHFP), of the form M_BHsigma^(3.0+-0.3)*R_e^(0.43+-0.19) or M_BHM_bulge^(0.54+-0.17)*sigma^(2.2+-0.5), similar to relations foundobservationally. The simulations indicate that the BHFP can be understoodroughly as a tilted intrinsic correlation between BH mass and spheroid bindingenergy, or the condition for feedback coupling to power a pressure-drivenoutflow. While changes in halo circular velocity, merger orbital parameters,progenitor disk redshifts and gas fractions, ISM gas pressurization, and otherparameters can drive changes in e.g. sigma at fixed M_bulge, and thereforechanges in the M_BH-sigma or M_BH-M_bulge relations, the BHFP is robust. Giventhe empirical trend of decreasing R_e for a given M_bulge at high redshift, theBHFP predicts that BHs will be more massive at fixed M_bulge, in good agreementwith recent observations. This evolution in the structural properties of mergerremnants, to smaller R_e and larger sigma (and therefore larger M_BH,conserving the BHFP) at a given M_bulge, is driven by the fact that bulgeprogenitors have characteristically larger gas fractions at high redshifts.Adopting the observed evolution of disk gas fractions with redshift, oursimulations predict the observed trends in both R_e(M_bulge) and M_BH(M_bulge).Comment: 22 pages, 19 figures, replaced with version accepted to ApJ. Companion paper to arXiv:0707.400