Abstract
We examine the origin and evolution of correlations between properties of supermassive BHs and their host galaxies using simulations of major galaxy mergers, including the effects of gas dissipation, cooling, star formation, and BH accretion and feedback. We demonstrate that the simulations predict the existence of a BH "fundamental plane" (BHFP), of the form MBH ∝ σ3.0±0.3R or MBH ∝ Mσ2.2±0.5, similar to relations found observationally. The simulations indicate that the BHFP can be understood roughly 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 for a given M* at high redshift (i.e., increasingly deep potential wells), the BHFP predicts that 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 a given 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.
Highlights
Correlations between the masses of supermassive black holes (BHs) in the centers of galaxies and the properties of their host spheroids (e.g., Kormendy & Richstone 1995) imply a fundamental bond between the growth of BHs and galaxy formation
The scatter is of critical importance at these masses: we consider the BH mass function (BHMF) derived from MBH − σ if we change the estimated intrinsic scatter by just 25%, all within the range allowed by the present observations (Tremaine et al 2002), and find that this relatively small difference in the intrinsic scatter estimate makes a larger difference at high MBH than the choice of correlation (MBH − σ, MBH − M∗, or BH “fundamental plane” (BHFP)) adopted
For example, the BH accretion rate is a pure function of the galactic star formation rate, it is difficult to explain how the BH mass would be sensitive to the central potential in the manner of the observed BHFP, and not trace the galaxy stellar mass
Summary
The Harvard community has made this article openly available. Please share how this access benefits you. “A Theoretical Interpretation of the Black Hole Fundamental Plane.”. ACCEPTED TO APJ, MAY 2007 Preprint typeset using LATEX style emulateapj v. ACCEPTED TO APJ, MAY 2007 Preprint typeset using LATEX style emulateapj v. 08/22/09
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