A Theoretical Interpretation of the Black Hole Fundamental Plane

By P. Hopkins, L. Hernquist, Thomas J. Cox, Brant Robertson, E. Krause. 2007

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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.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/e8b323dcc277667e61e00ea321c962f3f87cded0

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Citations in the corpus

THE SINFONI BLACK HOLE SURVEY: THE BLACK HOLE FUNDAMENTAL PLANE REVISITED AND THE PATHS OF (CO)EVOLUTION OF SUPERMASSIVE BLACK HOLES AND BULGES (2016, background): “(32) This is similar to the dependences found by Aller & Richstone (2007), Hopkins et al. (2007b) and Mancini & Feoli (2012).”
The Illustris simulation: the evolving population of black holes across cosmic time (2014, methodology): “…even in the case of the bolometric and hard X-ray luminosity functions large uncertainties remain due to poorly constrained bolometric corrections (Hopkins et al. 2007; Vasudevan & Fabian 2007, 2009; Lusso et al. 2012) and the c© 0000 RAS, MNRAS 000, 000–000 uncertain fraction of Compton-thick…”
MOLECULAR GAS IN z ∼ 6 QUASAR HOST GALAXIES (2010, background): “…velocity dispersion and supermassive black hole (SMBH) mass in nearby galaxies (Tremaine et al. 2002; Marconi & Hunt 2003; Hopkins et al. 2007a), which suggests that the formation of the SMBH and its spheroidal host are tightly coupled (Kauffmann & Haehnelt 2000; Hopkins et al. 2007b).”
THE METALLICITY EVOLUTION OF INTERACTING GALAXIES (2011, background): “…sense, the same gas that drives nuclear starbursts (Mihos & Hernquist 1994b, 1996; Iono et al. 2004) and triggers central AGN activity and black hole growth (Di Matteo et al. 2005; Springel et al. 2005; Hopkins & Hernquist 2006; Hopkins et al. 2007), also results in suppressed nuclear metallicity.”
HOW DO DISKS SURVIVE MERGERS? (2008, background): “…halo gas; Hernquist 1989; Barnes & Hernquist 1991, 1996; Hernquist et al. 1993; Mihos & Hernquist 1994b, 1996; Di Matteo et al. 2005; Naab et al. 2006; Jesseit et al. 2007; Cox et al. 2006a,b; Robertson et al. 2006b; Springel et al. 2005a; Burkert et al. 2007; Hopkins et al. 2007c, 2008a,g,b,c,d).”
A semi-analytic model for the co-evolution of galaxies, black holes and active galactic nuclei (2008, methodology): “Because the depth of the spheroid’s potential well determines the amount of momentum necessary to entrain the infalling gas, Hopkins et al. (2007a) find that this leads to a ‘black hole fundamental plane’, a correlation between the final black hole mass and sets of spheroid structural/dynamical…”
THE BULK OF THE BLACK HOLE GROWTH SINCE z ∼ 1 OCCURS IN A SECULAR UNIVERSE: NO MAJOR MERGER–AGN CONNECTION (2010, background): “…time (Peng 2007; Jahnke & Maccio 2010), these correlations have often been interpreted as the signature of coupled evolution between the BH and its host galaxy (Kauffmann & Haehnelt 2000; Volonteri et al. 2003; Wyithe & Loeb 2003; Granato et al. 2004; Hopkins et al. 2007; Somerville et al. 2008).”
The Coevolution of Galaxies and Supermassive Black Holes: Insights from Surveys of the Contemporary Universe (2014, methodology): “In terms of the luminosity function, this departure from a pure PLE model is primarily manifested as an evolution in the faint end slope with γ1 increasing from ∼0.3 at z = 3 to ∼0.9 at z = 0 (Hopkins et al. 2007).”
DISSIPATION AND EXTRA LIGHT IN GALACTIC NUCLEI. IV. EVOLUTION IN THE SCALING RELATIONS OF SPHEROIDS (2008, methodology): “Recall, motivated by observational and theoretical expectations of a black hole “fundamental plane” (Hopkins et al. 2007c,b) the fundamental “assumed” correlation here is between black hole mass and binding energy of the dissipational component of the bulge, determined at the time of that…”
A Cosmological Framework for the Co-Evolution of Quasars, Supermassive Black Holes, and Elliptical Galaxies. II. Formation of Red Ellipticals (2007, background): “…a comparison of the local mass density of supermassive black holes with the luminosity density of quasars integrated over redshift (Soltan 1982; Hopkins et al. 2007d) indicates that the mass growth through the radio mode must be negligible (Hopkins et al. 2006d), in agreement with preliminary…”
THE BLACK HOLE MASS, STELLAR MASS-TO-LIGHT RATIO, AND DARK HALO IN M87 (2009, background): “The correlation of black hole with velocity dispersion (Gebhardt et al. 2000, Ferrarese & Merritt 2000) has led to a large amount of theoretical research as to the cause of the correlation and the value of the slope (e.g., Hopkins et al. 2007).”
A Cosmological Framework for the Co-Evolution of Quasars, Supermassive Black Holes, and Elliptical Galaxies. I. Galaxy Mergers and Quasar Activity (2007, methodology): “…our halo occupationmodel predicts of orderk3 satellite M galaxies), and the expectation from a secular model, in which quasar clustering traces the observed clustering of star-forming galaxies (taken from the observations collected in Hopkins et al. 2007d)—neither agrees with the observations.”
DISSIPATION AND EXTRA LIGHT IN GALACTIC NUCLEI. II. “CUSP” ELLIPTICALS (2008, methodology): “Given the BHFP in terms of stellar mass and Re (i.e. scaling of BH mass with Re or, equivalently, σ at fixed galaxy stellar mass, as in Hopkins et al. 2007a, 2007b), and the scaling of Re with extra light fraction at fixed mass seen in Figure 22, we can estimate the dependence of BH mass on extra li”
An Observed Fundamental Plane Relation for Supermassive Black Holes (2007, background): “Both a pure relation between BH mass and spheroid binding energy, of the form MBH ∝ (M∗σ2)2/3, as studied in Aller & Richstone (2007), for example, and a mixed relation of the formMBH ∝M 1/2 ∗ σ 2 (see Hopkins et al. 2007), are within the∼ 1σ allowed range of the data.”
The correlation of star formation quenching with internal galaxy properties and environment (2008, background): “The critical mass is that at which the energy radiated by the black hole is sufficient to halt further accretion, i.e. the black hole growth is self-regulated (Hopkins et al. 2007).”
Discriminating Between the Physical Processes that Drive Spheroid Size Evolution (2009, background): “Generically, in such models, the ‘most fundamental’ correlation is between BH mass and some measure of the binding energy of the material which must be ‘halted’ to arrest further accretion; Hopkins et al. (2007a) show, in high-resolution C© 2009 The Authors.”
Structure and Star Formation in Galaxies out to z = 3: Evidence for Surface Density Dependent Evolution and Upsizing (2008, methodology): “The evolution of the mass-size relation for spheroidal galaxies is expected to evolve even faster (e.g., Kochfar & Silk 2006, Hopkins et al. 2007,2008) The first studies of the evolution of the size-mass relation to z = 3 were done by Trujillo et al. (2006), based on ISAAC imaging data on the…”
Black holes on FIRE: stellar feedback limits early feeding of galactic nuclei (2017, background): “…by BH feedback (e.g. Silk & Rees 1998; Di Matteo, Springel & Hernquist 2005; Murray, Quataert & E-mail: anglesd@northwestern.edu Thompson 2005; Hopkins et al. 2007) or (3) the result of a common gas supply for star formation and BH growth, regulated by gravitational torques (e.g. Kauffmann…”