A Log-Quadratic Relation for Predicting Supermassive Black Hole Masses from the Host Bulge Sérsic Index

By Alister W. Graham, S. Driver. 2006

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We reinvestigate the correlation between black hole mass and bulge concentration. With an increased galaxy sample (totaling 27) and updated estimates of galaxy distances, black hole masses, and Sérsic indices n—a measure of concentration—we perform a least-squares regression analysis to obtain a relation suitable for the purpose of predicting black hole masses in other galaxies. In addition to the linear relation, log Mbh = (7.81 ± 0.08) + (2.69 ± 0.28) log(n/3) with ϵintrinsic = 0.31 dex, we investigated the possibility of a higher order Mbh-n relation, finding the second-order term in the best-fitting quadratic relation to be inconsistent with a value of zero at greater than the 99.99% confidence level. The optimal relation is given by log Mbh = (7.98 ± 0.09) + (3.70 ± 0.46) log(n/3) - (3.10 ± 0.84) [log(n/3)]2, with ϵintrinsic = 0.18 dex and a total absolute scatter of 0.31 dex. When the quadratic relation is extrapolated, it predicts black holes with masses of ~103 M☉ in n = 0.5 dwarf elliptical galaxies, compared to ~105 M☉ from the linear relation, and an upper bound on the largest black hole masses in the local universe equal to 1.2 × 109 M☉. In addition, we show that the nuclear star clusters at the centers of low-luminosity elliptical galaxies follow an extrapolation of the same quadratic relation, strengthening suggestions for a possible evolutionary link between supermassive black holes and nuclear star clusters. Moreover, we speculate that the merger of two such nucleated galaxies, accompanied by the merger and runaway collision of their central star clusters, could result in the late-time formation of some supermassive black holes. Finally, we predict the existence of, and provide equations for, an Mbh-μ0 relation, in which μ0 is the (extrapolated) central surface brightness of a bulge.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/7f58ff89051281ae7affd74344c78e36934bb3d8

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Citations in the corpus

Selection bias in dynamically measured supermassive black hole samples: its consequences and the quest for the most fundamental relation (2016, methodology): “…or Sérsic index (e.g., Magorrian et al. 1998; Richstone et al. 1998; Ferrarese & Merritt 2000; Gebhardt & et al. 2000; Graham et al. 2001; Graham & Driver 2007a; Marconi & Hunt 2003; Häring & Rix 2004; Graham 2007; Satyapal et al. 2008; c© 2016 RAS Graham 2012; Kormendy & Ho 2013;…”
Titans of the early Universe: The Prato statement on the origin of the first supermassive black holes (2018, background): “…galaxy and central black hole include a correlation between MBH and the galactic Sérsic index (nsph, a measure of bulge concentration see, e.g., Graham & Driver 2007; Savorgnan et al. 2016), and a correlation between the morphology of the spiral arms and the mass of the central black hole in…”
CONSTRAINTS ON BLACK HOLE GROWTH, QUASAR LIFETIMES, AND EDDINGTON RATIO DISTRIBUTIONS FROM THE SDSS BROAD-LINE QUASAR BLACK HOLE MASS FUNCTION (2010, background): “…relationship, e.g., Gebhardt et al. 2000; Merritt & Ferrarese 2001; Tremaine et al. 2002), concentration or Sersic index (e.g., Graham et al. 2001; Graham & Driver 2007), bulge mass (e.g., Magorrian et al. 1998; Marconi & Hunt 2003; Häring & Rix 2004), and binding energy (e.g., Aller &…”
A catalogue of 2D photometric decompositions in the SDSS-DR7 spectroscopic main galaxy sample: preferred models and systematics (2014, background): “Although such galaxies may exist in nature (e.g. Graham & Driver 2007; Kormendy et al. 2009), we find that higher values of the Sérsic index are often associated with fitting problems in this sample.”
Cosmic Evolution of Black Holes and Spheroids. II. Scaling Relations at z = 0.36 (2007, background): “…and luminosity of the spheroidal (or bulge) component, indicating a connection between nuclear activity and galaxy formation and evolution (Magorrian et al. 1998; Ferrarese & Merritt 2000; Gebhardt et al. 2000, 2001; Marconi & Hunt 2003; Häring & Rix 2004; Novak et al. 2006; Graham & Driver 2007).”
The black hole mass–stellar velocity dispersion correlation: bulges versus pseudo-bulges (2008, background): “…Drory & Fisher 2007; (4) Erwin et al. 2002; (5) Gadotti 2008; (6) Garcia-Rissmann et al. 2005; (7) Gebhardt et al. 2003; (8) Ghez et al. 2005; (9) Graham & Driver 2007; (10) Greenhill et al. 2003; (11) Kondratko et al. 2008; (12) Lodato & Bertin 2003; Huré 2002; (13) Nelson & Whittle 1995; (14)…”
THE MBH–LSPHEROID RELATION AT HIGH AND LOW MASSES, THE QUADRATIC GROWTH OF BLACK HOLES, AND INTERMEDIATE-MASS BLACK HOLE CANDIDATES (2012, methodology): “L relation is of course also important when using the galaxy/spheroid luminosity function to predict the black hole mass function, and sub- The Mbh–Lspheroid relation 13 sequently the black hole mass density (e.g. Graham & Driver 2007b, and references therein).”
An expanded Mbh–σ diagram, and a new calibration of active galactic nuclei masses (2010, methodology): “None the less, using a 5 per cent uncertainty, Gültekin et al. (2009b) report an intrinsic scatter of 0.44 ± 0.06 dex for their full sample Mbh–σ relation. relation (Graham & Driver 2007a), which uses the major-axis Sérsic index n, has a total scatter of only 0.31 dex.”
DISSIPATION AND EXTRA LIGHT IN GALACTIC NUCLEI. IV. EVOLUTION IN THE SCALING RELATIONS OF SPHEROIDS (2008, methodology): “Owing to the dependence ofns on stellar mass, there is an indirect correlation betweenMBH andns, consistent with that claimed in Graham & Driver (2007).”
The Effect of Radiation Pressure on Virial Black Hole Mass Estimates and the Case of Narrow-Line Seyfert 1 Galaxies (2008, background): “…a BH and its host galaxy is provided by the tight correlations between BH mass and luminosity, mass, velocity dispersion and surface brightness profile ofthe host spheroids (Kormendy & Richstone 1995; Gebhardt et al. 2000; Ferrarese & Merritt 2000; Marconi & Hunt 2003; Graham & Driver 2007).”
REVISITING THE SCALING RELATIONS OF BLACK HOLE MASSES AND HOST GALAXY PROPERTIES (2012, background): “…Manoa, Honolulu, HI; nmcc@ifa.hawaii.edu 2 Department of Astronomy, University of California at Berkeley, Berkeley, CA; cpma@berkeley.edu ity (e.g., Kormendy & Gebhardt 2001; Kormendy et al. 2011; B12), and bulge concentration or Sérsic index (e.g., Graham et al. 2001; Graham & Driver 2007; B12).”
WHAT TURNS GALAXIES OFF? THE DIFFERENT MORPHOLOGIES OF STAR-FORMING AND QUIESCENT GALAXIES SINCE z ∼ 2 FROM CANDELS (2011, result): “Given correlations between black hole mass, bulge mass, velocity dispersion and Sérsic index (Häring & Rix 2004; Peng et al. 2006; Graham & Driver 2007; Gültekin et al. 2009), our results tentatively support the AGN feedback paradigm, at least at the qualitative level.”
On the correlations between galaxy properties and supermassive black hole mass (2011, methodology): “The Sérsic index n has indeed been adopted by some as a good tracer for M• (Graham et al. 2001, 2003; Graham & Driver 2007).”
Quantifying the coexistence of massive black holes and dense nuclear star clusters (2009, methodology): “Here we have modelled the nuclear star cluster with a Sérsic function (dotted curve) and the underlying host bulge — which has an effective half-light radius of ∼4.5 degrees (e.g. Graham & Driver 2007) and is therefore basically a horizontal line — with an exponential function (Kent et al. 1991).”
A Cosmological Framework for the Co-Evolution of Quasars, Supermassive Black Holes, and Elliptical Galaxies. I. Galaxy Mergers and Quasar Activity (2007, background): “…mass to, e.g., the mass (Magorrian et al. 1998; McLure & Dunlop 2002; Marconi & Hunt 2003; Häring& Rix 2004), velocity dispersion (Ferrarese & Merritt 2000; Gebhardt et al. 2000; Tremaine et al. 2002), and concentration or Sersic index (Graham et al. 2001; Graham & Driver 2007) of the spheroid.”