Breaking the law: the M bh-M spheroid relations for core-Sersic and Sersic galaxies


Graham, Alister W.


The popular log-linear relation between supermassive black hole mass, M bh, and the dynamical mass of the host spheroid, M sph, is shown to require a significant correction. Core galaxies, typically with M bh 2 × 108 M ☉ and thought to be formed in dry merger events, are shown to be well described by a linear relation for which the median black hole mass is 0.36%—roughly double the old value of constancy. Of greater significance is that M bhM 2 sph among the (non-pseudobulge) lower-mass systems: specifically, log [M bh/M ☉] = (1.92 ± 0.38)log [M sph/7 × 1010 M ☉] + (8.38 ± 0.17). 'Classical' spheroids hosting a 106 M ☉ black hole will have M bh/M sph ~ 0.025%. These new relations presented herein (1) bring consistency to the relation M bhσ5 and the fact that Lσ x with exponents of 5 and 2 for bright (MB & 8211;20.5 mag) and faint spheroids, respectively, (2) mimic the non-(log-linear) behavior known to exist in the M bh-(Sérsic n) diagram, (3) necessitate the existence of a previously overlooked M bhL 2.5 relation for Sérsic (i.e., not core-Sérsic) galaxies, and (4) resolve past conflicts (in mass prediction) with the M bh-σ relation at the low-mass end. Furthermore, the bent nature of the M bh-M sph relation reported here for 'classical' spheroids will have a host of important implications that, while not addressed in this paper, relate to (1) galaxy/black hole formation theories, (2) searches for the fundamental, rather than secondary, black hole scaling relation, (3) black hole mass predictions in other galaxies, (4) alleged pseudobulge detections, (5) estimates of the black hole mass function and mass density based on luminosity functions, (6) predictions for space-based gravitational wave detections, (7) connections with nuclear star cluster scaling relations, (8) evolutionary studies over different cosmic epochs, (9) comparisons and calibrations matching inactive black hole masses with low-mass active galactic nucleus data, and more.

Publication year


Publication type

Journal article


Astrophysical Journal, Vol. 746, no. 1 (Feb 2012), article no. 113




Institute of Physics


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