Black Hole Mass Scaling Relations in Galaxies

Scaling relations linking supermassive black hole mass to host galaxy properties underpin our understanding of galaxy evolution and feedback processes. Empirically, black hole mass correlates with stellar velocity dispersion, bulge luminosity and stellar mass, suggesting a co-evolution between central engines and their galactic spheroids. The canonical relations include the M–σ relation, where black hole mass M_BH ∝ σ^κ, and the M–L and M–M_* relations tying mass to bulge luminosity and stellar mass. These relations exhibit intrinsic scatter and potential curvature at high masses, reflecting varied growth histories. Dynamical measurements via stellar or gas kinematics establish the local scaling laws, which serve as benchmarks for models of active galactic nuclei feedback, galaxy merger simulations and predictions of gravitational-wave backgrounds. Recent work refines these relations by accounting for sample selection biases, environmental effects, structural non-homology and morphological dependence. As observational capabilities extend to higher redshifts and fainter systems, evolving scaling relations offer insight into the assembly of black holes and their host galaxies across cosmic time.

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Black Hole Mass Scaling Relations in Galaxies publication trend

The graph below shows the total number of articles in black hole mass scaling relations in galaxies across all publications each year (not limited to Nature Index journals).

Technical terms

Scaling relation: An empirical correlation between black hole mass and a host galaxy property, such as velocity dispersion or bulge stellar mass.

Velocity dispersion (σ): The spread in stellar or gas velocities within a galaxy’s bulge, indicative of its gravitational potential depth.

Bulge: The central, spheroidal stellar component of a galaxy, distinct from the flattened disc and often housing the supermassive black hole.

Fundamental plane: A multi-parameter relation, combining variables such as σ, effective radius and luminosity, that reduces scatter in black hole–galaxy correlations.

Mass function: The distribution of black hole masses or galaxy stellar masses per unit volume, used to derive demographic and merger statistics.

References

1. Big Galaxies and Big Black Holes: The Massive Ends of the Local Stellar and Black Hole Mass Functions and the Implications for Nanohertz Gravitational Waves. The Astrophysical Journal Letters (2024).
2. A Breakdown of the Black Hole–Bulge Mass Relation in Local Active Galaxies. The Astrophysical Journal (2024).
3. Resequencing the Hubble sequence and the quadratic (black hole mass)–(spheroid stellar mass) relation for elliptical galaxies. Monthly Notices of the Royal Astronomical Society (2023).
4. Selection bias in dynamically measured supermassive black hole samples: its consequences and the quest for the most fundamental relation. Monthly Notices of the Royal Astronomical Society (2016).
5. The black hole mass – spheroid luminosity relation. Monthly Notices of the Royal Astronomical Society (2007).
6. An Observed Fundamental Plane Relation for Supermassive Black Holes. The Astrophysical Journal (2007).