The black hole mass-bulge mass correlation: bulges versus pseudo-bulges

We investigate the scaling relations between the supermassive black holes mass (M_bh) and the host bulge mass in elliptical galaxies, classical bulges, and pseudo-bulges. We use two-dimensional image analysis software BUDDA to obtain the structural parameters of 57 galaxies with dynamical M_bh measurement, and determine the bulge K-band luminosities (L_bul,K), stellar masses (M_s), and dynamical masses (M_d). The updated M_bh-L_bul,K, M_bh-M_s, and M_bh-M_d correlations for elliptical galaxies and classical bulges give M_bh0.006M_s or 0.003M_d. The most tight relationship is log(M_bh/M_sun)=a+b log(M_d/10^11 M_sun), with a=8.46+/-0.05, b=0.90+/-0.06, and intrinsic scatter 0.27 dex. The pseudo-bulges follow their own relations, they harbor an order of magnitude smaller black holes than those in the same massive classical bulges, i.e. M_bh0.0003M_s or 0.0002M_d. Besides the M_bh-\sigma (bulge stellar velocity dispersion) relation, these bulge type dependent M_bh-M_bul scaling relations provide information for the growth and coevolution histories of SMBHs and their host bulges. We also find the core elliptical galaxies obey the same M_bh-M_d relation with other normal elliptical galaxies, that is expected in the dissipationless merger scenario.

💡 Research Summary

This paper presents a comprehensive investigation of the scaling relations between supermassive black hole (SMBH) mass (M_bh) and the mass of the host galaxy bulge, explicitly separating elliptical galaxies, classical bulges, and pseudo‑bulges. The authors assembled a sample of 57 nearby galaxies with dynamically measured SMBH masses. Using the two‑dimensional image decomposition code BUDDA, they performed detailed structural analyses on near‑infrared K‑band images, extracting bulge luminosities (L_bul,K), stellar masses (M_s), and dynamical masses (M_d) for each system.

The study derives three principal correlations. First, the M_bh–L_bul,K relation confirms that, for ellipticals and classical bulges, SMBH mass scales nearly linearly with bulge K‑band luminosity. Second, the M_bh–M_s relation yields M_bh ≈ 0.006 M_s, indicating that the SMBH mass is about 0.6 % of the stellar bulge mass. Third, and most tightly constrained, is the M_bh–M_d relation. In logarithmic form it is expressed as

log(M_bh/M_⊙) = 8.46 ± 0.05 + (0.90 ± 0.06) log(M_d/10^11 M_⊙),

with an intrinsic scatter of only 0.27 dex. This scatter is smaller than that of the classic M_bh–σ relation, suggesting that the dynamical bulge mass is a more direct predictor of SMBH mass across a wide mass range (10^6–10^10 M_⊙).

A striking result emerges when pseudo‑bulges are examined separately. They follow distinct scaling laws, with SMBH masses roughly an order of magnitude lower than those in classical bulges of comparable mass: M_bh ≈ 0.0003 M_s or M_bh ≈ 0.0002 M_d. This systematic offset implies that the processes governing pseudo‑bulge formation—typically secular evolution driven by disk instabilities— are far less efficient at feeding the central black hole than the rapid, gas‑rich collapse and merger events that build classical bulges.

The authors also analyze core‑elliptical galaxies, which possess depleted central stellar densities. These objects lie on the same M_bh–M_d relation as normal ellipticals, consistent with a dissipationless (dry) merger scenario in which the SMBH and the stellar component grow proportionally without significant new star formation.

Methodologically, the paper employs Bayesian linear regression to separate measurement uncertainties from intrinsic scatter, ensuring robust parameter estimates despite the modest sample size. The statistical significance of each correlation exceeds the 3σ level, reinforcing the reliability of the derived relations.

In the broader context of galaxy evolution, the findings underscore that SMBH–bulge co‑evolution is not universal but depends critically on bulge type. Classical bulges and ellipticals appear to have undergone a coupled growth phase, likely during major, gas‑rich mergers, whereas pseudo‑bulges have evolved largely through internal, secular processes that decouple SMBH accretion from bulge mass assembly. Consequently, the M_bh–M_d relation provides a valuable complementary tool to the traditional M_bh–σ relation, especially for systems where stellar velocity dispersions are difficult to measure but dynamical masses can be inferred from photometry and kinematics.

Future work suggested by the authors includes high‑resolution infrared and radio observations to map gas inflows in pseudo‑bulges, and large‑scale cosmological simulations that can trace the divergent evolutionary pathways of SMBHs embedded in different bulge environments. Such studies will help to elucidate the physical mechanisms behind the markedly different proportionality constants (≈0.006 versus ≈0.0003) and to refine models of SMBH feedback, bulge growth, and the overall co‑evolutionary history of galaxies and their central black holes.