Cosmic evolution and physical origin of the supermassive black hole–host galaxy scaling relations: what sets their zero point and scatter

Supermassive black hole (SMBH) masses correlate tightly with bulge properties of their host galaxies, but whether these scaling relations evolve with cosmic time, and what physical processes set their normalization (zero point) and intrinsic scatter, remains unsettled. Zhao, Ho, Shangguan, Kim, Zhao and Gao (2021) showed that 35 low-redshift Palomar-Green quasars roughly obey the local black-hole–host relations but stressed that the sample was far too small to establish whether the relations evolve, or whether their zero point and scatter depend on the Eddington ratio, the star-formation history or type of the bulge, the large-scale environment, or the role of major mergers. Later work has delivered substantially larger low-redshift samples, reverberation-mapped intermediate-redshift samples, and JWST detections at z>3, yet the literature now contains both strong claims that high-redshift black holes are overmassive relative to their hosts and galaxy-selected samples consistent with no evolution, with selection and virial-mass systematics of the same order as the claimed effects. The problem is to determine, with large, bias-controlled samples, whether and how the SMBH–host scaling relations evolve with redshift, and to identify the physical drivers—accretion phase, star-formation history, mergers, or environment—of their zero point and scatter.

Background

Supermassive black holes (SMBHs), with masses of roughly $10^6$ – $10^{10}$ solar masses, sit at the centers of massive galaxies. Their masses correlate with properties of the host bulge—the classical scaling relations, chiefly $M_{\rm BH}$ – $\sigma$ (black hole mass versus bulge stellar velocity dispersion), $M_{\rm BH}$ – $M_{\rm bulge}$ (versus bulge stellar mass), and $M_{\rm BH}$ – $M_{\rm total}$ (versus total galaxy stellar mass), together with $M_{\rm BH}$ – $M_{\rm core}$ (versus the mass of the central "core" component of elliptical galaxies, the component most directly linked to their compact high-redshift progenitors). These relations are the central empirical pillar of the idea that black holes and galaxies coevolve (Kormendy & Ho 2013), but whether the correlations reflect causal feedback, hierarchical merging that merely averages black-hole-to-stellar mass ratios, or observational selection remains debated.

An active galactic nucleus (AGN) is a growing SMBH that outshines its host; quasars are the most luminous AGNs. The Eddington ratio $L_{\rm bol}/L_{\rm Edd}$ compares the bolometric luminosity to the Eddington limit set by the black hole mass, and measures the instantaneous accretion rate. In AGNs the black hole mass is usually estimated indirectly: single-epoch virial estimates combine the velocity width of broad emission lines with continuum luminosity, calibrated against reverberation mapping, the time-domain technique that infers the size of the broad-line region from light-travel delays. These virial masses carry a poorly known geometry-dependent virial factor and orientation systematics. Host galaxy properties require separating the galaxy light from the bright nucleus by point-spread-function (PSF) matching and two-dimensional image decomposition, and converting luminosity to stellar mass through a mass-to-light ratio that depends on stellar population age—sources of systematic uncertainty identified already in the source paper.

Bulges come in two flavors: classical bulges, built by mergers and dynamically hot, and pseudo bulges, built gradually by secular disk evolution, with low bulge-to-total light ratio and low Sérsic index (a concentration parameter of the light profile). Narrow-line Seyfert 1 galaxies (NLS1s), AGNs with narrow broad lines signaling small black hole masses accreting at high Eddington ratios, preferentially occur in barred disk galaxies with pseudo bulges. Zhao et al. (2021) analyzed Hubble Space Telescope imaging of 35 low-redshift ( $z<0.5$ ) Palomar-Green quasars: roughly half the hosts are disks, often barred with pseudo bulges; mergers are a minority (≲20%); the sample roughly obeys the local scaling relations, with less massive black holes (mostly NLS1s) behaving like pseudo bulges; and pseudo-bulge hosts show evidence of recent or ongoing central star formation. They emphasized that this sample is far too small to establish the intrinsic scatter of the relations, whether they evolve with cosmic time, or whether the zero point and scatter depend on the Eddington ratio, the color or star-formation history of the bulge, or the environment—questions they left open, framing their low-redshift focus as laying the foundation for future investigations of possible cosmic evolution.

Subsequent work has transformed the observational landscape. At low redshift, Zhuang & Ho (2023) measured the $M_{\rm BH}$ – $M_*$ relation for about 11,500 broad-line AGNs and found that the position of an AGN on this plane is connected with both its star-formation and accretion properties. At intermediate redshift, reverberation-mapped samples find the $M_{\rm BH}$ – $M_*$ relation already in place by $z\sim1$ (Li et al. 2023), and X-ray selected samples find no evolution of the mean mass ratio to $z\sim2$ (Mountrichas 2023), while Farrah et al. (2025) show that selection and measurement biases at $z\sim0.8$ reach ~0.6 dex, comparable to claimed evolutionary offsets. At $z\gtrsim3$ , JWST broad-line AGN samples have been reported to violate the local relation at >3σ with black holes overmassive by 1–2 dex and intrinsic scatter near 0.9 dex (Pacucci et al. 2024; Jones et al. 2025; Young et al. 2026), including a dormant black hole at $z=6.68$ about 1000 times above the local mass ratio (Juodžbalis et al. 2024). Yet stacked JADES spectra reveal a population of low-mass black holes within the local relation's scatter (Geris et al. 2025), and a galaxy-selected (rather than AGN-luminosity-selected) sample at $z\sim3$ –5 finds a mean mass ratio consistent with the local value (Li, Shen & Zhuang 2025), implying that selection effects remain a central, unresolved issue. On the physical side, a non-causal scenario in which galaxy mergers average the mass ratio and reduce the scatter over cosmic time has been quantitatively developed (Tanaka et al. 2026), and cosmological simulations with heavy seeds and super-Eddington growth can reproduce overmassive black holes (Chon et al. 2026), while direct reverberation-mapping-based local benchmarks (Bennert et al. 2026) anchor the low-redshift zero point. Whether the relations' zero point and scatter genuinely depend on Eddington ratio, star-formation history, or environment—and what that dependence means physically—is therefore still open.

Problem Statement

Using large, selection-bias-controlled samples of active-galaxy and quasar hosts spanning redshift from the local universe to the highest redshifts at which black hole and host properties can currently be measured, determine: (i) whether the supermassive black hole–host galaxy scaling relations ( $M_{\rm BH}$ – $M_{\rm bulge}$ , versus bulge stellar mass; $M_{\rm BH}$ – $M_{\rm core}$ , versus the mass of the central core component of elliptical galaxies; $M_{\rm BH}$ – $M_{\rm total}$ , versus total galaxy stellar mass; and $M_{\rm BH}$ – $\sigma$ , versus bulge stellar velocity dispersion—increasingly difficult, if not impossible, to measure for the most powerful quasars, especially at higher redshift, for which the source paper notes bulge stellar mass offers a promising alternative) evolve in zero point or intrinsic scatter with cosmic time, quantifying any evolution and its redshift dependence; (ii) whether and how the zero point and scatter of these relations depend on the mass accretion rate as measured by the Eddington ratio $L_{\rm bol}/L_{\rm Edd}$ , on the color or star-formation history of the bulge (including the classical-versus-pseudo bulge distinction), and on the large-scale environment; and (iii) what role galaxy major mergers play in establishing the relations, as tested against the merger fraction and merger signatures in the same samples. These questions are facets of one coherent objective—an empirically grounded physical account of what sets the normalization, scatter, and cosmic evolution of the black hole–host scaling relations. (i), (ii), and (iii) are all required sub-questions, and a resolution must address each; an answer that determines the cosmic evolution or a single dependence axis while leaving the remaining axes or the merger attribution untested does not resolve the task. Where a named relation cannot be measured over part of the demanded redshift range— $M_{\rm BH}$ – $M_{\rm core}$ is defined only for the local elliptical galaxies whose central core component can be resolved, and $M_{\rm BH}$ – $\sigma$ is increasingly difficult, if not impossible, for the most powerful quasars at higher redshift—report the redshift range and sample over which it can be measured and state explicitly what remains unconstrained; such a bounded measurement limit is part of the answer to (i) but does not by itself resolve (ii) or (iii).

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