Physical validation of the central-molecular-cloud-fed growth scenario for supermassive black holes: origin and gigayear persistence of the quasi-universal CMC parameters

The tight correlation between supermassive black hole (SMBH) mass and host bulge mass, and the down-sizing of active galactic nuclei (AGN), are cornerstone observations of black-hole-galaxy co-evolution whose mechanistic origin is still debated. Inoue (2025) proposed a semi-analytic scenario in which the SMBH grows from a Population II seed black hole embedded in the dense core of a persistent central molecular cloud (CMC) sitting at the bottom of the potential of the nuclear region of a $z\sim10$ proto-bulge, is fed beyond the CMC mass by gas supplied through interactions of the CMC with the ambient molecular cloud population while its wandering motion is sustained, and stops growing when dynamical friction from field stars halts the wandering; with a CMC of mass $\sim10^7M_\odot$ and radius $\sim10$ pc adopted as fitted inputs, the scenario reproduces both observed relations. The open problem is the physical validation of this scenario beyond the order-of-magnitude level: the origin and $\sim1$ Gyr maintenance of CMC parameters nearly independent of nuclear-region mass — the selection of which the source explicitly leaves open to future study — together with the efficiency of CMC gas replenishment by cloud-cloud interactions, the sensitivity of the result to the star-formation law and cloud-population assumptions, the behavior below nuclear-region masses $\sim10^8M_\odot$ and its demographic signature in relic nuclear star clusters, and the justification for neglecting accretion-rate suppression and outflows. No detailed dynamical or hydrodynamical test, refinement, or refutation of the scenario exists in the literature.

Background

Nearly every massive galaxy hosts a supermassive black hole (SMBH, $10^6$-$10^{10}M_\odot$) whose mass is tightly correlated with properties of the host bulge (the spheroidal central stellar component of a galaxy), approximately $M_{\rm smbh}\simeq5\times10^{-3}M_{\rm blg}$ (Kormendy & Ho 2013). X-ray surveys of active galactic nuclei (AGN, i.e. accreting SMBHs) further show down-sizing: the most luminous, most massive AGN were most active earliest in cosmic history, expressible as $t_{\rm agn}\simeq10^{9.5}(M_{\rm bh}/10^7M_\odot)^{-0.25}$ yr for the age of the Universe at peak AGN activity (Ueda et al. 2014; the observational trend box adopted by Inoue is Figure 7 of Fan, Bañados & Simcoe 2023). Explaining both relations from a growth mechanism is a central problem of black-hole-galaxy co-evolution; the standard explanations regulate growth through AGN feedback, e.g. momentum-driven winds in which radiation pressure from the accreting black hole drives a wind whose thrust balances the weight of the galaxy's interstellar gas (King 2003).

Inoue (2025) proposes an alternative channel in which feedback plays no regulatory role. Primordial gas collapsing at $z\sim10$ forms a proto-bulge modeled as a self-gravitating isothermal sphere; its dense core, called the nuclear region (NR, mass $M_{\rm nr}$), is fragmented into molecular clouds (MCs, cold dense gas clouds with typical Galactic masses of $10^5$-$10^6M_\odot$ and sizes of tens of parsecs; Fukui & Kawamura 2010). Black-hole seeds formed from Population II stars (metal-poor early-generation stars) born in the core of the central molecular cloud (CMC) — the most massive gas condensation, sitting at the bottom of the NR potential — accrete at the high ambient density ($\sim3\times10^8\ \mathrm{cm}^{-3}$ for a CMC of $10^7M_\odot$ and boundary radius $10$ pc) needed to grow from $\lesssim10^2M_\odot$ to $10^6$-$10^9M_\odot$ within $\sim1$ Gyr, as down-sizing requires; seeds formed from Population III stars in mini-halos at $z\sim20$-30 are argued to fail this residence-time requirement. The most massive black hole (MMBH) monopolizes the CMC core gas, because its Bondi radius (the radius within which the black hole's gravity dominates the gas thermal energy) becomes comparable to the core size, and it can grow beyond the CMC mass only if interactions between the CMC and the ambient, restlessly rearranging MC population replenish the CMC gas. The MMBH wanders through the central region under the gravitational pull of the nearest MCs; above a boundary mass, set by the balance between that pull and dynamical friction (the braking force on a massive body moving through a stellar system, produced by gravitational deflection of the ambient field stars), the wandering is damped and accretion ceases. The boundary mass can be made proportional to $M_{\rm nr}$, reproducing the SMBH-bulge relation for a specific parameter set: a saturated MC number $N_{\rm mc}=N_{\rm mc,1}$ (the regime in which typical-size MCs fill the whole NR volume), typical MC radius $R_{\rm mc,0}=30$ pc, star-formation-law exponent $\beta\approx1.8$ (versus the canonical $\beta\simeq1.4$), and an MC-direction-change time $t_{\rm mc}=\alpha t_{\rm sf}$ with $\alpha\approx0.02$, where $t_{\rm sf}$ is the NR star-formation time scale. Sustained growth assumes no suppression of the accretion rate, justified by advection in super-Eddington accretion (accretion above the classical Eddington luminosity limit, made possible when the flow is so dense that much of the generated radiation is swallowed inward rather than radiated — the slim-disk regime; Inoue 2024). Relic CMCs are identified with nuclear star clusters (NSCs, compact massive star clusters at galactic centers), whose observed masses and radii indeed peak near $10^7M_\odot$ and a few parsecs, and whose incidence is observed to drop in galaxies above $\sim10^{10}M_\odot$ (Neumayer, Seth & Böker 2020) — a trend the scenario attributes to CMC disruption once the MMBH outgrows it.

All of this is order-of-magnitude and semi-analytic: the CMC is treated as a static isothermal sphere, the MC system through average properties, and the MMBH orbit through a nearest-cloud force balance, and the CMC mass and radius are fitted inputs rather than derived quantities. The paper itself states that the study depends on disputable premises, is on the level of order estimation, and that more detailed studies are needed.

Problem Statement

Inoue (2025) proposes that SMBHs grow from Population II seed black holes embedded in the dense core of a central molecular cloud at the bottom of the potential of the nuclear region of a $z\sim10$ proto-bulge, with the most massive black hole sustained beyond the CMC mass by gas supplied through interactions of the CMC with the ambient molecular cloud population, until dynamical friction from field stars halts its wandering and its growth; the order-of-magnitude analytic treatment reproduces the SMBH-bulge mass correlation ($M_{\rm smbh}\simeq5\times10^{-3}M_{\rm blg}$) and the AGN down-sizing relation ($t_{\rm agn}\simeq10^{9.5}(M_{\rm bh}/10^7M_\odot)^{-0.25}$ yr) for a fitted CMC of mass $\sim10^7M_\odot$ and radius $\sim10$ pc, a saturated MC number $N_{\rm mc}=N_{\rm mc,1}$ with typical MC radius $R_{\rm mc,0}=30$ pc, star-formation exponent $\beta\approx1.8$, and $t_{\rm mc}=\alpha t_{\rm sf}$ with $\alpha\approx0.02$. The open problem, in the generality stated by the source, is to establish — through detailed dynamical and hydrodynamical modelling beyond order-of-magnitude estimates, and/or through observational tests — whether this scenario is physically viable, by resolving its interlinked unresolved premises:

(1) the physical origin and maintenance of the CMC parameters: why a CMC of mass $\sim10^7M_\odot$ and radius $\sim10$ pc is selected, and kept nearly constant over the $\sim1$ Gyr growth interval, almost independently of the NR mass, although the ambient MC distribution is expected to change on a $\sim10$ Myr scale — the selection of these parameters being what the source explicitly leaves open to future study, and their persistence being reconciled there only qualitatively;

(2) the efficiency and time-dependence of CMC gas replenishment through CMC-MC interactions, and the assumed time scale $t_{\rm mc}$ for direction changes of the nearest MC, which together determine whether the MMBH can grow beyond the CMC mass up to the boundary mass at which dynamical friction halts the wandering;

(3) the sensitivity of the reproduced SMBH-bulge proportionality to the adopted MC-population and star-formation-law parameters ($N_{\rm mc}=N_{\rm mc,1}$, $R_{\rm mc,0}=30$ pc, $\beta\approx1.8$, $\alpha\approx0.02$);

(4) the fate of the scenario at low NR masses ($M_{\rm nr}\lesssim10^8M_\odot$), where the MC number drops to order unity, CMC-MC interactions cannot drive the extra gas supply, and the mass-correlation argument breaks down — with observable consequences for relic nuclear star clusters versus SMBHs; and

(5) whether neglecting accretion-rate suppression and outflow-mediated mass loss (i.e. assuming sustained, effectively advective super-Eddington accretion) is justified.

These premises are individually necessary and jointly load-bearing for one overarching objective: a complete answer either demonstrates, with self-consistently determined rather than fitted CMC parameters, that the scenario quantitatively reproduces both target relations and the observed NSC demographics — resolving all five premises and matching the normalizations and slopes of the two relations rather than only their order of magnitude — or identifies which premise fails and shows that this failure is load-bearing, i.e. that it breaks the reproduction of those relations or demographics, and thereby refutes the scenario as the origin of the SMBH-bulge correlation and AGN down-sizing.

References

1. Inoue, H. 2025, 'Evolution of massive black holes in galactic nuclei', Publications of the Astronomical Society of Japan 77, 208, DOI 10.1093/pasj/psae110, arXiv:2412.20492, https://arxiv.org/abs/2412.20492
2. Inoue, H. 2021, 'Wandering of the central black hole in a galactic nucleus and correlation of the black hole mass with the bulge mass', Publications of the Astronomical Society of Japan 73, 431, DOI 10.1093/pasj/psab009, arXiv:2102.03478, https://arxiv.org/abs/2102.03478
3. Inoue, H. 2024, 'Relativistic jet ejections from slim disks', The Astrophysical Journal 967, 3, DOI 10.3847/1538-4357/ad3937, arXiv:2404.03684, https://arxiv.org/abs/2404.03684
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