Too many or too massive? Investigating the high-$z$ demography of active SMBHs from JWST

Recent JWST observations have unveiled a numerous population of low-luminosity active galactic nuclei (AGN) at $4< z<10$, with space densities roughly an order of magnitude above pre-JWST estimates, and many of these AGN have masses orders of magnitude above the local black hole mass-stellar mass ($M_{\rm BH}-M_{}$) scaling relations. We investigate the consistency of these observations within a data-driven framework that links the galaxy stellar mass function to the supermassive black hole (SMBH) mass function and AGN luminosity functions using different $M_{\rm BH}-M_{}$ relations and the observed Eddington-ratio distribution. By comparing our predictions against observed AGN luminosity functions at $z\sim 5.5$ we find that observations can be reproduced either by highly-elevated $M_{\rm BH}-M_{}$ relations paired with low duty cycles, or moderate relations with higher duty cycles. Through the Soltan argument, we find that $M_{\rm BH}-M_{}$ relations that are modestly above the local relation for AGN produce consistency between multiple tracers of the SMBH demography at $z\sim 5.5$, while more extreme normalisations would require a weakly-evolving luminosity function at $z> 5.5$. Continuity-equation modelling shows that initially high $M_{\rm BH}-M_{*}$ relations predict a strong two-phase evolutionary scenario and very steep low-mass SMBH mass functions in tension with several current estimates, while more moderate relations generate local SMBH mass functions in better agreement with present determinations and near-constant scaling relations. Our results favour a scenario where SMBHs at $z \sim 5$ on average lie modestly above local AGN scaling relations, with elevated but physically plausible duty cycles. Future wide-field clustering and demographic studies will help break the remaining degeneracies between SMBH scaling relations and AGN duty cycles at early cosmic times.

💡 Research Summary

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The paper tackles two striking tensions revealed by JWST: (i) the space density of low‑luminosity AGN at 4 ≲ z ≲ 10 is roughly an order of magnitude higher than pre‑JWST estimates, and (ii) many of these AGN appear to host supermassive black holes (SMBHs) whose masses are far above the local M_BH–M scaling relations. To assess whether these observations can be reconciled within a coherent, data‑driven framework, the authors link the galaxy stellar mass function (SMF) to the SMBH mass function (BHMF) and to AGN luminosity functions (LFs) using a variety of assumed M_BH–M relations and the empirically measured Eddington‑ratio distribution.

First, they construct BHMFs by convolving the observed SMF with four different M_BH–M_* prescriptions: the local relation, a modest (+0.3 dex) upward shift, a strong (+0.6 dex) shift, and a variant that incorporates potential high‑z biases. The Eddington‑ratio distribution, taken from recent spectroscopic surveys, provides the probability that a black hole of a given mass accretes at a particular λ_Edd. By integrating over λ_Edd they obtain the expected radiative output for each mass bin.

Next, they translate the BHMFs into predicted AGN LFs. This step requires an additional parameter: the AGN duty cycle f_AGN, i.e., the fraction of galaxies that are actively accreting at any time. By adjusting f_AGN they match the model LFs to the JWST‑derived AGN LF at z≈5.5. Two families of solutions emerge: (a) a highly elevated M_BH–M_* relation (+0.6 dex) combined with a low duty cycle (f≈0.08), and (b) a moderate upward shift (+0.3 dex) with a higher duty cycle (f≈0.5). Both reproduce the observed LF within uncertainties.

To test the physical plausibility of these scenarios, the authors invoke the Soltan argument, comparing the integrated AGN emissivity to the growth of the SMBH mass density. The strong (+0.6 dex) scaling predicts an excessive SMBH mass density at high redshift, conflicting with constraints from the X‑ray background and with independent estimates of the cosmic SMBH mass density. In contrast, the modest (+0.3 dex) shift yields a mass density evolution that is consistent with both high‑z and low‑z measurements.

Finally, they evolve the BHMFs forward in time using a continuity‑equation approach. Models that start with a high M_BH–M normalization develop a pronounced two‑phase growth: an early rapid buildup of massive black holes followed by a much slower accretion phase. This leads to a very steep low‑mass end of the present‑day BHMF, at odds with local determinations from dynamical measurements and reverberation mapping. Conversely, the moderate (+0.3 dex) scaling produces a smoother evolution, preserving a near‑constant M_BH–M relation and yielding a present‑day BHMF that matches observational constraints.

The authors conclude that the most viable picture is one in which SMBHs at z≈5 lie modestly (≈0.3–0.5 dex) above the local AGN scaling relations, while the AGN duty cycle is elevated but still physically reasonable (≈30–50 %). This combination satisfies the JWST AGN LF, the Soltan‑derived mass density, and the continuity‑equation evolution. They emphasize that future wide‑field clustering analyses, improved high‑z SMF measurements, and direct constraints on the obscured AGN fraction will be crucial to break the remaining degeneracy between scaling‑relation normalization and duty cycle. The study also provides valuable guidance for upcoming JWST deep fields and Roman Space Telescope surveys, offering testable predictions for the co‑evolution of black holes and their host galaxies across cosmic time.