The implications of overmassive black holes at $z > 5$ for quasar and black hole growth

TL;DR

The paper investigates the implications of overmassive black holes at $z>5$ for the growth and co-evolution of quasars and their host galaxies. By combining BH mass density arguments (Soltan-like growth constraints) with an observed high-$z$ BH–host mass relation and a detailed modeling of halo and galaxy growth, it shows that either the high-$z$ overmassive BH population is extremely rare or that accretion must proceed with unusually high radiative efficiency, or else BH growth from $z\sim5$ to the present would place these systems far from the local $M_{ m BH}$–$M_{*}$ relation. The study also demonstrates that, under average growth histories, these BHs would remain significantly overmassive unless their growth is suppressed by factors ~10 relative to contemporary models, or the high-$z$ sample is not representative. These results have important consequences for understanding quasar feedback, seed formation, and the evolution of the BH–galaxy connection across cosmic time.

Abstract

Recent JWST surveys of high-redshift galaxies have found surprisingly large black holes, with many being measured to be $\sim100$ times more massive than local galaxies with the same stellar mass. Here, we find that a population of these black holes would have dramatic implications for our understanding of their growth across cosmic time. We first show that the global black hole mass density at $z \sim 5$ would be comparable to local values. This would not occur if these black holes occupy a small fraction of galaxies, though it would be expected if these black holes radiate at high efficiencies (requiring that the central engines of AGN spin rapidly). We then show that the individual detected $z \sim 5$ black holes would remain overmassive compared to the local relation if they grow according to the average rates of state-of-the-art models. These systems must instead grow at least an order of magnitude more slowly than expected if they are to fall within the observed scatter of the local black hole mass-stellar mass relation. Such slow growth is surprising in comparison to other estimates of the radiative efficiency of AGN, especially because growth must be rapid at $z > 5$ in order to build up such massive black holes quickly. Finally, we highlight the challenges that overmassive black holes have on our understanding of the impact of quasar feedback on galaxies.

Figures (5)

• Figure 1: A demonstration of scenarios that reconcile the local and high-$z$$M_{\rm BH}$--$M_{*}$ relations on a global level. The black point shows the black hole mass density assuming all galaxies host overmassive black holes described by the $M_{\rm BH}$--$M_{*}$ relation from Pacucci2023_Mbh-Mstar. We use the $z \sim 6$ stellar mass function from Stefanon2021 in the conversion (larger, light gray points). The solid red line is the result of the Soltan argument using the QLF fits from Shen2020_quasar, assuming a radiative efficiency $\epsilon_{r} = 0.1$. The light orange curves show other choices for the radiative efficiency, which depends on the spin of the BH, using the Soltan argument, including $\epsilon_{r} = 0.067$, which is the radiative efficiency estimated by Zhang2025_TrinityVI. Assuming $\epsilon_r=0.1$, we scale the black point to the curve from Shen2020_quasar, and find the fraction of galaxies hosting overmassive black holes to be $f_{\rm over} \lesssim 0.002$, or $\lesssim 0.2 \%$ of galaxies host overmassive black holes. For reference, we show a number of $z = 0$ black hole mass function measurements Marconi2004_local_rhoBHGraham2007_local_rhoBHShankar2009_local_rhoBH and stellar mass function measurements across redshift Stefanon2021Weaver2023_COSMO2020.
• Figure 2: The connection between stellar mass and halo mass in the galaxy growth model, using results from Behroozi2019_UniverseMACHINE. The solid colored curves are the relations from Behroozi2019_UniverseMACHINE spanning $z = 10$ to $z = 0$, marked on the plot. The dotted curves extending from the solid lines are the linear extrapolation of the solid curves in log space. The conversions of the individual galaxies are marked as red stars, with most having $f_{*} = 0.01$--$0.05$. A single galaxy had a particularly high fitted stellar mass which went beyond the stellar mass range in Behroozi2019_UniverseMACHINE for that redshift, so we set it to be $f_*=0.01$.
• Figure 3: The Eddington ratios, $\bar{\eta}$, chosen for each of the galaxies in the sample across redshift, assuming an average BH growth rate according to Zhang2025_TrinityVI (black curves). The initial $\bar{\eta}$ for each of the galaxies is marked as a red star. We choose the average values for $\bar{\eta}$ from Zhang2025_TrinityVI as in this section we explore the evolution of these galaxies hosting overmassive BHs as average galaxies, although we relax the black hole mass growth rate later. We note that the data from Zhang2025_TrinityVI are binned in $\Delta z = 1$, which we interpolated linearly in time for our calculation. When plotted in redshift space for a more convenient presentation, the curves appear to have kinks.
• Figure 4: Top left panel: The predicted evolution across $M_{\rm BH}$--$M_{*}$ of each galaxy using our set of models explained in section \ref{['sec:gal_evol']}. The red points are the starting measurements from our samples Harikane2023_AGNUbler2023Juodvbalis2025_jadesbh, with their respective errorbars (although four points from Harikane2023_AGN are presented with stellar mass upper limits, which we show as upper limits here). The starting points evolve using our set of models across the $M_{\rm BH}$--$M_{*}$ relation in gray to the blue points, which are the predicted end values at $z = 0$, assuming average growth rates. We compare the results to the local relation Reines2015_RV15 in green, with progressively lighter green shades representing the $1$ and $2 \sigma$ scatter in the relation. The majority of the data points lie $> 3 \sigma$ away from the relation, in tension with the belief that these observed high-$z$ galaxies hosting overmassive black holes are universal. Top right panel: The same plot as the top left panel, though we assume a radiative efficiency of $\epsilon_{r} = 0.2$. The errors in the final black hole masses are calculated in the same manner as the top left panel. Here, the points remain above the local relation, but at $1$--$2\sigma$, relaxing but not resolving the tension in the top left panel. This result is interesting in context of figure \ref{['fig:rho_bhs']}, which found black holes radiating at a high efficiency can recover the black hole mass density at $z \sim 5$ assuming all black holes are as overmassive as recent observations suggest. Bottom panel: The same plot as the top panels, except we assume there is zero black hole growth. The errors in the final black hole mass are the original measurement errors. In this case, the points settle near the local relation, and surprisingly recover (approximately) the scatter in the local relation.
• Figure 5: Estimated upper limits on the accretion efficiency, $\bar{\eta}$, for our galaxy sample to connect the observed high-$z$ overmassive black holes to the local $M_{\rm BH}$--$M_{*}$ relation, allowing for the black holes to occupy the upper tail of the local distribution. We show the limits for three scenarios (see text) with occupation fractions of the overmassive black holes, $f_{\rm over} = 0.002,\,0.06,$ and $0.0004$ as black circles, green stars, and red diamonds, respectively. Each point corresponds to one galaxy in our sample. To compare these results with the average results in the Zhang2025_TrinityVI model, we plot the average $\bar{\eta}$ as solid colored lines, spanning $z = 10$ to $z = 0$. As the upper limits on $\bar{\eta}$ are time averages, we plot as a dot-dash blue line the time average of the Zhang2025_TrinityVI model for each initial black hole mass at $z = 5$. The time average is far above the upper limit on $\bar{\eta}$ for nearly every data point, signaling that a much lower BH growth rate is needed for these overmassive BHs than models expect.