How Fast Could Supermassive Black Holes Grow At the Epoch of Reionization?

TL;DR

This work demonstrates that while an early, brief super-Eddington accretion phase can rapidly grow seed black holes in high-redshift halos, AGN feedback subsequently halts this rapid growth, initiating a self-regulated, sub-Eddington regime. Continuous Eddington-limited accretion then provides the fastest sustainable path to assembling SMBHs by z~7–10, implying seed masses of order ten thousand to one hundred thousand solar masses are necessary and must arise from mechanisms other than the self-generated super-Eddington phase. The findings help reconcile the existence of luminous z>6 quasars with the observed SMBH demographics, and they suggest that the common progenitors of massive quasars require substantial initial seeds rather than relying on prolonged super-Eddington accretion alone.

Abstract

Utilizing cosmological hydrodynamic simulations we show that there is a brief super-Eddington accretion phase in typical halos at high redshift, impervious to AGN self-regulation. However, once having attained a black hole mass of $10^4-10^5\msun$, AGN feedback process can self-regulate to guide the SMBHs to grow at a significantly slower, sub-Eddington rate. By redshift $z\sim 10$ the black hole mass with an initial super-Eddington jump-start is caught up by that in the case with a steady Eddington limited case. Thus a continuous Eddington limit case represents the fastest possible route to maximally grow SMBHs. To account for the observed $z=7-10$ quasars with supermassive black holes of billions of solar masses, our analysis establishes firmer ground for the need of seed masses of $10^4-10^5\msun$ that are not grown via an earlier super-Eddington phase.

Figures (4)

• Figure 1: The dark matter projected density, the gas projected density as well as the gas temperature plot shown on the bottom panel, upper right panel and upper right panel respectively at $z=10$. All the length unit in the figure is in physical unit. The zoom-in region contains two halos with $2 \times 10^9 {\rm\,M_\odot} < M_{\rm halo} < 5 \times 10^9 {\rm\,M_\odot}$ at $z \sim 10$.
• Figure 2: Left: The gas density and temperature profiles of our zoom-in halo at $z=10$ are shown in the upper and lower panels, respectively. While the gas density profiles are broadly consistent across different simulations, which agree well with the analytical form presented in 2016MNRAS.459.3738I, the temperature profiles exhibit significant variation. This contrast highlights that, although gravitational collapse governs the overall gas distribution, the thermal state of the gas is highly sensitive to the feedback prescriptions and physical processes included in each simulation. Right: (a) The black hole mass growth curves over time are shown, revealing two distinct phases. Once the black hole reaches a mass of $10^4 - 10^5 {\rm\,M_\odot}$ during the super-Eddington accretion phase, AGN feedback self-regulates its growth, causing it to transition to a slower, approximately Eddington-limited rate. We refer to this stage as the self-regulation phase. (b) The evolution of the black hole accretion rate ($\dot{M}_{acc}$, BHAR) over cosmic time is shown, along with (c) the Eddington ratio $\lambda_{Edd}$, and $\lambda_{Edd} = \dot{M}_{acc}/\dot{M}_{Edd}$, which represents the accretion rate relative to the Eddington limit. During the super-Eddington phase, the black hole accretion rate $\dot{M}_{acc}$ remains close to its maximum $3\times \dot{M}_{Edd}$ in the super-Eddington case and $\dot{M}_{Edd}$ in the Eddington-limited case. However, upon entering the self-regulation phase, only the simulations without feedback or with SN-only feedback in the super-Eddington case can sustain the maximum accretion rate. In contrast, in simulations with AGN feedback, the accretion rate inevitably declines to the Eddington limit, for the range of the implemented AGN feedback strength or the suite of SN feedback models employed.
• Figure 3: (a) The distribution of the transition black hole mass $M_{\rm sink}^t$ determined by the average gas density $<n>$, and the average gas temperature $<T>$. The black star represents the typical value obtained from our simulations, while the red region highlights the range where $M_{\rm sink}^t$ falls between $10^4 - 10^5 \, M_{\odot}$.(b) The time evolution of the sound speed near the black hole, $c_s$, is shown, while (c) presents the squared gas density in spherical shells as a function of radius centered on the black hole times radius cubed, $n^2 R^3$, where the area under the curve is proportional to the cooling rate contribution. (d, e, f) The evolution of stellar mass, total gas mass, hot gas mass, and cold gas mass over time for two regions: the galaxy region ($0.1 R_{\rm vir}$) and the black hole region ($0.01 R_{\rm vir}$). Panel (d) corresponds to the SN-only case with $\lambda_{\rm Edd} < 3$, panel (e) to $\epsilon_q = 0.15$, $\epsilon_j = 0.05$, and $\lambda_{\rm Edd} < 3$, and panel (f) to $\epsilon_q = 0.15$, $\epsilon_j = 0.05$, and $\lambda_{\rm Edd} < 1$. Once SMBHs reach masses of $10^4 - 10^5 \, M_{\odot}$, their growth transitions to a self-regulated phase, driven by AGN feedback that expels gas from the surrounding region. This process ultimately regulates accretion, with higher accretion rates leading to stronger feedback.
• Figure 4: Following 2025arXiv250504609T, we present the redshifts and black hole masses from our simulations, along with the population of spectroscopically confirmed quasars at $z > 6$. We also include a simple growth model for $10^2\,{\rm\,M_\odot}$ (blue shading) and $10^4\,{\rm\,M_\odot}$ (red shading) black hole seeds accreting at the Eddington limit. A vertical black dotted line marks the transition from the super-Eddington accretion phase to the self-regulation phase. By $z \sim 10$, the SMBH in the more steady, Eddington-limited scenario surpasses its initially super-Eddington jump-start counterpart in mass, indicating that the Eddington-limited mode provides the fastest sustainable pathway for SMBH growth. To account for the $\gtrsim 10^9\,{\rm\,M_\odot}$ quasars observed at $z = 7$–10, seed black holes with initial masses of $10^4$–$10^5\,{\rm\,M_\odot}$ are required.