Super-Eddington accretion in protogalactic cores

The presence of massive black holes (BHs) exceeding $10^9,{\rm M}{\odot}$ already at redshift $z > 6$ challenges standard models of BH growth. Super-Eddington (SE) accretion has emerged as a promising mechanism to solve this issue, yet its impact on early BH evolution in tailored numerical experiments remains largely unexplored. In this work, we investigate the growth of BH seeds embedded in a gas-rich, metal-poor protogalaxy at $z \sim 15$, using a suite of high-resolution hydrodynamical simulations that implement a slim-disc-based SE accretion model. We explore a broad parameter space varying the initial BH mass, feedback efficiency, and spin. We find that SE accretion enables rapid growth in all cases, allowing BHs to accrete up to $10^5,{\rm M}{\odot}$ within a few $10^3$-$10^4$ years, independent of seed properties. Feedback regulates this process, both by depleting central gas and altering BH dynamics via star formation-driven potential fluctuations, yet even the strongest feedback regimes permit significantly greater growth than the Eddington-limited case. Growth stalls after less than $\sim$1 Myr due to local gas exhaustion, as no large-scale inflows are present in the adopted numerical setup. Our results show that SE accretion naturally leads to BHs that are over-massive relative to their host galaxy stellar content, consistent with JWST observations. We conclude that short, low-duty-cycle SE episodes represent a viable pathway for assembling the most massive BHs observed at early cosmic times, even starting from light seeds.

💡 Research Summary

The paper addresses the long‑standing problem of how supermassive black holes (SMBHs) with masses ≳10⁹ M⊙ could already exist at redshifts z > 6, a challenge for standard Eddington‑limited growth models. The authors explore whether super‑Eddington (SE) accretion, modeled with a slim‑disc prescription that reduces the radiative efficiency ϵᵣ as a function of accretion rate and black‑hole spin, can enable rapid early growth in a controlled, high‑resolution environment.

Using an updated version of the SPH code G asoline 2, they embed black‑hole seed particles in an idealized, metal‑poor (Z≈10⁻³ Z⊙), gas‑rich protogalactic core at z≈15. The host halo has a total mass of 10⁸ M⊙, with gas densities >5 mp cm⁻³ and temperatures below 1.5×10⁴ K. The black‑hole seeds are assigned initial masses of 10², 10³, or 10⁴ M⊙. For each seed mass the authors vary two additional parameters: (i) the feedback coupling efficiency ϵ_c (0.01, 0.05, 0.1) and (ii) the spin parameter a (non‑rotating a = 0 and near‑maximally rotating a = 0.99). Accretion follows the Bondi‑Hoyle‑Lyttleton formula with a boost factor α = 1, evaluated over 64 neighbour particles. Crucially, the Eddington cap is removed and the radiative efficiency is computed from the analytic fit of Madau et al. (2014) to the relativistic slim‑disc solutions (eqs. 5‑7). Thermal feedback injects a fraction ϵ_c L into the surrounding gas.

Across the entire parameter space, the simulations show that SE accretion drives black‑hole masses up to ≈10⁵ M⊙ within a few 10³–10⁴ yr, essentially independent of the seed mass. Stronger feedback depletes the central gas more quickly, shortening the growth phase, but even the most aggressive feedback cases still produce final masses 1–2 dex higher than any Eddington‑limited run. Spin influences the radiative efficiency modestly: the a = 0.99 runs have ≈20 % lower growth rates because of higher ϵᵣ, yet the overall growth pattern remains robust. After ≈1 Myr the central gas reservoir is exhausted, and accretion stalls because the simulation does not include large‑scale inflows or mergers. This “closed‑box” limitation makes the results a conservative lower bound; in a realistic cosmological setting, repeated gas supply episodes could sustain SE phases for longer periods.

The authors connect these findings to recent JWST observations that reveal high‑z quasars with black‑hole‑to‑stellar‑mass ratios well above the local M_BH–M_* relation. The short, low‑duty‑cycle SE bursts demonstrated here naturally produce over‑massive black holes relative to their host stellar content, supporting the idea that SE accretion is a viable pathway for building the earliest SMBHs, even from light Pop III remnants.

The paper also discusses limitations: (1) the absence of external gas inflow, (2) the assumption of a fixed spin (no angular momentum evolution), and (3) the use of purely thermal feedback without explicit radiation‑transfer or jet physics. The authors suggest future work incorporating cosmological inflows, spin evolution, and more sophisticated radiative‑hydrodynamic treatments to assess the long‑term co‑evolution of black holes and their host galaxies. In summary, the study provides a detailed, high‑resolution demonstration that SE accretion can dramatically accelerate early black‑hole growth, offering a compelling solution to the high‑redshift SMBH problem and aligning with the emerging JWST data.