Super-Eddington accretion in protogalactic cores

Abstract

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 explored 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 overmassive 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 when starting from light seeds.

Figures (11)

• Figure 1: Evolution of the BH mass for all the tested BH seeds, grouped by $\epsilon_{\rm c}$. Different colours indicate the initial BH mass, whereas the line style denotes the BH spin: solid lines for $a = 0.99$ and dashed lines for $a = 0$. The $x$-axis is shown using a symmetric logarithmic scale with a linear threshold of $10^{-2}$ to allow visibility near $t = 0$ while preserving a logarithmic behaviour at larger values.
• Figure 2: Evolution of the accreted mass $\Delta M_{\rm BH} \equiv M_{\rm BH}(t)-M_{\rm BH}(t_{\rm i})$ for all the tested BH seeds with $a = 0.99$ and different coupling efficiencies. Each plot refers to a different initial mass. Different colours indicate the coupling efficiency $\epsilon_{\rm c}$. The same symmetric logarithmic scale and linear threshold of Fig. \ref{['fig:bhmass_evol_eps']} are adopted here.
• Figure 3: Accreted mass $\Delta M_{\rm BH}~[{\rm M_{\sun}}]$ (left-hand column) and Eddington ratio $f_{\rm Edd} \equiv \dot{M}_{\rm acc} / \dot{M}_{\rm Edd}$ (right-hand column) evolution grouped by feedback intensity for three regimes -- $\epsilon_{\rm c} = 0$, $10^{-3}$, and $5 \times 10^{-3}$ -- from top to bottom, assuming a spin of $a = 0.99$. The Eddington limit is marked by the dashed black line. The same colour-coding and symmetric logarithmic $x$-axis as in Fig. \ref{['fig:bhmass_evol_eps']} are used throughout. In the bottommost left-hand panel, the yellow curve is nearly indistinguishable from the purple one, as the two are almost perfectly overlapped.
• Figure 4: Evolution of the BH mass for rapidly rotating seeds ($a = 0.99$) in the absence of feedback ($\epsilon_{\rm c} = 0$). Solid lines show the SE runs for $M_{\rm BH}(t_{\rm i}) = 5 \times 10^2$ (blue) and $10^5~\mathrm{M}_{\sun}$ (purple), whereas dashed lines indicate the corresponding Eddington-limited cases, shown for comparison with a fixed radiative efficiency of $\epsilon_{\rm r} = 0.1$.
• Figure 5: Left-hand panels: Evolution of the total gas mass (solid lines) and stellar mass (dashed lines) within the entire disc for the three feedback cases under analysis (i.e. $\epsilon_{\rm c} = 0$, $10^{-3}$, and $5 \times 10^{-3}$, from top to bottom). The inset magnifies the terminal part of the stellar evolution lines in the top-left panel (the no-feedback case), where the curves overlap. The right-hand panels show the evolution of the $M_{\rm BH}/M_{*}$ ratio. Different colours indicate the various initial BH masses, following the same colour scheme used in Fig. \ref{['fig:bhmass_evol_eps']}. For reference, the Eddington-limited ('EL' in the figure) cases with $M_{\rm BH}(t_{\rm i})=5\times10^2$ and $M_{\rm BH}(t_{\rm i})=10^5$ and $\epsilon_{\rm c} = 0$ are included in the corresponding panel. The same symmetric logarithmic scale and linear threshold of Fig. \ref{['fig:bhmass_evol_eps']} are applied to the $x$-axis in the left-hand column, whereas a full logarithmic scale is used in the right-hand column, with the origin set at $t = 10^{-2}$ Myr, approximately corresponding to the onset of the first SF episodes.