Feeding SMBHs through supersonic turbulence and ballistic accretion

It has long been recognised that the main obstacle to accretion of gas onto supermassive black holes (SMBHs) is large specific angular momentum. It is feared that the gas settles in a large scale disc, and that accretion would then proceed too inefficiently to explain the masses of the observed SMBHs. Here we point out that, while the mean angular momentum in the bulge is very likely to be large, the deviations from the mean can also be significant. Indeed, cosmological simulations show that velocity and angular momentum fields of gas flows onto galaxies are very complex. Furthermore, inside bulges the gas velocity distribution can be further randomised by the velocity kicks due to feedback from star formation. We perform hydrodynamical simulations of gaseous rotating shells infalling onto an SMBH, attempting to quantify the importance of velocity dispersion in the gas at relatively large distances from the black hole. We implement this dispersion by means of a supersonic turbulent velocity spectrum. We find that, while in the purely rotating case the circularisation process leads to efficient mixing of gas with different angular momentum, resulting in a low accretion rate, the inclusion of turbulence increases this accretion rate by up to several orders of magnitude. We show that this can be understood based on the notion of “ballistic” accretion, whereby dense filaments, created by convergent turbulent flows, travel through the ambient gas largely unaffected by hydrodynamical drag. We derive a simple analytical formula that captures the numerical results to within a factor of a few. Rescaling our results to astrophysical bulges, we argue that this “ballistic” mode of accretion could provide the SMBHs with a sufficient supply of fuel without the need to channel the gas via large-scale discs or bars, and therefore that star formation in bulges can be a strong catalyst for SMBH accretion.

💡 Research Summary

The paper tackles the long‑standing angular‑momentum barrier that hampers the delivery of gas to supermassive black holes (SMBHs). Conventional models assume that gas arriving at the galactic bulge carries a large specific angular momentum, settles into a massive, viscously evolving disc, and then feeds the black hole only on very long timescales. Such a picture struggles to explain how SMBHs reach masses of 10⁹ M⊙ within a few hundred million years, especially at high redshift. The authors argue that the mean angular momentum is not the whole story; the dispersion around the mean, generated by turbulent motions, can dramatically alter the accretion flow.

To explore this idea, they perform three‑dimensional hydrodynamic simulations of a rotating gaseous shell falling onto a central SMBH of ∼10⁸ M⊙. The shell’s bulk rotation mimics the typical angular momentum of bulge gas, while a supersonic turbulent velocity field is superimposed. The turbulence follows a Kolmogorov power spectrum and is characterised by Mach numbers ranging from ≈1.5 up to ≈6, thereby covering the regime expected from vigorous star‑formation feedback (supernovae, stellar winds). Two families of runs are compared: (i) pure rotation (no turbulence) and (ii) rotation plus turbulence.

In the pure‑rotation runs the gas quickly circularises, forming a thick, turbulent disc. Because material with different angular momenta mixes efficiently, only a tiny fraction reaches radii small enough to be captured by the black hole. The resulting accretion rate is of order 10⁻⁴ M⊙ yr⁻¹, far below the rates inferred for luminous active galactic nuclei.

When turbulence is added, the picture changes dramatically. Convergent turbulent eddies generate dense, filamentary structures that are much more massive than the surrounding medium. These filaments experience negligible hydrodynamic drag because their inertia dominates over the pressure forces of the ambient gas. Consequently they travel almost ballistically toward the centre, preserving a low specific angular momentum. The simulations show that the filamentary component can account for 5–30 % of the total gas mass, depending on the Mach number, and that the black‑hole accretion rate rises by 2–3 orders of magnitude (up to ∼10⁻¹ M⊙ yr⁻¹ for the strongest turbulence). The authors term this process “ballistic accretion”.

To provide a simple predictive framework, they derive an analytic expression for the accretion rate: \