On the convective instability of hot radiative accretion flows

How many fraction of gas available at the outer boundary can finally fall onto the black hole is an important question. It determines the observational appearance of accretion flows, and is also related with the evolution of black hole mass and spin. Previous two-dimensional hydrodynamical simulations of hot accretion flows find that the flow is convectively unstable because of its inward increase of entropy. As a result, the mass accretion rate decreases inward, i.e., only a small fraction of accretion gas can fall onto the black hole, while the rest circulates in the convective eddies or lost in convective outflows. Radiation is usually neglected in these simulations. In many cases, however, radiative cooling is important. In the regime of the luminous hot accretion flow (LHAF), radiative cooling is even stronger than the viscous dissipation. In the one dimensional case, this implies that the inward increase of entropy will become slower or the entropy even decreases inward in the case of an LHAF. We therefore expect that convective instability becomes weaker or completely disappears when radiative cooling is important. To examine the validity of this expectation, in this paper we perform two-dimensional hydrodynamical simulations of hot accretion flows with strong radiative cooling. We find that compared to the case of negligible radiation, convection only becomes slightly weaker. Even an LHAF is still strongly convectively unstable, its radial profile of accretion rate correspondingly changes little. We find the reason is that the entropy still increases inward in the two-dimensional case.

💡 Research Summary

The paper addresses a fundamental question in accretion theory: what fraction of gas supplied at large radii ultimately reaches the black hole? Earlier two‑dimensional (2‑D) hydrodynamic simulations of hot, radiatively inefficient accretion flows (ADAFs) have shown that the inward increase of entropy makes the flow convectively unstable. Convection then transports a large part of the inflowing material into turbulent eddies or outflows, causing the mass accretion rate to decline with decreasing radius. Those simulations, however, ignored radiative cooling, which can be significant in many astrophysical contexts. In the luminous hot accretion flow (LHAF) regime, radiative losses even exceed viscous heating, and one‑dimensional analytical models predict that the entropy gradient may flatten or become negative, potentially suppressing convection.

To test this expectation, the authors performed new 2‑D axisymmetric hydrodynamic simulations that explicitly include radiative cooling processes (Bremsstrahlung, synchrotron emission, and inverse‑Compton scattering) together with an α‑viscosity prescription (α = 0.01) and a Paczyński‑Wiita pseudo‑Newtonian potential. They initialized the simulations with a self‑similar ADAF solution and explored a range of mass accretion rates (ṁ ≈ 10⁻³–10⁻¹) that span the transition from ADAF to LHAF. The computational grid (256 × 128 in r–θ) was fine enough to resolve convective eddies and the vertical transport of heat.

The results are strikingly contrary to the naive expectation that strong cooling would quench convection. Even in the LHAF cases where cooling dominates, the entropy still rises inward, albeit with a slightly reduced gradient compared to the cooling‑free runs. Consequently, the Solberg‑Høiland criterion remains satisfied for convective instability, and vigorous convective motions persist. The convective vigor is modestly weakened (by roughly 10–20 % in velocity amplitude), but the radial profile of the accretion rate (ṁ ∝ r^s with s ≈ 0.5) changes little. The authors attribute this resilience of convection to the two‑dimensional nature of the flow: vertical (θ‑direction) heat transport and centrifugal support redistribute entropy in a way that a one‑dimensional model cannot capture.

In summary, the study demonstrates that radiative cooling, even when energetically dominant, does not eliminate convection in hot accretion flows. The entropy gradient stays positive, convection remains strong, and the inward decline of the mass accretion rate is largely unchanged. The work suggests that future three‑dimensional magnetohydrodynamic simulations, which incorporate both magnetic stresses and realistic radiation physics, are needed to fully understand how convection, cooling, and outflows interact in the vicinity of black holes.