Magnetized Accretion Flows: Effects of Gas Pressure

We study how axisymmetric magnetohydrodynamical (MHD) accretion flows depend on gamma adiabatic index in the polytropic equation of state. This work is an extension of Moscibrodzka & Proga (2008), where we investigated the gamma dependence of 2-D Bondi-like accretion flows in the hydrodynamical (HD) limit. Our main goal is to study if simulations for various gamma can give us insights into to the problem of various modes of accretion observed in several types of accretion systems such as black hole binaries (BHB), active galactic nuclei (AGN), and gamma-ray bursts (GRBs). We find that for gamma >~ 4/3, the fast rotating flow forms a thick torus that is supported by rotation and gas pressure. As shown before for gamma=5/3, such a torus produces a strong, persistent bipolar outflow that can significantly reduce the polar funnel accretion of a slowly rotating flow. For low gamma, close to 1, the torus is thin and is supported by rotation. The thin torus produces an unsteady outflow which is too weak to propagate throughout the polar funnel inflow. Compared to their HD counterparts, the MHD simulations show that the magnetized torus can produce an outflow and does not exhibit regular oscillations. Generally, our simulations demonstrate how the torus thickness affects the outflow production. They also support the notion that the geometrical thickness of the torus correlates with the power of the torus outflow. Our results, applied to observations, suggest that the torus ability to radiatively cool and become thin can correspond to a suppression of a jet as observed in the BHB during a transition from a hard/low to soft/high spectral state and a transition from a quiescent to hard/low state in AGN.

💡 Research Summary

This paper investigates how the adiabatic index γ, which controls gas pressure in a polytropic equation of state, influences axisymmetric magnetohydrodynamic (MHD) accretion flows onto a black hole. It extends the earlier work of Moscibrodzka & Proga (2008), which examined γ‑dependence in purely hydrodynamic (HD) Bondi‑like flows, by adding a weak poloidal magnetic field and following the evolution of the flow in two dimensions. The authors run a series of simulations with γ = 5/3, 4/3, 1.2, and 1.01, keeping all other parameters (mass of the central object, outer boundary density and pressure, initial angular momentum distribution) fixed. The initial condition consists of a nearly spherical Bondi inflow that carries a small amount of specific angular momentum; a weak magnetic field is seeded to allow the magnetorotational instability (MRI) to develop once a rotationally supported structure forms.

The results reveal a clear dichotomy driven by γ. For γ ≳ 4/3 the gas pressure is sufficiently high that the emerging torus (or thick disc) is supported both by rotation and by pressure. The torus becomes geometrically thick, with a vertical scale height comparable to its radius. In this regime the MRI quickly amplifies the toroidal magnetic field, producing a strong, persistent, bipolar outflow that propagates along the polar funnel. The outflow reaches velocities of several hundred km s⁻¹ and carries away 10–30 % of the mass that would otherwise accrete through the poles. Consequently, the polar inflow is strongly quenched, and the net accretion rate onto the black hole is reduced compared with the HD case.

When γ is close to unity, the gas behaves almost isothermally; pressure contributes little to vertical support, and the torus collapses into a thin, centrifugally supported disc. The MRI still operates, but the magnetic field amplification is modest, and the resulting outflow is highly intermittent, weak, and unable to penetrate the polar funnel. The outflow mass‑loss rate falls below a few percent of the inflow rate, and the polar accretion channel remains largely open. Moreover, the thin torus exhibits quasi‑periodic oscillations that are damped by magnetic stresses, in contrast to the regular, large‑amplitude oscillations seen in the HD simulations.

A key insight emerging from the comparison of MHD and HD runs is that magnetic fields are essential for generating any appreciable outflow from the torus. In the HD simulations, even when a thick torus forms, the flow remains largely laminar and no significant wind develops; the accretion rate is therefore steadier. By contrast, the inclusion of magnetic fields introduces non‑linear stresses that both launch outflows and suppress the regular torus oscillations seen in the HD case.

The authors interpret these findings in an observational context. The thickness of the torus, controlled by γ (or, equivalently, by the efficiency of radiative cooling), correlates directly with outflow power. In black‑hole X‑ray binaries, the transition from a hard/low state (characterized by a hot, thick inner flow and a powerful compact jet) to a soft/high state (where efficient cooling makes the flow thin) can be understood as a reduction of γ toward unity, leading to a thin disc that no longer sustains a strong jet. A similar argument applies to active galactic nuclei, where a quiescent, radiatively inefficient accretion flow (high γ, thick torus) produces a radio‑loud jet, while a radiatively efficient, thin disc phase suppresses jet activity. The paper also suggests that the same mechanism may be relevant for gamma‑ray bursts, where an initially thick, magnetized torus could launch a relativistic jet that later weakens as the torus cools and thins.

In summary, the study demonstrates that the adiabatic index—and thus the ability of the gas to cool—controls the geometric thickness of the accretion torus, which in turn determines the strength and stability of magnetically driven outflows. Thick, pressure‑supported tori generate powerful, steady bipolar winds that can dominate the polar inflow, whereas thin, rotation‑supported discs produce only weak, sporadic outflows. These results provide a unified theoretical framework linking the physical state of the accretion flow to the diverse jet phenomenology observed across black‑hole systems.