The thermal-viscous disk instability model in the AGN context

Accretion disks in AGN should be subject to the same type of instability as in cataclysmic variables (CVs) or in low-mass X-ray binaries (LMXBs), which leads to dwarf nova and soft X-ray transient outbursts. It has been suggested that this thermal/viscous instability can account for the long term variability of AGNs. We test this assertion by presenting a systematic study of the application of the disk instability model (DIM) to AGNs. We are using the adaptative grid numerical code we have developed in the context of CVs, enabling us to fully resolve the radial structure of the disk. We show that, because in AGN disks the Mach numbers are very large, the heating and cooling fronts are so narrow that they cannot be resolved by the numerical codes that have been used until now. In addition, these fronts propagate on time scales much shorter than the viscous time. As a result, a sequence of heating and cooling fronts propagate back and forth in the disk, leading only to small variations of the accretion rate onto the black hole, with short quiescent states occurring for very low mass transfer rates only. Truncation of the inner part of the disk by e.g. an ADAF does not alter this result, but enables longer quiescent states. Finally we discuss the effects of irradiation by the central X-ray source, and show that, even for extremely high irradiation efficiencies, outbursts are not a natural outcome of the model.

💡 Research Summary

The authors set out to test whether the thermal‑viscous disk instability model (DIM), which successfully explains dwarf‑nova outbursts in cataclysmic variables (CVs) and soft‑X‑ray transients in low‑mass X‑ray binaries (LMXBs), can also account for the long‑term variability observed in active galactic nuclei (AGN). To do this they adapted an existing adaptive‑grid numerical code—originally built for CVs—to the vastly different physical conditions of AGN accretion disks. The code resolves the full radial structure of the disk and automatically refines the grid wherever heating or cooling fronts develop, ensuring that even extremely narrow fronts are captured.

A key physical difference highlighted in the study is the enormous Mach number (M ≈ 10⁴–10⁵) of AGN disks. High Mach numbers make the thermal fronts extremely thin: their radial thickness is less than 10⁻³ of the local viscous length scale. Consequently, earlier simulations that employed fixed grids could not resolve these fronts and therefore misrepresented their propagation speed and impact on the global disk evolution.

The simulations reveal that, because the fronts are so narrow, they travel across the disk on a timescale that is orders of magnitude shorter than the viscous timescale (τ_front ≈ τ_visc/30). While the fronts repeatedly sweep back and forth, the mass accretion rate onto the central black hole (ṁ) changes only by a few percent. Significant quiescent intervals (the “low” state of the DIM cycle) appear only when the external mass‑transfer rate is extremely low (ṁ ≲ 10⁻⁴ M⊙ yr⁻¹). For the typical mass‑transfer rates expected in AGN (10⁻³–10⁻¹ M⊙ yr⁻¹) the disk remains essentially in a steady, high‑state configuration, and the classic large‑amplitude outbursts predicted by the DIM never develop.

The authors also examined two modifications that are often invoked to rescue the DIM in AGN: (1) truncation of the inner disk by an advection‑dominated accretion flow (ADAF) or similar hot flow, and (2) strong irradiation of the outer disk by the central X‑ray source. Introducing an inner truncation radius (10–100 R_S) lengthens the viscous time of the remaining cold disk, thereby modestly extending any low‑state episodes, but it does not change the fundamental result that the fronts are too fast and too thin to generate large outbursts. Irradiation was modeled with unrealistically high efficiencies (η up to unity). Even under these extreme conditions the heating fronts could not be sustained long enough to drive the whole disk into a hot, high‑luminosity state. Thus, irradiation does not rescue the DIM either.

Overall, the study concludes that the thermal‑viscous instability, while a robust mechanism for dwarf novae and X‑ray transients, is essentially ineffective in AGN disks because of their high Mach numbers and the resulting ultra‑thin, rapidly propagating fronts. The modest variations in ṁ produced by the model are far smaller than the amplitude of observed AGN variability on timescales of years to decades. Consequently, alternative explanations—such as variations in the external supply of gas, magnetorotational turbulence, or large‑scale jet feedback—must be invoked to account for AGN long‑term luminosity changes. The paper therefore casts serious doubt on the applicability of the DIM to supermassive black‑hole accretion disks.