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.
Aims: We test this assertion by systematically studying how the disk instability model (DIM) is applied to AGNs.
Methods: We use the adaptative grid numerical code we developed in the context of CVs, enabling us to fully resolve the radial structure of the disk.
Results: We show that, because the Mach numbers are very large in AGN disks, 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 much shorter time scales 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 in the accretion rate onto the black hole, with short quiescent states only occurring for very low mass-transfer rates. 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.