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We discuss two important instability mechanisms that may lead to the limit‐cycle oscillations of the luminosity of the accretion discs around compact objects: ionization instability and radiation pressure instability. Ionization instability is well established as a mechanism of X‐ray novae eruptions in black hole binary systems, but its applicability to active galactic nuclei (AGN) is still problematic. Radiation pressure theory has still a very weak observational background in any of these sources. In this paper, we attempt to confront the parameter space of these instabilities with the observational data. At the basis of this simple survey of sources properties, we argue that the radiation pressure instability is likely to be present in several Galactic sources with the Eddington ratios being above 0.15 and in AGN with the Eddington ratio above 0.025. Our results favour the parametrization of the viscosity through the geometrical mean of the radiation and gas pressure in both Galactic sources and AGN. More examples of the quasi‐regular outbursts in the time‐scales of 100 s in Galactic sources and hundreds of years in AGN are needed to formulate firm conclusions. We also show that the disc sizes in the X‐ray novae are consistent with the ionization instability. This instability may also considerably influence the lifetime cycle and overall complexity in the supermassive black hole environment.

On different types of instabilities in black hole accretion discs: implications for X‐ray binaries and active galactic nuclei