Stability and oscillations of thermal accretion discs around black holes.

We perform perturbation calculations on accretion discs by using the formula proposed by Liang & Wandel which bridges the optically thin and optically thick cases. Using the α model, the steady-structure solutions fall into two groups, one for hot optically thin solutions and the other for cool optically thick solutions. We note that there are oscillatory modes with relatively short wavelengths only in the cool solutions, with typical frequencies below tens of Hz. The oscillation only exists within a certain range of accretion rate, and its frequency changes with the accretion rate.

This result may be used to explain certain quasi-periodic oscillations (QPOs) observed in X-ray sources, where the frequency is several Hz in most cases for keV photons, as well as the very low QPO frequencies of about 100 keV recently found for GRO J 0422+32 and Cygnus X-1. In future observations, we expect to see a strong correlation between QPO frequency and the observed photon spectrum.