Overstable oscillations in accretion discs

Abstract

In this study the accretion disc is taken to be axially symmetric. Vertical averaging and a polytropic equation of state are assumed valid. The rotation rate is not assumed to be Keplerian, but rather the angular momentum equation is explicitly treated. The important inner boundary region, where the angular rotation rate suddenly drops from near the Keplerian value to the much lower stellar value, is thus incorporated into this study. The viscosity model used is a modification of the standard Shakura and Sunyaev ‘α-model’. In this paper the mixing length used varies from H to H p / β, where H is the disc scale height and H p is the radial pressure scale length. Two distinct regions of oscillations are shown to exist. The first set consists of out-going waves from the inner boundary. These give measurable variations in the luminosity of such a system. Their amplitude and periodicity are found to be governed by the value of β. These are separated by an evanescent region from a set of trapped waves at the outer boundary. Criteria for the stabilisation of the disc are shown. The relevance of these results to QPO's, Dwarf Novae and Cataclysmic Variables is included.