Adiabatic oscillations of accretion disks

Abstract

We have used a variational principle to derive an integral expression for the frequencies of adiabatic oscillations of an accretion disk and have applied this expression to vertical oscillations. A number of examples show that this expression generally gives fairly good results with a simple trial function. In particular, the oscillatory periods of vertical oscillations in some of the low modes are found to be of the order of the corresponding Keplerian periods (or less, if self-gravity is taken into account), regardless of the detailed structure of the disk model. These times are of the order of those observed in the quasi-periodic oscillations of dwarf novae or in variable quasars. Physical arguments, based mostly on the virial theorem, make these results plausible. We have also obtained the differential equation for the vertical, adiabatic oscillations of an accretion disk. This equation embraces the equations derived by two other groups as special cases. Exact solutions are found in a number of cases. These solutions agree with results based on the variational principle.