On the oscillations and the stability of a uniformly rotating gaseous gravitating disc, including viscosity and heat exchange

This paper presents a critical revision of the problem of small oscillation s and stability of a thin, homogeneous and uniformly rotating gas disc, wit h regard to self-gravitation, viscosity and dissipative factors. We allow f or the possibility of heat exchange between this disc and the non-equilibri um thermodynamic surrounding medium. A combined method for the study of dis cs is applied, which takes into account both the elements of the perturbati on method and those of the variational description. The general dispersion equations of this task are obtained, and a careful analysis of these equati ons is carried out. We establish that dissipative factors lead to two compl etely different modes of slow instabilities. The first mode is the ordinary secular instability, and the other mode is an amplification of gravitation al sound oscillations under heal exchange with the external medium. The cri teria for these modes of instability of the disc are found.