Equilibrium and stability of a self-gravitating torus in a field of a large central mass

A model is generated for a selfgravitating uniform liquid torus in a field of a central mass. The model is a generalization of the known Laplacian model for the case with differential rotation and allows, unlike the latter, equilibrium configurations with a rather lange mass of the central body. A study of the stability of the stability of these models is made. The emphasis is placed on radial disturbances. It is shown that there exist two types of disturbances, i.e. symmetrical and antisymmetrical about the outer contour of the torus. Only symmetrical disturbances can be unstable. Two types of instability are possible, dynamical and secular, arising in the presence of dissipation in the system. It is shown that the secular instability has a universal character and develops even in a dynamically stable system. Stability boundaries of all radial modes are obtained. Nonradial disturbances have also been investigated for the case when the azimuthal wavelength exceeds considerably the torus cross-section size. Instability analysis results are used for interpreting radial divisions in Saturn's rings