A model for tidally driven eccentric instabilities in fluid disks

Abstract

The eccentric instabilities generated in fluid disks by tidal mechanisms are examined by means of a model in which a companion object is in a circular orbit about a disk. The perturbing-potential component causes a tidal response which generates density waves at the eccentric Lindblad resonances based on the eccentricity. The eccentricity increases because of the stress introduced by the coupling of the tidal response and the eccentricity; this stress is considered in theory and in terms of eccentric planetary rings and superhump phenomena. The growth rate of the eccentricity is defined for the ideal case of minimal dissipation in a narrow ring, and a general relation is given relating eccentricity growth rates to changes in resonant angular momentum. An ideal eccentricity growth rate is developed for superhump phenomena based on the dominant eccentric Lindblad resonance.