Simulations of tidally driven eccentric instabilities with application to superhumps

The eccentric evolution of fluid disks in close binaries is examined analytically with a 2D smooth-particle hydrodynamics code to develop a model of superhumps. The perturbing potential is limited to eliminate orbit crossings near resonance, and two distinct stages of eccentricity growth are identified. The angular and time dependences and binary angular speed of the wave are described for both stages; a mild wave exists in stage 1 which develops and then dissipates somewhat due to shocks in stage 2. The imbalance of the developing disk causes modifications of the apparent eccentricity of the two-armed inwardly propagating disturbance. A mode-coupling model for eccentricity growth is supported by the results of the analysis, and disks in close binaries can be truncated by a 3:1 resonance.