Nonlinear Density Waves in Self-Gravitating Gas Sheets
The dynamical evolution of spiral density waves of finite amplitude in a thin, self-gravitating, rotating gas sheet is investigated. The analysis proceeds through three stages. First the basic model is described. Next a linear stability analysis of the sheet, subjected to spiral perturbations, is carried out. The evolution of the wave amplitudes is then followed from initial exponential growth into the regime of finite amplitudes. The result is a non-deterministic oscillation of the perturbed surface density. This may be related to recurrent spiral instabilities of stellar disks as studied by Toomre (1989 and these proceedings) and also observed in numerical simulations of the global dynamical evolution of stellar disks (Sellwood and Athanassoula, 1986).
- Toomre, A. 1989, in Dynamics of Astro-physical Disks, J. Sellwood (ed.), (in press).Google Scholar