Nonlinear Stellar Oscillations: Dynamics of Directly Coupled and Parametrically Coupled Three-Mode Systems.

In most studies of stellar oscillations, the excited modes are treated as linear perturbations to the background star. However, in some stars the mode amplitudes are so large that the linear approximation breaks down and nonlinear three-mode coupling becomes important. There are two types of three-mode coupling to consider: (1) direct coupling, in which two linearly excited modes nonlinearly drive a third mode, and (2) parametric coupling, in which one linearly excited mode nonlinearly drives two modes. Previous studies of three-mode coupling tended to focus on either direct or parametric coupling and ignored the possibility that both could be active in the same star. We study this possibility and show that the mode dynamics can be significantly altered by the presence of both types of coupling. As an example, we consider oscillation modes of delta Scuti variable stars and find that direct and parametric coupling can both be dynamically important and together impact the observed oscillation spectrum.