1996A&A...308...66V

The strength of nonlinear interactions of oscillation modes of stars is determined by the amplitudes as well as by the eigenfunctions of the oscillation modes. The intrinsic coupling of modes through their eigenfunctions can be described by coupling coefficients. We derive values of coupling coefficients for isentropic oscillation modes of polytropic models with degrees of central condensation that correspond to central condensations of main sequence stars to highly condensed evolved stars and study the influence of the radial order and the degree of the oscillation mode on the coupling coefficients. For modes with equal amplitude of the radial displacement at the surface, coupling coefficients are larger for higher overtones and usually smaller for higher degrees. With increasing polytropic index, and thus increasing central condensation of the model, the coupling coefficients increase in absolute values for the lowest-order modes and decrease in absolute value for the higher-order modes. We discuss the implications of the nonlinear couplings on the frequencies and the radial-velocity variations in the case of single, linearly excited, nonresonant modes, and comment on the amplitudes of the modes. The nonlinear frequencies and velocity curves for single modes are calculated without the use of the Galerkin approximation, which is found to be inadequate. We conclude that the nonlinear frequencies are slightly smaller than the linear ones, and that the lowest-order Fourier coefficients of the radial-velocity variations are in good general agreement with observations.