Date of this Version
THE ASTROPHYSICAL JOURNAL, 237: 175-186, 1980 April 1
The iterative nonlinear pulsation theory is extended to the bimodal case, and a series of equations derived which are complete to second order. Solutions to these equations are obtained for a number of long-period double-mode Cepheid models in the vicinity of the interaction resonance Ѡl + Ѡ0 = Ѡ3 and the harmonic resonance P2/P0 = 0.5. We show that the resonant second-order amplitudes and phases change abruptly as the center of the resonance is approached. In addition, it is demonstrated that, inward of the hydrogen ionization zone, the amplitudes strongly resemble the linear eigenfunctions to which they are resonantly linked. Thus the resonances are shown to have spatial as well as temporal content. Due to nonadiabatic effects the second-order terms are particularly strong in the H I ionization zone, a circumstance which suggests that this region could play an important role in determining limiting-amplitude behavior.