Abstract
If one is only interested in the behaviour of a few longlived modes, the simplest model for the evolution to steady nonlinear stellar pulsation is nonresonant interaction. As the coupled-mode equations are generically not dependent upon a particular stellar model, qualitative ideas about the eventual evolution of mode energies give scenarios that depend mainly upon nonlinear coupling constants and linear growth rates. Two linearly unstable modes are considered in the presence of a representative stable or slave mode. One scenario models a double-mode pulsator, without it being necessary that all coupling constants be negative, if only the model is well behaved enough in excluding unbounded solutions and in avoiding finite amplitudes for the slave modes. The influence of driving on slave modes is then such that all slave modes ultimately decay away. Other scenarios show evolution to classic pulsators. A discussion is given of the modelling of a classic Cepheid in a mode which is not the linearly most unstable one. Findings of the present paper show the need for additional theoretical and numerical modelling and a cautious discussion thereof.
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Verheest, F. Nonresonant three-mode coupling as a model for double-mode pulsators. Astrophys Space Sci 166, 77–91 (1990). https://doi.org/10.1007/BF00655609
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DOI: https://doi.org/10.1007/BF00655609