Nonresonant three-mode coupling as a model for double-mode pulsators

Details Nonresonant three-mode coupling as a model for double-mode pulsators Nonresonant three-mode coupling as a model for double-mode pulsators

Apr 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990ap%26ss.166...77v&link_type=abstract

Astrophysics and Space Science (ISSN 0004-640X), vol. 166, no. 1, April 1990, p. 77-91. Research supported by FNRS.

Physics

Optics

3

Pulsars, Stellar Models, Stellar Oscillations, Variable Stars, Cepheid Variables, Coupled Modes, Nonlinear Optics, Nonresonance

Scientific paper

If one is only interested in the behavior 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 modeling 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 modeling and a cautious discussion thereof.

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