Astronomy and Astrophysics – Astrophysics
Scientific paper
Apr 1980
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980apj...237..175s&link_type=abstract
Astrophysical Journal, Part 1, vol. 237, Apr. 1, 1980, p. 175-186.
Astronomy and Astrophysics
Astrophysics
9
Cepheid Variables, Pulsars, Stellar Models, Eigenvectors, Hydrogen Ions, Iteration, Nonadiabatic Theory, Nonlinearity, Optical Resonance, Propagation Modes
Scientific paper
The iterative nonlinear pulsation theory is extended to the bimodal case, and a series of eqations 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 omega(1) + omega(0) = omega(3) and the harmonic resonance P(2)/P(0) = 0.5. It is shown 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.
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