Astronomy and Astrophysics – Astrophysics
Scientific paper
Dec 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993ap%26ss.210..269a&link_type=abstract
Astrophysics and Space Science (ISSN 0004-640X), vol. 210, no. 1-2, p. 269-280 (IAU Colloquium 134)
Astronomy and Astrophysics
Astrophysics
1
Cepheid Variables, Hydrodynamics, Stellar Models, Stellar Oscillations, Chaos, Harmonic Oscillation, Resonance, Supergiant Stars
Scientific paper
Phenomena of bifurcation in hydrodynamic stellar models of radial pulsation are reviewed. By changing control parameters of models, we can see qualitatively different pulsation behaviors in hydrodynamic models with transitions due to various types of bifurcation. In weakly dissipative models (classical Cepheids), the bifurcation is induced by modal resonances. Two types of the modal resonances found in models are discussed: The higher-harmonic resonances of the second overtone mode in the fundamental mode pulsator and of the fourth ovetone mode in the first overtone pulsator are relevant to observations. The subharmonic resonance between the fundamental and first overtone modes is confirmed in classical Cepheid models. In strongly dissipative models (less-massive supergiant stars), the bifurcation of nonlinear pulsation is induced by the hydrodynamics of ionization zones as well as modal resonances. The sequence of the bifurcation sometimes leads to chaotic behaviors in nonlinear pulsation. The transition routes from regular to the chaotic pulsations found in models are discussed with respect to the theory of chaos in simple dynamical systems: The cascade of period-doubling bifurcation is confirmed to cause chaotic pulsation in W Virginis models. For models of higher luminosity, the tangent bifurcation is found to lead intermittent chaos. Finally, hydrodynamic models for chaotic pulsation with small amplitudes observed in the post Asymptotic Giant Branch (AGB) stars are briefly discussed.
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