Astronomy and Astrophysics – Astrophysics
Scientific paper
Feb 1984
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984mnras.206..497d&link_type=abstract
Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 206, Feb. 1, 1984, p. 497-519. Research supported by th
Astronomy and Astrophysics
Astrophysics
50
Astrophysics, Cepheid Variables, Resonance, Stellar Oscillations, Vibration Mode, Amplitudes, Coupled Modes, Equilibrium, Numerical Stability
Scientific paper
Attention is given to the simultaneous effects of resonant coupling and nonlinear saturation of the linear driving mechanism on the finite amplitude solution of the multimodal pulsation problem and on its stability. The calculations of both effects are in the lowest order of approximation in terms of amplitudes. The 2:1 resonance between one of the two linearly unstable modes and a higher frequency mode gives rise to double-mode (fundamental and first overtone) pulsation. It is noted that within a certain range of parameters, such as the frequency mismatch, the linear growth, and damping rates, it is the only stable solution to the problem. It is also shown that three-mode resonance promotes a single-mode rather than a double-mode pulsation. Under certain conditions, the nonresonant interaction occurring through the collective saturation of the driving rates may lead to multimodal variability. It is contended here, however, that this condition is unlikely to be met in Cepheids and RR Lyrae stars.
Dziembowski Wojciech
Kovacs Gabor
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