Astronomy and Astrophysics – Astrophysics
Scientific paper
Jan 1975
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975apj...195..441s&link_type=abstract
Astrophysical Journal, vol. 195, Jan. 15, 1975, pt. 1, p. 441-466.
Astronomy and Astrophysics
Astrophysics
269
Astronomical Models, Cepheid Variables, Dynamic Stability, Modal Response, Stellar Structure, Astronomical Catalogs, Globular Clusters, Harmonic Oscillation, Hydrodynamics, Mathematical Models, Nonadiabatic Theory, Nonlinear Systems, Stellar Envelopes, Tables (Data)
Scientific paper
The modal stability of a survey of RR Lyrae models has been investigated using linear nonadiabatic analysis and relaxation to the exact periodic nonlinear limit cycles. With these techniques both the growth rates of the small-amplitude solutions and the mode switching rates of the large-amplitude solutions are obtained, resulting in a complete description of the long-term modal behavior of the model. The systematics of the nonlinear models are described, and an accurate fitting formula for the periods is derived. The nonlinear stability results show a narrow region of 'fundamental or first harmonic' behavior whose blue edge is nearly the same as the linear fundamental blue edge. This situation suggests that the Oosterhoff dichotomy of globular clusters is caused by an evolutionary hysteresis effect. In a large region toward the red these models show aperiodic mixed-mode behavior similar to that observed for several stars.
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