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Period-doubling as a limit to pulsation of short-period population II Cepheid models

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Abstract

The short-period limiting pulsation found by Fadeyev and Fokin (1985) in a short-period, Population II Cepheid model is examined by means of the Baker-von Sengbush-Stellingwerf (BSS) algorithm of limit cycles.

It is shown that the model has a stable limit cycle of the fundamental mode and an unstable limit cycle of the first overtone mode. When the method is applied for pulsations spanning the time interval of twice the period of the fundamental mode, we find only the fundamental cycle repeated doubly or the first overtone limit cycle repeated three times, depending on initial conditions of the integration.

We thus conclude that the period-doubling limiting pulsation found by Fadeyev and Fokin (1985) is a transient feature of the model.

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References

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Aikawa, T. Period-doubling as a limit to pulsation of short-period population II Cepheid models. Astrophys Space Sci 125, 325–330 (1986). https://doi.org/10.1007/BF00648031

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Keywords

  • Fundamental Mode
  • Stable Limit
  • Stable Limit Cycle
  • Transient Feature
  • Unstable Limit Cycle