Abstract
We discuss, in general, the problem of deriving a vibrational stability coefficient of stars in thermal imbalance on the basis of an energy principle.
The damped harmonic oscillator with variable spring ‘constant’ provides a typical illustration of the problem. In fact, for systems with variable parameters (as evolving stars), the vibrational stability coefficients, defined respectively in terms of the behaviour of the small displacement and of the total pulsation energy, are basically different. Davey and Cox's so-called ‘modified’ energy method, proposed in order to recover the small displacement stability coefficient, is also shown to be unsatisfactory.
The use of results obtained in the first two papers by asymptotic methods yields a simple compact general expression for the vibrational stability coefficient relative to the pulsation energy of arbitrary evolving stars. This allows the easy recovery of results obtained by more complicated approaches due to Kato and Unno, Simon and Sastri and Axel and Perkins, valid only in particular cases.
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Demaret, J. Vibrational stability of stars in thermal imbalance. Astrophys Space Sci 45, 31–45 (1976). https://doi.org/10.1007/BF00642139
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DOI: https://doi.org/10.1007/BF00642139