Vibrational stability of stars in thermal imbalance. III - A general discussion of energy methods

Details Vibrational stability of stars in thermal imbalance. III - A general discussion of energy methods Vibrational stability of stars in thermal imbalance. III - A general discussion of energy methods

Nov 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976ap%26ss..45...31d&link_type=abstract

Astrophysics and Space Science, vol. 45, Nov. 1976, p. 31-45.

Computer Science

Numerical Analysis

7

Astrophysics, Dynamic Stability, Energy Methods, Harmonic Oscillators, Stellar Models, Thermodynamics, Asymptotic Methods, Conservation Equations, Numerical Analysis, Perturbation Theory, Stellar Envelopes, Taylor Series, Wave Equations

Scientific paper

The paper discusses, in general, the problem of deriving a vibrational stability coefficient for 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 behavior of the small displacement and the total pulsation energy, are basically different. Davey and Cox's (1974) 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 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 that are valid only in particular cases.

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