On the vibrational stability of stars in thermal imbalance

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Asymptotic Methods, Dynamic Stability, Mechanical Oscillators, Stellar Evolution, Thermal Stability, Variable Stars, Harmonic Oscillation, Hydrostatics, Mathematical Models, Nonlinear Systems, Perturbation Theory

Scientific paper

Pulsational-stability conditions are derived for stars in thermal imbalance as a simple application of a two-time asymptotic method, previously developed as a practical tool to evolve stars through pulsational phases. In the case of soft oscillations the known results are recovered, but in a more straightforward and transparent way. In the case of hard oscillations, not accessible to the usual linear analysis, a simple method is outlined for studying the nature of the stability and, in particular, the range of stability. The ineluctable difference between stability coefficients as derived from amplitude or energy considerations is briefly discussed, and another, more natural, definition is suggested in terms of the action variable.

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