Pulsational stabilities of a star in thermal imbalance - Comparison between the methods

The stability coefficients for quasi-adiabatic pulsations for a model in thermal imbalance are evaluated using the dynamical energy (DE) approach, the total (kinetic plus potential) energy (TE) approach, and the small amplitude (SA) approaches. From a comparison among the methods, it is found that there can exist two distinct stability coefficients under conditions of thermal imbalance as pointed out by Demaret. It is shown that both the TE approaches lead to one stability coefficient, while both the SA approaches lead to another coefficient. The coefficient obtained through the energy approaches is identified as the one which determines the stability of the velocity amplitudes. For a prenova model with a thin hydrogen-burning shell in thermal imbalance, several radial modes are found to be unstable both for radial displacements and for velocity amplitudes. However, a new kind of pulsational instability also appears, viz., while the radial displacements are unstable, the velocity amplitudes may be stabilized through the thermal imbalance terms.