Pulsational stability of stars in thermal inbalance. II. An energy approach

A general expression is derived for the rate of change of the total pulsation energy (kinetic plus potential) of a star in thermal imbalance. It is shown that no intrinsically second-order terms appear for the case of infinitesimal oscillations. The present analysis does not explicitly invoke the quasi-adiabatic approximation. Quantitative agreement with Simon and with Kato and Unno is obtained in certain special cases. It is shown, however, that this energy approach does not correctly describe the growth or decay of the pulsation amplitude, and hence cannot be the correct approach to the thermal imbalance problem (as must also, presumably, be the case with the energy approaches used by the above authors). Moreover, this approach leads to disagreement with a result due to Unno and also with the results of the "small perturbation" approach used by Cox, Hansen, and Davey. Exact agreement with this latter approach can be obtained in at least a certain class of cases if the stability coefficient is defined in terms of the average rate of change of total pulsation kinetic energy alone. Also, this new definition agrees precisely with the direct solution of the appropriate differential equation in at least two cases. Subject headings: interiors, stellar - pulsation