Theoretical growth rates, periods, and pulsation constants for long-period variables

An extensive set of linear, nonadiabatic pulsation models for red giant and supergiant stars is computed, in order that the dependence of pulsation periods (P), pulsation constants (Q), and growth rate on physical input parameters can be determined from the systematic behavior seen in the models. Also investigated is the extent of the dependence of P, Q, and growth rate on uncertain quantities such as atmospheric molecular opacity, surface boundary conditions, and effective temperature. The growth rate for the fundamental mode is found to increase with luminosity on the giant branch while the growth rate for the first overtone decreases. Dynamical instabilities found in previous adiabatic models of extreme red giants do not occur when nonadiabatic effects are included in the models.