Theoretical aspects of pulsation and envelope ejection in red giants

Observational Q values for globular cluster red variables, Mira variables and red supergiant variables have been compared with appropriate theoretical Q values in an attempt to find the mode(s) of pulsation of these variables. The results are inconclusive for the globular cluster red variables, with the observed Q values scattering between the values expected for fundamental and first overtone modes. The Q values and period ratios in Mira-variables support first overtone pulsation in stars of mass 0.8 - 1.2 solar masses. The red supergiant variables in our galaxy appear to be fundamental mode pulsators with masses of 10-25 solar masses, and a similar class of variables occurs in the LMC. In the SMC and LMC there is another class of fundamental mode pulsator which lies on the AGB and which has a mass of approximately 4.5 solar masses. It is suggested that the type II OH/IR sources are the galactic counterparts of these variables. The cases for first overtone and fundamental mode pulsation in Mira variables are examined in detail, and little support is found for the fundamental mode unless Miras have masses on the AGB of approximately 2 solar masses. Finally, some aspects of the interaction between pulsation, evolution and mass loss in red giant stars are reviewed, following the models of Wood and Cahn (1977) and Tuchman, Sack and Barkat (1979). (Auth.)