The pulsational stability of intermediate- and low-luminosity red giants in globular clusters *

Some theoretical calculations of linear non-adiabatic pulsations of intermediate- and low- luminosity red giants in globular clusters have been carried out using a time-dependent theory of nonlocal stellar convection. As shown by the results, for all models with temperatures higher than 5400 K the modes up to the fourth overtone are pulsationally stable. With the increase of stellar luminosity, the low-order overtones also become pulsationally unstable. For red giants of intermediate and low luminosities, the pulsational stability is exceedingly low and is close to neutral stability. Therefore, they will be either non-variables or short-period variables (P < 2 days) with extremely small amplitudes.