The fundamental mode of radial pulsation has been calculated for convective envelopes in adiabatic equilibrium including radiation pressure. The theoretical Q-values are compared with the observational Q-values of variable M supergiants in galactic associations. The variability of these massive red super- giants can be explained on the pulsation hypothesis if a suitable readjustment of some of the observed periods is made. Pulsation seems to be suggested by (1) the cyclical variations in magnitude, spectrum, and radius in individual stars, (2) a period-luminosity relation, and (3) a period-spectrum relation for the group of stars
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Richard B. Stothers (1969) studied this question.