Stothers, R., 1972: Convective envelopes and radial pulsation of massive red supergiants. Astron. Astrophys., 18, 325-328.
A grid of convective envelope models covering a wide range of astrophysical parameters (including mass low) haa been constructed for M-type supergiants with the help of theoretical evolutionary tracks, mixing length theory, and the inclusion of hydrogen and helium ionization zones. Linear adiabatic pulsation theory has been used to obtain the first four normal modes of radial pulsation for all the models. For the fundamental mode, the quantity W = P(M/M☉)(R/R☉)-2 is found to be more nearly constant than is the usual quantity Q = P(M/M☉)1/2(R/R☉)-3/2, although the overtone Q values are practically constant. All the convective envelopes are found to be dynamically stable. The theoretical pulsation calculations confirm that the primary observed period in variable M-type supergiants is probably due to the fundamental mode of radial pulsation and that the long secondary period is not due to a normal mode of radial pulsation.