Luminosities, masses and periodicities of massive red supergiants.

Luminosities and masses of M-type supergiants belonging to extreme Population I have been derived from (a) cluster membership and other strictly empirical luminosity and mass criteria and (b) the pulsational Q value method applied to the known variables. New periods for eight variables have been determined from AAVSO data. It is found, in general, that the primary period and the long secondary period both increase with brighter luminosity class and later spectral type. This reflects, partly, the increase of mass with increasing luminosity if the primary period is interpreted as being due to the fundamental mode of radial pulsation and if the appropriate theoretical mass-luminosity relation is adopted. The long secondary period is tentatively interpreted as the convective turnover time of giant convection cells in the stellar envelope. A possible alternative interpretation is that the primary and secondary periods represent, respectively, the first overtone and the fundamental mode of radial pulsation. Luminosities based on methods (a) and (b) are in good agreement, and yield a self-consistent calibration of the mean absolute visual magnitudes of the different luminosity classes. The pulsational masses of variables in associations are in satisfactory agreement with the masses inferred from the main-sequence turnoffs, thereby implying that little mass has been lost. The evidence is very strong that the majority of red supergiants are in the early stages of core helium burning. Key words: red supergiants - periodicities - luminosities - masses