Galactic stars applied to tests of the criterion for convection and semiconvection in an inhomogeneous star

The question of the effective criterion for convection and semiconvection to use in the inhomogeneous layers of models of massive stars is addressed here in terms of a choice between the Schwarzschild (temperature-gradient) criterion and the Ledoux (density-gradient) criterion. These two extremes give rise to and suppress, respectively, a fully convective zone (FCZ) in the layers immediately above the hydrogen-burning shell, if the star's mass is neither too low nor too high. Specifically, the existence of a large FCZ delays or prevents the star during core helium burning from becoming a red supergiant. The applicable range of initial stellar masses for a solar metallicity is approximately 13 to 30 solar mass. Nine different tests for the effective criterion for convection and semiconvection in Galactic supergiants, as well as a test using SN 1987A of the Large Magellanic Cloud, are performed, or reexamined, by using both old and new theoretical data, while three of the Galactic tests are repeated for association supergiants separately from cluster supergiants. Although eight of the 13 tests yield inconclusive results, five do support the Ledoux criterion, and three do so strongly.