Context. Current massive star evolution grids are not able to simultaneously reproduce the empirical upper luminosity limit of red supergiants, the Humphrey–Davidson (HD) limit, nor the blue-to-red (B/R) supergiant ratio at high and low metallicity. Although previous studies have shown that the treatment of convection and semi-convection plays a role in the post-main-sequence (MS) evolution to blue or red supergiants (RSGs), a unified treatment for all metallicities has not been achieved so far.
Aims. We focus on developing a better understanding of what drives massive star evolution to blue and red supergiant phases, with the ultimate aim of reproducing the HD limit at varied metallicities. We discuss the consequences of classifying B and R in the B/R ratio and clarify what is required to quantify a relatable theoretical B/R ratio for comparison with observations.
Methods. For solar, Large Magellanic Cloud (50% solar), and Small Magellanic Cloud (20% solar) metallicities, we develop eight grids of MESA models for the mass range 20–60 M⊙ to probe the effect of semi-convection and overshooting on the core helium-burning phase. We compare rotating and non-rotating models with efficient (αsemi = 100) and inefficient semi-convection (αsemi = 0.1), with high and low amounts of core overshooting (αov of 0.1 or 0.5). The red and blue supergiant evolutionary phases are investigated by comparing the fraction of core He-burning lifetimes spent in each phase for a range of masses and metallicities.
Results. We find that the extension of the convective core by overshooting αov = 0.5 has an effect on the post-MS evolution that can disable semi-convection, leading to more RSGs, but a lack of BSGs. We therefore implement αov = 0.1, which switches on semi-convective mixing, but for standard αsemi = 1 would result in an HD limit that is higher than observed at low Z (Large and Small Magellanic Clouds). Therefore, we need to implement very efficient semi-convection of αsemi = 100, which reproduces the HD limit at log L/L⊙ ∼ 5.5 for the Magellanic Clouds while simultaneously reproducing the Galactic HD limit of log L/L⊙ ∼ 5.8 naturally. The effect of semi-convection is not active at high metallicities because the envelope structure is depleted by strong mass loss such that semi-convective regions could not form.
Conclusions. Metallicity-dependent mass loss plays an indirect, yet decisive role in setting the HD limit as a function of Z. For a combination of efficient semi-convection and low overshooting with standard Ṁ(Z), we find a natural HD limit at all metallicities.
Wolf--Rayet binaries in the Magellanic Clouds and implications for massive-star evolution -- I. Small Magellanic Cloud
