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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 heliumburning phase. We compare rotating and non-rotating models with efficient (ffsemi = 100) and inefficient semi-convection (ffsemi = 0:1), with high and low amounts of core overshooting (ffov 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 ffov = 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 ffov = 0:1, which switches on semi-convective mixing, but for standard ffsemi = 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 ffsemi = 100, which reproduces the HD limit at log L=Lβ ~ 5:5 for the Magellanic Clouds while simultaneously reproducing the Galactic HD limit of log L=Lβ ~ 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. [ABSTRACT FROM AUTHOR]

Context. Massive star evolution is dominated by various physical effects, including mass loss, overshooting, and rotation, but the prescriptions of their effects are poorly constrained and even affect our understanding of the main sequence. Aims. We aim to constrain massive star evolution models using the unique test-bed eclipsing binary HD 166734 with new grids of MESA stellar evolution models, adopting calibrated prescriptions of overshooting, mass loss, and rotation. Methods. We introduce a novel tool, called the mass-luminosity plane or M−L plane, as an equivalent to the traditional HR diagram, utilising it to reproduce the test-bed binary HD 166734 with newly calibrated MESA stellar evolution models for single stars. Results. We can only reproduce the Galactic binary system with an enhanced amount of core overshooting (αov = 0.5), mass loss, and rotational mixing. We can utilise the gradient in the M−L plane to constrain the amount of mass loss to 0.5–1.5 times the standard prescription test-bed, and we can exclude extreme reduction or multiplication factors. The extent of the vectors in the M−L plane leads us to conclude that the amount of core overshooting is larger than is normally adopted in contemporary massive star evolution models. We furthermore conclude that rotational mixing is mandatory to obtain the correct nitrogen abundance ratios between the primary and secondary components (3:1) in our test-bed binary system. Conclusions. Our calibrated grid of models, alongside our new M−L plane approach, present the possibility of a widened main sequence due to an increased demand for core overshooting. The increased amount of core overshooting is not only needed to explain the extended main sequence, but the enhanced overshooting is also needed to explain the location of the upper-luminosity limit of the red supergiants. Finally, the increased amount of core overshooting has – via the compactness parameter – implications for supernova explodability. [ABSTRACT FROM AUTHOR]