  The Humphreys-Davidson (HD) limit empirically defines a region of high
luminosities (log L > 5.5) and low effective temperatures (T < 20kK) on the
Hertzsprung-Russell Diagram in which hardly any supergiant stars are observed.
Attempts to explain this limit through instabilities arising in near- or
super-Eddington winds have been largely unsuccessful. Using modern stellar
evolution we aim to re-examine the HD limit, investigating the impact of
enhanced mixing on massive stars. We construct grids of stellar evolution
models appropriate for the Small and Large Magellanic Clouds (SMC, LMC), as
well as for the Galaxy, spanning various initial rotation rates and convective
overshooting parameters. Significantly enhanced mixing apparently steers
stellar evolution tracks away from the region of the HD limit. To quantify the
excess of over-luminous stars in stellar evolution simulations we generate
synthetic populations of massive stars, and make detailed comparisons with
catalogues of cool (T < 12.5kK) and luminous (log L > 4.7) stars in the SMC and
LMC. We find that adjustments to the mixing parameters can lead to agreement
between the observed and simulated red supergiant populations, but for hotter
supergiants the simulations always over-predict the number of very luminous
(log L > 5.4) stars compared to observations. The excess of luminous
supergiants decreases for enhanced mixing, possibly hinting at an important
role mixing has in explaining the HD limit. Still, the HD limit remains
unexplained for hotter supergiants.
