## The excess of cool supergiants from contemporary stellar evolution models defies the metallicity-independent Humphreys-Davidson limit

The Humphreys-Davidson (HD) limit empirically defines a region of high luminosities (log10(L/L⊙) ≳ 5.5) and low effective temperatures ( $T_{\rm eff} \lesssim 20 , {\rm kK}$ ) 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 Magellanic Cloud (SMC) and Large Magellanic Cloud (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 overluminous stars in stellar evolution simulations, we generate synthetic populations of massive stars and make detailed comparisons with catalogues of cool ( $T_\mathrm{eff} \le 12.5, \mathrm{kK}$ ) and luminous (log10(L/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 overpredict the number of very luminous (log10(L/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.