Metallicity dependence of envelope inflation in massive stars

Context. Recently it has been found that models of massive stars reach the Eddington limit in their interior, which leads to dilute extended envelopes.
Aims: We perform a comparative study of the envelope properties of massive stars at different metallicities, with the aim to establish the impact of the stellar metallicity on the effect of envelope inflation.
Methods: We analysed published grids of core-hydrogen burning massive star models computed with metallicities appropriate for massive stars in the Milky Way, the Large Magellanic Cloud, and the Small Magellanic Cloud, the very metal poor dwarf galaxy I Zwicky 18, and for metal-free chemical composition.
Results: Stellar models of all the investigated metallicities reach and exceed the Eddington limit in their interior, aided by the opacity peaks of iron, helium, and hydrogen, and consequently develop inflated envelopes. Envelope inflation leads to a redward bending of the zero-age main sequence and a broadening of the main-sequence band in the upper part of the Hertzsprung-Russell diagram. We derive the limiting L/M-values as a function of the stellar surface temperature above which inflation occurs, and find them to be higher for lower metallicity. While Galactic models show inflation above 29 M_⊙, the corresponding mass limit for Population III stars is 150 M_⊙. While the masses of the inflated envelopes are generally low, we find that they can reach 1-100 M_⊙ in models with effective temperatures below 8000 K, with higher masses reached by models of lower metallicity.
Conclusions: Envelope inflation is expected to occur in sufficiently massive stars at all metallicities, and is expected to lead to rapidly growing pulsations, high macroturbulent velocities, and might well be related to the unexplained variability observed in luminous blue variables such as S Doradus and η Carina.