Massive main-sequence stars evolving at the Eddington limit⋆

Context. Massive stars play a vital role in the Universe, however, their evolution even on the main-sequence is not yet well understood. Aims. Because of the steep mass-luminosity relation, massive main-sequence stars become extremely luminous. This brings their envelopes very close to the Eddington limit. We analyse stellar evolutionary models in which the Eddington limit is reached and exceeded, explore the rich diversity of physical phenomena that take place in their envelopes, and investigate their observational consequences. Methods. We use published grids of detailed stellar models, computed with a state-of-the-art, one-dimensional hydrodynamic stellar evolution code using LMC composition, to investigate the envelope properties of core hydrogen burning massive stars. Results. We find that the Eddington limit is almost never reached at the stellar surface, even for stars up to 500 M . When we define an appropriate Eddington limit locally in the stellar envelope, we can show that most stars more massive than ∼40 M actually exceed this limit, in particular, in the partial ionisation zones of iron, helium, or hydrogen. While most models adjust their structure such that the local Eddington limit is exceeded at most by a few per cent, our most extreme models do so by a factor of more than seven. We find that the local violation of the Eddington limit has severe consequences for the envelope structure, as it leads to envelope inflation, convection, density inversions, and, possibly to, pulsations. We find that all models with luminosities higher than 4× 105 L , i.e. stars above ∼40 M show inflation, with a radius increase of up to a factor of about 40. We find that the hot edge of the S Dor variability region coincides with a line beyond which our models are inflated by more than a factor of two, indicating a possible connection between S Dor variability and inflation. Furthermore, our coolest models show highly inflated envelopes with masses of up to several solar masses, and appear to be candidates for producing major luminous blue variable eruptions. Conclusions. Our models show that the Eddington limit is expected to be reached in all stars above ∼40 M in the LMC, even in lower mass stars in the Galaxy, or in close binaries or rapid rotators. While our results do not support the idea of a direct super-Eddington wind driven by continuum photons, the consequences of the Eddington limit in the form of inflation, pulsations and possibly eruptions may well give rise to a significant enhancement of the time averaged mass-loss rate.