The relationship between the Eddington limit, the observed upper luminosity limit for massive stars, and the luminous blue variables

The observed upper luminosity limits in the Galaxy and the LMC are compared with the Eddington limit as estimated for plane-parallel LTE model atmospheres which include the full effects of metal line opacities in the ultraviolet. It is shown that the Humphreys-Davidson (HD) limit corresponds to the locus of extremely low effective gravities. This result suggests that stars approaching the HD limit will suffer high mass-loss rates because of the reduction of the effective gravity due to radiation pressure. These high mass-loss rates ultimtely lead to the core mass fraction reaching its critical value and the reversal of the stellar evolution tracks. It is shown that radiation pressure, as an agent for producing enhanced mass loss near the HD limit, can in a natural way explain the kink in the HD limit near T(eff) roughly 10,000 K and the upper luminosity limit for yellow and red supergiants. The high mass-loss rates of the luminous blue variables, their location in the HR diagram, and their evolutionary stage are also discussed.