Astronomy Colloquium

The well-known Eddington limit for stars is thought to correspond to the maximum luminosity which a star may have in hydrostatic equilibrium. We show that in our
galaxy, stars above 40 Msun reach or even exceed this limit. Stellar models show that these stars do not become unstable, but inflate their radius. We discuss the observational evidence for this picture, its relation to the truely unstable so called Luminous Blue Variable stars and to dynamical pulsations, and derive consequences for massive single and binary star evolution and for the early stages of supernova explosions.