FUNDAMENTAL PARAMETERS OF GALACTIC LUMINOUS OB STARS .2. A SPECTROSCOPIC ANALYSIS OF HDE-226-868 AND THE MASS OF CYGNUS-X-1

We present a spectroscopic analysis of the O9.7 Iab star HDE 226 868, which is the optical counterpart of Cygnus X-1. We use this extreme su pergiant to test the differences in the stellar parameters derived usi ng plane parallel hydrostatic model atmospheres and spherical non-hydr ostatic models (''Unified Model''). We find that the difference is sig nificant, but smaller than it is needed to explain the mass and helium discrepancy between the theories of stellar atmospheres and evolution . We also find that the dilution effect of He I 4471 is not due only t o the presence of a strong wind. We use the derived atmospheric parame ters to show that Cygnus X-1 has to be a black hole (provided it is a single compact object) in a way that is independent of the distance to the system and assumptions about the mass-luminosity relation of the visible star. We also derive a probable mass for Cygnus X-1.