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The Ultraviolet Spectrum and Physical Properties of the Mass Donor Star in HD 226868 = Cygnus X-1

We present an examination of high resolution, ultraviolet spectroscopy from Hubble Space Telescope of the photospheric spectrum of the O-supergiant in the massive X-ray binary HD 226868 = Cyg X-1. We analyzed this and ground-based optical spectra to determine the effective temperature and gravity of the O9.7 Iab supergiant. Using non-local thermodynamic equilibrium (non-LTE), line blanketed, plane parallel models from the TLUSTY grid, we obtain T_eff = 28.0 +/- 2.5kK and log g > 3.00 +/- 0.25, both lower than in previous studies. The optical spectrum is best fit with models that have enriched He and N abundances. We fit the model spectral energy distribution for this temperature and gravity to the UV, optical, and IR fluxes to determine the angular size of and extinction towards the binary. The angular size then yields relations for the stellar radius and luminosity as a function of distance. By assuming that the supergiant rotates synchronously with the orbit, we can use the radius - distance relation to find mass estimates for both the supergiant and black hole as a function of the distance and the ratio of stellar to Roche radius. Fits of the orbital light curve yield an additional constraint that limits the solutions in the mass plane. Our results indicate masses of 23^{+8}_{-6} M_sun for the supergiant and 11^{+5}_{-3} M_sun for the black hole.