Comprehensive UV and optical spectral analysis of Cygnus X-1

Context. Cygnus X-1 contains the only dynamically confirmed black hole in a persistent high-mass X-ray binary in the Milky Way. Previous studies have suggested that the black hole in Cyg X-1 is one of the most massive stellar-mass black holes known in an X-ray binary, despite its high-metallicity environment. While the source has been actively investigated, a comprehensive UV and optical spectral analysis of the donor using modern stellar atmosphere models incorporating stellar winds and X-ray ionization has been lacking.Aims. We aim to determine the stellar parameters, chemical abundances, and wind parameters of the donor star in Cyg X-1 along with the mass of the black hole. We also aim to investigate the system's current evolutionary state and its future evolution toward a binary black hole system, exploring its potential as a gravitational wave source.Methods. We used archival high-resolution UV and optical spectra of Cyg X-1 taken at multiple orbital phases and X-ray states. We employed state-of-the-art, non-local thermodynamic equilibrium (non-LTE), Potsdam Wolf-Rayet (PoWR) atmosphere models that account for stellar winds, X-ray photoionization, metal line blanketing, and wind clumping. We performed a simultaneous analysis of UV and optical spectra. We further used the stellar evolution code MESA to model the further evolution of the system.Results. Our analysis yields notably lower masses for both the donor ( approx 29 M_{⊙) and the black hole ( 12.7 to 17.8 M⊙), depending on inclination), and confirms that the donor's radius is close to reaching the inner Lagrangian point. We find super-solar Fe, Si, and Mg abundances (1.3-1.8 times solar) at the surface of the donor star, while the total CNO abundance remains solar despite evidence of CNO processing (N enrichment, O depletion) and He enrichment. This abundance pattern is distinct from the surrounding Cyg OB3 association. We observed a clear difference in wind parameters between X-ray states: v∞ ≈ 1200 km s^{-1 and Ṁ ≈ 3 ⨯ 10−7 M⊙ yr−1in the high-soft state, increasing to v∞ ≲ 1800 km s−1 and Ṁ ≲ 5 ⨯ 10−7 M⊙ yr−1 in the low-hard state. The observed X-ray luminosity is consistent with wind-fed accretion. Evolutionary models show that Cyg X-1 will undergo Roche-lobe overflow in the near future. Under a fully conservative mass accretion scenario, our models predict a future binary black hole merger for Cyg X-1 within ∼ 5 Gyr.Conclusions. Our comprehensive analysis provides refined stellar and wind parameters of the donor star in Cyg X-1, highlighting the importance of using advanced atmospheric models and considering X-ray ionization and wind clumping. The observed abundances suggest a complex formation history involving a high initial metallicity. The potential for a future gravitational wave merger under highly conservative mass accretion makes Cyg X-1 crucial for understanding binary evolution.}}