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 −1 in 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.