Evolutionary constraints on the masses of the components of the HDE 226868/Cyg X-1 binary system

Calculations carried out to model the evolution of HDE 226868, under different assumptions about the stellar wind mass-loss rate, provide robust limits on the present mass of the star. It has to be in the range 40 ± 5 M⊙ if the distance to the system is in the range 1.95–2.35 kpc and the effective temperature of HDE 226868 in the range 30 000–31 000 K. Extending the possible intervals of these parameters to 1.8–2.35 kpc and 28 000–32 000 K, one gets for the mass of the star the range 40 ± 10 M⊙. Including into the analysis observational properties such as the profiles of the emission lines, rotational broadening of the absorption lines and the ellipsoidal light variations, one can estimate also the mass of the compact component. It has to be in the ranges 20 ± 5 M⊙ and 13.5–29 M⊙ for the cases described above. The same analysis (using the evolutionary models and the observational properties listed above) yields a lower limit to the distance to the system of ∼2.0 kpc, if the effective temperature of HDE 226868 is higher than 30 000 K. This limit to the distance does not depend on any photometric or astrometric considerations.