Understanding Compact Object Formation and Natal Kicks. III. The Case of Cygnus X-1

In recent years, accurate observational constraints have become available for an increasing number of Galactic X-ray binaries (XRBs). Together with proper-motion measurements, we could reconstruct the full evolutionary history of XRBs back to the time of compact object formation. In this paper, we present the first study of the persistent X-ray source Cygnus X-1 that takes into account all available observational constraints. Our analysis accounts for three evolutionary phases: orbital evolution and motion through the Galactic potential after the formation of a black hole (BH), and binary orbital dynamics at the time of core collapse. We find that the mass of the BH immediate progenitor is 15.0-20.0 M _⊙, and at the time of core collapse, the BH has potentially received a small kick velocity of <=77 km s^-1 at 95% confidence. If the BH progenitor mass is less than ~17 M _⊙, a non-zero natal kick velocity is required to explain the currently observed properties of Cygnus X-1. Since the BH has only accreted mass from its companion's stellar wind, the negligible amount of accreted mass does not explain the observationally inferred BH spin of a _* > 0.95, and the origin of this extreme BH spin must be connected to the BH formation itself. Right after the BH formation, we find that the BH companion is a 19.8-22.6 M _⊙ main-sequence star, orbiting the BH at a period of 4.7-5.2 days. Furthermore, recent observations show that the BH companion is currently super-synchronized. This super-synchronism indicates that the strength of tides exerted on the BH companion should be weaker by a factor of at least two compared to the usually adopted strength.