Diagnosing the Properties and Evolutionary Fates of Black Hole and Wolf-Rayet X-ray Binaries as Potential Gravitational Wave Sources for the LIGO-Virgo-KAGRA Network

IC 10 X-1, NGC 300 X-1, and Cyg X-3 constitute a unique class of X-ray binaries in which a stellar-mass black hole (BH) accretes material from a Wolf–Rayet (WR). These systems are particularly intriguing because of their short orbital periods, which make them promising progenitors of gravitational-wave (GW) sources detectable by the LIGO–Virgo–KAGRA (LVK) network. Adopting a revised accretion efficiency within the standard Bondi–Hoyle–Lyttleton framework, we perform detailed binary evolution calculations using MESA to characterize their properties at different evolutionary stages and to assess their ultimate fates as potential LVK-detectable GW sources. By applying additional constraints from the observed properties of IC 10 X-1 and NGC 300 X-1, we find that the upper limits on the BH masses in these systems (MBH ≲ 25 M⊙ for IC 10 X-1 and MBH ≲ 15 M⊙ for NGC 300 X-1) are significantly lower than previous estimates. Both systems are expected to form binary black holes (BBHs) that will merge within a Hubble time, except in the case where the BH in NGC 300 X-1 has a mass of 9 M⊙, corresponding to the lower limit inferred in a previous study using the continuum-fitting method with a relativistic slim-disc model. For Cyg X-3, we find that the BH spin magnitude is constrained to be ≲ 0.6. Moreover, the WR star in Cyg X-3 is likely to form a lower-mass-gap BH, and the resulting BBH system is also expected to merge within a Hubble time.