Rapid population synthesis of black-hole high-mass X-ray binaries: implications for binary stellar evolution

We conduct a binary population synthesis study to investigate the formation of wind-fed high-mass X-ray binaries containing black holes (BH-HMXBs). We evolve multiple populations of high-mass binary stars and consider BH-HMXB formation rates, masses, spins and separations. We find that systems similar to Cygnus X-1 likely form after stable Case A mass transfer (MT) from the main sequence progenitors of black holes, provided such MT is characterised by low accretion efficiency, $\beta \lesssim 0.1$, with modest orbital angular momentum losses from the non-accreted material. Additionally, BH-HMXB formation relies on a new simple treatment for Case A MT that allows donors to retain larger core masses compared to traditional rapid population-synthesis procedures. At solar metallicity, our Preferred model yields $\mathcal{O}(1)$ observable BH-HMXBs in the Galaxy today, consistent with observations. In this simulation, $8\%$ of BH-HMXBs go on to merge as binary black holes or neutron star-black hole binaries within a Hubble time. Compact-object mergers that evolve via a BH-HMXB phase may contribute $\gtrsim20$~Gpc$^{-3}$~yr$^{-1}$ to the merger rate inferred from gravitational-wave observations. We also suggest that MT efficiency is higher during stable Case B MT than during Case A MT.