Population Synthesis of Black Hole Binaries with Compact Star Companions

Abstract

We perform a systematic study of merging black hole (BH) binaries with compact star (CS) companions, including black hole--white dwarf (BH--WD), black hole--neutron star (BH--NS) and black hole--black hole (BH--BH) systems. Previous studies have shown that mass transfer stability and common envelope evolution can significantly affect the formation of merging BH--CS binaries through isolated binary evolution. With detailed binary evolution simulations, we obtain easy-to-use criteria for the occurrence of the common envelope phase in mass-transferring BH binaries with a nondegenerate donor, and incorporate into population synthesis calculations. To explore the impact of possible mass gap between NSs and BHs on the properties of merging BH--CS binary population, we adopt different supernova mechanisms involving the \textit{rapid}, \textit{delayed} and \textit{stochastic} prescriptions to deal with the compact remnant masses and the natal kicks. Our calculations show that there are $ \sim 10^{5} -10^{6}$ BH--CS binaries in the Milky Way, among which dozens are observable by future space-based gravitational wave detectors. We estimate that the local merger rate density of all BH--CS systems is $ \sim 60-200 \,\rm Gpc^{-3}yr^{-1}$. While there are no low-mass BHs formed via \textit{rapid} supernovae, both \textit{delayed} and \textit{stochastic} prescriptions predict that $ \sim 100\% $/$ \sim 70\% $/$ \sim 30\% $ of merging BH--WD/BH--NS/BH--BH binaries are likely to have BH components within the mass gap.