Formation rate of LB-1-like systems through dynamical interactions

We estimate formation rates of LB-1-like systems through dynamical interactions in the framework of the theory of stellar evolution before the discovery of the LB-1 system. The LB-1 system contains a ∼70 ${M_{\odot}}$ black hole (BH), a so-called pair instability (PI) gap BH, and a B-type star with solar metallicity, and has nearly zero eccentricity. The most efficient formation mechanism is as follows. In an open cluster, a naked helium star (with ∼20 ${M_{\odot}}$ ) collides with a heavy main sequence star (with ∼50 ${M_{\odot}}$ ) which has a B-type companion. The collision results in a binary consisting of the collision product and the B-type star with a high eccentricity. The binary can be circularized through the dynamical tide with radiative damping of the collision product envelope. Finally, the collision product collapses to a PI-gap BH, avoiding pulsational pair instability and pair instability supernovae because its He core is as massive as the pre-colliding naked He star. We find that the number of LB-1-like systems in the Milky Way galaxy is ∼0.01(ρ_oc/10⁴ ${M_{\odot}}$ pc^-3), where ρ_oc is the initial mass densities of open clusters. If we take into account LB-1-like systems with O-type companion stars, the number increases to ∼0.03(ρ_oc/10⁴ ${M_{\odot}}$ pc^-3). This mechanism can form LB-1-like systems at least ten times more efficiently than the other mechanisms: captures of B-type stars by PI-gap BHs, stellar collisions between other types of stars, and stellar mergers in hierarchical triple systems. We conclude that no dynamical mechanism can explain the presence of the LB-1 system.