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 $\sim 70M_\odot$ black hole (BH), so-called pair instability (PI)-gap BH, and 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 (He) star (with $\sim 20M_\odot$) collides with a heavy main-sequence (MS) star (with $\sim 50M_\odot$) which has a B-type companion. The collision results in a binary consisting of the collision product and 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 $\sim 0.01 (\rho_{\rm oc} / 10^4 M_\odot \mbox{pc}^{-3})$, where $\rho_{\rm oc}$ 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 $\sim 0.03 (\rho_{\rm oc} / 10^4 M_\odot \mbox{pc}^{-3})$. This mechanism can form LB-1-like systems at least 10 times more efficiently than the other mechanisms: captures of B-type stars by PI-gap BHs, stellar collisions between other type stars, and stellar mergers in hierarchical triple systems. We conclude that no dynamical mechanism can explain the presence of the LB-1 system.