Compact binary formation in open star clusters - I. High formation efficiency of Gaia BHs and their multiplicities

Gaia BHs, black hole (BH) binaries discovered from data base of an astrometric telescope Gaia, pose a question to the standard binary evolution model. We have assessed whether Gaia BHs can be formed through dynamical capture in open clusters rather than through isolated binary evolution. We have performed gravitational N-body simulations of 100 open clusters with 10(5) M-circle dot in total for each metallicity Z = 0.02, 0.01, and 0.005. We have discovered one Gaia BH-like binary escaping from an open cluster, and found that the formation efficiency of Gaia BHs in open clusters (similar to 10(-5) M-circle dot(-1)) is larger than in isolated binaries (similar to 10(-8) M-circle dot(-1)) by 3 orders of magnitude. The Gaia BH-like binary is the inner binary of a triple star system. Gaia BHs can have tertiary stars frequently, if they are formed in open clusters. Combining additional N-body simulations with 8000 open clusters with 8 x 10(6) M-circle dot, we have estimated the number of Gaia BHs in the Milky Way disc to 10(4)-10(5) (depending on the definitions of Gaia BHs), large enough for the number of Gaia BHs discovered so far. Our results indicate that the discoveries of Gaia BHs do not request the reconstruction of the standard binary evolution model, and that Gaia BHs are a probe for the dynamics of open clusters already evaporated.