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Soon after the Gaia data release (DR) 3 in June 2022, some candidates (andone confirmed) of detached black hole (BH) - luminous companion (LC) binarieshave been reported. Existing and future detections of astrometric BH-LCbinaries will shed light on the spatial distribution of these systems, whichcan deepen our understanding of the natal kicks and the underlying formationmechanism of BHs. By tracking Galactic orbits of BH-LC binaries obtained fromBSE, we find that distributions of BH mass and the height from the Galacticplane |z| would help us give a constraint on supernova model. We also indicatethat the correlations of (i) orbital periods and eccentricities, and (ii) BHmass and $|z|$ could be clues for the strength of natal kick, and that thecorrelations of ($P$, $Z/Z_\odot$) may tell us a clue for common envelope (CE)efficiency. We also discuss the possibility of forming BH-LC binaries like theBH binary candidates reported in Gaia DR3 and Gaia BH 1, finding that if thecandidates as well as the confirmed binary originate from isolated binaries,they favor models which produce low-mass BHs and have high CE efficienciesexceeding unity.

Spatial and Binary Parameter Distributions of Black Hole Binaries in the Milky Way Detectable with Gaia