  Detection of black holes (BHs) with detached luminous companions (LCs) can be
instrumental in connecting the BH properties with their progenitors' since the
latter can be inferred from the observable properties of the LC. Past studies
showed the promise of Gaia astrometry in detecting BH-LC binaries. We build
upon these studies by: 1) initialising the zero-age binary properties based on
realistic, metallicity-dependent star-formation history in the Milky Way (MW),
2) evolving these binaries to current epoch to generate realistic MW
populations of BH-LC binaries, 3) distributing these binaries in the MW
preserving the complex age-metallicity-Galactic position correlations, 4)
accounting for extinction and reddening using three-dimensional dust maps, 5)
examining the extended Gaia mission's ability to resolve BH-LC binaries. We
restrict ourselves to detached BH-LC binaries with orbital period <10 yr such
that Gaia can observe at least one full orbit. We find: 1) the extended Gaia
mission can astrometrically resolve 30-300 detached BH-LC binaries depending on
our assumptions of supernova physics and astrometric detection threshold; 2)
Gaia's astrometry alone can indicate BH candidates for 10-100 BH-LC binaries by
constraining the dark primary mass >3 Msun; 3) distributions of observables
including orbital periods, eccentricities, and component masses are sensitive
to the adopted binary evolution model, hence can directly inform binary
evolution models. Finally, we comment on the potential to further characterise
these BH binaries through radial velocity measurements and observation of X-ray
counterparts.
