Uncovering astrometric black hole binaries with massive main-sequence companions with

Context. In the era of gravitational wave astrophysics and with the precise astrometry of billions of stellar sources, the hunt for compact objects is more alive than ever. Rarely seen massive binaries with a compact object are a crucial phase in the evolution towards compact object mergers. With the upcoming third Gaia data release (DR3), the first Gaia astrometric orbital solutions for binary sources will become available, potentially revealing many such binaries. Aims. We investigate how many black holes (BHs) with massive main-sequence dwarf companions (OB+BH binaries) are expected to be detected as binaries in Gaia DR3 and at the end of the nominal 5-year mission. We estimate how many of those are identifiable as OB+BH binaries and discuss the distributions of the masses of both components as well as of their orbital periods. We also explore how different BH-formation scenarios affect these distributions. Methods. We apply observational constraints to tailored models for the massive star population, which assume a direct collapse and no kick upon BH formation, to estimate the fraction of OB+BH systems that will be detected as binaries by Gaia, and consider these the fiducial results. These OB+BH systems follow a distance distribution according to that of the second Alma Luminous Star catalogue (ALS II). We use a method based on astrometric data to identify binaries with a compact object and investigate how many of the systems detected as binaries are identifiable as OB+BH binaries. Different scenarios for BH natal kicks and supernova mechanisms are explored and compared to the fiducial results. Results. In the fiducial case we conservatively estimate that 77% of the OB+BH binaries in the ALS II will be detected as binaries in DR3, of which 89% will be unambiguously identifiable as OB+BH binaries. By the end of the nominal 5-year mission, the detected fraction will increase to 85%, of which 82% will be identifiable. The 99% confidence intervals on these fractions are of the order of a few percent. These fractions become smaller for different BH-formation scenarios. Conclusions. Assuming direct collapse and no natal kick, we expect to find around 190 OB+BH binaries in Gaia DR3 among the sources in the ALS II, which increases the known sample of OB+BH binaries by more than a factor of 20 and covers an uncharted parameter space of long-period binaries (10 ≲ P ≲ 1000 d). Our results further show that the size and properties of the OB+BH population that is identifiable using Gaia DR3 will contain crucial observational constraints that will help us improve our understanding of BH formation. An additional ∼5 OB+BH binaries could be identified at the end of the nominal 5-year mission, which are expected to have either very short (P ≲ 10 d) or long periods (P ≳ 1000 d)