Detection of single-degenerate massive binaries with Gaia: The impact of blue supergiants, triples, mass precision, and high-precision parallax requirements

Hundreds of black holes with massive main-sequence companions (OB+BHs) might be identified from Gaia astrometry with the Astrometric Mass-Ratio Function (AMRF). We investigate the impact of blue supergiant companions (BSG) instead of dwarfs and the presence of additional companions in the system that are unresolved by Gaia on the astrometric identification of OB+BHs. We also explore how accurate the primary mass needs to be constrained. Moreover, we assess how the high-precision publishing constraints of astrometric binary orbits in the latest Gaia data release DR3 impact the detection of OB+BHs. We establish a BSG mass-magnitude relation and compute BSG AMRF curves. From a mock population of non- and single-degenerate massive binaries and triples with OB or BSG primaries, we asses the false-positive identification fraction and the effect of the BSG AMRF curves. We compare the number of stars with astrometric DR3 orbits in the second Alma Luminous Star catalogue (ALSII) with new predictions on the OB+BH detection using the conservative DR3 publishing criteria. BSG primaries and triples are not expected to impact the false-positive identification fractions significantly. However, if the evolutionary stage of the primary star is unknown, the usage of the BSG curves is still recommended. This also reduces the OB+BH identification fraction significantly. The primary mass does not need to be known to benefit from the high identification fraction of OB+BHs, while keeping the fraction of false-positives low. We find no OB+BH candidates in the ALS II among the DR3 orbits. This null-detection cannot be attributed to the underlying BH-formation scenario, but rather to the stringent DR3 selection criteria. To infer the BH-formation scenario with Gaia, we propose that the constraint on the relative parallax precision in DR4 should be 95% less conservative than the DR3 criterion.(Abridged)