The boring history of Gaia BH3 from isolated binary evolution

Gaia BH3 is the first observed dormant black hole (BH) with a mass of \(\approx{30}\) M\(_\odot\) and represents the first confirmation that such massive BHs are associated with metal-poor stars. Here, we explore the isolated binary formation channel for Gaia BH3 focusing on the old and metal-poor stellar population of the Milky Way halo. We use the MIST stellar models and our open-source population synthesis code SEVN to evolve \(5.6 \times 10^8\) binaries exploring 20 sets of parameters. We find that systems like Gaia BH3 form preferentially from binaries initially composed of a massive star (\(40-60\) M\(_\odot\)) and a low mass companion (\(10^3\) days) and eccentric orbit (\(e>0.6\)). Such progenitor binary stars do not undergo any Roche-lobe overflow episode during their entire evolution, so that the final orbital properties of the BH-star system are determined at the core collapse of the primary star. Low natal kicks (\(\lesssim\) 10~km/s) significantly favour the formation of Gaia BH3-like systems, but high velocity kicks up to \(\approx 220\) km/s are also allowed. We estimate the formation efficiency for Gaia BH3-like systems in old (\(t>10\) Gyr) and metal-poor (\(Z