Formation of the dormant black holes with luminous companions from binary or triple systems

Context. Recently, a class of dormant black hole (BH) binaries with luminous companions (dBH-LCs) has been observed, such as Gaia BH1, BH2, and BH3. Unlike previously discovered X-ray BH binaries, the observed dBH-LCs have relatively long orbital periods (typically more than several tens to a few hundred days) and show very weak X-ray emission. Aims. Studying the formation and evolution of the whole dBH-LC population is a very interesting problem. Our aim is to study the contribution of massive stars to the dBH-LC population under different evolutionary models, namely, isolated binary evolution (IBE) and hierarchical triple evolution, and different formation channels (i.e., mass transfer and common envelope evolution). Methods. Using the Massive Objects in Binary Stellar Evolution code, the Triple Stellar Evolution code, and the latest initial multiple-star distributions, we modeled the populations of massive stars. We then calculated the orbital properties, mass distributions, and birth rates of the dBH-LC populations formed under these different conditions. Results. In the Milky Way, we calculate that the birth rate of dBH-LCs formed through IBE is about 4.35 × 10−5 yr−1, while the birth rate through triple evolution is about 1.47 × 10−3 yr−1. This means that the birth rate from triple evolution is one to two orders of magnitude higher than that from IBE. We find that in triple evolution, the main formation channel of dBH-LCs is post-merger binaries formed from inner binary mergers triggered by von Zeipel−Lidov−Kozai oscillations. In particular, if the merger product is formed from a central helium-burning star and a main-sequence star, the resulting star usually has a small core mass and a large envelope mass. The stars with this structure can form BHs in the pair-instability supernova range (about 60 M⊙ ∼ 120 M⊙), and they are about three times more massive than the maximum BH mass formed through IBE. Conclusions. Due to the presence of dynamical effects in triple evolution, the inner binaries in triples are more likely to interact than isolated binaries. As a result, dBH-LCs formed through triple evolution mainly come from the channel where the inner binary merges. The birth rate of dBH-LCs from triple evolution is about two orders of magnitude higher than that from IBE. In addition, some dBH-LCs with heavy BHs are also formed through the inner binary merger channel in triples. These results strongly indicate that the triple evolution can be the most important channel for dBH-LC formation.