Formation of the Dormant Black Holes with Luminous Companions from Binary or Triple Systems

Abstract

Recently, a class of dormant black hole binaries with luminous companions (dBH-LC) has been observed, such as $Gaia$ BH1, BH2, and BH3. Unlike previously discovered X-ray BH binaries, this type of dBH-LC has relatively long orbital periods (typically more than several tens to a few hundred days) and shows very weak X-ray emission. Therefore, studying the formation and evolution of the whole dBH-LC population is also a very interesting problem. Our aim is to study the contribution of massive stars to the dBH-LC population under different evolutionary models (isolated binary evolution (IBE) and hierarchical triple evolution), and different formation channels (such as mass transfer, common envelope evolution). Using the Massive Objects in Binary Stellar Evolution (MOBSE) code, the Triple Stellar Evolution (TSE) code, and the latest initial multiple-star distributions, we model the populations of massive stars. Finally, we calculate the orbital properties, mass distributions, and birthrates of the BH-LC populations formed under these different conditions. In the Milky Way, we calculate that the birthrate of dBH-LC formed through IBE is about 4.35$\times$$10^{-5}$ ${\rm yr}^{-1}$, while the birthrate through triple evolution is about 1.47$\times$$10^{-3}$ ${\rm yr}^{-1}$. This means that the birthrate 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-LC is post-merger binaries formed from inner binary mergers triggered by von Zeipel$-$Lidov$-$Kozai oscillations.