Young Star Clusters Dominate the Production of Detached Black Hole-Star Binaries

The recent discovery of two detached black hole-star (BH-star) binaries from Gaia's third data release has sparkled interest in understanding the formation mechanisms of these systems. We investigate the formation of these systems by dynamical processes in young open star clusters (SCs) and via isolated binary (IB) evolution, using a combination of direct $N$-body models and population synthesis simulations. By comparing dynamical and isolated systems created using the same model of binary stellar evolution, we find that dynamical formation in SCs is nearly 40 times as efficient per unit of star formation at producing BH-star binaries compared to IB evolution. We expand this analysis to the full Milky Way (MW) using a FIRE-2 hydrodynamical simulation of a MW-mass galaxy. Even assuming that only $10\%$ of star formation produces SCs with masses $> 1000\,\mathrm{M_{\odot}}$, we find that the MW contains $\sim 2 \times 10^5$ BH-star systems, with approximately 4 out of every 5 systems being formed dynamically. Many of these dynamically-formed systems have larger orbital periods, eccentricities, and black hole masses than their isolated counterparts. For binaries older than 100 Myr, we show that any detectable system with $e\gtrsim0.5$ or $M_{\rm BH}\gtrsim 10\,\mathrm{M_{\odot}}$ can only be formed through dynamical processes. Our MW model predicts between 61 and 210 such detections from the complete DR4 Gaia catalog, with the majority of systems being dynamically formed in massive and metal-rich SCs. Finally, we compare our populations to the recently discovered Gaia BH1 and Gaia BH2, and conclude that the dynamical scenario is the most favorable formation pathway for both systems.