Dynamical formation of dormant black holes: Predictions for Gaia DR4

Dormant black holes (dormant BHs, i.e., X-ray quiet binaries comprising a BH and a companion star) are probes of the effect of cluster dynamics and binary stellar evolution on compact-object binaries. A dozen dormant BH binaries are known, a number that will increase substantially with the upcoming Gaia Data Release 4 (DR4). Their origin is uncertain, and dynamical formation is proposed as one possible channel. Here, we study the formation of dormant BHs in low-mass star clusters, accounting for the interplay of binary stellar evolution and cluster dynamics. We present new simulations with the N-body code PeTar, interfaced with the population synthesis code SEVN for single and binary star evolution. Our grid spans a range of cluster masses (300-4800, M), metallicities (1.4 times10-2, 1.4 times10-4), and natal kick models (with and without fallback). We find that almost all dormant BH binaries escape the parent cluster within about1, Gyr (about10, Myr) when assuming weak (strong) natal kicks. Most (73%) dormant BHs form via the exchange of a BH (or its progenitor star) into a stellar binary, or of a star into a binary with a BH. Dormant BHs in low-mass clusters have a wide orbital period distribution (from a few hours to 10 8, d), with an upper limit set by natal kicks, a bimodal eccentricity distribution (a first peak at zero eccentricity for circularised systems and a second at high eccentricity), and stellar masses that follow the (evolved) initial mass function. Large BH masses are a smoking gun of dynamical formation, via exchanges and stellar collisions. We expect Gaia DR4 to contain about1-64 high-metallicity and about0.4-48 low-metallicity dormant BHs, with a period distribution peaking at about10 cubed, d, 90% of them with eccentricity e>0.1, and about20% with large BH masses (m BH 30, M).