Dynamical formation of dormant black holes: Predictions for Gaia DR4

Abstract

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$_\odot$), 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 $\sim1\,$Gyr ($\sim10\,$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 $\sim1-64$ high-metallicity and $\sim0.4-48$ low-metallicity dormant BHs, with a period distribution peaking at $\sim10^3\,$d, $\gtrsim90\%$ of them with eccentricity $e>0.1$, and $\sim20\%$ with large BH masses ($m_{\rm BH} \gtrsim 30\,$M$_\odot$).