Black hole dynamics in star clusters: Eccentric mergers and star-black hole binaries

[eng] Star clusters are dense stellar systems, where the gravitational interactions between stars and black holes (BH) play a crucial role in shaping their structure and evolution. These interactions can produce exotic systems, including merging binary black holes (BBH) and BHs with stellar companions (hereafter, star-BH binaries). Understanding the formation channels and properties of these systems sheds light on the dynamical processes within star clusters, and is essential for interpreting gravitational wave (GW) detections. The goal of this Thesis is to understand the outcome of few-body interactions in star clusters, specifically the ones leading to BBH mergers with detectable eccentricity and dormant star-BH binaries. We discuss the formation of these sources, as well as the implications for current and future observations. In the first paper, we study the population of dynamically assembled BBHs – commonly referred to as ‘three-body’ BBHs – in star clusters. In contrast to those BBHs that formed from the unperturbed evolution of binaries of massive stars that originated as part of the cluster formation process (so-called primordial binaries), three-body BBHs are assembled via the interaction of at least three previously unbound BHs. The motivation for this first paper is two-fold: firstly, we test the suggestion that the binaries that lead to BBH mergers are three-body binaries, so it is important to understand their formation; secondly, a high efficiency of in-cluster BBH mergers was found in numerical simulations of low-mass clusters, a not yet understood finding that we aim to shed light on. By using gravitational N-body simulations of stars clusters we find that, contrary to theoretical predictions, each cluster has, on average, only one three-body BBH, because the formation of new binaries is suppressed by a high rate of binary–binary interactions, which efficiently ionize one of the binaries involved. In the second paper, we study in detail the aforementioned BBHBBH interactions with numerical N-body scattering experiments with post-Newtonian dynamics. Specifically, we are interested in how these interactions lead to GW captures – and their associated eccentricities at the frequencies of ground-based GW detectors – as well as BH triple formation and their contribution to BBH mergers via the von ZeipelLidov-Kozai mechanism. We confirm the idea presented in the first paper that most BBH-BBH interactions involve three-body BBHs, and we show that the BBH-BBH interaction rate is comparable to the threebody BBH formation rate. Using a population synthesis model, we derive the merger rate for GW captures, its evolution with redshift, and the eccentricity distribution. We argue that dynamically formed triples contribute less to the merger rate than GW captures in BBH-BBH interactions. In the second part of this Thesis (paper three), we study the formation of dormant star-BH systems. This work was prompted by the announcement of the discovery of Gaia BH3, a binary of a massive BH (33M⊙) in a wide orbit around a giant star. The properties of this system, as well as its orbit around the Milky Way, challenge models of binary stellar evolution. We show that this system likely formed dynamically in the progenitor cluster of the ED-2 stream. The results shown in this Thesis have paved the way to understanding the population of BHs in star clusters and the outcomes of their dynamical effects. We have shed light on the dynamical formation of BBH mergers, especially those with detectable eccentricity, and the dynamical assembly of dormant star-BH systems. These results are key to understand current and future observations of GWs, and dormant star-BHs from, e.g. Gaia and other surveys.