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Abstract The recent discovery of two detached black hole–star (BH–star) binaries from Gaia’s third data release has sparked interest in understanding the formation mechanisms of these systems. We investigate the formation of these systems by dynamical processes in young star clusters (SCs) and via isolated binary (IB) evolution, using a combination of directN-body and population synthesis simulations. We find that dynamical formation in SCs is nearly 50 times more efficient per unit of star formation at producing BH–star binaries than IB evolution. We expand this analysis to the full Milky Way (MW) using a FIRE-2 hydrodynamical simulation of an MW-mass galaxy. Even assuming that only 10% of star formation goes into SCs, we find that approximately four out of every five BH–star systems are formed dynamically, and that the MW contains a total of ∼2 × 10⁵BH–star systems. Many of these dynamically formed systems have longer orbital periods, greater eccentricities, and greater black hole masses than their isolated counterparts. For binaries older than 100 Myr, we show that any detectable system withe≳ 0.5 orM_BH≳ 10M_⊙canonlybe formed through dynamical processes. Our MW model predicts between 64 and 215 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. 

Abstract The dense environments in the cores of globular clusters (GCs) facilitate many strong dynamical encounters among stellar objects. These encounters have been shown to be capable of ejecting stars from the host GC, whereupon they become runaway stars, or hypervelocity stars (HVSs) if unbound to the galactic potential. We study high-speed stellar ejecta originating from GCs by using Monte CarloN-body models, in particular focusing on binary–single encounters involving compact objects. We pair our model-discriminated populations with observational catalogs of Milky Way GCs (MWGCs) to compose a present-day Galactic population of stellar ejecta. We find that these kinds of encounters can accelerate stars to velocities in excess of 2000 km s⁻¹, to speeds beyond the previously predicted limits for ejecta from star-only encounters and in the same regime of Galactic center ejections. However, the same ejections can only account for 1.5%–20% of the total population of stellar runaways, and only 0.0001%–1% of HVS, with similar relative rates found for runaway white dwarfs. We also provide credible regions for ejecta from 149 MWGCs, which we hope will be useful as supplementary evidence when pairing runaway stars with origin GCs. 

ABSTRACT The current generation of galaxy simulations can resolve individual giant molecular clouds, the progenitors of dense star clusters. But the evolutionary fate of these young massive clusters, and whether they can become the old globular clusters (GCs) observed in many galaxies, is determined by a complex interplay of internal dynamical processes and external galactic effects. We present the first star-by-star N-body models of massive (N ∼ 105–107) star clusters formed in a FIRE-2 MHD simulation of a Milky Way-mass galaxy, with the relevant initial conditions and tidal forces extracted from the cosmological simulation. We select 895 (∼30 per cent) of the YMCs with >6 × 104 M⊙ from Grudić et al. 2022 and integrate them to z = 0 using the cluster Monte Carlo code, CMC. This procedure predicts a MW-like system with 148 GCs, predominantly formed during the early, bursty mode of star formation. Our GCs are younger, less massive, and more core-collapsed than clusters in the Milky Way or M31. This results from the assembly history and age-metallicity relationship of the host galaxy: Younger clusters are preferentially born in stronger tidal fields and initially retain fewer stellar-mass black holes, causing them to lose mass faster and reach core collapse sooner than older GCs. Our results suggest that the masses and core/half-light radii of GCs are shaped not only by internal dynamical processes, but also by the specific evolutionary history of their host galaxies. These results emphasize that N-body studies with realistic stellar physics are crucial to understanding the evolution and present-day properties of GC systems. 

ABSTRACT The properties of young star clusters formed within a galaxy are thought to vary in different interstellar medium conditions, but the details of this mapping from galactic to cluster scales are poorly understood due to the large dynamic range involved in galaxy and star cluster formation. We introduce a new method for modelling cluster formation in galaxy simulations: mapping giant molecular clouds (GMCs) formed self-consistently in a FIRE-2 magnetohydrodynamic galaxy simulation on to a cluster population according to a GMC-scale cluster formation model calibrated to higher resolution simulations, obtaining detailed properties of the galaxy’s star clusters in mass, metallicity, space, and time. We find $$\sim 10{{\ \rm per\ cent}}$$ of all stars formed in the galaxy originate in gravitationally bound clusters overall, and this fraction increases in regions with elevated Σgas and ΣSFR, because such regions host denser GMCs with higher star formation efficiency. These quantities vary systematically over the history of the galaxy, driving variations in cluster formation. The mass function of bound clusters varies – no single Schechter-like or power-law distribution applies at all times. In the most extreme episodes, clusters as massive as 7 × 106 M⊙ form in massive, dense clouds with high star formation efficiency. The initial mass–radius relation of young star clusters is consistent with an environmentally dependent 3D density that increases with Σgas and ΣSFR. The model does not reproduce the age and metallicity statistics of old ($$\gt 11\rm Gyr$$) globular clusters found in the Milky Way, possibly because it forms stars more slowly at z > 3. 

The surface brightness profiles of globular clusters are conventionally described with the well-known King profile. However, observations of young massive clusters (YMCs) in the local Universe suggest that they are better fit by simple models with flat central cores and simple power-law densities in their outer regions (such as the Elson-Fall-Freeman, or EFF, profile). Depending on their initial central density, YMCs may also facilitate large numbers of stellar collisions, potentially creating very massive stars that will directly collapse into intermediate-mass black holes (IMBHs). Using Monte CarloN-body models of YMCs, we show that EFF-profile clusters transform to Wilson or King profiles through natural dynamical evolution, but that their finalW₀parameters do not strongly correlate to their initial concentrations. In the densest YMCs, runaway stellar mergers can produce stars that collapse into IMBHs, with their final masses depending on the treatment of the giant star envelopes during collisions. If a common-envelope prescription is assumed, where the envelope is partially or entirely lost, stars form with masses up to 824M_⊙, collapsing into IMBHs of 232M_⊙. Alternatively, if no mass loss is assumed, stars as massive as 4000M_⊙can form, collapsing into IMBHs of ∼4000M_⊙. In doing so, these runaway collisions also deplete the clusters of their primordial massive stars, reducing the number of stellar-mass BHs by as much as ∼40%. This depletion will accelerate the core collapse, suggesting that the process of IMBH formation itself may produce the high densities observed in some core-collapsed clusters. 

The long-term relaxation of rotating, spherically symmetric globular clusters is investigated through an extension of the orbit-averaged Chandrasekhar non-resonant formalism. A comparison is made with the long-term evolution of the distribution function in action space, measured from averages of sets ofN-body simulations up to core collapse. The impact of rotation on in-plane relaxation is found to be weak. In addition, we observe a clear match between theoretical predictions andN-body measurements. For the class of rotating models considered, we find no strong gravo-gyro catastrophe accelerating core collapse. Both kinetic theory and simulations predict a reshuffling of orbital inclinations from overpopulated regions to underpopulated ones. This trend accelerates as the amount of rotation is increased. Yet, for orbits closer to the rotational plane, the non-resonant prediction does not reproduce numerical measurements. We argue that this mismatch stems from these orbits’ coherent interactions, which are not captured by the non-resonant formalism that only addresses local deflections. 

Context.Despite the nearly hundred gravitational-wave detections reported by the LIGO-Virgo-KAGRA Collaboration, the question of the cosmological origin of merging binary black holes (BBHs) remains open. The two main formation channels generally considered are from isolated field binaries or via dynamical assembly in dense star clusters. Aims.Here we focus on understanding the dynamical formation of merging BBHs within massive clusters in galaxies of different masses. Methods.To this end, we applied a new framework to consistently model the formation and evolution of massive star clusters in zoom-in cosmological simulations of galaxies. Each simulation, taken from the FIRE project, provides a realistic star formation environment, with a unique star formation history, that hosts realistic giant molecular clouds that constitute the birthplace of star clusters. Combined with the code for star cluster evolutionCMC, we are able to produce populations of dynamically formed merging BBHs across cosmic time in different environments. Results.As the most massive star clusters preferentially form in dense massive clouds of gas, we find that, despite their low metallicities favouring the creation of black holes, low-mass galaxies contain few massive clusters and therefore make a limited contribution to the global production of dynamically formed merging BBHs. Furthermore, we find that massive clusters can host hierarchical BBH mergers with clear, identifiable physical properties. Looking at the evolution of the BBH merger rate in different galaxies, we find strong correlations between BBH mergers and the most extreme episodes of star formation. Finally, we discuss the implications for future LIGO-Virgo-KAGRA gravitational wave observations.