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We present a novel, few-body computational framework designed to shed light on the likelihood of forming intermediate-mass (IM) and supermassive (SM) black holes (BHs) in nuclear star clusters (NSCs) through successive BH mergers, initiated with a single BH seed. Using observationally motivated NSC profiles, we find that the probability of an ${\sim }100\hbox{-}\mathrm{M}_\odot$ BH to grow beyond ${\sim }1000 \, \mathrm{M}_\odot$ through successive mergers ranges from ${\sim }0.1~{{\ \rm per\ cent}}$ in low-density, low-mass clusters to nearly 90  per cent in high-mass, high-density clusters. However, in the most massive NSCs, the growth time-scale can be very long ($\gtrsim 1\,$ Gyr); vice versa, while growth is least likely in less massive NSCs, it is faster there, requiring as little as ${\sim }0.1\,$Gyr. The increased gravitational focusing in systems with lower velocity dispersions is the primary contributor to this behaviour. We find that there is a simple ‘7-strikes-and-you’re-in’ rule governing the growth of BHs: Our results suggest that if the seed survives 7–10 successive mergers without being ejected (primarily through gravitational wave recoil kicks), the growing BH will most likely remain in the cluster and will then undergo runaway, continuous growth all the way to the formation of an SMBH (under the simplifying assumption adopted here of a fixed background NSC). Furthermore, we find that rapid mergers enforce a dynamically mediated ‘mass gap’ between about ${50\!-\!300 \, \mathrm{M}_\odot }$ in an NSC.

The theory of stellar escape from globular clusters (GCs) dates back nearly a century, especially the gradual evaporation of GCs via two-body relaxation coupled with external tides. More violent ejection can also occur via strong gravitational scattering, supernovae, gravitational wave-driven mergers, tidal disruption events, and physical collisions, but comprehensive study of the many escape mechanisms has been limited. Recent exquisite kinematic data from the Gaia space telescope has revealed numerous stellar streams in the Milky Way (MW) and traced the origin of many to specific MWGCs, highlighting the need for further examination of stellar escape from these clusters. In this study, the first of a series, we lay the groundwork for detailed follow-up comparisons between Cluster Monte Carlo GC models and the latest Gaia data on the outskirts of MWGCs, their tidal tails, and associated streams. We thoroughly review escape mechanisms from GCs and examine their relative contributions to the escape rate, ejection velocities, and escaper demographics. We show for the first time that three-body binary formation may dominate high-speed ejection from typical MWGCs, potentially explaining some of the hypervelocity stars in the MW. Due to their mass, black holes strongly catalyze this process, and their loss at the onset of observable core collapse, characterized by a steep central brightness profile, dramatically curtails three-body binary formation, despite the increased post-collapse density. We also demonstrate that even when born from a thermal eccentricity distribution, escaping binaries have significantly nonthermal eccentricities consistent with the roughly uniform distribution observed in the Galactic field.

The existence of black holes (BHs) with masses in the range between stellar remnants and supermassive BHs has only recently become unambiguously established. GW190521, a gravitational wave signal detected by the LIGO/Virgo Collaboration, provides the first direct evidence for the existence of such intermediate-mass BHs (IMBHs). This event sparked and continues to fuel discussion on the possible formation channels for such massive BHs. As the detection revealed, IMBHs can form via binary mergers of BHs in the “upper mass gap” (≈40–120M_⊙). Alternatively, IMBHs may form via the collapse of a very massive star formed through stellar collisions and mergers in dense star clusters. In this study, we explore the formation of IMBHs with masses between 120 and 500M_⊙in young, massive star clusters using state-of-the-art Cluster Monte Carlo models. We examine the evolution of IMBHs throughout their dynamical lifetimes, ending with their ejection from the parent cluster due to gravitational radiation recoil from BH mergers, or dynamical recoil kicks from few-body scattering encounters. We find thatallof the IMBHs in our models are ejected from the host cluster within the first ∼500 Myr, indicating a low retention probability of IMBHs in this mass range for globular clusters today. We estimate the peak IMBH merger rate to be$\mathit{}\approx 2{\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-1}$at redshiftz≈ 2.

Many recent observational and theoretical studies suggest that globular clusters (GCs) host compact object populations large enough to play dominant roles in their overall dynamical evolution. Yet direct detection, particularly of black holes and neutron stars, remains rare and limited to special cases, such as when these objects reside in close binaries with bright companions. Here we examine the potential of microlensing detections to further constrain these dark populations. Based on state-of-the-art GC models from theCMC Cluster Catalog, we estimate the microlensing event rates for black holes, neutron stars, white dwarfs (WDs), and, for comparison, also for M dwarfs in Milky Way GCs, as well as the effects of different initial conditions on these rates. Among compact objects, we find that WDs dominate the microlensing rates, simply because they largely dominate by numbers. We show that microlensing detections are in general more likely in GCs with higher initial densities, especially in clusters that undergo core collapse. We also estimate microlensing rates in the specific cases of M22 and 47 Tuc using our best-fitting models for these GCs. Because their positions on the sky lie near the rich stellar backgrounds of the Galactic bulge and the Small Magellanic Cloud, respectively, these clusters are among the Galactic GCs best suited for dedicated microlensing surveys. The upcoming 10 yr survey with the Rubin Observatory may be ideal for detecting lensing events in GCs.

The globular cluster 47 Tucanae (47 Tuc) is one of the most massive star clusters in the Milky Way and is exceptionally rich in exotic stellar populations. For several decades it has been a favorite target of observers, and yet it is computationally very challenging to model because of its large number of stars (N≳ 10⁶) and high density. Here we present detailed and self-consistent 47 Tuc models computed with theCluster Monte Carlocode (CMC). The models include all relevant dynamical interactions coupled to stellar and binary evolution, and reproduce various observations, including the surface brightness and velocity dispersion profiles, pulsar accelerations, and numbers of compact objects. We show that the present properties of 47 Tuc are best reproduced by adopting an initial stellar mass function that is both bottom-heavy and top-light relative to standard assumptions (as in, e.g., Kroupa 2001), and an initial Elson profile (Elson et al. 1987) that is overfilling the cluster’s tidal radius. We include new prescriptions inCMCfor the formation of binaries through giant star collisions and tidal captures, and we show that these mechanisms play a crucial role in the formation of neutron star binaries and millisecond pulsars in 47 Tuc; our best-fit model contains ∼50 millisecond pulsars, 70% of which are formed through giant collisions and tidal captures. Our models also suggest that 47 Tuc presently contains up to ∼200 stellar-mass black holes, ∼5 binary black holes, ∼15 low-mass X-ray binaries, and ∼300 cataclysmic variables.