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Abstract We explore three-body binary formation (3BBF), the formation of a bound system via gravitational scattering of three initially unbound bodies (3UB), using direct numerical integrations. For the first time, we consider systems with unequal masses, as well as finite-size and post-Newtonian effects. Our analytically derived encounter rates and numerical scattering results reproduce the 3BBF rate predicted by Goodman & Hut for hard binaries in dense star clusters. We find that 3BBF occurs overwhelmingly through nonresonant encounters and that the two most-massive bodies are never the most likely to bind. Instead, 3BBF favors pairing the two least-massive bodies (for wide binaries) or the most- plus least-massive bodies (for hard binaries). 3BBF overwhelmingly favors wide-binary formation with superthermal eccentricities, perhaps helping to explain the eccentric wide binaries observed by Gaia. Hard-binary formation is far rarer, but with a thermal eccentricity distribution. The semimajor axis distribution scales cumulatively asa³for hard and slightly wider binaries. Although mergers are rare between black holes when including relativistic effects, direct collisions occur frequently between main-sequence stars—more often than hard 3BBF. Yet, these collisions do not significantly suppress hard 3BBF at the low-velocity dispersions typical of open or globular clusters. Energy dissipation through gravitational radiation leads to a small probability of a bound, hierarchical triple system forming directly from 3UB. 

Abstract Very massive stars (VMSs) formed via a sequence of stellar collisions in dense star clusters have been proposed as the progenitors of massive black hole seeds. VMSs could indeed collapse to form intermediate-mass black holes, which would then grow by accretion to become the supermassive black holes observed at the centers of galaxies and powering high-redshift quasars. Previous studies have investigated how different cluster initial conditions affect the formation of a VMS, including mass segregation, stellar collisions, and binaries, among others. In this study, we investigate the growth of VMSs with a new grid of Cluster Monte Carlo star cluster simulations—the most expansive to date. The simulations span a wide range of initial conditions, varying the number of stars, cluster density, stellar initial mass function (IMF), and primordial binary fraction. We find a gradual shift in the mass of the most massive collision product across the parameter space; in particular, denser clusters born with top-heavy IMFs provide strong collisional regimes that form VMSs with masses easily exceeding 1000M_⊙. Our results are used to derive a fitting formula that can predict the typical mass of a VMS formed as a function of the star cluster properties. Additionally, we study the stochasticity of this process and derive a statistical distribution for the mass of the VMS formed in one of our models, recomputing the model 50 times with different initial random seeds. 

Abstract Intermediate-mass black holes (IMBHs) are believed to be the missing link between the supermassive black holes (BHs) found at the centers of massive galaxies and BHs formed through stellar core collapse. One of the proposed mechanisms for their formation is a collisional runaway process in high-density young star clusters, where an unusually massive object forms through repeated stellar collisions and mergers, eventually collapsing to form an IMBH. This seed IMBH could then grow further through binary mergers with other stellar-mass BHs. Here we investigate the gravitational-wave (GW) signals produced during these later IMBH–BH mergers. We use a state-of-the-art semi-analytic approach to study the stellar dynamics and to characterize the rates and properties of IMBH–BH mergers. We also study the prospects for detection of these mergers by current and future GW observatories, both space-based (LISA) and ground-based (LIGO Voyager, Einstein Telescope, and Cosmic Explorer). We find that most of the merger signals could be detected, with some of them being multiband sources. Therefore, GWs represent a unique tool to test the collisional runaway scenario and to constrain the population of dynamically assembled IMBHs. 

Abstract Globular clusters (GCs) are particularly efficient at forming millisecond pulsars. Among these pulsars, about half lack a companion star, a significantly higher fraction than in the Galactic field. This fraction increases further in some of the densest GCs, especially those that have undergone core collapse, suggesting that dynamical interaction processes play a key role. For the first time, we createN-body models that reproduce the ratio of single-to-binary pulsars in Milky Way–like GCs. We focus especially on NGC 6752, a typical core-collapsed cluster with many observed millisecond pulsars. Previous studies suggested that an increased rate of neutron star binary disruption in the densest clusters could explain the overabundance of single pulsars in these systems. Here, we demonstrate that binary disruption is ineffective and instead we propose that two additional dynamical processes play dominant roles: (1) tidal disruption of main-sequence stars by neutron stars and (2) gravitational collapse of heavy white dwarf binary merger remnants. Neutron stars formed through these processes may also be associated with fast radio bursts similar to those observed recently in an extragalactic GC. 

Abstract We apply for the first time orbit-averaged Monte Carlo star cluster simulations to study tidal tail and stellar stream formation from globular clusters (GCs), assuming a circular orbit in a time-independent spherical Galactic potential. Treating energetically unbound bodies—potential escapers (PEs)—as collisionless enables this fast but spherically symmetric method to capture asymmetric extratidal phenomena with exquisite detail. Reproducing stream features such as epicyclic overdensities, we show howreturning tidal tailscan form after the stream fully circumnavigates the Galaxy, enhancing the stream's velocity dispersion by several kilometers per second in our ideal case. While a truly clumpy, asymmetric, and evolving Galactic potential would greatly diffuse such tails, they warrant scrutiny as potentially excellent constraints on the Galaxy’s history and substructure. Reexamining the escape timescale Δtof PEs, we find new behavior related to chaotic scattering in the three-body problem; the Δtdistribution features sharp plateaus corresponding to distinct locally smooth patches of the chaotic saddle separating the phase-space basins of escape. We study for the first time Δtin an evolving cluster, finding that $\mathrm{\Delta }t\sim (E_{\mathrm{J}}^{-0.1},E_{\mathrm{J}}^{-0.4})$for PEs with (low, high) Jacobi energyE_J, flatter than for a static cluster ( $E_{\mathrm{J}}^{-2}$). Accounting for cluster mass loss and internal evolution lowers the median Δtfrom ∼10 Gyr to ≲100 Myr. We finally outline potential improvements to escape in the Monte Carlo method intended to enable the first large grids of tidal tail/stellar stream models from full GC simulations and detailed comparison to stream observations. 

ABSTRACT The motion of the centre of mass of a coalescing binary black hole (BBH) in a gravitational potential, imprints a line-of-sight acceleration (LOSA) on to the emitted gravitational-wave (GW) signal. The acceleration could be sufficiently large in dense stellar environments, such as globular clusters (GCs), to be detectable with next-generation space-based detectors. In this work, we use outputs of the cluster monte carlo (cmc) simulations of dense star clusters to forecast the distribution of detectable LOSAs in DECIGO and LISA eras. We study the effect of cluster properties – metallicity, virial and galactocentric radii – on the distribution of detectable accelerations, account for cosmologically motivated distributions of cluster formation times, masses, and metallicities, and also incorporate the delay time between the formation of BBHs and their merger in our analysis. We find that larger metallicities provide a larger fraction of detectable accelerations by virtue of a greater abundance of relatively lighter BBHs, which allow a higher number of GW cycles in the detectable frequency band. Conversely, smaller metallicities result in fewer detections, most of which come from relatively more massive BBHs with fewer cycles but larger LOSAs. We similarly find correlations between the virial radii of the clusters and the fractions of detectable accelerations. Our work, therefore, provides an important science case for space-based GW detectors in the context of probing GC properties via the detection of LOSAs of merging BBHs. 

ABSTRACT It has been argued that heavy binaries composed of neutron stars (NSs) and millisecond pulsars (MSPs) can end up in the outskirts of star clusters via an interaction with a massive black hole (BH) binary expelling them from the core. We argue here, however, that this mechanism will rarely account for such observed objects. Only for primary masses ≲100 M⊙ and a narrow range of orbital separations should a BH–BH binary be both dynamically hard and produce a sufficiently low recoil velocity to retain the NS binary in the cluster. Hence, BH binaries are in general likely to eject NSs from clusters. We explore several alternative mechanisms that would cause NS/MSP binaries to be observed in the outskirts of their host clusters after a Hubble time. The most likely mechanism is a three-body interaction involving the NS/MSP binary and a normal star. We compare to Monte Carlo simulations of cluster evolution for the globular clusters NGC 6752 and 47 Tuc, and show that the models not only confirm that normal three-body interactions involving all stellar-mass objects are the dominant mechanism for putting NS/MSP binaries into the cluster outskirts, but also reproduce the observed NS/MSP binary radial distributions without needing to invoke the presence of a massive BH binary. Higher central densities and an episode of core collapse can broaden the radial distributions of NSs/MSPs and NS/MSP binaries due to three-body interactions, making these clusters more likely to host NSs in the cluster outskirts. 

Abstract Over 60 yr after the discovery of the first quasar, more than 275 such sources are identified in the epoch of reionization atz> 6. JWST is now exploring higher redshifts (z≳ 8) and lower-mass (≲10⁷M_⊙) ranges. The discovery of progressively farther quasars is instrumental to constraining the properties of the first population of black holes (BHs), or BH seeds, formed atz∼ 20–30. For the first time, we use Bayesian analysis of the most comprehensive catalog of quasars atz> 6 to constrain the distribution of BH seeds. We show that the mass distribution of BH seeds can be effectively described by combining a power law and a lognormal function tailored to the mass ranges associated with light and heavy seeds, assuming Eddington-limited growth and early seeding time. Our analysis reveals a power-law slope of $-{0.70}_{-0.46}^{+0.46}$and a lognormal mean of ${4.44}_{-0.30}^{+0.30}$. The inferred values of the Eddington ratio, the duty cycle, and the mean radiative efficiency are ${0.82}_{-0.10}^{+0.10}$, ${0.66}_{-0.23}^{+0.23}$, and ${0.06}_{-0.02}^{+0.02}$, respectively. Models that solely incorporate a power law or a lognormal distribution within the specific mass range corresponding to light and heavy seeds are statistically strongly disfavored, unlike models not restricted to this specific range. Our results suggest that including both components is necessary to comprehensively account for the masses of high-redshift quasars, and that both light and heavy seeds formed in the early Universe and grew to form the population of quasars we observe. 

ABSTRACT 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. 

Abstract 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.