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Close encounters and physical collisions between stars in young dense clusters may lead to the formation of very massive stars and black holes via runaway merging. We examine critically some details of this process, using N-body simulations and simple analytical estimates to place limits on the cluster parameters for which it expected to occur. For small clusters, the mass of the runaway is effectively limited by the total number of high-mass stars in the system. For sufficiently dense larger clusters, the runaway mass is determined by the fraction of stars that can mass segregate to the cluster core while still on the main sequence. The result is in the range commonly cited for intermediate-mass black holes, such as that recently reported in the Galactic center.
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Hierarchical triples are expected to be produced by the frequent binary-mediated interactions in the cores of globular clusters. In some of these triples, the tertiary companion can drive the inner binary to merger following large eccentricity oscillations, as a result of the eccentric Kozai-Lidov mechanism. In this paper, we study the dynamics and merger rates of black hole (BH) hierarchical triples, formed via binary--binary encounters in the CMC Cluster Catalog, a suite of cluster simulations with present-day properties representative of the Milky Ways globular clusters. We compare the properties of the mergers from triples to the other merger channels in dense star clusters, and show that triple systems do not produce significant differences in terms of mass and effective spin distribution. However, they represent an important pathway for forming eccentric mergers, which could be detected by LIGO--Virgo/KAGRA (LVK), and future missions such as LISA and DECIGO. We derive a conservative lower limit for the merger rate from this channel of $0.35$ Gpc$^{-3}$yr$^{-1}$ in the local Universe and up to $sim9%$ of these events may have a detectable eccentricity at LVK design sensitivity. Additionally, we find that triple systems could play an important role in retaining second-generation BHs, which can later merge again in the core of the host cluster.
More than two hundred supermassive black holes (SMBHs) of masses $gtrsim 10^9,mathrm{M_{odot}}$ have been discovered at $z gtrsim 6$. One promising pathway for the formation of SMBHs is through the collapse of supermassive stars (SMSs) with masses $sim 10^{3-5},mathrm{M_{odot}}$ into seed black holes which could grow upto few times $10^9,mathrm{M_{odot}}$ SMBHs observed at $zsim 7$. In this paper, we explore how SMSs with masses $sim 10^{3-5},mathrm{M_{odot}}$ could be formed via gas accretion and runaway stellar collisions in high-redshift, metal-poor nuclear star clusters (NSCs) using idealised N-body simulations. We explore physically motivated accretion scenarios, e.g. Bondi-Hoyle-Lyttleton accretion and Eddington accretion, as well as simplified scenarios such as constant accretions. While gas is present, the accretion timescale remains considerably shorter than the timescale for collisions with the most massive object (MMO). However, overall the timescale for collisions between any two stars in the cluster can become comparable or shorter than the accretion timescale, hence collisions still play a crucial role in determining the final mass of the SMSs. We find that the problem is highly sensitive to the initial conditions and our assumed recipe for the accretion, due to the highly chaotic nature of the problem. The key variables that determine the mass growth mechanism are the mass of the MMO and the gas reservoir that is available for the accretion. Depending on different conditions, SMSs of masses $sim10^{3-5} ,mathrm{M_{odot}}$ can form for all three accretion scenarios considered in this work.
The observations of high redshifts quasars at $zgtrsim 6$ have revealed that supermassive black holes (SMBHs) of mass $sim 10^9,mathrm{M_{odot}}$ were already in place within the first $sim$ Gyr after the Big Bang. Supermassive stars (SMSs) with masses $10^{3-5},mathrm{M_{odot}}$ are potential seeds for these observed SMBHs. A possible formation channel of these SMSs is the interplay of gas accretion and runaway stellar collisions inside dense nuclear star clusters (NSCs). However, mass loss due to stellar winds could be an important limitation for the formation of the SMSs and affect the final mass. In this paper, we study the effect of mass loss driven by stellar winds on the formation and evolution of SMSs in dense NSCs using idealised N-body simulations. Considering different accretion scenarios, we have studied the effect of the mass loss rates over a wide range of metallicities $Z_ast=[.001-1]mathrm{Z_{odot}}$ and Eddington factors $f_{rm Edd}=L_ast/L_{mathrm{Edd}}=0.5,0.7,,&, 0.9$. For a high accretion rate of $10^{-4},mathrm{M_{odot}yr^{-1}}$, SMSs with masses $gtrsim 10^3MSun$ could be formed even in a high metallicity environment. For a lower accretion rate of $10^{-5},mathrm{M_{odot}yr^{-1}}$, SMSs of masses $sim 10^{3-4},mathrm{M_{odot}}$ can be formed for all adopted values of $Z_ast$ and $f_{rm Edd}$, except for $Z_ast=mathrm{Z_{odot}}$ and $f_{rm Edd}=0.7$ or 0.9. For Eddington accretion, SMSs of masses $sim 10^3,mathrm{M_{odot}}$ can be formed in low metallicity environments with $Z_astlesssim 0.01mathrm{Z_{odot}}$. The most massive SMSs of masses $sim 10^5,mathrm{M_{odot}}$ can be formed for Bondi-Hoyle accretion in environments with $Z_ast lesssim 0.5mathrm{Z_{odot}}$.
Using state-of-the-art dynamical simulations of globular clusters, including radiation reaction during black hole encounters and a cosmological model of star cluster formation, we create a realistic population of dynamically-formed binary black hole mergers across cosmic space and time. We show that in the local universe, 10% of these binaries form as the result of gravitational-wave emission between unbound black holes during chaotic resonant encounters, with roughly half of those events having eccentricities detectable by current ground-based gravitational-wave detectors. The mergers that occur inside clusters typically have lower masses than binaries that were ejected from the cluster many Gyrs ago. Gravitational-wave captures from globular clusters contribute 1-2 Gpc^-3 yr^-1 to the binary merger rate in the local universe, increasing to ~10 Gpc^-3 yr^-1 at z~3. Finally, we discuss some of the technical difficulties associated with post-Newtonian scattering encounters, and how care must be taken when measuring the binary parameters during a dynamical capture.
Stellar encounters potentially affect the evolution of the protoplanetary discs in the Orion Nebula Cluster (ONC). However, the role of encounters in other cluster environments is less known. We investigate the effect of the encounter-induced disc-mass loss in different cluster environments. Starting from an ONC-like cluster we vary the cluster size and density to determine the correlation of collision time scale and disc-mass loss. We use the NBODY6++ code to model the dynamics of these clusters and analyze the effect of star-disc encounters. We find that the disc-mass loss depends strongly on the cluster density but remains rather unaffected by the size of the stellar population. The essential outcome of the simulations are: i) Even in clusters four times sparser than the ONC the effect of encounters is still apparent. ii) The density of the ONC itself marks a threshold: in less dense and less massive clusters it is the massive stars that dominate the encounter-induced disc-mass loss whereas in denser and more massive clusters the low-mass stars play the major role for the disc mass removal. It seems that in the central regions of young dense star clusters -- the common sites of star formation -- stellar encounters do affect the evolution of the protoplanetary discs. With higher cluster density low-mass stars become more heavily involved in this process. This finding allows for the extrapolation towards extreme stellar systems: in case of the Arches cluster one would expect stellar encounters to destroy the discs of most of the low- and high-mass stars in several hundred thousand years, whereas intermediate mass stars are able to retain to some extant their discs even under these harsh environmental conditions.
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