Black Hole Accretion and Spin-up through Stellar Collisions in Dense Star Clusters

ABSTRACTIntermediate-mass black holes (IMBHs) in the mass range $10^2\!-\!10^5\, \mathrm{M_{\odot }}$ bridge the gap between stellar black holes (BHs) and supermassive BHs. Here, we investigate the possibility that IMBHs form in young star clusters via runaway collisions and BH mergers. We analyse 104 simulations of dense young star clusters, featuring up-to-date stellar wind models and prescriptions for core collapse and (pulsational) pair instability. In our simulations, only nine IMBHs out of 218 form via binary BH mergers, with a mass ∼100–140 M⊙. This channel is strongly suppressed by the low escape velocity of our star clusters. In contrast, IMBHs with masses up to ∼438 M⊙ efficiently form via runaway stellar collisions, especially at low metallicity. Up to ∼0.2 per cent of all the simulated BHs are IMBHs, depending on progenitor’s metallicity. The runaway formation channel is strongly suppressed in metal-rich (Z = 0.02) star clusters, because of stellar winds. IMBHs are extremely efficient in pairing with other BHs: ∼70 per cent of them are members of a binary BH at the end of the simulations. However, we do not find any IMBH–BH merger. More massive star clusters are more efficient in forming IMBHs: ∼8 per cent (∼1 per cent) of the simulated clusters with initial mass 104–3 × 104 M⊙ (103–5 × 103 M⊙) host at least one IMBH.

Young star clusters are the most common birthplace of massive stars and are dynamically active environments. Here, we study the formation of black holes (BHs) and binary black holes (BBHs) in young star clusters, by means of 6000 N-body simulations coupled with binary population synthesis. We probe three different stellar metallicities (Z = 0.02, 0.002, and 0.0002) and two initial-density regimes (density at the half-mass radius ρh ≥ 3.4 × 104 and ≥1.5 × 102 M⊙ pc−3 in dense and loose star clusters, respectively). Metal-poor clusters tend to form more massive BHs than metal-rich ones. We find ∼6, ∼2, and <1 per cent of BHs with mass mBH > 60 M⊙ at Z = 0.0002, 0.002, and 0.02, respectively. In metal-poor clusters, we form intermediate-mass BHs with mass up to ∼320 M⊙. BBH mergers born via dynamical exchanges (exchanged BBHs) can be more massive than BBH mergers formed from binary evolution: the former (latter) reach total mass up to ∼140 M⊙ (∼80 M⊙). The most massive BBH merger in our simulations has primary mass ∼88 M⊙, inside the pair-instability mass gap, and a mass ratio of ∼0.5. Only BBHs born in young star clusters from metal-poor progenitors can match the masses of GW 170729, the most massive event in first and second observing run (O1 and O2), and those of GW 190412, the first unequal-mass merger. We estimate a local BBH merger rate density ∼110 and ∼55 Gpc−3 yr−1, if we assume that all stars form in loose and dense star clusters, respectively.

Current theoretical models predict a mass gap with a dearth of stellar black holes (BHs) between roughly 50 M ⊙ and 100 M ⊙, while above the range accessible through massive star evolution, intermediate-mass BHs (IMBHs) still remain elusive. Repeated mergers of binary BHs, detectable via gravitational-wave emission with the current LIGO/Virgo/Kagra interferometers and future detectors such as LISA or the Einstein Telescope, can form both mass-gap BHs and IMBHs. Here we explore the possibility that mass-gap BHs and IMBHs are born as a result of successive BH mergers in dense star clusters. In particular, nuclear star clusters at the centers of galaxies have deep enough potential wells to retain most of the BH merger products after they receive significant recoil kicks due to anisotropic emission of gravitational radiation. Using for the first time simulations that include full stellar evolution, we show that a massive stellar BH seed can easily grow to ∼103–104 M ⊙ as a result of repeated mergers with other smaller BHs. We find that lowering the cluster metallicity leads to larger final BH masses. We also show that the growing BH spin tends to decrease in magnitude with the number of mergers so that a negative correlation exists between the final mass and spin of the resulting IMBHs. Assumptions about the birth spins of stellar BHs affect our results significantly, with low birth spins leading to the production of a larger population of massive BHs.

Theoretical modeling of massive stars predicts a gap in the black hole (BH) mass function above ∼40–50 M ⊙ for BHs formed through single star evolution, arising from (pulsational) pair-instability supernovae (PISNe). However, in dense star clusters, dynamical channels may exist that allow construction of BHs with masses in excess of those allowed from single star evolution. The detection of BHs in this so-called “upper-mass gap” would provide strong evidence for the dynamical processing of BHs prior to their eventual merger. Here, we explore in detail the formation of BHs with masses within or above the pair-instability gap through collisions of young massive stars in dense star clusters. We run a suite of 68 independent cluster simulations, exploring a variety of physical assumptions pertaining to growth through stellar collisions, including primordial cluster mass segregation and the efficiency of envelope stripping during collisions. We find that as many as ∼20% of all BH progenitors undergo one or more collisions prior to stellar collapse and up to ∼1% of all BHs reside within or above the pair-instability gap through the effects of these collisions. We show that these BHs readily go on to merge with other BHs in the cluster, creating a population of massive BH mergers at a rate that may compete with the “multiple-generation” merger channel described in other analyses. This has clear relevance for the formation of very massive BH binaries as recently detected by the Laser Interferometer Gravitational-Wave Observatory/Virgo in GW190521. Finally, we describe how stellar collisions in clusters may provide a unique pathway to PISNe and briefly discuss the expected rate of these events and other electromagnetic transients.

When two black holes merge in a dense star cluster, they form a new black hole with a well-defined mass and spin. If that "second-generation" black hole remains in the cluster, it will continue to participate in dynamical encounters, form binaries, and potentially merge again. Using a grid of 96 dynamical models of dense star clusters and a cosmological model of cluster formation, we explore the production of binary black hole mergers where at least one component of the binary was forged in a previous merger. We create four hypothetical universes where every black hole born in the collapse of a massive star has a dimensionless Kerr spin parameter, $\chi_{\rm birth}$, of 0.0, 0.1, 0.2, or 0.5. We show that if all stellar-born black holes are non-spinning ($\chi_{\rm birth} = 0.0$), then more than 10% of merging binary black holes from clusters have components formed from previous mergers, accounting for more than 20% of the mergers from globular clusters detectable by LIGO/Virgo. Furthermore, nearly 7% of detectable mergers would have a component with a mass $\gtrsim 55M_{\odot}$, placing them clearly in the mass "gap" region where black holes cannot form from isolated collapsing stars due to the pulsational-pair instability mechanism. On the other hand, if black holes are born spinning, then the contribution from these second-generation mergers decreases, making up as little as 1% of all detections from globular clusters when $\chi_{\rm birth} = 0.5$. We make quantitative predictions for the detected masses, mass ratios, and spin properties of first- and second-generation mergers from dense star clusters, and show how these distributions are highly sensitive to the birth spins of black holes.

The rapid formation of supermassive black holes (SMBHs) at high redshifts is still a puzzle. One hypothesis is that intermediate-mass black holes (IMBHs) serve as seeds for their formation, which could arise from hierarchical mergers in dense star clusters. There are two possible pathways for IMBH formation: 1) very massive stars may form in young star clusters, such as Pop3 clusters, and evolve into IMBHs within a few million years; 2) multiple stellar-mass black holes can merge into IMBHs in dense nuclear star clusters. Detailed insights into these scenarios can be obtained through high-resolution star-by-star simulations of dense star clusters. Furthermore, upcoming observations of faint quasars, nuclear star clusters, and Pop3 stars with the James Webb Space Telescope (JWST) will offer valuable data to constrain theoretical models and deepen our understanding of the rapid formation of SMBHs.

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” (≈40–120 M ⊙). 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 500 M ⊙ 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 that all of 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 at redshift z ≈ 2.

Dense star clusters are thought to contribute significantly to the merger rates of stellar-mass binary black holes (BBHs) detected by the LIGO–Virgo–KAGRA collaboration. We combine N -body dynamic models of realistic dense star clusters with cluster formation histories to estimate the merger rate distribution as a function of primary mass for merging BBHs formed in these environments. It has been argued that dense star clusters—most notably old globular clusters—predominantly produce BBH mergers with primary masses M p ≈ 30 M ⊙ . We show that dense star clusters forming at lower redshifts—and thus having higher metallicities—naturally produce lower-mass BBH mergers. We find that cluster BBH mergers span a wide range of primary mass, from about 6 M ⊙ to above 100 M ⊙ , with a peak near 8 M ⊙ , reproducing the overall merger rate distribution inferred from gravitational wave detections. Our results show that most low-mass BBH mergers (about 95% with M p ≲ 20 M ⊙ ) originate in metal-rich ( Z ∼ Z ⊙ ) dense star clusters, while more massive BBH mergers form predominately in metal-poor globular clusters. We also discuss the role of hierarchical mergers in shaping the BBH mass distribution. Gravitational wave detection of dynamically formed low-mass BBH mergers—potentially identifiable by features such as isotropic spin distributions—may serve as probes of cluster formation histories in metal-rich environments at low redshifts.

GW190521 is the most massive binary black hole (BBH) merger observed to date, and its primary component lies in the pair-instability (PI) mass gap. Here, we investigate the formation of GW190521-like systems via three-body encounters in young massive star clusters. We performed 2 × 105 simulations of binary-single interactions between a BBH and a massive $\ge {60}\,$M⊙ black hole (BH), including post-Newtonian terms up to the 2.5 order and a prescription for relativistic kicks. In our initial conditions, we take into account the possibility of forming BHs in the PI mass gap via stellar collisions. If we assume that first-generation BHs have low spins, $\sim {0.17}{{\ \rm per\ cent}}$ of all the simulated BBH mergers have component masses, effective and precessing spin, and remnant mass and spin inside the $90{{\ \rm per\ cent}}$ credible intervals of GW190521. Seven of these systems are first-generation exchanged binaries, while five are second-generation BBHs. We estimate a merger rate density $\mathcal {R}_{\rm GW190521}\sim {0.03}\,$Gpc$^{-3}\,$yr−1 for GW190521-like binaries formed via binary-single interactions in young star clusters. This rate is extremely sensitive to the spin distribution of first-generation BBHs. Stellar collisions, second-generation mergers and dynamical exchanges are the key ingredients to produce GW190521-like systems in young star clusters.

Merging binary black holes (BBHs) formed dynamically in dense star clusters are expected to have uncorrelated spin–orbit orientations since they are assembled through many random interactions. However, measured effective spins in BBHs detected by LIGO/Virgo/KAGRA hint at additional physical processes that may introduce anisotropy. Here we address this question by exploring the impact of stellar collisions and accretion of collision debris on the spin–orbit alignment in merging BBHs formed in dense star clusters. Through hydrodynamic simulations, we study the regime where the disruption of a massive star by a BBH causes the stellar debris to form individual accretion disks bound to each black hole (BH). We show that these disks, which are randomly oriented relative to the binary orbital plane after the initial disruption of the star, can be reoriented by strong tidal torques in the binary near pericenter passages. Following accretion by the BHs on longer timescales, BBHs with small but preferentially positive effective spin parameters (χ eff ≲ 0.2) are formed. Our results indicate that BBH collisions in young massive star clusters could contribute to the observed trend toward small positive χ eff, and we suggest that the standard assumption often made that dynamically assembled BBHs should have isotropically distributed BH spins is not always justified.

GW231123, the most massive binary black hole (BBH) merger detected by LIGO–Virgo–KAGRA, highlights the need to understand the origins of massive, high-spin stellar black holes (BHs). Dense star clusters provide natural environments for forming such systems, beyond the limits of standard massive star evolution to core collapse. While repeated BBH mergers can grow BHs through dynamical interactions (the so-called “hierarchical merger” channel), most star clusters with masses ≲10 6 M ⊙ have escape speeds too low to retain higher-generation BHs, limiting growth into or beyond the mass gap. In contrast, BH–star collisions with subsequent accretion of the collision debris can grow and retain BHs irrespective of the cluster escape speed. Using N -body ( Cluster Monte Carlo ) simulations, we study BH growth and spin evolution through this process, and we find that accretion can drive BH masses up to at least ∼200 M ⊙ , with spins set by the details of the growth history. BHs up to about 150 M ⊙ can reach dimensionless spins χ ≳ 0.7 via single coherent episodes, while more massive BHs form through multiple stochastic accretion events and eventually spin down to χ ≲ 0.4. These BHs later form binaries through dynamical encounters, producing BBH mergers that contribute up to ∼10% of all detectable events, comparable to predictions for the hierarchical channel. However, the two pathways predict distinct signatures: hierarchical mergers yield more unequal mass ratios, whereas accretion-grown BHs preferentially form near-equal-mass binaries. The accretion-driven channel allows dense clusters with low escape speeds, such as globular clusters, to produce highly spinning BBHs with both components in or above the mass gap, providing a natural formation pathway to GW231123-like systems.

Dynamical interactions in dense star clusters are considered one of the most effective formation channels of binary black holes (BBHs). Here, we present direct N-body simulations of two different star cluster families: low-mass (∼500–800 M⊙) and relatively high-mass star clusters (≥5000 M⊙). We show that the formation channels of BBHs in low- and high-mass star clusters are extremely different and lead to two completely distinct populations of BBH mergers. Low-mass clusters host mainly low-mass BBHs born from binary evolution, while BBHs in high-mass clusters are relatively massive (chirp mass up to ∼100 M⊙) and driven by dynamical exchanges. Tidal disruption dramatically quenches the formation and dynamical evolution of BBHs in low-mass clusters on a very short time-scale (≲100 Myr), while BBHs in high-mass clusters undergo effective dynamical hardening until the end of our simulations (1.5 Gyr). In high-mass clusters, we find that 8 per cent of BBHs have primary mass in the pair-instability mass gap at metallicity Z = 0.002, all of them born via stellar collisions, while only one BBH with primary mass in the mass gap forms in low-mass clusters. These differences are crucial for the interpretation of the formation channels of gravitational-wave sources.

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.

Young dense massive star clusters are promising environments for the formation of intermediate mass black holes (IMBHs) through collisions. We present a set of 80 simulations carried out with nbody6++gpu of 10 models of compact $\sim 7 \times 10^4 \, \mathrm{M}_{\odot }$ star clusters with half-mass radii Rh ≲ 1 pc, central densities $\rho _\mathrm{core} \gtrsim 10^5 \, \mathrm{M}_\odot \, \mathrm{pc}^{-3}$, and resolved stellar populations with 10 per cent primordial binaries. Very massive stars (VMSs) up to $\sim 400 \, \mathrm{M}_\odot$ grow rapidly by binary exchange and three-body scattering with stars in hard binaries. Assuming that in VMS–stellar black hole (BH) collisions all stellar material is accreted on to the BH, IMBHs with masses up to $M_\mathrm{BH} \sim 350 \, \mathrm{M}_\odot$ can form on time-scales of ≲15 Myr, as qualitatively predicted from Monte Carlo mocca simulations. One model forms an IMBH of 140 $\mathrm{M_{\odot }}$ by three BH mergers with masses of 17:28, 25:45, and 68:70 $\mathrm{M_{\odot }}$ within ∼90 Myr. Despite the stochastic nature of the process, formation efficiencies are higher in more compact clusters. Lower accretion fractions of 0.5 also result in IMBH formation. The process might fail for values as low as 0.1. The IMBHs can merge with stellar mass BHs in intermediate mass ratio inspiral events on a 100 Myr time-scale. With 105 stars, 10 per cent binaries, stellar evolution, all relevant dynamical processes, and 300 Myr simulation time, our large suite of 80 simulations indicate another rapid IMBH formation channel in young and compact massive star clusters.

A significant number of stellar binary black hole (sBBH) mergers may be lensed and detected by the third generation of gravitational wave (GW) detectors. Their lensed host galaxies may be detectable, which would thus help to accurately localize these sources and provide a new approach to study the origin of sBBHs. In this paper, we investigate the detectability of lensed host galaxies for lensed sBBH mergers. We find that the detection fraction of galaxies hosting lensed GW events can be significantly different for a survey with a given limiting magnitude if sBBHs are produced by different mechanisms, such as the evolution of massive binary stars, dynamical interactions in dense star clusters, and production assisted by active galactic nuclei or massive black holes. Furthermore, we illustrate that the statistical spatial distributions of those lensed sBBHs in their hosts resulting from different sBBH formation channels can differ. Therefore, with the third generation of GW detectors and future large-scale galaxy surveys, it is possible to independently constrain the origin of sBBHs via the detection fraction of those lensed events with identifiable lensing host signatures and/or even to constrain the fractional contributions from different sBBH formation mechanisms.