Rotating Supergiants: How Stellar Mergers in Dense Clusters Spin Up Black Holes
The influence of massive star mergers in young clusters on the spin distribution of black holes and gravitational-wave sources is studied. Hypothesis: angular momentum transferred during merger significantly spins up the merger product and the resulting black hole; some objects evolve as collapsars with a thick accretion disk, which promotes efficient spin-up. Analysis of about 150 N-body models (CMC code) identified mergers leading to black holes, prioritizing events with mass ratio q>0.1. Detailed post-merger structure and evolution were computed in MESA to capture pre-collapse profiles. In data typical for Milky Way globular clusters, up to half of black holes form via mergers, including ~10% from major ones with q>0.1. Angular momentum estimates indicate strong spin-up, correlating with mass ratio and properties; in a number of cases, a dimensionless spin parameter a ≳ 0.5 is expected. The results are important for the dynamical formation and retention of gravitational-wave sources in clusters.
Context
The origin of black hole spins is one of the central mysteries of astrophysics. Isolated massive stars lose angular momentum through winds and envelope expansion, so the black holes born from them typically have low spin. However, observations from gravitational waves detectors point to the existence of black holes with appreciable rotation. Dense stellar clusters provide ideal conditions for stellar mergers before collapse, helping to spin up future black holes. Early research, including work by Jacob Bekenstein on gravitational-wave recoil, showed that spin is critical for retaining merger products and enabling the growth of intermediate-mass black holes.
Methods
The study used a hybrid approach: dynamical modeling of globular clusters with the CMC (Cluster Monte Carlo) code and detailed simulations of post-merger stellar evolution in MESA. An initial sample of 148 CMC models spanned typical Galactic cluster parameters: up to 4×10^6 stars, metallicities from 0.01 to solar, and radii from 0.5 to 4 pc. Additional calculations varied the initial binary fraction (up to 100% for massive stars) and the presence of primordial mass segregation. To estimate black hole spins, MESA results were interpolated onto CMC data; the critical parameter was the mass ratio of the merger components, q. Spectroscopic determination of effective temperature separated blue supergiants with T > 10^3.9 K, which retain a hydrogen envelope.
Results
The analysis showed that up to half of all black holes in a typical cluster have undergone at least one stellar merger; about 10% have a significant mass ratio q > 0.1. For q > 0.3, the merger product becomes a compact blue supergiant that preserves a rapid envelope. According to MESA models, such objects collapse into black holes with dimensionless spins between 0.5 and 0.8. In models with an increased binary fraction (100% for massive stars) and primordial segregation, the number of rapidly spinning black hole candidates increases by an order of magnitude. Meanwhile, about 15% of all binary black hole mergers contain at least one component born through this channel, comparable to the fraction of second-generation hierarchical mergers. The gravitational-wave recoil speeds for these systems, calculated accounting for spins, exceed the escape velocity from the cluster (about 66 km/s for a mass of 10^6 M⊙), preventing retention of merger products.
Implications
The results significantly advance our understanding of the formation of black hole populations with nonzero spin detected by gravitational-wave observatories. They show that dynamical processes in clusters can naturally explain the high spins of some events without invoking exotic mechanisms. Moreover, refined distributions of black hole merger recoil affect predictions of hierarchical merger rates and the potential to form intermediate-mass black holes. These findings tie together stellar evolution, cluster dynamics, and gravitational-wave astronomy into a unified picture.
Future development
Future prospects involve directly incorporating merger hydrodynamics and subsequent evolution in a single code, enabling more precise spin predictions. It is also important to explore dependencies on the initial mass function, stellar wind rates, and supernova explosion prescriptions. Data from future observations by the Hubble Space Telescope and its successors will help refine properties of young massive clusters. Joint analysis of gravitational-wave and electromagnetic signals from such events could shed light on the nature of collapsars—the sources of long gamma-ray bursts.
Impact
The work impacts the interpretation of data from LIGO–Virgo–KAGRA gravitational-wave detectors and the theory of hierarchical merger formation. It also touches on the study of globular clusters, massive star evolution, and modeling of electromagnetic transients associated with blue supergiant collapse.
Next steps
Immediate next steps include direct computation of hydrodynamic mergers and evolution with feedback in the CMC code, as well as a detailed investigation of how metallicity affects the mass ratio threshold for spin-up.
Key open problems
The research is directly linked to the problem of black hole spin origin, which remains a key issue in compact-object astrophysics. It also relates to the unsolved question of black hole retention mechanisms in clusters and the formation of intermediate-mass black holes, plus the physics of stellar collapse and the nature of long gamma-ray bursts. These processes unfold in an evolving Universe from the Big Bang era to the present day.
🎯 Although the standard picture has isolated massive stars lose almost all their angular momentum and give birth to black holes with negligible spin, a single close encounter in a dense cluster can "stir up" a future black hole to spin speeds near the limit. Interestingly, even minor tweaks to initial conditions—like the binary fraction among massive stars—can boost the number of such rapidly rotating objects by an order of magnitude.
Key numbers
- fraction of black holes that have experienced a stellar merger: up to 50%
- fraction of significant interactions (mass ratio > 0.1): ~10%
- mass ratio threshold for a blue supergiant: 0.3
- dimensionless spin parameter: 0.5–0.8
- escape velocity for a 10^6 M⊙ cluster: 66 km/s