Shadows of the Colossus: Hierarchical Black Hole Mergers in a 10-million-body Globular Cluster Simulation

The LIGO/Virgo/Kagra (LVK) Collaboration has detected numerous binary black hole mergers with properties that challenge standard binary evolution scenarios, such as component masses above the pair-instability gap and high spin magnitudes. Dense stellar environments such as globular clusters provide a natural channel for producing such systems through hierarchical mergers, where black hole remnants formed in earlier mergers are retained in the cluster and undergo successive mergers. However, gravitational-wave recoil kicks often eject merger remnants from typical globular clusters, which limits hierarchical growth. Massive clusters with deeper potential wells, such as those found in giant elliptical galaxies like M87, may overcome this barrier, but direct simulations of such massive globular clusters remains computationally challenging. In this study, we present a 10-million-body cluster simulation performed with the $\texttt{Cluster Monte Carlo}$ ($\texttt{CMC}$) code, referred to as $\texttt{colossus}$, which serves as a proxy for the most massive low-metallicity globular clusters observed in the local Universe. This simulation demonstrates that extended chains of hierarchical mergers can occur in massive globular clusters, producing black holes up to fifth generation with masses approaching $250,M_\odot$, comparable to the most massive LVK events observed to date (e.g., GW231123). Combining the $\texttt{colossus}$ simulation with the previous $\texttt{CMC Cluster Catalog}$, we develop a framework to extrapolate binary black hole merger predictions for the thousands of globular clusters seen in the Virgo Supercluster.

💡 Research Summary

The paper addresses the puzzling LIGO/Virgo/KAGRA detections of binary black hole (BBH) mergers that feature component masses above the pair‑instability gap and high spin magnitudes—properties that are difficult to reconcile with isolated binary stellar evolution. Dense stellar systems, especially massive globular clusters (GCs), provide a natural dynamical pathway: hierarchical mergers, where black‑hole (BH) remnants from earlier mergers are retained and subsequently merge again. The main obstacle to this channel is the gravitational‑wave recoil kick: typical kicks of 100–2000 km s⁻¹ easily exceed the escape velocities of ordinary GCs (≈50 km s⁻¹), limiting hierarchical growth to at most one or two generations.

The authors target the most massive, low‑metallicity GCs that reside in giant elliptical galaxies such as M87, where escape velocities can be substantially higher. To explore this regime they perform a state‑of‑the‑art Monte‑Carlo simulation with the CMC code, modeling a cluster of ten million stars (N = 10⁷), an initial total mass of 6 × 10⁶ M⊙, half‑mass radius ≈4 pc, metallicity Z = 0.1 Z⊙, and a modest 5 % primordial binary fraction. The simulation incorporates modern prescriptions for stellar evolution (COSMIC), BH formation (Fryer et al. fallback, Belczynski et al. pair‑instability), post‑Newtonian dynamics, and recoil‑kick calculations based on numerical‑relativity fits.

Over a 12 Gyr evolution the cluster—named “colossus”—exhibits classic phases: rapid early mass loss from stellar evolution, mass segregation of BHs within ~100 Myr, formation of a dense BH subsystem, and a long‑lasting “BH burning” phase where three‑body encounters continually create and harden BBHs, providing dynamical heating to the core. Because the cluster’s central escape speed is roughly 66 km s⁻¹ (scaling as √(Mcl/rh)), many merger remnants are retained despite typical recoil velocities exceeding 100 km s⁻¹. Consequently, the retained remnants sink back into the BH core and can merge again.

Quantitatively, colossus produces 1 367 BBH mergers, of which 448 (≈33 %) are hierarchical (generation ≥ 2). Fourteen mergers are third‑generation, two are fourth‑generation, and two fifth‑generation BHs reach masses of ~240–250 M⊙ with spin magnitudes χ≈0.8–0.9. By contrast, five lower‑mass CMC models (N = 2 × 10⁵–3.2 × 10⁶) combined yield no mergers beyond the second generation. The stark difference underscores the importance of deep potential wells for retaining high‑kick remnants.

The authors also map colossus onto the broader Virgo Supercluster GC population using a three‑dimensional distance metric in mass‑radius‑metallicity space. Extrapolating the BBH merger rates suggests that massive GCs could contribute 20–30 % of the observable BBH merger budget, and that a non‑negligible fraction of detected events should display signatures of hierarchical growth: masses well above the pair‑instability gap and high effective spins.

In summary, this work delivers the first published N = 10⁷ Monte‑Carlo GC simulation with full modern physics, demonstrates that hierarchical mergers up to the fifth generation are viable in realistic massive GCs, and provides a concrete link between such clusters and the most extreme GW events observed to date (e.g., GW231123). The study paves the way for future investigations into how variations in metallicity, primordial binary fraction, and the presence of intermediate‑mass black holes may further shape the hierarchical merger landscape.