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

TL;DR

This work addresses how the LVK detections, including high-mass and high-spin BBHs, might arise from hierarchical mergers in dense stellar systems. It uses the colossus 10‑million‑body cluster simulation, built on the CMC framework with COSMIC stellar evolution, to model extended chains of BH mergers over ~12 Gyr in a massive, low-metallicity GC ($M_{cl}\approx 6\times10^6\,M_\odot$, $Z=0.1Z_\odot$, $r_v=2$ pc). The key result is that hierarchical growth can proceed to generation 5, producing BHs up to $\sim 250\,M_\odot$ and multiple LVK-like events, aided by a deep escape velocity ($v_{esc}\approx 150$ km/s) that retains merger remnants against GW recoil kicks. The study also provides a framework to extrapolate BBH merger predictions to thousands of Virgo‑Supercluster GCs, linking local dense‑cluster dynamics to LVK observations such as GW231123 and offering insight into the population of high-generation BHs in the universe.

Abstract

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.

Figures (6)

• Figure 1: Top panel: Half-light radius ($r_h$) and core radius ($r_c$) of colossus plotted over time. Bottom panel: Lagrange radii of colossus plotted over time, calculated separately for black holes (solid curves) and stellar objects (dotted lines). Each Lagrange radii curve encloses a fixed fraction of mass for the particular type of object: from bottom to top, 0.1%, 1%, 10%, 50%, and 90%. Stellar objects steadily expand in radius over time, while black holes segregate towards the core; by 2 Gyr, the 90% BH threshold is smaller than the 10% stellar threshold.
• Figure 2: Evolution of cluster mass (top panel), number of BHs ($N_{\rm BH}$, center panel), and number of BBHs ($N_{\rm BBH}$, bottom panel) over time for colossus and five other models with varying initial mass.
• Figure 3: Primary vs. secondary mass for all binary black hole mergers in colossus (right panel), and an aggregate of five lower-mass models from the CMC Catalog with matching parameters except for initial mass (left panel). Each merger is colored by the higher generation of the two progenitor black holes, as described in the text. The ten current highest-mass GW observations from LVK are plotted in green, the three most massive of which lie exclusively within the high-generation G3+ merger space of colossus, including GW231123 (the upper-rightmost star in both panels). Not only do high-mass globular clusters like colossus produce many more mergers than lower-mass globular clusters, but high-generation mergers proportionally compose a much larger fraction of total mergers.
• Figure 4: Net $\chi_{\rm eff}$ distributions for all BBH mergers in colossus, versus total merger mass (left panel) and hierarchical generation (right panel). $\chi_{\rm eff}$ distributions for individual BBH mergers were obtained through $10^3$ random angle draws on $\theta_i$ (Equation \ref{['eq:spin']}), which were then pooled into corresponding bins based on total mass and hierarchical generation. Since all 1G+1G mergers have $\chi_{\rm eff} = 0$, the net $\chi_{\rm eff}$ distribution at $< 75~M_\odot$ is tightly centered about $\chi_{\rm eff} = 0$. Between $75~M_\odot$ and $125~M_\odot$, nearly all mergers involve at least one 2G black hole ($\chi \approx 0.7$), significantly broadening the $\chi_{\rm eff}$ distribution. Past $125~M_\odot$, many mergers involve a 3G or 4G black hole (which typically have lower spins than 2G), resulting in smaller $\chi_{\rm eff}$.
• Figure 5: Hierarchical merger trees of the two highest-mass black hole in colossus, both generation 5 black holes with masses $243.7\:M_\odot$ and $181.6\:M_\odot$. Each black hole is colored according to its hierarchical generation, as described in the text. The mass, spin ($\chi$), GW kick velocity ($v_k$, applicable for generation 2+ BHs only), and merger time of each black hole is also listed. Solid lines indicate 2-body inspiral mergers, and dashed lines indicate 3-body capture mergers. Many BH mergers within both merger trees resulted in kick velocities of over 100 km/s, and would have been ejected from a typical lower-mass GC with $v_\text{esc} \lesssim 50~\text{km/s}$, but were retained in colossus ($v_\text{esc} \approx 150~\text{km/s}$).