Investigating the formation channel of GW231123: Population III stars or hierarchical mergers?

This study utilizes a self-consistent cosmological framework to demonstrate that the gravitational wave event GW231123 is best explained by a hierarchical merger channel in dense globular clusters rather than isolated binary evolution or Population III stars, as the latter fail to reproduce the event's inferred merger redshift and mass constraints.

The Gist

Imagine the universe as a giant, cosmic construction site. For a long time, astronomers thought they understood the rules of how "black holes" (the ultimate cosmic vacuum cleaners) are built. They believed these objects were born from the death of massive stars, much like how a building collapses when its support beams give way.

However, a new event called GW231123 has thrown a wrench into the works. It's a collision between two black holes so massive that, according to the old rulebook, they shouldn't exist. It's like finding a skyscraper built out of materials that are supposed to explode if you try to stack them that high.

This paper is the story of two teams of detectives trying to figure out how this "impossible" skyscraper was built. They had two main theories:

Theory 1: The "Lone Wolf" Construction (Population III Stars)

The Idea: Maybe these black holes were born from the very first generation of stars in the universe. These ancient stars were like giant, pure-metal-free giants. Because they had no "dirt" (metals) in them, they didn't lose weight as they aged, allowing them to grow huge and collapse directly into massive black holes.

The Investigation: The authors used a super-computer simulation to see if this "Lone Wolf" method could work. They tried to build these massive black holes in two different ways (using two different sets of math rules).

• The Problem: In one set of rules, the stars were too far apart to ever crash into each other. In the other, the stars were so rare and the conditions so extreme that it was like trying to find a needle in a haystack the size of a galaxy.
• The Verdict: This theory failed. The "Lone Wolf" stars just couldn't explain why these black holes merged at the specific time and place we observed.

Theory 2: The "Cosmic Mosh Pit" (Hierarchical Mergers)

The Idea: Instead of being born alone, maybe these black holes are the result of a cosmic game of "musical chairs" in a crowded room. Imagine a dense cluster of stars (a Globular Cluster) where black holes are constantly bumping into each other.

1. Two small black holes crash and merge into a medium one.
2. That medium one crashes with another, becoming a big one.
3. That big one crashes again, becoming a giant.

This is called a hierarchical merger. It's like a snowball rolling down a hill, picking up more snow until it becomes an avalanche.

The Investigation: The authors simulated these crowded "mosh pits." They found that:

• The Math Works: The snowball effect naturally creates black holes heavy enough to match GW231123.
• The Spin Matches: When black holes crash, they spin faster, just like figure skaters pulling their arms in. The observed spin of GW231123 fits perfectly with this "crashing" theory.
• The Timing: The simulation showed that these massive collisions happen most often in the early universe (around 4 to 6 billion years after the Big Bang), and the remnants can travel to us today.

The Big Picture Analogy

Think of the universe as a giant factory.

• The Old Theory (Isolated Stars): Tried to build a massive black hole by taking a single, perfect brick and hoping it grew into a skyscraper on its own. The paper says, "Nope, the bricks are too far apart, or the factory is too empty."
• The New Theory (Hierarchical Mergers): Says the factory is a busy, chaotic construction site. Small bricks (small black holes) keep getting glued together by the chaos of the crowd. Eventually, you get a massive structure.

Why Does This Matter?

The paper concludes that GW231123 is likely the "low-hanging fruit" of a much larger population of these "cosmic snowballs." It suggests that the universe is full of these massive black holes formed by repeated crashes in crowded star clusters, especially in the early, metal-poor days of the universe.

In short: The "impossible" black hole wasn't built by a single star standing alone. It was built by a chaotic, crowded dance of smaller black holes crashing into each other over and over again in the dense clusters of the early universe. This discovery helps us rewrite the history books on how the heaviest objects in the cosmos are made.

Technical Summary

1. Problem Statement

The gravitational wave event GW231123 presents a significant challenge to standard stellar evolution models. The event involves the merger of two black holes (BHs) with source-frame masses of $M_1 \approx 137 M_\odot$ and $M_2 \approx 103 M_\odot$ at a redshift of $z \approx 0.39$.

• The Mass Gap Challenge: These masses lie within or above the pair-instability (PI) mass gap (typically $\sim 60 - 130 M_\odot$), where standard single-star evolution predicts that massive stellar cores are completely disrupted by pair-instability supernovae, leaving no remnant.
• The Spin Challenge: The event exhibits exceptionally high dimensionless spins ($\chi_1 \approx 0.9, \chi_2 \approx 0.8$), which are difficult to reproduce via isolated binary evolution without fine-tuning.
• The Question: The paper investigates whether GW231123 originated from isolated Population III (Pop III) binary evolution (first-generation stars in the early Universe) or hierarchical mergers within dense stellar systems (globular clusters).

2. Methodology

The authors developed a novel, self-consistent framework to compare these formation channels within a single cosmological context, avoiding the need to stitch together disparate models.

• Cosmological Framework (GAMESH): They utilized the GAMESH pipeline, which couples $N$-body dark matter dynamics (GCD+ code) with semi-analytic prescriptions for star formation, radiative/mechanical feedback, and reionization.
  • Simulation Volume: A multi-resolution "zoom-in" simulation of a $(4 \text{ cMpc})^3$ volume centered on a Milky Way-like halo ($1.7 \times 10^{12} M_\odot$ at $z=0$), representing a Local Group-like environment.
• Binary Population Synthesis (BPS): The GAMESH framework was coupled with two distinct BPS codes to model isolated binary evolution:
  • SEVN: A code focusing on stellar evolution.
  • BSEEMP: A code specifically tuned for low-metallicity environments.
  • Initial Conditions: Assumed a binary fraction $f_b=1$, a Kroupa IMF for standard stars, and a log-flat IMF for Pop III stars ($5-300 M_\odot$).
• Cluster Dynamics (RAPSTER): To model hierarchical mergers, they coupled GAMESH with RAPSTER, a cluster population synthesis code.
  • Cluster Formation: Globular clusters (GCs) were formed in galaxies with high gas surface densities ($\Sigma_g > 10^3 M_\odot \text{ pc}^{-2}$).
  • Evolution: The code tracked the dynamical evolution, disruption, and merger chains of BHs within these clusters, accounting for gravitational wave recoil kicks and retention probabilities.

3. Key Contributions

• First Self-Consistent Comparison: This is the first study to reconstruct the life cycle of GW231123-like candidates within the same cosmological simulation, allowing for a direct, unbiased comparison between isolated evolution and dynamical hierarchical channels.
• Redshift-Dependent Constraints: The study explicitly tests formation channels against the inferred merger redshift ($z \approx 0.39$), not just the final masses.
• Spin Consistency: The framework evaluates whether the predicted spin distributions match the high spins observed by the LIGO-Virgo-KAGRA (LVK) collaboration.

4. Results

A. Failure of Isolated Binary Evolution

Despite theoretical possibilities, isolated evolution failed to reproduce the event in the simulated volume:

• SEVN: Massive Pop III progenitors ($240-300 M_\odot$) formed BH binaries with semi-major axes $> 10^3 R_\odot$. These wide orbits prevent coalescence within a Hubble time.
• BSEEMP: While this code produced massive BHs, they only formed at extremely low metallicities ($Z \approx 10^{-10}$). In the GAMESH simulation, the star formation rate density at such low metallicities is negligible, making the probability of detecting such an event effectively zero.
• Conclusion: Isolated Pop III evolution cannot account for the observed masses and the merger redshift of GW231123.

B. Success of Hierarchical Mergers

The dynamical channel in dense globular clusters successfully reproduced the event's properties:

• Mass Reproduction: Successive mergers in massive GCs naturally populate the PI mass gap.
• Spin Alignment: The high observed spins are consistent with the hierarchical population, where merger remnants inherit a dimensionless spin of $\sim 0.7$ (consistent with the observed $\chi \approx 0.8-0.9$).
• Merger Rate & Redshift:
  • The predicted local merger rate density for GW231123-like candidates is $0.78 \text{ Gpc}^{-3} \text{ yr}^{-1}$. (Note: This is higher than the LVK inference of $\sim 0.08$, attributed to the simulated volume being an overdense region with $\sim 8\times$ the cosmic average star formation rate).
  • Formation Epoch: These systems predominantly form at high redshift ($z \approx 4-6$) in metal-poor environments ($Z \approx 0.006$) and merge quickly (delay times $\sim 100 \text{ Myr}$).
  • Metallicity Constraint: While hierarchical mergers can occur at very low metallicities, the specific constraint of merging at $z \approx 0.39$ selects systems formed in environments with $Z > 0.006$, as these environments had already undergone significant chemical enrichment by that epoch.

5. Significance and Conclusions

• Benchmark Event: GW231123 is identified as a benchmark event for a robust population of hierarchical black holes formed in the early Universe.
• Resolution of the Mass Gap: The study confirms that the PI mass gap is not an absolute barrier but can be populated via dynamical interactions in dense stellar systems, specifically massive globular clusters ($M_{cl} > 10^5 M_\odot$).
• Cosmological Implication: The event likely represents the "low-redshift tail" of a broader population of hierarchical mergers that peaked at $z \approx 4-6$.
• Future Outlook: The detection of such events suggests that future gravitational wave observatories will be crucial for uncovering this hidden population and constraining the formation history of massive black holes in the early Universe.

In summary, the paper rules out isolated Pop III binary evolution as the origin of GW231123 due to orbital and redshift constraints, providing strong evidence that the event resulted from hierarchical mergers in massive globular clusters.