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GW231123 Formation from Population III Stars: Isolated Binary Evolution

This paper demonstrates that isolated Population III binary evolution can account for the formation of the extremely massive black hole merger GW231123, provided specific conditions regarding convective overshooting, nuclear reaction rates, and initial orbital parameters are met, thereby placing tighter constraints on single-star evolution models.

Original authors: Ataru Tanikawa, Shuai Liu, WeiWei Wu, Michiko S. Fujii, Long Wang

Published 2026-04-21

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CC BY 4.0

Original authors: Ataru Tanikawa, Shuai Liu, WeiWei Wu, Michiko S. Fujii, Long Wang

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Cosmic Detective Story: Solving the Mystery of GW231123

Imagine the universe as a giant, dark ocean. For years, we've been listening to the ripples on the surface—Gravitational Waves—to find out what's making waves underneath. Recently, scientists detected a particularly loud splash called GW231123.

This splash was caused by two black holes crashing into each other. But here's the twist: these weren't just any black holes. They were giants, weighing in at over 100 times the mass of our Sun. In fact, they are the heaviest black holes we've ever found via these waves.

The big question is: How did these two cosmic giants get together?

This paper is like a detective story where the authors (Tanikawa and his team) try to solve the mystery using a "simulator" of the universe. They test different theories to see which one explains how these monsters were born.

The Suspects: Ancient Stars

The main suspect in this case is a type of star called a Population III star. Think of these as the "Great-Grandparents" of the universe.

Modern Stars (Pop I/II): Like us, they are made of "stardust" (heavy elements like carbon and oxygen).
Population III Stars: These are the very first stars ever born. They were made of pure hydrogen and helium, with zero heavy elements. Because they were so pure, they could grow to be absolutely massive—much bigger than modern stars.

The authors asked: Could two of these ancient, massive stars have evolved into the two giant black holes we saw in GW231123?

The Simulation: A Cosmic Cooking Show

To answer this, the team ran a massive computer simulation (a "cooking show" for stars). They tried different recipes to see if they could "cook up" a pair of black holes that matched the GW231123 data.

They tested two main "kitchen styles" (models of how stars grow):

The "Efficient" Kitchen (Model L): In this style, the stars mix their ingredients very well. They grow huge, puffy, and expand like a balloon.
The "Inefficient" Kitchen (Model M): In this style, the stars don't mix as much. They stay smaller and more compact.

They also tested different "spices" (nuclear reaction rates), specifically how fast carbon turns into oxygen inside the star.

The Verdict: What Worked and What Didn't

The "Efficient" Kitchen Failed:
When they used the "Efficient" model (where stars get huge and puffy), the simulation showed that the stars would get so big they would crash into each other too early. They would lose too much mass or merge in a way that created black holes that were too small (around 70 solar masses) or too far apart to ever meet again. Result: No GW231123.

The "Inefficient" Kitchen Succeeded (With a Catch):
The "Inefficient" model worked, but only if they adjusted the "spices."

The Catch: They had to assume that the nuclear reaction turning Carbon into Oxygen was slower than we usually think (about 2 standard deviations slower).
The Result: With this slower reaction and the "inefficient" mixing, the stars stayed compact. They didn't lose much mass. They survived their lives, collapsed into black holes, and stayed close enough to eventually spiral into each other and merge. Result: A perfect match for GW231123!

The Spin Mystery

One of the weird things about GW231123 is that the black holes seem to be spinning very fast.

The authors found that in their successful simulation, the second black hole spins fast, but the first one spins very slowly.
Why? The first star gave away a tiny bit of its outer skin (mass) to its partner before dying. This act stripped away its spin, like a figure skater losing their momentum when they let go of a partner.
Surprisingly, this mix of "one fast, one slow" still fits the data we have, even though we aren't 100% sure about the spins yet.

Why This Matters

This paper is a big deal because it puts strict rules on how the universe works.

If GW231123 really came from isolated stars (like a couple living alone in a house, rather than a crowded party), then our understanding of how stars mix their insides and how fast they turn carbon into oxygen must be slightly different than we thought.
It's like finding a fingerprint at a crime scene that proves the suspect must be wearing a specific size of shoe. If our "shoe size" (physics models) doesn't match, we have to change our theory.

The Bottom Line

The authors conclude that yes, it is possible for these massive black holes to form from ancient, lonely stars, BUT only if:

The stars didn't mix their insides very well (inefficient overshooting).
The nuclear "cooking" inside them was a bit slower than standard recipes.

If these conditions are true, then the universe is full of these ancient giants waiting to be discovered. If not, we might need to look for other explanations, like black holes forming in crowded star clusters or near black hole nurseries in the centers of galaxies.

In short: The universe is a complex puzzle, and GW231123 is a new piece that forces us to redraw the picture of how the very first stars lived and died.

1. Problem Statement

The recent detection of GW231123, a binary black hole (BH) merger with component masses estimated at $137^{+22}_{-17} M_\odot$ and $103^{+20}_{-51} M_\odot$ , presents a significant challenge to standard astrophysical models. These masses place the primary BH firmly within or above the Pair Instability (PI) mass gap ( $\sim60–130 M_\odot$ ), where standard stellar evolution predicts complete disruption via Pair-Instability Supernovae (PISN) or Pulsational PISN (PPISN), leaving no remnant.

While dynamical formation channels (e.g., in dense star clusters or AGN disks) are often invoked for such massive mergers, this paper investigates whether isolated binary evolution of Population III (Pop III) stars (metal-free stars formed in the early universe) can naturally produce GW231123-like events. The study aims to determine the specific physical conditions required for isolated Pop III binaries to survive PISN/PPISN and merge as massive BHs within the age of the universe.

2. Methodology

The authors employed binary population synthesis calculations using the BSEEMP code (a derivation of the original BSE code capable of handling near-zero metallicities, $Z = 2 \times 10^{-10}$ ).

Stellar Evolution Models: Two distinct single-star evolution models for Pop III stars were utilized, based on 1D hydrodynamic simulations (HOSHI code):
- M Model: Inefficient convective overshooting.
- L Model: Efficient convective overshooting.
Nuclear Reaction Rates: The study systematically varied the $^{12}\text{C}(\alpha, \gamma)^{16}\text{O}$ reaction rate, a critical parameter determining the onset of PISN/PPISN. Rates were tested at standard, $1\sigma$ , $2\sigma$ , and $3\sigma$ lower than the standard value.
Initial Conditions:
- IMF: Top-heavy Initial Mass Function (power-law index $-1$) for masses $10–150 M_\odot$ .
- Binaries: Binary fraction of 0.5, with mass ratios, orbital periods, and eccentricities distributed according to observations of massive Pop I/II stars (H. Sana et al. 2012).
- Sample Size: Evolution of 3 million binary systems.
Supernova Models: The study defined remnant masses based on helium core mass ( $m_c$ ) thresholds for PPISN, PISN, and Direct Collapse (DC), which shift significantly depending on the $^{12}\text{C}(\alpha, \gamma)^{16}\text{O}$ rate.
Definition of "GW231123-like": Mergers where component masses fall within the 90% credible intervals of GW231123 ( $137^{+22}_{-17} M_\odot$ primary, $103^{+20}_{-51} M_\odot$ secondary).

3. Key Contributions

Identification of Necessary Conditions: The paper establishes that isolated Pop III binaries can produce GW231123-like events only if three specific conditions are met simultaneously:
1. Pop III stars evolve with inefficient convective overshooting (M model).
2. The $^{12}\text{C}(\alpha, \gamma)^{16}\text{O}$ reaction rate is at least $2\sigma$ lower than the standard value.
3. Pop III binaries share initial orbital parameters similar to Pop I/II binaries (specifically, short initial periods allowing for compact mergers).
Differentiation from GW190521: The study demonstrates that while GW190521 (a lighter PI-gap event) can be formed under standard conditions or with the L model, GW231123 imposes much stricter constraints, ruling out efficient overshooting models entirely.
Spin Predictions: The models predict that in GW231123-like events, the primary BH has a near-zero spin ( $a_1 \sim 0$ ) while the secondary is rapidly rotating ( $a_2 \sim 1$ ), resulting in an effective inspiral spin ( $\chi_{\text{eff}}$ ) consistent with observations.

4. Results

Merger Rates:
- Under the M2 $\sigma$ (inefficient overshooting, $2\sigma$ lower reaction rate) and M3 $\sigma$ scenarios, the local merger rate density for GW231123-like events is $2.1 \times 10^{-2} \text{ Gpc}^{-3} \text{ yr}^{-1}$ . This is consistent with the single-event rate estimate from LIGO/Virgo ( $0.08^{+0.19}_{-0.07} \text{ Gpc}^{-3} \text{ yr}^{-1}$ ).
- Under the L model (efficient overshooting), even with a $3\sigma$ lower reaction rate, zero GW231123-like events were produced.
Physical Mechanism for Disparity:
- M Model: Stars with $m_{\text{ZAMS}} \sim 150 M_\odot$ reach small maximum radii ( $\lesssim 10^2 R_\odot$ ). They undergo stable mass transfer with negligible mass loss, preserving their high masses and tight orbits, allowing them to merge within a Hubble time.
- L Model: Stars expand significantly ( $\sim 3 \times 10^3 R_\odot$ ), triggering intense Common Envelope (CE) evolution or mass transfer that strips them down to $\sim 70 M_\odot$ (too light for GW231123) or widens their orbits (preventing merger).
Spin and Eccentricity:
- The simulated events exhibit effective inspiral spins ( $\chi_{\text{eff}}$ ) within the 90% credible interval of GW231123.
- Effective precessing spins ( $\chi_p$ ) are negligible ( $\sim 0$ ), consistent with current data limitations regarding precession claims.
- Orbits are circularized ( $e \lesssim 0.5$ ) before entering the LISA band, distinguishing them from dynamical formation channels which often produce highly eccentric mergers.

5. Significance

Constraining Stellar Physics: The discovery of GW231123 acts as a powerful constraint on single-star evolution models. It suggests that if these events originate from isolated binaries, convective overshooting must be inefficient and the $^{12}\text{C}(\alpha, \gamma)^{16}\text{O}$ rate must be significantly lower than standard nuclear physics predictions.
Progenitor Identification: The results strongly favor a Pop III origin for GW231123 over Pop I/II, as the latter cannot produce such massive remnants without violating PI limits.
Observational Discrimination: The paper proposes that the orbital eccentricity of such massive mergers is a key discriminator. Isolated binary evolution predicts circularized orbits (detectable by LISA/TianQin/Taiji as circular sources), whereas dynamical formation in clusters predicts high eccentricity.
Future Implications: The findings suggest that GW231123-like events are rare but plausible outcomes of early-universe star formation, provided specific nuclear and stellar physics parameters are tuned. This places unprecedented constraints on the fundamental parameters of stellar evolution models.