Can GW231123 have a stellar origin?

The gravitational wave event GW231123 detected by the LIGO interferometers during their fourth observing run features two black holes with source-frame masses of $137^{+23}{-18} M\odot$ and $101^{+22}{-50} M\odot$ – in the range of the pair-instability black hole mass gap predicted by standard stellar evolution theory. Both black holes are also inferred to be rapidly spinning ($χ_1 \simeq 0.9$, $χ_2 \simeq 0.8$). The primary object in GW231123 is the heaviest stellar mass black hole detected to date, which, together with its extreme rotation, raises questions about its astrophysical origin. Accounting for the unusually large spin of $\sim 0.9$ with hierarchical mergers requires some degree of fine tuning. We investigate whether such a massive, highly spinning object could plausibly form from the collapse of a single rotating massive star. We simulate stars with an initial core mass of $160,M_\odot$ – sufficient to produce BH masses at the upper edge of the 90% credible interval for $m_1$ in GW231123 – across a range of rotation rates and $^{12}\mathrm{C}(α,γ)^{16}\mathrm{O}$ reaction rates. We allow for differential rotation to explore the high-spin regime. In this limit of weak angular momentum transport, we find that: (i) rotation shifts the pair-instability mass gap to higher masses, introducing an important correlation between masses and spins in gravitational wave predictions; and (ii) highly spinning BHs with masses $\gtrsim 150 \rm M_\odot$ can form above the mass gap. Our results suggest that the primary object of GW231123 may be the first directly observed black hole that formed via direct core collapse following the photodisintegration instability.

💡 Research Summary

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The paper addresses the puzzling nature of the gravitational‑wave event GW231123, detected during LIGO’s fourth observing run. The merger involves two black holes with source‑frame masses of 137 M⊙ (±23/−18) and 101 M⊙ (±22/−50) and dimensionless spins χ₁≈0.9 and χ₂≈0.8. These values place the primary component well within the canonical pair‑instability black‑hole mass gap (≈60–130 M⊙) and give it an unusually high spin. Hierarchical merger scenarios, which are often invoked to explain massive black holes, predict a spin distribution peaked near χ≈0.7 and would require fine‑tuned mass ratios or near‑perfect spin alignment to reach χ≈0.9. Consequently, the authors explore whether a single, rapidly rotating massive star could directly collapse to produce such an object.

The study focuses on the impact of rotation on the pair‑instability (PI) regime. In non‑rotating massive helium cores, electron‑positron pair production softens the equation of state (adiabatic index Γ₁<4/3) once core temperatures exceed ~10⁹ K, triggering pulsational pair‑instability supernovae (PPISN) or full pair‑instability supernovae (PISN) that leave no remnant. For cores above ≈130 M⊙, the temperature becomes high enough that photons photodisintegrate iron‑group nuclei, causing a rapid loss of pressure support (the photodisintegration instability) and leading to direct collapse into a black hole – this defines the upper edge of the mass gap.

Rotation modifies this picture in two ways. First, centrifugal support lowers the central temperature at a given density, effectively raising the mass at which Γ₁ drops below 4/3. Second, if the core contracts while conserving angular momentum, it spins up, further increasing centrifugal support and stabilising the star against pair‑instability. The net effect is an upward shift of both the lower and upper edges of the PI mass gap, while preserving roughly the same gap width (~80 M⊙).

To quantify these effects, the authors use the one‑dimensional stellar evolution code MESA (v15140) to evolve a grid of bare helium cores with an initial mass of 160 M⊙ and metallicity Z=10⁻⁵. They vary the initial rotation rate Ω/Ω_crit from 0 to 1, where Ω_crit is the critical angular velocity at which centrifugal force balances effective gravity at the equator. They also explore the uncertainty in the key nuclear reaction ¹²C(α,γ)¹⁶O by scaling its rate by ±3σ around the median value, reflecting current experimental disagreements. Crucially, they omit the Spruit‑Tayler dynamo, thereby assuming inefficient internal angular‑momentum transport and allowing the core to retain substantial differential rotation up to collapse. Mass loss is treated with the Brott et al. (2011) wind prescription, including rotationally enhanced mass loss near critical rotation.

The simulation outcomes reveal several important trends. In non‑rotating models, a 160 M⊙ core either undergoes a PISN (if the ¹²C(α,γ)¹⁶O rate is low, leading to a larger carbon fraction) or collapses directly after photodisintegration, producing a black hole of roughly 140 M⊙. As the rotation rate increases, the centrifugal term stabilises the core against pair‑instability, allowing more massive remnants to survive. For Ω/Ω_crit≈0.8–1.0 and for ¹²C(α,γ)¹⁶O rates at or below the median (−1σ to −2σ), the final black hole masses exceed 150 M⊙ and acquire dimensionless spins χ≈0.9–0.95. These high‑mass, high‑spin remnants lie squarely within the 90 % credible intervals of GW231123’s primary component. Conversely, models with faster rotation combined with a higher ¹²C(α,γ)¹⁶O rate undergo PPISN and lose too much mass to be relevant.

The authors emphasize that the shift of the mass gap depends sensitively on the nuclear reaction rate. Lower ¹²C(α,γ)¹⁶O rates increase the carbon fraction, making the core more prone to pair‑instability and lowering the gap’s lower edge, while higher rates increase the oxygen fraction, strengthening the explosion and raising the upper edge. Rotation amplifies these shifts, moving the entire gap upward without dramatically changing its width.

Limitations of the study are openly discussed. The use of a one‑dimensional code precludes fully capturing multi‑dimensional effects such as bar‑mode instabilities, magnetic torques, or anisotropic mass loss. The assumption of negligible angular‑momentum transport is optimistic; real massive stars may experience some coupling, which would reduce the final spin. The mass‑loss prescriptions near critical rotation are uncertain, and the exact treatment of photodisintegration collapse in MESA remains approximate. Moreover, binary interactions, metallicity variations, and environmental factors could alter the evolutionary pathways. Therefore, the results should be viewed as an “optimistic upper bound” on what rotating massive stars can achieve.

Despite these caveats, the paper provides the first systematic exploration of how rapid rotation can push the pair‑instability mass gap to higher masses and produce black holes with χ≈0.9. It demonstrates that a single, rapidly rotating 160 M⊙ helium core can plausibly generate a ~150 M⊙ black hole with the spin inferred for GW231123, without invoking hierarchical mergers. This opens a new channel for the formation of massive, high‑spin black holes and suggests that future gravitational‑wave observations, especially those measuring both mass and spin, can be used to constrain stellar rotation physics and the ¹²C(α,γ)¹⁶O reaction rate. The work thus bridges the gap between nuclear astrophysics, massive‑star evolution, and gravitational‑wave astronomy, and it motivates more detailed multi‑dimensional simulations and observational campaigns to test the viability of the proposed “direct collapse after photodisintegration” pathway.