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Explosions from Rotating Very Massive Star Collapses to Black Holes: Effects of Nuclear Burning

Numerical relativity simulations of rotating very massive and supermassive stellar core collapses reveal that lower-mass, pair-unstable cores undergo runaway collapse to form rapidly rotating black holes with massive disks that drive energetic ejecta capable of producing significant iron-group elements, whereas higher-mass cores experience homologous collapse with less efficient disk formation.

Original authors: Sho Fujibayashi, Alan Tsz-Lok Lam, Yuichiro Sekiguchi, Masaru Shibata

Published 2026-08-17

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CC BY 4.0

Original authors: Sho Fujibayashi, Alan Tsz-Lok Lam, Yuichiro Sekiguchi, Masaru Shibata

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 Heavyweights: When Stars Collapse and Explode

Imagine the universe as a giant, chaotic construction site where stars are the buildings. Most of these buildings are made of gas and dust, held together by their own weight. But sometimes, a building gets so heavy that gravity wins the tug-of-war, and the whole thing implodes. This is called gravitational collapse. Usually, when a star like our Sun runs out of fuel, it just puffs up and fades away. But the "very massive" stars—those hundreds of times heavier than our Sun—are a different story. They are so heavy that they can't even hold themselves up; they collapse into black holes, the universe's ultimate vacuum cleaners.

Now, here is the tricky part: what happens when these giants collapse? Do they just silently disappear into a black hole, or do they throw a tantrum and explode? Scientists have long wondered if the spin of the star matters. If a star is spinning fast, like a figure skater pulling in their arms, it might fling some of its material outward instead of swallowing it all. This paper dives into that exact question, using supercomputer simulations to watch what happens when these spinning giants collapse, specifically looking at how nuclear reactions (the same kind that power the Sun) and invisible particles called neutrinos change the outcome.

The Great Stellar Collapse: A Race Between Gravity and Spin

In this study, a team of scientists used a powerful digital laboratory to simulate the final moments of rotating "very massive" and "supermassive" stars. Think of these stars as cosmic giants, with cores ranging from 2,000 to 50,000 times the mass of our Sun ( $2 \times 10^3$ to $5 \times 10^4 M_\odot$ ). The researchers wanted to see if these spinning giants would simply collapse into a black hole or if they would explode, sending a massive shockwave of material back out into space.

The simulation revealed that the size of the star's core changes the story completely. It's like comparing a heavy, slow-moving truck to a lightweight, high-speed sports car.

The Heavy Truck (Supermassive Cores):
For the most massive stars (those around $5 \times 10^4 M_\odot$ ), the collapse is almost perfectly uniform. Imagine a giant balloon shrinking evenly from all sides. This is called a "homologous collapse." Because the star is so huge, it doesn't get hot and dense enough in the center to trigger a runaway reaction immediately. Instead, it collapses steadily until a black hole forms. In these cases, the black hole swallows almost everything—about 95% of the star's mass—leaving very little behind to explode.

The Sports Car (Lower-Mass Cores):
For the slightly lighter giants (around $2 \times 10^3 M_\odot$ ), the story is wilder. These cores are less dense initially, but as they collapse, they get hot and dense very quickly. This triggers a "runaway" collapse. It's like a snowball rolling down a hill, gathering speed and mass until it becomes a landslide. Because these cores are less compact, they can spin faster relative to their size. As they collapse, the center implodes so fast that the outer layers don't have time to fall in. They get flung outward, forming a massive, spinning disk of debris around the newborn black hole.

The Great Bounce:
Here comes the explosion. When this massive disk forms, it hits a wall of gravity and "bounces." Imagine a trampoline being hit by a heavy weight; it snaps back up. This "disk bounce" sends a powerful shockwave racing outward, blasting material into space. The simulations show that for these lower-mass, fast-spinning stars, this explosion can eject anywhere from 10 to over 1,000 times the mass of our Sun ( $10\text{--}10^3 M_\odot$ ) with energies reaching $10^{53}$ to $10^{55}$ erg. That is an unimaginable amount of energy, far more than a typical supernova.

The Secret Ingredient: Nuclear Burning and Neutrinos
The researchers also looked at what happens inside the star's core during this chaos. They included a detailed "recipe" for nuclear burning, tracking how elements like oxygen turn into heavier things like nickel. They found that in the lower-mass models, the core gets hot enough to create a nuclear statistical equilibrium (a state where elements are constantly being made and broken). This leads to the creation of huge amounts of Nickel-56 ( $^{56}\text{Ni}$ ), the radioactive element that powers the glow of supernovae.

However, there's a catch. In the lower-mass models, the collapse is so fast and the densities so high that invisible particles called neutrinos act like a super-efficient cooling system. They carry heat away, making the core collapse even faster. The team tested what would happen if they turned off this cooling (a "what-if" scenario in the simulation). They found that without this cooling, the collapse would be slower and more uniform, and the black hole would form with more mass. But in the real simulations, the cooling makes the lower-mass cores collapse in a runaway fashion, leaving more matter outside the black hole to be ejected.

The Role of Viscosity (The Sticky Factor)
After the initial explosion, the disk of debris doesn't just sit there; it swirls and interacts. The scientists simulated what happens if this disk has "viscosity" (imagine the friction or stickiness in a fluid). This friction causes the disk to heat up and push more material outward over time. In the lower-mass models, this "viscosity-driven" ejection adds even more mass and energy to the explosion, sometimes doubling or tripling the amount of material thrown out. Crucially, this extra material comes from the hottest parts of the disk, meaning it is rich in the heavy elements created by nuclear burning.

What About the "Exceptional" Case?
One specific model, the $2 \times 10^3 M_\odot$ star spinning very fast, showed a particularly dramatic explosion, ejecting a huge amount of mass. The authors suggest this might be because the black hole formed with an incredibly high spin, allowing the disk to bounce deeper in the gravity well and create a stronger shock. However, they are careful to note that this result is sensitive to the resolution of their computer simulation. It's like trying to photograph a tiny, fast-moving object with a slightly blurry camera; the details might shift if they zoom in closer. So, while the explosion is real in the simulation, the exact size of the blast is still being tested.

The Bottom Line
This paper suggests that rotating very massive stars don't just quietly vanish into black holes. If they are spinning fast enough and aren't too massive, they can explode with tremendous force, creating massive disks and ejecting huge clouds of material. These explosions could produce some of the heaviest elements in the universe, including iron-group elements like Nickel-56. While the exact brightness and duration of the resulting light show depend on the star's surroundings (which we don't know yet), these events are predicted to be incredibly bright and long-lasting, potentially visible across the universe as a new type of cosmic firework. The study confirms that the interplay between gravity, spin, and nuclear physics can turn a collapsing star into a spectacular, element-spewing explosion.

Technical Summary: Explosions from Rotating Very Massive Star Collapses to Black Holes: Effects of Nuclear Burning

Problem Statement
The collapse of very massive stars (VMS, $M \gtrsim 130 M_\odot$ ) and supermassive stars (SMS, $M \gtrsim 10^4 M_\odot$ ) is a critical mechanism for forming seed black holes and potentially powering luminous transients. Previous studies have explored these collapses, often focusing on general-relativistic (GR) instability in high-mass SMS or pair-instability in lower-mass VMS. However, the interplay between rotation, nuclear burning, and neutrino cooling in the collapse of rotating cores with masses in the range $2 \times 10^3 - 5 \times 10^4 M_\odot$ remains under-explored. In this mass regime, the collapsing matter reaches higher densities and temperatures than in more massive SMS, making microphysical processes—specifically alpha-chain nuclear reactions and neutrino cooling—more efficient and potentially significant for the dynamics, explosion mechanism, and nucleosynthetic yields.

Methodology
The authors employ numerical relativity simulations to model the core collapse of rotating stellar cores. The study utilizes the same Einstein equation and radiation hydrodynamics solvers as in Fujibayashi et al. (2025), with specific enhancements to address microphysics:

Nuclear Burning: An approximate alpha-chain nuclear reaction network consisting of 13 species (from $^4$ He to $^{56}$ Ni) is evolved using operator splitting. Reaction rates are derived from JINA REACLIB v2.2. For temperatures $T > 10^{10}$ K, the system is assumed to be in Nuclear Statistical Equilibrium (NSE).
Neutrino Cooling: The simulations include neutrino cooling via electron-positron pair annihilation, Bremsstrahlung, and plasmon decay, using fitting formulae from Itoh et al. (1996). Charged-current weak interactions (electron/positron captures) are excluded, and neutrino trapping is modeled by artificially suppressing cooling above critical densities ( $\rho_{crit} = 10^{10}$ and $10^8$ g cm $^{-3}$ ) to assess its impact.
Initial Conditions: Rotating equilibrium configurations are constructed to be marginally stable against either pair instability (for $M_0 \lesssim 10^4 M_\odot$ ) or GR instability (for $M_0 \gtrsim 10^4 M_\odot$ ). The survey covers initial core masses $M_0 = 2 \times 10^3 - 5 \times 10^4 M_\odot$ with varying rotation parameters ( $T_{rot}/|W| \approx 0.004$ and $0.009$).
Viscous Evolution: For selected models, the post-collapse viscous evolution of the accretion disk is simulated using an $\alpha$ -viscosity prescription ( $\alpha_{vis} = 0.03, 0.10$ ) after the disk-bounce ejecta saturates.

Key Results

Collapse Dynamics: The collapse profile depends systematically on core mass. High-mass models ( $M_0 \gtrsim 10^4 M_\odot$ ), triggered by GR instability, undergo a nearly homologous collapse. In contrast, lower-mass models ( $M_0 \lesssim 10^4 M_\odot$ ), triggered by pair instability, exhibit a "runaway-like" collapse in the central region. This is driven by more efficient neutrino cooling at the higher densities and temperatures of lower-mass cores, which reduces pressure and accelerates the central infall.
Black Hole and Disk Formation: Due to the runaway collapse, lower-mass models form black holes that initially contain a smaller fraction of the total core mass ( $\sim 5\%$ for $2E3-09$ vs. $\sim 20\%$ for $5E4-09$ ). Consequently, a larger amount of matter remains outside the black hole, leading to the formation of more massive disks. The lower compactness of pair-unstable cores allows for larger dimensionless angular momentum, favoring the formation of rapidly rotating black holes (spin $\chi_{BH} \approx 0.87$ for $2E3-09$ ) and massive disks.
Explosion Mechanism: The formation of the massive disk triggers a violent disk bounce, launching a strong shock that causes a stellar core explosion.
- Ejecta Properties: Disk-bounce ejecta masses range from $\sim 10$ to $10^3 M_\odot$ with kinetic energies of $10^{53} - 10^{55}$ erg. The average ejecta velocity decreases for lower-mass cores because a larger fraction of the stellar mass remains outside the black hole at the time of disk formation, dissipating more kinetic energy through interaction with infalling matter.
- Exceptional Case: The $2E3-09$ model ( $2 \times 10^3 M_\odot$ ) shows exceptional behavior, producing a significantly larger ejecta mass ( $\sim 100 M_\odot$ ) and kinetic energy than the trend suggests. This is attributed to the early formation of a compact disk around a rapidly spinning black hole, generating a stronger shock. However, the authors note this result is sensitive to numerical resolution and requires higher-resolution verification.
Nucleosynthesis:
- Disk-Bounce Ejecta: Significant $^{56}$ Ni production in the prompt disk-bounce ejecta occurs only in the lowest-mass models ( $M_0 \lesssim 10^4 M_\odot$ ), where temperatures are sufficiently high.
- Viscous Ejecta: Viscosity drives additional mass ejection from the disk, increasing both the total ejecta mass and kinetic energy. In models with $M_0 \lesssim 10^4 M_\odot$ , the disk reaches temperatures $> 5$ GK, approaching NSE. Consequently, the viscosity-driven ejecta becomes rich in $^{56}$ Ni and other iron-group elements, substantially increasing the total synthesized mass compared to the prompt ejecta alone.
Resolution Dependence: The authors highlight that lower-mass models form smaller, more rapidly rotating black holes, which are challenging to resolve. Finite-resolution effects can spuriously increase the black hole mass and decrease the spin in late-time evolution. While the broad trends (e.g., viscosity enhancing ejecta) remain robust, quantitative values for the lowest-mass, rapidly rotating models (like $2E3-09$ ) are tentative.

Significance and Claims
The paper claims that rotating very massive star collapses can produce massive, energetic ejecta ($10 $–$ 10^3 M_\odot$, $10^{53}$ – $10^{55}$ erg) capable of powering luminous transients. The study emphasizes that microphysical processes (nuclear burning and neutrino cooling) are essential for accurately modeling the collapse dynamics and the resulting ejecta properties in the $10^3$ – $10^4 M_\odot$ mass range.

Regarding observational signatures, the authors suggest these transients are promising targets for deep near-infrared surveys (e.g., JWST, Euclid, Roman). They argue that if the progenitor retains a hydrogen-rich envelope, the emission may manifest as a long-lasting plateau phase powered by shock cooling and recombination, rather than radioactive decay, unless an exceptionally large amount of $^{56}$ Ni is synthesized.

The authors modestly qualify their nucleosynthetic predictions. Since charged-current weak interactions (which alter the electron fraction $Y_e$ ) are not included, the calculated $^{56}$ Ni masses should be interpreted as representative of iron-group nuclei produced under nearly symmetric conditions ( $Y_e \approx 0.5$ ). They note that if weak interactions operate efficiently, the ejecta could be neutron-rich or proton-rich, potentially altering the specific isotopic yields. Furthermore, they acknowledge that the exceptional mass ejection in the $2E3-09$ model is tentative and requires future high-resolution simulations to confirm.

The Cosmic Heavyweights: When Stars Collapse and Explode

The Great Stellar Collapse: A Race Between Gravity and Spin

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