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Impact of Sub-2.5 MeV 12C+12CResonances on the Production of Elements from C to Pd in Core-Collapse Supernovae

This study demonstrates that adopting a more efficient sub-2.5 MeV $^{12}$ C+ $^{12}$ C reaction rate significantly alters the pre-supernova structure of massive stars, thereby enhancing the production of elements heavier than iron via the s-process and dominating over the effects of different explosion mechanisms in core-collapse supernovae.

Original authors: L. Roberti, S. Palmerini, A. Falla, L. Boccioli, F. Andreis, A. Chieffi, M. La Cognata, M. Limongi, M. Masci, A. Nurmukhanbetova, A. Oliva, R. Spartá, A. Tumino

Published 2026-07-01

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Original authors: L. Roberti, S. Palmerini, A. Falla, L. Boccioli, F. Andreis, A. Chieffi, M. La Cognata, M. Limongi, M. Masci, A. Nurmukhanbetova, A. Oliva, R. Spartá, A. Tumino

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 Big Picture: Rewriting the Recipe for Star Explosions

Imagine a massive star as a giant, multi-layered onion made of different nuclear ingredients. As the star ages, it burns through these layers like a furnace, fusing lighter elements into heavier ones (turning Hydrogen into Helium, Helium into Carbon, and so on) until it runs out of fuel and collapses, exploding as a supernova.

This paper asks a very specific question: What happens if we change the "recipe" for how Carbon atoms fuse together?

For decades, scientists have used a standard recipe (called CF88) to calculate how stars burn Carbon. However, new, more precise experiments (using a clever technique called the Trojan Horse Method, or THM) suggest that Carbon atoms actually fuse together much more easily and quickly than we thought—especially at the lower temperatures found inside stars.

The authors of this paper took this new, "faster" recipe and ran computer simulations of massive stars (ranging from 15 to 40 times the mass of our Sun) to see how it changes the star's life, its death, and the elements it scatters into the universe.

The Main Findings: A Slower Burn, A Bigger Core

1. The "Slow-Motion" Carbon Phase
In the old recipe (CF88), Carbon burning was a quick, intense sprint. In the new recipe (THM), because the reaction is more efficient, the star doesn't need to get as hot to burn the Carbon.

The Analogy: Imagine lighting a campfire. The old recipe was like throwing a bucket of gasoline on the wood—it burns hot and fast. The new recipe is like using a high-quality, slow-burning log. It burns longer and steadier.
The Result: The Carbon-burning phase lasts about three times longer. Because it burns longer, the "fire" (the convective core) spreads out and becomes much larger, consuming more of the star's interior.

2. A Less "Tight" Star
Because the star burns its fuel more slowly and efficiently, it doesn't collapse as tightly as we previously thought.

The Analogy: Think of a sponge. The old models suggested the star was a sponge that had been squeezed dry and compressed into a tiny, dense ball. The new models show the star is a fluffier, more expanded sponge.
The Result: When the star is ready to explode, it is "less compact." This structural change is crucial because it dictates how the explosion behaves.

The Explosion: What Gets Ejected?

When these stars finally die, they explode, shooting material out into space. This material is what eventually forms new stars, planets, and even us. The paper found that the new "faster fusion" recipe changes what gets thrown out:

1. More Heavy Elements (The "Gold" and "Silver" of the Universe)
The most surprising result is that the new recipe produces significantly more elements heavier than Iron (like Strontium, Yttrium, and Palladium).

The Analogy: Inside the star, there are tiny "neutron factories" that build heavy elements. In the old model, these factories were only active for a short time. In the new model, because the Carbon burning is more efficient, these factories get a head start and run longer.
The Result: The star ejects about twice as much of these heavy elements (specifically those made by the "s-process," or slow neutron capture) compared to the old models.

2. The "Odd" Elements
In one specific case (a 16-solar-mass star), the new recipe caused a dramatic event where the Carbon layer and the Oxygen layer merged.

The Analogy: Imagine two distinct layers of a cake suddenly mixing together. This merger created a burst of energy that produced a huge amount of odd-numbered elements (like Phosphorus and Titanium) that wouldn't have been made otherwise.

3. The Explosion Itself
The authors tested two different ways the star might explode (like setting off a firecracker in the center vs. at the edge). They found that while the way the explosion happens matters, the structure of the star before the explosion (determined by the new Carbon recipe) is the dominant factor. Even if you change how you trigger the explosion, the new recipe still results in a different chemical mix because the "ingredients" inside the star were different to begin with.

Why This Matters

This paper doesn't just tweak a number; it suggests our understanding of how the universe is chemically enriched needs an update.

The Takeaway: If Carbon fuses more easily than we thought, then massive stars are actually better "factories" for creating the heavy elements that make up the Earth and life. The universe might be richer in these elements than our old models predicted.

In short: By updating the recipe for how Carbon atoms stick together, the authors found that massive stars live longer, burn more steadily, and explode with a richer, more diverse chemical payload than we previously believed.

Technical Summary: Impact of Sub-2.5 MeV $^{12}$ C + $^{12}$ C Resonances on the Production of Elements from C to Pd in Core-Collapse Supernovae

Problem Statement
The evolution and nucleosynthesis of massive stars ( $>9 M_\odot$ ) are critically governed by the carbon fusion reaction ( $^{12}$ C + $^{12}$ C). This reaction determines the ignition conditions for subsequent burning phases, the structure of the pre-supernova core, and the resulting compactness, which influences whether a star explodes as a core-collapse supernova (CCSN) or collapses directly to a black hole. Historically, stellar models have relied on the reaction rate from Caughlan & Fowler (1988, hereafter CF88). However, significant experimental uncertainties persist in the astrophysically relevant energy range ( $0.9 < E_{cm} < 3.4$ MeV), where the cross-section is dominated by complex resonance structures. Recent experimental efforts, specifically the Trojan Horse Method (THM) measurements by Tumino et al. (2018), suggest a significant enhancement of the reaction rate at low energies due to previously unpredicted resonances, contrasting with standard estimates and alternative extrapolations suggesting a hindrance effect. This paper investigates the specific impact of adopting this more efficient THM rate on the stellar structure, hydrostatic nucleosynthesis, and explosive yields of massive stars.

Methodology
The authors computed non-rotating stellar evolution models with initial masses of 15, 16, 18, 20, 22, 25, and 40 $M_\odot$ at solar metallicity ( $Z=0.01345$ ) using the FRANEC code. The models utilized the THM $^{12}$ C + $^{12}$ C rate, which is up to a factor of 20–30 higher than CF88 below $\sim1.5$ GK, compared against standard models using the CF88 rate. The nuclear network included 356 nuclei (from n to Cd) and over 3000 reactions to resolve the weak s-process peak, including the short-lived isotope $^{107}$ Pd.

Core-collapse supernova explosions were simulated using the thermal bomb technique with the HYPERION hydrodynamic code. Two distinct explosion prescriptions were employed to test the robustness of the results:

Set A: Energy deposition at $0.8 M_\odot$ (inside the Fe core) to ensure full mantle ejection, with the remnant mass constrained to eject exactly $0.07 M_\odot$ of $^{56}$ Ni.
Set B: Energy deposition at the Si/Si-O interface (mimicking neutrino-driven shock revival), with the explosion energy scaled to the pre-supernova compactness ( $\xi_{2.5}$ ) via a semi-analytical fit derived from 1D+ simulations.

Key Contributions and Results

Stellar Structure and Evolution:
The adoption of the THM rate leads to carbon burning activation at lower temperatures and densities. Consequently, the central carbon burning lifetime increases by a factor of roughly three, and the convective core becomes more massive. However, the transition to radiative carbon burning occurs at lower initial masses in THM models compared to CF88 models.
- Shell Burning: THM models develop fewer, more massive, and longer-lasting convective carbon shell episodes. For masses up to $20 M_\odot$ , THM models typically form a single C convective shell that vanishes before central Neon ignition, whereas CF88 models often form two or three.
- Pre-Supernova Structure: The enhanced C burning in THM models results in a less compact pre-supernova structure (lower $\xi_{2.5}$ ) for most masses, particularly between 20 and $22 M_\odot$ . The ONe core mass is systematically smaller in THM models due to the extended C burning shells, while the CO core mass remains comparable.
- Mass Dependence: Differences between THM and CF88 models diminish for initial masses $>40 M_\odot$ (He core mass $>11 M_\odot$ ), as the reaction rate scales with the square of the $^{12}$ C abundance, which decreases with increasing initial mass.
Hydrostatic Nucleosynthesis:
The structural changes significantly alter the chemical composition of the pre-supernova star.
- Elemental Ratios: THM models generally overproduce elements between Neon and Aluminum (C burning products) and underproduce elements between Silicon and Calcium (Ne and O burning products) compared to CF88 models.
- s-Process Nucleosynthesis: A critical finding is the enhancement of the weak s-process component (elements heavier than Fe up to Sr). The earlier and more efficient activation of C burning shells in THM models leads to a more efficient activation of the $^{13}$ C( $\alpha$ , n) $^{16}$ O neutron source. In the $15 M_\odot$ model, the THM rate allows the $^{13}$ C( $\alpha$ , n) $^{16}$ O source to contribute equally to neutron production alongside the standard $^{22}$ Ne( $\alpha$ , n) $^{25}$ Mg source, whereas the latter dominates in CF88 models. This results in an overproduction of s-process elements (up to Sr) by a factor of $\sim2$ in models with $M \le 20 M_\odot$ .
- Shell Mergers: In the $16 M_\odot$ THM model, a C–O shell merger occurs, drastically increasing the production of odd-Z elements and $\alpha$ -nuclei from O burning, an event not present in the corresponding CF88 model.
Explosive Yields:
The differences in pre-supernova structure largely dictate the final ejecta composition, dominating over the effects of different explosion prescriptions (Set A vs. Set B).
- Robustness: While Set B explosions (energy dependent on compactness) result in narrower explosive burning zones and less reprocessing of the pre-supernova structure compared to Set A, the primary trends (enhanced C-burning products and s-process elements in THM models) persist.
- Specific Isotopes: The overproduction of weak s-process elements (Kr, Rb, Sr) remains a factor of $\sim2$ in THM models. The $16 M_\odot$ THM model shows extreme overproduction (factor of 10–20) of elements from P to Ti due to the C–O shell merger.
- Short-Lived Radioactive (SLR) Nuclei: No significant differences were found for most SLRs, except for $^{107}$ Pd, which follows the s-process trend. In the $16 M_\odot$ THM model, SLRs such as $^{36}$ Cl, $^{40}$ K, $^{41}$ Ca, and $^{44}$ Ti are significantly overproduced due to the shell merger.

Significance and Claims
The paper claims that the adoption of the THM $^{12}$ C + $^{12}$ C rate fundamentally alters the evolutionary path of massive stars, leading to less compact pre-supernova cores and distinct nucleosynthetic signatures. The authors assert that these structural differences are the primary driver of the chemical composition of CCSN ejecta, outweighing the uncertainties introduced by different explosion mechanisms. Specifically, the work highlights that a more efficient carbon burning rate enhances the production of elements heavier than iron via the s-process in massive stars, potentially improving the agreement between massive star yields and galactic chemical evolution models, particularly for the weak s-process component. The study concludes that while the "hindrance" scenario (lower rates) is debated, the existence of resonant structures at low energies (as measured by THM) is sufficient to induce significant changes in stellar evolution and nucleosynthesis compared to standard CF88-based models.

The Big Picture: Rewriting the Recipe for Star Explosions

The Main Findings: A Slower Burn, A Bigger Core

The Explosion: What Gets Ejected?

Why This Matters

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