Self-consistent explosion modeling and nucleosynthetic yields of zero-metallicity (Population III) core-collapse supernovae versus the abundance patterns of the most metal-poor stars

Whether the abundance patterns of the most iron-poor Galactic halo stars can be reproduced by the ejecta of zero-metallicity (Population III) core-collapse supernovae is a central open question of stellar archaeology. Limongi & Chieffi (2012) showed that one-dimensional, spherical, canonical-energy explosion models of a 13-80 solar-mass zero-metallicity grid, with mass cuts calibrated to the observed "average" extremely metal-poor star, fit C, Mg, Si, Ca, and Mn but systematically underproduce Sc, Ti, Co, Ni, and Zn, overproduce Cr, and fail to reproduce primary nitrogen - and that no single model, nor a generation of models, fits the full pattern. They traced the failure to the absence of a first-principles explosion prediction: the mass cut, fallback, and explosion energy remain free parameters, proton ingestion at zero metallicity is treatment-dependent, rotation is unexplored, and inter-group yield differences are unexplained.

Background

The first generation of stars (Population III, or Pop III) formed from gas with the primordial Big-Bang composition - hydrogen, helium, and trace lithium, with essentially no "metals" (elements heavier than helium). Massive Pop III stars, roughly $13$-$80\,M_{\odot}$ and above, end their lives as core-collapse supernovae: the growing iron core collapses to a neutron star or black hole, and a shock wave - revived and powered largely by neutrino heating acting through multidimensional fluid motions - ejects the stellar mantle, synthesizing and dispersing new elements. Because these stars contained no heavier elements to begin with, their explosions produced the first chemical enrichment of the universe. The surviving witnesses of that epoch are the most iron-poor stars of the Galactic halo - "extremely metal-poor" (EMP) stars, with $[{\rm Fe/H}]<-3$, where $[{\rm A/B}]=\log_{10}({\rm A/B})-\log_{10}({\rm A/B})_{\odot}$ is the logarithmic abundance ratio relative to the Sun. Their atmospheres may preserve the ejecta of one or a few first supernovae, so decoding their abundance patterns ("stellar archaeology") is the most direct observational window on the first stars.

The observational benchmark for this program is the homogeneous abundance study of Cayrel et al. (2004) and Spite et al. (2005), which measured elements from carbon to zinc in a sample of EMP giants and distilled an "average" EMP star - the abundance pattern shared by the majority of stars with $[{\rm Fe/H}]<-3$. The central theoretical question is whether the ejecta of zero-metallicity massive stars can reproduce this pattern.

Predicting a supernova yield requires three linked steps: presupernova stellar evolution, an explosion model, and the explosive nucleosynthesis. The bottleneck is the second step. The explosion mechanism cannot yet be simulated from first principles across the full progenitor range, so traditional yield calculations use "induced" explosions - a piston, a thermal bomb, or an instantaneous velocity imposed inside the iron core, with the ejecta kinetic energy prescribed - in spherical symmetry. The mass cut, $M_{\rm cut}$, the mass coordinate separating the final compact remnant from the ejecta, and the fallback, the mass that falls back onto the remnant after shock launch, are then outcomes of a parameterized prescription rather than predictions. In this framework Limongi & Chieffi (2012) computed a homogeneous grid of nonrotating zero-metallicity models from $13$ to $80\,M_{\odot}$ (with the FRANEC stellar-evolution code, simultaneous convective mixing and burning, and a 297-isotope network up to $^{98}{\rm Mo}$), exploded them one-dimensionally with a Lagrangian piecewise-parabolic-method hydrocode, and calibrated each model's $M_{\rm cut}$ by minimizing the mismatch between the predicted $[{\rm X/Fe}]$ ratios and the average EMP star of Cayrel et al. (2004) and Spite et al. (2005).

The outcome is a partial success with systematic failures. With spherical explosions of canonical energy ($\sim 10^{51}$ erg) and no artificial mixing or fallback, the models reproduce the relative abundances of C, Mg, Si, and Ca - a check on both the presupernova structures and the explosive burning - and also Mn. But the iron-peak elements (the elements around iron, from scandium to zinc, synthesized in the deepest ejected layers during explosive silicon burning) fail systematically: Sc, Ti, Co, Ni, and Zn relative to Fe are significantly underproduced while Cr is overproduced. Since Mn and Cr form in the same zone of incomplete explosive silicon burning (the regime where silicon burns without reaching full nuclear statistical equilibrium), fitting Mn while overproducing Cr is an internal inconsistency that no single adjustment of the mass cut can cure. Moreover $[{\rm N/Fe}]$ is severely underproduced except in models with proton ingestion, and no single model - nor a generation of models - reproduces the entire pattern from C to Ca simultaneously. Only "nonstandard" parameterized physics - very energetic explosions, artificial mixing and fallback, asphericity, or an electron fraction $Y_e>0.5$ (where $Y_e$, the number of electrons per baryon, set by weak interactions, controls the neutron richness of the matter) - improves the iron-peak fit, and even then not completely.

Zero metallicity brings a further peculiarity. With no initial CNO nuclei to catalyze the CNO cycle, Pop III stars must burn hydrogen at temperatures where the triple-alpha process produces its own carbon; hydrogen and helium burning then proceed at similar temperatures, the entropy barrier between the hydrogen and helium layers weakens, and protons are mixed into the helium-burning convective shell. Such convective-reactive "proton ingestion" episodes release bursts of nuclear energy and produce primary nitrogen (nitrogen synthesized from carbon newly made in the star, rather than from pre-existing CNO seeds), Na, and Mg. Different research groups obtain different results for the same phenomenon because it depends on the numerical coupling of convective mixing and burning - which one-dimensional diffusion treatments capture only approximately - and on inherently multidimensional convective flows. Rotation is expected to modify both the shell structure and the primary-nitrogen production.

Finally, yield sets from different groups disagree for identical progenitors. Comparing their $20\,M_{\odot}$ zero-metallicity model (tuned to eject the same $^{56}{\rm Ni}$ mass) with the analogous model of the Heger & Woosley (2010) zero-metallicity grid, Limongi & Chieffi (2012) found that the latter produces more weak-s-process nuclei (nuclei up to krypton made by the slow neutron-capture process) and more O, N, and F, while their model produces more C and more nuclei between Kr and Mo; the suggested explanation - a different carbon abundance at the end of central helium burning - was explicitly untested. Understanding such inter-group differences is a precondition for attributing any remaining model-data mismatch to physics rather than numerics.

Limongi & Chieffi (2012) state plainly what would be needed to go beyond these limitations: a proper computation of $M_{\rm cut}$ "would require a much more sophisticated multidimensional hydrodynamical simulation of the core collapse explosion extending at late times that, at present, is not available", and a comprehensive study including rotating models "is not available yet".

Problem Statement

Can the nucleosynthetic yields of zero-metallicity (Population III) core-collapse supernovae be predicted from physically self-consistent explosion models - multidimensional simulations that determine the explosion energy, the mass cut $M_{\rm cut}$ (the mass coordinate separating the newly formed compact remnant from the ejecta), and the fallback (the matter that falls back onto the remnant after shock launch) from the explosion mechanism itself rather than by calibration - and can such explosions reproduce the observed abundance patterns of the most metal-poor stars?

Building on the $13$-$80\,M_{\odot}$ zero-metallicity grid and findings of Limongi & Chieffi (2012), this objective has the following linked components:

1. Explosion prediction. Obtain, from multidimensional core-collapse simulations of zero-metallicity progenitors extended to late times (including the fallback phase), the explosion energy, remnant mass, $M_{\rm cut}$, and fallback as emergent outcomes - removing the fitted mass cut of the one-dimensional induced-explosion framework - and propagate them into the coupled explosive nucleosynthesis.

2. Yield confrontation. From those self-consistently exploded yields, determine whether standard core-collapse explosions - without artificial mixing, fallback tuning, or ad hoc explosion parameters - can simultaneously reproduce the observed $[{\rm X/Fe}]$ pattern (where $[{\rm X/Fe}]=\log_{10}({\rm X/Fe})-\log_{10}({\rm X/Fe})_{\odot}$ is the logarithmic abundance ratio of element X to iron, relative to the solar ratio) of the most metal-poor stars from carbon through zinc; in particular, resolve the persistent underproduction of Sc, Ti, Co, Ni, and Zn and the overproduction of Cr relative to Fe, and establish the behavior of primary N (nitrogen synthesized from carbon newly made in the star, together with Na and Mg) given the sensitivity of convective-reactive proton ingestion (protons mixed into a helium-burning shell, where they burn on freshly synthesized carbon) at zero metallicity to the multidimensional mixing-burning coupling and to rotation.

3. Attribution of required physics. Identify which physical ingredients (multidimensional or aspherical explosion dynamics, fallback, rotation, modified $Y_e$ (the number of electrons per baryon, which sets the neutron richness of the matter) through weak-interaction rates, nuclear reaction rates) are required to reconcile the yields with the data - or demonstrate that no standard explosion physics does - and, where nonstandard explosions are required, assess their physical plausibility and their frequency in the first-star population.

4. Numerics-versus-physics control. Establish, through controlled comparison, which of the known inter-group yield differences (for example, in weak-s-process production (light nuclei heavier than iron made by the slow neutron-capture process) and C/O outcomes between the Limongi-Chieffi and Heger-Woosley zero-metallicity grids) stem from numerical treatment rather than physics, so that residual discrepancies with observations can be attributed unambiguously.

The objective is to replace calibrated, one-dimensional, parameterized yield sets for the first supernovae with physically self-consistent predictions and to confront them with the observed abundance patterns of the most metal-poor stars.

References

1. M. Limongi and A. Chieffi, "Presupernova evolution and explosive nucleosynthesis of zero metal massive stars", The Astrophysical Journal Supplement Series 199, 38 (2012). DOI: 10.1088/0067-0049/199/2/38; arXiv:1202.4581; https://arxiv.org/abs/1202.4581 (primary source of the open question)
2. R. Cayrel, E. Depagne, M. Spite, V. Hill, F. Spite, P. Francois, B. Plez, T. C. Beers, F. Primas, J. Andersen, B. Barbuy, P. Bonifacio, P. Molaro, and B. Nordstrom, "First stars V - Abundance patterns from C to Zn and supernova yields in the early Galaxy", Astronomy & Astrophysics 416, 1117 (2004). DOI: 10.1051/0004-6361:20034074; https://doi.org/10.1051/0004-6361:20034074
3. M. Spite, R. Cayrel, B. Plez, V. Hill, F. Spite, E. Depagne, P. Francois, P. Bonifacio, B. Barbuy, T. C. Beers, J. Andersen, P. Molaro, B. Nordstrom, and F. Primas, "First stars VI - Abundances of C, N, O, Li, and mixing in extremely metal-poor giants. Galactic evolution of the light elements", Astronomy & Astrophysics 430, 655 (2005). DOI: 10.1051/0004-6361:20041274; https://doi.org/10.1051/0004-6361:20041274
4. A. Heger and S. E. Woosley, "Nucleosynthesis and Evolution of Massive Metal-Free Stars", The Astrophysical Journal 724, 341 (2010). DOI: 10.1088/0004-637X/724/1/341; arXiv:0803.3161; https://arxiv.org/abs/0803.3161
5. S. Jones, R. Hirschi, M. Pignatari, A. Heger, C. Georgy, N. Nishimura, C. L. Fryer, and F. Herwig, "Code dependencies of pre-supernova evolution and nucleosynthesis in massive stars: Evolution to the end of core helium burning", Monthly Notices of the Royal Astronomical Society 447, 3115 (2015). DOI: 10.1093/mnras/stu2657; arXiv:1412.6518; https://arxiv.org/abs/1412.6518
6. O. Clarkson and F. Herwig, "Convective H-He Interactions in Massive Population III Stellar Evolution Models", Monthly Notices of the Royal Astronomical Society 500, 2685 (2020). DOI: 10.1093/mnras/staa3328; arXiv:2005.07748; https://arxiv.org/abs/2005.07748
7. L. Roberti, M. Limongi, and A. Chieffi, "Zero and extremely low metallicity rotating massive stars: evolution, explosion, and nucleosynthesis up to the heaviest nuclei", The Astrophysical Journal Supplement Series 270, 28 (2024). DOI: 10.3847/1538-4365/ad1686; arXiv:2312.02942; https://arxiv.org/abs/2312.02942
8. B. Sykes and B. Mueller, "Long-Time 2D Simulations of Fallback Supernovae: A Systematic Investigation of Explosions Dynamics and Mass Ejections", Monthly Notices of the Royal Astronomical Society 538, 572 (2025). DOI: 10.1093/mnras/staf317; arXiv:2410.04944; https://arxiv.org/abs/2410.04944
9. R. Hatami, N. Tominaga, T. Yoshida, H. Umeda, and T. Takiwaki, "Physical Conditions for Synthesis of Sc, Ti, and V in Neutrino-driven Supernovae", arXiv:2512.19101 (2025); https://arxiv.org/abs/2512.19101
10. R. Jiang, H. Li, G. Zhao, Q. Xing, and W. Xin, "Abundance Pattern Fitting with Bayesian Inference: Constraining First Stars' Properties and Their Explosion Mechanism with Extremely Metal-poor Stars", The Astrophysical Journal 995, 165 (2025). DOI: 10.3847/1538-4357/ae10b9; arXiv:2510.05712; https://arxiv.org/abs/2510.05712
11. F. Rizzuti, G. Cescutti, P. Molaro, L. Roberti, A. Chieffi, M. Limongi, L. Magrini, and F. Matteucci, "Explaining the 12C/13C ratio in the Galactic halo: the contribution from shell mergers in primordial massive stars", Astronomy & Astrophysics 698, A118 (2025). DOI: 10.1051/0004-6361/202453603; arXiv:2503.20876; https://arxiv.org/abs/2503.20876
12. A. P. Ji, S. Curtis, N. Storm, V. Chandra, K. C. Schlaufman, K. G. Stassun, A. Heger, M. Pignatari, A. M. Price-Whelan, M. Bergemann, G. S. Stringfellow, C. Frohlich, H. Reggiani, E. M. Holmbeck, J. Tayar, S. P. Shah, E. J. Griffith, C. F. P. Laporte, A. R. Casey, K. Hawkins, D. Horta, W. Cerny, P. Thibodeaux, S. A. Usman, J. A. S. Amarante, R. L. Beaton, P. A. Cargile, C. Chiappini, C. Conroy, J. A. Johnson, J. A. Kollmeier, H. Li, S. Loebman, G. Meynet, D. Bizyaev, J. R. Brownstein, P. Gupta, S. Morrison, K. Pan, S. V. Ramirez, H.-W. Rix, and J. Sanchez-Gallego, "Spectacular nucleosynthesis from early massive stars", arXiv:2401.02484 (2024); https://arxiv.org/abs/2401.02484 (abundance pattern of the metal-poor star J0931+0038, unexplained by current early-massive-star yield models)
13. W. Xin, K. Nomoto, C.-M. Yip, X. Zhang, Q.-F. Xing, S. Bi, and G. Zhao, "Nucleosynthesis of Pop III and Fe-enriched Pop II Pair-Instability Supernovae", arXiv:2607.10612 (2026); https://arxiv.org/abs/2607.10612