The delayed neutrino-heating mechanism is the leading explanation of core-collapse supernova explosions, but a definitive first-principles prediction — which massive-star progenitors explode, which collapse to black holes, and with what explosion energies, remnant properties, and multi-messenger signals — still requires the combination of capabilities distilled from the urgent tasks summarized in the outlook of Kotake, Nakamura, Kuroda and Takiwaki (2014): three-dimensional general-relativistic simulations coupled to full energy- and angle-dependent (Boltzmann) neutrino transport, including rotation and nuclear burning, followed to seconds after bounce with demonstrated numerical convergence. The decade since has resolved the pieces individually: 3D simulations with spectral approximate transport now produce explosions (Lentz et al. 2015), seconds-long 3D models reach realistic energies of about one bethe (Bollig et al. 2021), a multidimensional Boltzmann transport code in full general relativity exists (Akaho et al. 2021), and reviews describe the neutrino mechanism as emerging but not yet definitively established (Burrows & Vartanyan 2021; Janka 2025). The surviving open core is the combination itself: no full-GR 3D Boltzmann simulation of core collapse through explosion has been published; angular- and energy-resolution effects demonstrably flip explosion outcomes (Akaho 2026); and which stars explode remains contested between modeling groups. This problem asks for that definitive progenitor-to-outcome determination.

Background

A core-collapse supernova (CCSN) begins when the electron-degenerate iron core of a massive star grows beyond its effective Chandrasekhar mass and collapses. Collapse is halted when the matter reaches supra-nuclear density and the nuclear equation of state (EOS) stiffens; the rebound ('core bounce') launches a shock wave that promptly stalls, because it loses enormous energy to dissociating infalling nuclei and to neutrinos streaming out of the newly formed proto-neutron star (PNS). In the standard 'delayed neutrino-heating' mechanism, the stalled shock is revived hundreds of milliseconds after bounce by reabsorption of a small fraction of the intense neutrino flux radiated by the PNS, in the 'gain region' between the PNS surface and the shock; multi-dimensional fluid instabilities — convection and the standing accretion shock instability (SASI, a global oscillation of the stalled shock) — assist the heating. Whether this mechanism robustly explodes realistic stars, and with what energies, has been a central open question of supernova theory for over half a century.

The computational crux is neutrino transport. The neutrino distribution function lives on a six-dimensional (6D) phase space — three spatial coordinates, neutrino energy, and two propagation angles — and evolves according to the (relativistic) Boltzmann equation coupled to the stellar fluid. Direct solution is so expensive that simulations approximate it: 'gray' schemes discard energy dependence; 'multi-group' (spectral) schemes discretize energy; and angular dependence is treated by ray-by-ray transport (independent one-dimensional transport along each radial ray, ignoring lateral coupling), by two-moment 'M1' schemes that evolve the neutrino energy density and flux with an algebraic closure relation, or by leakage schemes (which replace the transport solution by free streaming outside the neutrinospheric trapping surface and diffusion inside it). Gravity is equally demanding: near the PNS, full general relativity (GR) rather than Newtonian gravity changes neutrino luminosities and heating rates enough to affect explodability. A 'light-bulb' scheme replaces transport entirely with prescribed neutrino luminosities and spectra.

In a 2014 conference contribution, Kotake, Nakamura, Kuroda and Takiwaki took stock of this frontier. Three-dimensional (3D) simulations with spectral transport found explosions harder to obtain in 3D than in 2D; their own 'first generation' of full-GR 3D simulations used a gray M1 closure and could be followed only a few hundred milliseconds after bounce; Newtonian 3D runs used ray-by-ray multi-group IDSA (isotropic diffusion source approximation) transport; and rotation and nuclear burning had been explored only in light-bulb parametrizations. They identified the field's urgent tasks (from the paper's discussion and outlook): extend 3D-GR models to late postbounce times (hundreds of milliseconds to seconds) to see whether successful explosions with realistic asymptotic energies develop; couple full energy- and angle-dependent (multi-group, multi-angle, ultimately 6D Boltzmann) neutrino transport to GR; include rotation and nuclear burning self-consistently; map the dependence on progenitor structure and weak-interaction microphysics (which progenitors are explodable); and establish numerical convergence and inter-code reliability.

A decade of subsequent work transformed this landscape piecewise — 3D spectral-transport explosions, seconds-long 3D models, a full-GR multidimensional Boltzmann transport code — but the full combination called for by the source has not been achieved: no 3D-GR Boltzmann simulation of core collapse through explosion has been published, momentum-space resolution demonstrably flips explosion outcomes, and reviews as late as 2025 state it is currently unclear which stars explode or form black holes. Throughout, 'one bethe' (1 B, equal to 105110^{51} erg) is the customary unit of explosion energy.

Problem Statement

Determine, from first principles, the outcomes of stellar core collapse.

For massive-star progenitors spanning a realistic range of structures — including the consequences of precollapse rotation, of self-consistent nuclear burning, and of microphysical input choices (nuclear equation of state, weak-interaction rates) — establish by self-consistent three-dimensional general-relativistic neutrino-radiation hydrodynamics, in which the neutrino transport solves the full energy- and angle-dependent (multi-group, multi-angle, 6D Boltzmann) transport equation coupled to general relativity rather than gray, ray-by-ray, or closure-based approximations, followed from core bounce through seconds of postbounce evolution, with numerical convergence demonstrated in the statistical sense specified below:

  1. the progenitor-to-outcome mapping: which progenitors explode by the neutrino-driven mechanism and which collapse to black holes;
  2. the asymptotic explosion energies and remnant properties: final energy in bethe (105110^{51} erg), neutron-star mass, kick, and spin, and the ejecta composition;
  3. the associated neutrino and gravitational-wave signals, confronted with the SN 1987A record and the statistical observables on which empirical comparison currently relies (neutron-star kick and mass distributions, supernova-energy systematics), and predictive for prospective multi-messenger observations of future supernovae.

These three parts are components of one scientific objective — a definitive, predictive account of the core-collapse explosion mechanism: the mapping in (1) is established by the converged full-fidelity simulations, its quantitative content is the energies and remnant properties in (2), and its empirical validation is the signal confrontation in (3). The admissible progenitor class must be stated explicitly: a specified grid over the progenitor structure parameters (mass, metallicity, rotation, binary history), representative of massive-star progenitors, and the mapping must be predictive within that stated coverage, in the sense that outcomes for progenitors between grid points follow from the simulations and their systematics with quantified uncertainties rather than being left open. Any such mapping and its quantitative predictions must be stable under refinement of spatial and neutrino momentum-space resolution and under stated microphysics variations, with quantified uncertainties; since outcomes are realization-dependent, this standard is statistical — stability of the ensemble-level mapping and its uncertainties under refinement, separating robust trends from realization noise — not pointwise reproducibility of any single chaotic model. Because this full standard lies at the frontier of current capability, converged full-fidelity results for a stated progenitor subset over an achievable postbounce window, with quantified systematics, determine the corresponding part of the mapping, while the full mapping requires the complete ensemble-level standard above.

References

  1. Kei Kotake, Ko Nakamura, Takami Kuroda, Tomoya Takiwaki, 'Cutting-edge issues of core-collapse supernova theory', AIP Conference Proceedings 1594, 250-257 (2014). DOI: 10.1063/1.4874078, https://doi.org/10.1063/1.4874078
  2. Eric J. Lentz, Stephen W. Bruenn, W. Raphael Hix, Anthony Mezzacappa, O. E. Bronson Messer, Eirik Endeve, John M. Blondin, J. Austin Harris, Pedro Marronetti, Konstantin N. Yakunin, 'Three-dimensional core-collapse supernova simulated using a 15 M⊙M_\odot progenitor', The Astrophysical Journal Letters 807, L31 (2015). DOI: 10.1088/2041-8205/807/2/L31, arXiv:1505.05110, https://arxiv.org/abs/1505.05110
  3. Luke F. Roberts, Christian D. Ott, Roland Haas, Evan P. O'Connor, Peter Diener, Erik Schnetter, 'General Relativistic Three-Dimensional Multi-Group Neutrino Radiation-Hydrodynamics Simulations of Core-Collapse Supernovae', The Astrophysical Journal 831, 98 (2016). DOI: 10.3847/0004-637X/831/1/98, arXiv:1604.07848, https://arxiv.org/abs/1604.07848
  4. Wakana Iwakami, Hirotada Okawa, Hiroki Nagakura, Akira Harada, Shun Furusawa, Kosuke Sumiyoshi, Hideo Matsufuru, Shoichi Yamada, 'Simulations of the Early Postbounce Phase of Core-collapse Supernovae in Three-dimensional Space with Full Boltzmann Neutrino Transport', The Astrophysical Journal 903, 82 (2020). DOI: 10.3847/1538-4357/abb8cf, arXiv:2004.02091, https://arxiv.org/abs/2004.02091
  5. Ryuichiro Akaho, Akira Harada, Hiroki Nagakura, Kohsuke Sumiyoshi, Wakana Iwakami, Hirotada Okawa, Shun Furusawa, Hideo Matsufuru, Shoichi Yamada, 'Multidimensional Boltzmann Neutrino Transport Code in Full General Relativity for Core-collapse Simulations', The Astrophysical Journal 909, 210 (2021). DOI: 10.3847/1538-4357/abe1bf, arXiv:2010.10780, https://arxiv.org/abs/2010.10780
  6. Robert Bollig, Naveen Yadav, Daniel Kresse, Hans-Thomas Janka, Bernhard Müller, Alexander Heger, 'Self-consistent 3D Supernova Models From -7 Minutes to +7 s: A 1-bethe Explosion of a ~19 M⊙ Progenitor', The Astrophysical Journal 915, 28 (2021). DOI: 10.3847/1538-4357/abf82e, arXiv:2010.10506, https://arxiv.org/abs/2010.10506
  7. Takami Kuroda, Tobias Fischer, Tomoya Takiwaki, Kei Kotake, 'Core-collapse supernova simulations and the formation of neutron stars, hybrid stars, and black holes', The Astrophysical Journal 924, 38 (2022). DOI: 10.3847/1538-4357/ac31a8, arXiv:2109.01508, https://arxiv.org/abs/2109.01508
  8. Adam Burrows, David Vartanyan, 'Core-Collapse Supernova Explosion Theory', Nature 589, 29-39 (2021). DOI: 10.1038/s41586-020-03059-w, arXiv:2009.14157, https://arxiv.org/abs/2009.14157
  9. Ko Nakamura, Tomoya Takiwaki, Kei Kotake, 'Three-dimensional simulation of a core-collapse supernova for a binary star progenitor of SN 1987A', Monthly Notices of the Royal Astronomical Society 514, 3941-3952 (2022). DOI: 10.1093/mnras/stac1586, arXiv:2202.06295, https://arxiv.org/abs/2202.06295
  10. Damiano F. G. Fiorillo, Malte Heinlein, Hans-Thomas Janka, Georg Raffelt, Edoardo Vitagliano, Robert Bollig, 'Supernova Simulations Confront SN 1987A Neutrinos', Physical Review D 108, 083040 (2023). DOI: 10.1103/PhysRevD.108.083040, arXiv:2308.01403, https://arxiv.org/abs/2308.01403
  11. Hans-Thomas Janka, 'Long-Term Multidimensional Models of Core-Collapse Supernovae: Progress and Challenges', Annual Review of Nuclear and Particle Science 75, 425-461 (2025). DOI: 10.1146/annurev-nucl-121423-100945, arXiv:2502.14836, https://arxiv.org/abs/2502.14836
  12. Ryuichiro Akaho, 'Momentum Space Resolution Dependence in Boltzmann Neutrino Radiation Hydrodynamics Simulations of Core-collapse Supernovae', arXiv:2607.12891 (2026, submitted to MNRAS). arXiv:2607.12891, https://arxiv.org/abs/2607.12891