The "56^{56}Ni problem" of core-collapse supernovae (CCSNe) is the tension between the radioactive nickel-56 masses synthesized and ejected in modern neutrino-driven explosion models and the larger nickel masses inferred from observations. Sawada & Suwa (2023) sharpened the problem with one-dimensional light-bulb simulations and a self-consistent inner boundary: although 56^{56}Ni is synthesized to nearly the same mass coordinate independent of the explosion-energy growth rate E˙expl\dot{E}_{\mathrm{expl}}, at low E˙expl\dot{E}_{\mathrm{expl}} the innermost nickel-rich material fails to escape, so the ejectable nickel mass decreases as explosions get slower. Matching the observed median of stripped-envelope supernovae (SE-SNe, ≈0.07 M⊙\approx 0.07\,M_{\odot}) would require E˙expl≳2\dot{E}_{\mathrm{expl}}\gtrsim 2 Bethe s−1^{-1} — far faster than standard multi-dimensional neutrino-driven models achieve — while the hydrogen-rich Type II median (≈0.03 M⊙\approx 0.03\,M_{\odot}) is reachable in principle but the observed high-nickel tail is not explained. The open problem is whether this mapping between energy growth rate and ejected 56^{56}Ni, and the mechanism constraints it implies, survive in self-consistent multi-dimensional simulations with detailed neutrino transport across progenitor types — hydrogen-rich and stripped-envelope — including the contribution of late proto-neutron-star outflows to the nickel budget. As of 2026 the problem remains open: the growth-rate mapping, the high-nickel tail, and the SE-SN branch remain untested in self-consistent multi-dimensional models.

Background

Core-collapse supernovae (CCSNe) terminate the lives of massive stars (≳8 M⊙\gtrsim 8\,M_{\odot} at birth). When the iron core of the star exceeds its effective Chandrasekhar mass (the limiting mass above which electron-degeneracy pressure can no longer support the core), it collapses to a proto-neutron star (PNS, the hot, newly formed compact remnant), and the infalling stellar mantle rebounds into a shock wave that initially stalls. In the standard "delayed neutrino" mechanism, the shock is revived after a fraction of a second because a small fraction of the neutrinos emitted from the hot PNS deposit energy in the layer behind the shock, helped by multi-dimensional (multi-D) fluid motions such as convection and the standing-accretion-shock instability (a large-scale sloshing oscillation of the stalled shock front). Modern axisymmetric (2D) and three-dimensional (3D) simulations with increasingly detailed neutrino transport succeed in exploding many progenitors, but the explosion energy in these models grows slowly, over seconds, rather than appearing promptly.

The radioactive isotope 56^{56}Ni (decaying through 56^{56}Co, with half-lives of 6.1 and 77 days, to stable 56^{56}Fe) is synthesized in the innermost ejected layers by explosive silicon burning (rapid, high-temperature fusion of silicon into iron-group nuclei), and its decay powers supernova light curves. The 56^{56}Ni mass is therefore one of the most widely and robustly inferred observables of a core-collapse event, and it depends directly on how much inner material is heated hot enough — and later escapes the remnant's gravity — that is, on the explosion mechanism itself.

The "56^{56}Ni problem" is the tension between this observable and the slow explosions of modern simulations. Sawada & Maeda (2019) showed, using one-dimensional (1D) parameterized explosions, that slow growth of the explosion energy underproduces 56^{56}Ni relative to observed masses, concluding that the energy must be injected on timescales of order 0.10.1 s — much faster than the seconds-scale growth of neutrino-driven models. Sawada & Suwa (2021) found that the late neutrino-driven wind (a slow outflow from the PNS surface powered by neutrino energy deposition) adds at most ∼0.01 M⊙\sim 0.01\,M_{\odot} and cannot resolve the shortfall. Imasheva et al. (2022) then showed that this anti-correlation between the nickel yield and the energy-injection timescale is largely an artifact of thermal-bomb setups that omit the initial core collapse: when collapse is included, the anti-correlation vanishes or even reverses. Sawada & Suwa (2023) — the source of the present problem — re-examined the question with 1D Lagrangian hydrodynamics (equations solved by following individual mass shells rather than fixed spatial grid points) in the "light-bulb" approximation (an idealized scheme in which the neutrino heating behind the shock is prescribed as a source term rather than computed from transported neutrino distributions), but with the PNS mass and the inner boundary determined self-consistently. They found that 56^{56}Ni is synthesized to nearly the same mass coordinate independent of the explosion-energy growth rate E˙expl\dot{E}_{\mathrm{expl}} (throughout, 1 Bethe =1051=10^{51} erg), but that in slowly exploding models the innermost nickel-rich material fails to reach escape velocity and falls back onto the remnant, shifting the inner edge of the ejecta outward and reducing the ejectable 56^{56}Ni mass. Comparing against observed nickel-mass distributions, they concluded that "modern slow" explosions (E˙expl≲1\dot{E}_{\mathrm{expl}}\lesssim 1 Bethe s−1^{-1}) can in principle reproduce standard hydrogen-rich Type II supernovae but not stripped-envelope supernovae (SE-SNe — Types IIb, Ib, and Ic, whose hydrogen and in some cases helium envelopes were removed before explosion), whose observed median nickel mass would require rapid early energy growth, E˙expl≳2\dot{E}_{\mathrm{expl}}\gtrsim 2 Bethe s−1^{-1} (reaching ∼1\sim 1 Bethe within t≲0.5t\lesssim 0.5 s), a rate current multi-D self-consistent models do not achieve.

The observational basis is substantial: Anderson (2019) compiled 258 literature nickel masses, finding medians of 0.032 M⊙0.032\,M_{\odot} for Type II supernovae versus 0.100.10–0.37 M⊙0.37\,M_{\odot} for the SE-SN subtypes; Meza & Anderson (2020) confirmed that this separation survives uniform re-inference of the nickel masses; and Afsariardchi et al. (2021) showed that Arnett's rule (the widespread empirical assumption that the supernova's peak luminosity equals its instantaneous radioactive-decay heating) overestimates SE-SN nickel masses by roughly a factor of two and that some of the peak luminosity may come from non-nickel power sources such as shock cooling or magnetar spin-down (energy loss from a strongly magnetized newborn neutron star) — yet the SE-SN nickel masses remain about three times that of Type II, implying genuinely different progenitor structures or explosion physics. Because 1D explosions convert almost all injected energy into radial motion while multi-D explosions divert part of it into turbulence and non-radial kinetic energy (lowering the post-shock temperatures that set nickel synthesis), the 1D results are best read as an optimistic upper bound whose multi-D correction is itself part of the open question. The problem is thus a sharp, quantitative constraint on the explosion mechanism: the growth rate of the explosion energy is a direct fingerprint of the neutrino-heating timescale, and the nickel mass is a directly observable consequence of how much hot inner material escapes the forming compact remnant.

Problem Statement

Determine whether the ejected 56^{56}Ni masses of core-collapse supernovae are consistent with the standard delayed neutrino-driven explosion mechanism, using self-consistent multi-dimensional simulations with detailed neutrino transport as the arbiter. The single scientific objective uniting the requested results is to close the loop between the explosion-energy growth rate E˙expl\dot{E}_{\mathrm{expl}} (throughout, 1 Bethe =1051=10^{51} erg) — the characteristic fingerprint of the neutrino-heating timescale — and the observable nickel mass, across core-collapse supernova types. Concretely, as posed by Sawada & Suwa (2023):

  1. Does the mapping found in 1D light-bulb models — the ejectable 56^{56}Ni mass decreasing with decreasing E˙expl\dot{E}_{\mathrm{expl}}, caused by a shift of the innermost ejecta mass coordinate as the innermost nickel-rich material fails the escape condition — carry over to full multi-dimensional self-consistent simulations, or do multi-D effects (turbulent and non-radial motions lowering post-shock temperatures, asymmetric accretion, neutrino-driven winds) alter or erase it?

  2. Do modern slow explosions (E˙expl≲1\dot{E}_{\mathrm{expl}}\lesssim 1 Bethe s−1^{-1}), typical of state-of-the-art simulations, actually achieve the observed median nickel mass of hydrogen-rich Type II supernovae (≈0.03 M⊙\approx 0.03\,M_{\odot}) — and do they explain the observed high-mass tail (more than ∼20%\sim 20\% of Type II events above 0.075 M⊙0.075\,M_{\odot})?

  3. Can the higher nickel masses of stripped-envelope supernovae (observed median ≈0.07 M⊙\approx 0.07\,M_{\odot}, robustly ∼3×\sim 3\times the Type II values according to Afsariardchi et al. 2021) be reproduced by the neutrino-driven mechanism without fine-tuning, given that the 1D mapping requires rapid early energy growth E˙expl≳2\dot{E}_{\mathrm{expl}}\gtrsim 2 Bethe s−1^{-1} (reaching ∼1\sim 1 Bethe within t≲0.5t\lesssim 0.5 s) that standard multi-D neutrino-driven models do not reach — or do SE-SNe require different progenitor structures, missing physics, or an alternative explosion channel?

  4. What is the integrated contribution of late-time neutrino-driven outflows from the proto-neutron-star surface — their magnitude, composition (proton- or neutron-rich), and ejectable mass — to the nickel budget, across progenitors and explosion regimes?

The task is to establish, with quantified comparison to the observed nickel-mass distributions of both hydrogen-rich and stripped-envelope events, whether the neutrino-driven mechanism can account for the observed nickel masses — and, if not, which ingredient (progenitor structure, energy-injection timescale, or explosion channel) must change. The four questions above are posed jointly toward this objective: the multi-dimensional fate of the growth-rate mapping (question 1), the quantified Type II and stripped-envelope distribution comparisons (questions 2 and 3), and the integrated contribution of late proto-neutron-star outflows (question 4).

References

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