Multidimensional core-collapse supernova simulations show that progenitors with high pre-collapse compactness undergo robust neutrino-driven shock revival, overturning the long-standing assumption that such stars fail. What remains unsettled is the final fate after revival: whether the revived shock invariably grows into an explosion that ejects the envelope, and with what asymptotic explosion energy, remnant mass, and fallback, or whether late-time accretion and early black-hole formation can abort the explosion. Different simulation groups still report divergent late-time outcomes for comparable progenitors, and the answer is sensitive to neutrino transport treatment and the nuclear equation of state. Establishing the robust mapping from pre-collapse compactness to final outcome — explosion energy, neutron-star or black-hole remnant mass, and fallback — through long-term multidimensional simulations reconciled across codes and microphysics remains an open problem at the heart of the core-collapse explosion mechanism.

Background

A core-collapse supernova (CCSN) marks the death of a massive star whose iron core, once it exceeds its effective Chandrasekhar mass, collapses to a proto-neutron star (PNS). The stellar infall drives a bounce shock that promptly stalls, because neutrinos and nuclear dissociation drain its energy; reviving that stalled shock is the central problem of the explosion mechanism. In the prevailing neutrino-driven picture, a fraction of the neutrinos radiated by the hot PNS is reabsorbed in the gain region, the layer between the stalled shock and the neutrinosphere where net neutrino heating is positive, and if heating wins over accretion power the shock runs away. A standard one-parameter measure of the pre-collapse core structure is the compactness

ξM=M/M⊙R(M)/1000 km,\xi_{M}=\frac{M/M_{\odot}}{R(M)/1000\,{\rm km}},

where R(M)R(M) is the radius enclosing baryonic mass MM, usually evaluated at M=2.0 M⊙M=2.0\,M_{\odot} (written ξ2.0\xi_{2.0}): high compactness means a dense, tightly bound core with large post-collapse accretion rates. Many one-dimensional explodability frameworks, calibrated against SN 1987A or on parametrized engines, assumed or predicted that high-compactness progenitors fail and form black holes. Boccioli, Vartanyan, O'Connor and Kasen (2025) challenged this for the revival phase itself: analyzing roughly 150 two-dimensional simulations with the FLASH and Fornax codes and 20 three-dimensional Fornax simulations, they showed that the maximum net neutrino heating rises steeply with compactness, so that for ξ2.0≳0.5\xi_{2.0}\gtrsim 0.5 the shock is essentially always revived despite the heavier accretion. They further showed that so-called 1D+ models — spherically symmetric simulations that mimic neutrino-driven convection through a mixing-length theory prescription (the STIR model, with mixing-length parameter αMLT\alpha_{\rm MLT}) — reproduce this compactness trend, and that the divergent predictions of other 1D engines trace to how each parametrizes convection, neutrino energies, or calibration. However, shock revival is not yet an explosion: all simulations they analyzed stop only 1–5 seconds after bounce, before the explosion energy asymptotes, before fallback is decided, and often before the remnant's fate (neutron star versus black hole) is settled. The late-time behavior is exactly where groups disagree — some obtain late-time shock expansion and successful explosions, others early black-hole formation that shuts off the neutrino source and can stop the explosion, and others no revival at all — and microphysics matters, since stiffer nuclear equations of state give colder neutrinospheres and systematically weaker heating. Recent long-term simulations have introduced the intermediate category of black hole supernovae (BHSNe), in which a black hole forms after shock revival yet the explosion, powered by the energy already deposited and by the drop in accretion, still succeeds; whether this is the generic high-compactness outcome, and what final energies and remnant masses follow, is precisely what is not yet known.

Problem Statement

Determine the final outcome of high-compactness core-collapse supernova progenitors after the shock revival demonstrated by Boccioli et al. (2025). Specifically: for progenitors in the high-compactness range ξ2.0≳0.5\xi_{2.0}\gtrsim 0.5 (lower bound fixed, upper bound open), establish from long-term multidimensional simulations — evolved well past the 1-5 s post-bounce coverage of current ensembles, through late-time accretion, possible black-hole formation, fallback, and to the asymptote of the explosion energy — whether the revived shock invariably grows into an explosion that ejects the stellar envelope, and with what final (asymptotic) explosion energy, ejected and fallback mass, and compact-remnant mass and nature (neutron star versus black hole); or whether, and for which structures, late-time accretion and early black-hole formation abort the explosion. Establish the mapping from pre-collapse compactness to outcome class, asymptotic energy, and remnant mass, for at least one self-consistent simulation code, neutrino-transport treatment, opacity set, and nuclear equation of state. The mapping must span the high-compactness range with at least ten distinct progenitors, so that the compactness dependence (including any turnover) is resolved rather than sampled at isolated points. Also determine how code, neutrino-transport treatment, opacity set, and nuclear equation of state shift the outcome for comparable high-compactness progenitors, so that the divergent late-time outcomes reported by different groups are reconciled. The published long-term multidimensional simulation suites in the cited literature provide the relevant evidence base.

References

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