Robust three-dimensional outcomes and observable signatures of black hole supernovae across the progenitor range

Black hole supernovae (BHSNe) are core-collapse events in which the proto-neutron star collapses to a black hole after the stalled bounce shock has revived but before the explosion has cleared the star. Andersen et al. (2026, arXiv:2605.01405) mapped this channel in axisymmetry: among 23 single-star progenitors of 19.51-60 solar masses, 18 produced BHSNe, with black hole formation 0.7-4.4 s after bounce, final explosion energies of roughly $2\times10^{49}$ to $3\times10^{51}$ erg, black hole masses of roughly 3-26 solar masses, and a remnant-mass trend with carbon-oxygen-core mass. The open problem is to complete this characterization, following the two open questions posed in the source's Conclusion: whether the outcome mapping survives fully three-dimensional simulation with controlled numerical resolution, and what light curves, spectra, and ejecta yields BHSNe would produce once coupled to radiative-transfer and nucleosynthesis calculations. The source's Discussion additionally flags, as caveats bounding the present mapping, the sensitivity of the progenitor-to-remnant mapping to the nuclear equation of state, to progenitor stellar-evolution assumptions, and to late-time reverse-shock fallback.

Background

Core-collapse supernovae end the lives of massive stars. When the iron core grows beyond its effective Chandrasekhar mass it collapses; the stiffening of supranuclear-density matter halts the collapse and launches a shock, which promptly stalls because of neutrino losses and photodisintegration. The currently favored revival mechanism is neutrino heating of matter behind the stalled shock, aided by convection and by the standing accretion shock instability, a global sloshing instability of the shock. If the shock revives and the explosion proceeds, a neutron star remains; if it never revives, the star collapses quietly into a black hole (a failed supernova). Long-term multidimensional simulations have exposed an intermediate outcome: the shock revives and an explosion develops, but the proto-neutron star (PNS), the hot, transiently neutron-rich object whose neutrino emission powers the explosion, keeps gaining mass from accretion until it collapses to a black hole while the explosion is still in progress. Andersen and collaborators call these events black hole supernovae (BHSNe). They differ from fallback supernovae, in which a black hole forms late (tens of seconds to hours after shock revival) from the reversal of already-ejected material: in a BHSN accretion proceeds directly from the still-infalling star on a timescale of hundreds of milliseconds to seconds, and the early black hole formation substantially reshapes the explosion, the remnant mass, and the ejecta composition.

The standard structural diagnostic of a pre-collapse core is the compactness $\xi_{2.5}=(M/M_\odot)/(R_{2.5}/1000\ \mathrm{km})$, where $M=2.5\,M_\odot$ and $R_{2.5}$ is the radius enclosing that baryonic mass; it measures how concentrated the inner 2.5 solar masses of the progenitor are, and high compactness implies a high post-bounce mass accretion rate. Another is the carbon-oxygen (CO) core mass, the helium-depleted core that dominates the inner ejecta. The widely used Sukhbold, Woosley and Heger (2018) progenitor grid provides high-resolution pre-supernova structures for single stars across a range of zero-age-main-sequence (ZAMS) masses. Boccioli et al. (2025) showed, from roughly 150 two-dimensional and 20 three-dimensional simulations, that neutrino heating efficiency grows with compactness, so that even high-compactness progenitors revive their shocks - the physical reason BHSNe arise across a broad progenitor range rather than only in the most extreme stars. Individual three-dimensional BHSNe had been simulated before 2026, but never as a systematic survey: Chan et al. (2018) modeled a 40 solar-mass zero-metallicity progenitor whose entire helium core was eventually accreted; Burrows, Vartanyan and Wang (2023) simulated a vigorously exploding 40 solar-mass progenitor, estimating a final black hole mass near 3.5 solar masses at early times; and Burrows, Wang and Vartanyan (2025) followed that same model through hours of late-time fallback accretion to an asymptotic black hole mass of roughly 9 solar masses, and simulated a 19.56 solar-mass progenitor leaving a 3.12 solar-mass black hole. The predecessor study, Eggenberger Andersen et al. (2025), coined the term, simulated three axisymmetric 60 solar-mass models to 20-50 days after collapse with Skyrme-type equations of state (EOS) - a family of nuclear density-functional models - differing in the nucleonic effective mass, the parameter that sets the thermal pressure of hot dense matter, and found explosion energies of $0.06$-$0.72\times10^{51}$ erg, 21.8-23.3 solar masses of ejecta with 0-0.018 solar masses of radioactive nickel-56, a nuanced EOS dependence of the dynamics and remnant mass, and no significant accretion from the reverse shock (the inward-moving shock that forms when the outgoing explosion shock decelerates at the compositional interfaces or the stellar surface).

Andersen et al. (2026) then performed 23 long-term axisymmetric simulations with the FLASH code (a widely used adaptive-mesh hydrodynamics code for astrophysical explosions), using energy-dependent M1 neutrino transport (a two-moment approximation to radiative transfer closed by an analytic angular distribution) and the SFHo nuclear equation of state, a standard model of supranuclear-density matter. It evolved black-hole-forming models past black hole formation with an excision treatment (removing the collapsed region from the computational grid) to at least 5000 s. It found 18 BHSNe spanning nearly the full ZAMS range, black hole formation 0.7-4.4 s after bounce, final explosion energies of roughly $2\times10^{49}$ to $3\times10^{51}$ erg, final black hole gravitational masses of roughly 3-26 solar masses, a clear remnant-mass trend with CO-core mass (though the CO core alone is not an adequate predictor), and several remnants of roughly 2.8-3.9 solar masses inside the so-called lower mass gap, the paucity of observed compact objects between the heaviest neutron stars near 2.2 solar masses and about 5 solar masses, a region probed by gravitational-wave observations of merging compact objects. The study itself compared one pair of two- and three-dimensional FLASH simulations of a stripped 39 solar-mass progenitor (using the SRO95 equation of state, a stiffer alternative to SFHo that generally delays black hole formation relative to it) and reported that the black hole formation time may be delayed in 3D.

Problem Statement

For the black-hole-supernova channel of core collapse, establish the physical outcome mapping and its observable identifiability. Concretely: (1) determine whether the outcome mapping obtained in axisymmetry by Andersen et al. (2026) - in particular the remnant-mass-CO-core-mass relation, the black hole formation times (0.7-4.4 s after bounce in 2D, possibly delayed in 3D), the final explosion energies, and which progenitors produce BHSNe rather than neutron-star-forming, failed, or fallback supernovae - is robust in fully three-dimensional simulation, with numerical resolution controlled, including the resolution of the proto-neutron-star surface approaching collapse; and (2) quantify the observable signatures of BHSNe by coupling these explosion models to radiative-transfer and nucleosynthesis calculations, predicting their light curves, spectra, and ejecta yields, and thereby establishing how BHSNe could be identified observationally and how strongly they contribute to chemical enrichment. These two parts serve one overarching objective - establishing BHSNe as a quantitatively characterized core-collapse outcome, trustworthy in its remnant and ejecta production and recognizable in observation; part (2) builds on the outcome models whose robustness part (1) must establish. The source's Discussion additionally identifies uncertainty axes that bound the present mapping and frame the interpretation of parts (1) and (2): the sensitivity of the zero-age-main-sequence-mass-to-final-black-hole-mass mapping to the nuclear equation of state (the suite adopted SFHo, with SRO95 noted to delay black hole formation), to the assumptions of the progenitor stellar-evolution models (mass loss, rotation, binary interaction), and to late-time fallback from the reverse shock after the explosion has propagated through the star.

References

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