Parametrized spherically symmetric (1D) explosion methods such as PUSH map the pre-supernova structure of a massive star (compactness, carbon-oxygen core mass) to its explosion outcome: explodability, explosion energy, and neutron-star or black-hole birth masses. Ebinger et al. (2019, PUSH Paper II) showed this mapping reproduces observed supernova properties but explicitly identified six unresolved limitations: the 1D parametrization cannot capture multi-dimensional neutrino heating; progenitor models above roughly 30-40 solar masses are uncertain in semiconvection, overshooting, and wind mass loss; early and late fallback are not modeled; solar-metallicity grids cannot reach the black-hole masses observed by the LIGO/Virgo gravitational-wave detectors; rotation and magnetic fields are neglected; and the calibration itself depends on the compactness evaluation mass and the SN 1987A anchor model, with an alternative calibration shifting explodability and black-hole fractions. Later work closed one of these limitations (low-metallicity grids in Paper IV), while the others remain open. The open core is a single robustness question: which features of the predicted progenitor-to-outcome mapping are physically real and which are artifacts of the parametrization, calibration, and progenitor modeling.

Background

A core-collapse supernova (CCSN) is the terminal explosion of a star more massive than about 8 solar masses: its iron core collapses to a proto-neutron star, and, in the standard delayed neutrino-driven mechanism, a stalled bounce shock is revived because a fraction of the neutrinos emitted from the cooling proto-neutron star deposits energy in the matter behind the shock (the gain region). First-principles simulations of this mechanism require multi-dimensional (multi-D) neutrino radiation hydrodynamics, since convection and turbulence aid the revival, and remain too expensive for surveys of hundreds of progenitors. For such surveys the field uses effective spherically symmetric (1D) models in which an artificial, parametrized heating term mimics the net effect of multi-D neutrino transport. PUSH (Perego et al. 2015) is one such method: it augments the neutrino energy deposition inside the gain region of a 1D general-relativistic hydrodynamics simulation with two free parameters (kpushk_{\mathrm{push}} and triset_{\mathrm{rise}}), which must be calibrated against external anchors. In PUSH Paper II (Ebinger et al. 2019) the calibration used three observational constraints — reproduction of SN 1987A properties (anchored on the progenitor model s18.8), allowance of black-hole formation, and low explosion energies for the lowest-mass progenitors (Crab-like supernovae) — implemented as a compactness-dependent parabola for kpushk_{\mathrm{push}}. The compactness parameter ξM=M/M⊙ (R/1000 km)−1\xi_M = M/M_\odot \,(R/1000\,\mathrm{km})^{-1} measures how concentrated the progenitor's inner MM solar masses of mass coordinate are at collapse and is the standard structural proxy for explodability. Applying this calibrated setup to 133 non-rotating solar-metallicity progenitors (the WHW02 (Woosley, Heger and Weaver 2002) and Woosley-Heger 2007 model sets, 10.8-120 M⊙M_\odot), Paper II produced an explodability landscape (which initial masses explode, form neutron stars, or collapse to black holes, including a black-hole island near 22-26 M⊙M_\odot), trends of explosion energy and ejecta yields with compactness and carbon-oxygen (CO) core mass, and predicted neutron-star and black-hole birth-mass distributions. Fallback — material that is initially ejected but later re-accretes onto the compact remnant — has an early component that only multi-D simulations can determine and a late component that requires much longer simulation times than the PUSH setup affords, so the predicted remnant masses exclude it. The authors state that the true mechanism problem requires multi-D simulations with general relativity, sophisticated neutrino transport, magnetic fields and rotation, and they list the specific respects in which their mapping remains unestablished: the calibration depends on the compactness evaluation mass (their standard ξ2.0\xi_{2.0} versus an alternative ξ1.75\xi_{1.75} calibration, the latter lowering overall explodability and enlarging the black-hole fraction), on the chosen SN 1987A progenitor model, and on progenitor evolution physics (semiconvection, a slow doubly diffusive mixing process in stellar interiors; convective overshooting, mixing beyond the formal convective boundary; and wind mass loss driven by radiation) that is poorly constrained above roughly 30-40 M⊙M_\odot; rotation and magnetism, which power hypernovae (explosions roughly ten times more energetic than a typical core-collapse supernova) and gamma-ray-burst supernovae, are absent. Because predicted explodability prescriptions and remnant-mass distributions are consumed downstream — in binary population synthesis, gravitational-wave source modeling, and galactic chemical evolution — whether this mapping is physically robust or partly a calibration artifact is a question of direct astrophysical consequence.

Problem Statement

The problem, as posed by the limitations Ebinger et al. (2019) explicitly identify for their PUSH-based explodability study, is to establish the physical robustness of the mapping from pre-supernova stellar structure (compactness and CO-core mass) to explosion outcome (explodability, explosion energy, and neutron-star/black-hole birth masses) that calibrated parametrized spherically symmetric methods predict. Concretely, for the PUSH framework and its published solar- and low-metallicity grids, determine: (i) how sensitive the predicted explodability landscape and remnant-mass distributions are to the calibration choices — the compactness evaluation mass (ξ2.0\xi_{2.0} versus ξ1.75\xi_{1.75}) and the SN 1987A anchor progenitor model — and which features (for example the black-hole island near 22-26 solar masses initial mass and the compactness/CO-core trends) survive alternative reasonable calibrations; (ii) whether the calibration, performed on limited observational anchors, transfers across progenitor structures, by validating the 1D mapping against multi-dimensional neutrino-radiation-hydrodynamic simulations for a representative progenitor sample, given that the parametrized heating only approximates multi-dimensional neutrino transport; (iii) how the omitted multi-dimensional physics — early fallback requiring multi-D simulation and late fallback requiring much longer evolution times, as well as rotation and magnetic fields — changes the predicted ejecta and remnant masses and the boundary between successful and failed explosions; and (iv) how the substantial progenitor-model uncertainties above roughly 30-40 solar masses (semiconvection efficiency, convective overshooting, wind mass loss) propagate into compactness and hence into explodability and black-hole masses. The common objective uniting these components is a quantitative account of which features of the predicted progenitor-to-outcome mapping are physically robust and which are artifacts of the parametrization, calibration, or progenitor modeling. All four components are required for a resolution: addressing any one of them alone leaves the robustness question open.

References

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