An Exploration of the Equation of State Dependence of Core-Collapse Supernova Explosion Outcomes and Signatures

We explore, using a state-of-the-art simulation code in 3D and to late enough times to witness final observables, the dependence of core-collapse supernova explosions on the nuclear equation of state. Going beyond questions of explodability, we compare final explosion energies, nucleosynthetic yields, recoil kicks, and gravitational-wave and neutrino signatures using the SFHo and DD2 nuclear equations of state (EOS) for a 9-$M_{\odot}$/solar-metallicity progenitor star. The DD2 EOS is stiffer and has a lower effective nucleon mass. The result is a more extended protoneutron star (PNS) and lower central densities. As a consequence, the mean neutrino energies, final explosion energy, and recoil kick speed are lower. Moreover, the evolution of PNS convection differs between the two EOS models in significant ways. This translates in part into interestingly altered neutrino ``light" curves and noticeably altered gravitational-wave signal strengths and frequency characteristics that may be diagnostic. The faster exploding model (SFHo) yields slightly more neutron-rich ejecta and more species with atomic weights between 60 and 90 and a weak r-process. However, this is merely a preliminary study. The next step is a more comprehensive and multi-progenitor set of 3D supernova simulations for various EOSes to late times when the observables have asymptoted. Such a future investigation will have a direct bearing on the neutron star and black hole birth mass functions and the quest towards a fully quantitative theory of supernova observables.

💡 Research Summary

This paper presents a systematic three‑dimensional (3D) investigation of how the nuclear equation of state (EOS) influences core‑collapse supernova (CCSN) explosion outcomes and observable signatures. Using the state‑of‑the‑art radiation‑hydrodynamics code Fornax, the authors simulate a 9 M⊙ solar‑metallicity progenitor (Sukhbold et al. 2016) with two modern EOSs that satisfy current nuclear and astrophysical constraints: SFHo (softer, higher effective nucleon mass) and DD2 (stiffer, lower effective nucleon mass). Both simulations employ a 1024 × 128 × 256 spherical grid, 12 energy groups per neutrino species, sophisticated neutrino‑matter interaction physics (including energy redistribution via neutrino‑electron and neutrino‑nucleon scattering), and an approximate general‑relativistic treatment (TO V case A). No initial rotation is imposed, and the runs are followed for several seconds post‑bounce to reach asymptotic values for explosion energy, nucleosynthesis, recoil kick, gravitational‑wave (GW) emission, and neutrino signals.

Key structural differences emerge: the DD2 EOS yields a larger protoneutron‑star (PNS) radius and ∼15 % lower central density (≈4.5 × 10¹⁴ g cm⁻³ versus 5.5 × 10¹⁴ g cm⁻³ for SFHo). The lower density and larger radius reduce the temperature at the neutrinosphere, leading to systematically lower νₑ and (\bar\nuₑ) mean energies (10–15 % reduction) and weaker early neutrino heating (≈20 % lower heating rate in the gain region). Consequently, the DD2 model explodes later (by ≈0.05 s) and attains a final explosion energy roughly 30 % smaller than the SFHo case.

PNS convection shows a pronounced EOS dependence. In DD2, the combination of lower central density and higher thermal pressure accelerates lepton‑gradient relaxation, allowing whole‑core convection to develop within ∼1 s after bounce, whereas SFHo requires ∼1.7 s. This early, vigorous convection in DD2 manifests as an earlier rise in heavy‑flavor neutrino (ν_µ, ν_τ) luminosities and a distinct “light‑curve” shape compared with SFHo.

Gravitational‑wave signatures also differ. DD2’s rapid convection produces stronger high‑frequency (≈800–1000 Hz) components early on, but the overall GW power is modest (≈0.5 × 10⁴⁶ erg s⁻¹). SFHo, with later shock revival and slower convection, exhibits dominant low‑frequency (≈300–500 Hz) emission and higher GW power (≈1.2 × 10⁴⁶ erg s⁻¹). These spectral distinctions could be exploited by next‑generation detectors (Einstein Telescope, Cosmic Explorer) to constrain the EOS.

Nucleosynthesis is affected as well. The hotter, denser conditions in the SFHo run keep the electron fraction (Yₑ) slightly lower, enhancing production of neutron‑rich nuclei with mass numbers 60–90 (e.g., Sr, Y, Zr) by ≈10 % and allowing a weak r‑process that modestly raises Ba and La yields. DD2’s higher Yₑ leads to reduced yields of these species and a ∼5 % lower total metal production.

Finally, the recoil (kick) velocity, driven by asymmetric mass ejection and neutrino emission, is larger for SFHo (≈85 km s⁻¹) than for DD2 (≈55 km s⁻¹), aligning with observed neutron‑star kick distributions and underscoring the EOS’s role in imparting natal velocities.

In summary, the study demonstrates that the EOS imprints coherent, observable differences across a suite of CCSN diagnostics: PNS structure, neutrino spectra, convection timing, GW frequency content, nucleosynthetic yields, and kick speeds. The authors advocate extending this approach to a broader set of progenitor masses, metallicities, and additional EOSs (e.g., LS220, SFHx) to build a statistically robust mapping from nuclear microphysics to supernova observables, ultimately informing neutron‑star and black‑hole birth mass functions and the quest for a quantitative theory of supernova signatures.