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

Adam S. Burrows; Aleksandr Rusakov; David Vartanyan; Tianshu Wang

arxiv: 2602.09025 · v2 · submitted 2026-02-09 · 🌌 astro-ph.HE · astro-ph.SR

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

Aleksandr Rusakov , Adam S. Burrows , Tianshu Wang , David Vartanyan This is my paper

Pith reviewed 2026-05-16 05:14 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.SR

keywords core-collapse supernovanuclear equation of stateprotoneutron starneutrino signalsgravitational wavesexplosion energyrecoil kick

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The pith

Stiffer DD2 nuclear equation of state produces weaker core-collapse supernova explosions, lower kicks, and altered neutrino and gravitational-wave signals than SFHo.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper runs 3D simulations of a 9-solar-mass star's core collapse to late times using two nuclear equations of state. The DD2 EOS is stiffer and has a lower effective nucleon mass, producing a more extended protoneutron star at lower central densities. As a direct result, mean neutrino energies, final explosion energy, and recoil kick speed are all lower than with the SFHo EOS. PNS convection evolves differently between the models, which changes the neutrino light curves and gravitational-wave signal strength and frequency. The faster SFHo run also yields slightly more neutron-rich ejecta and a weak r-process component.

Core claim

In 3D simulations to late times for a 9-solar-mass progenitor, the DD2 equation of state produces a more extended protoneutron star with lower central densities than SFHo; this leads to lower mean neutrino energies, reduced final explosion energy, smaller recoil kick, altered neutrino light curves, and different gravitational-wave characteristics, plus slightly less neutron-rich ejecta.

What carries the argument

The stiffness and effective nucleon mass of the nuclear equation of state, which set the protoneutron star radius and density profile and thereby control neutrino emission and explosion dynamics.

Load-bearing premise

The observed differences in explosion energy, kicks, and signals arise primarily from the choice of equation of state rather than from numerical resolution or neutrino transport details in the single simulation setup.

What would settle it

Higher-resolution or improved-transport simulations of the same progenitor that eliminate the systematic differences between DD2 and SFHo, or a multi-progenitor survey showing no consistent EOS-dependent trends in final observables.

read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Single 3D runs per EOS show DD2 yielding lower explosion energy, kick, and neutrino energies than SFHo via a more extended PNS, but one realization each leaves room for numerical or stochastic contributions.

read the letter

DD2 produces a more extended protoneutron star than SFHo in these 3D runs of the 9 solar mass star, which leads to lower mean neutrino energies, a weaker final explosion, and a smaller recoil kick. The gravitational wave signals also differ in strength and frequency content, and the nucleosynthesis shows slightly more neutron-rich ejecta with the faster SFHo case. The work does a good job of carrying the simulations far enough to see the asymptotic behavior in energy, nucleosynthesis, and signals. Tracking all those outputs together for two EOS choices on the same progenitor is a useful addition to the literature. The trends line up with expectations from the EOS stiffness and effective mass, and the paper is honest about being a first look at one case. The main limitation is the lack of any resolution study or ensemble of runs. One 3D realization per EOS leaves open the possibility that differences in convection or explosion strength come from stochastic variations or grid details rather than the EOS itself. Without error bars or convergence checks, the quantitative claims are harder to weigh. This paper is aimed at supernova modelers who want to see how EOS choices play out in full 3D late-time results. It gives them concrete examples to think about when planning larger surveys. I would recommend sending it to referees. The core comparison is worth discussing, and feedback on the numerical side would strengthen the next steps the authors already outline.

Referee Report

2 major / 2 minor

Summary. The manuscript performs 3D core-collapse supernova simulations to late times for a single 9 M⊙ progenitor using the SFHo and DD2 nuclear equations of state. It reports that the stiffer DD2 EOS produces a more extended protoneutron star with lower central densities, leading to lower mean neutrino energies, reduced final explosion energy, lower recoil kick speed, altered PNS convection, modified neutrino light curves and gravitational-wave signals, and slightly different nucleosynthetic yields compared to SFHo.

Significance. If the reported differences can be shown to arise primarily from EOS properties rather than numerical or stochastic effects, the work would provide useful constraints on how nuclear physics shapes multi-messenger supernova observables and neutron-star birth properties. The single-progenitor, single-realization scope keeps the immediate significance modest and preliminary.

major comments (2)

[Simulation setup and results sections] The central claim that differences in explosion energy, kicks, neutrino energies, PNS convection, and GW signals are driven by EOS stiffness and effective nucleon mass requires that the two runs differ only in the EOS table. However, only one 3D realization per EOS is presented with no resolution study, grid-convergence test, or ensemble of initial perturbations reported. In 3D CCSN models, turbulent convection and neutrino-driven heating are known to be sensitive to spatial/angular resolution and small perturbations, so the observed differences could reflect numerical details rather than EOS properties.
[Nucleosynthesis and yields discussion] The nucleosynthesis comparison (slightly more neutron-rich ejecta and weak r-process for the faster SFHo model) is based on this single-progenitor, single-run setup. Without multi-progenitor explorations or resolution checks, it is unclear whether these yield differences are robust or generalizable.

minor comments (2)

[Abstract and conclusions] The abstract and introduction appropriately flag the work as preliminary, but the limitations section could more explicitly quantify the absence of convergence tests and the single-realization nature.
[Methods] Ensure all EOS-specific quantities (e.g., effective nucleon mass, stiffness parameters) are defined with explicit references to the input tables upon first use.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the thoughtful and constructive review. We agree that the study is preliminary, as already stated in the abstract and conclusion, and that the single-realization, single-progenitor scope limits the robustness of the conclusions. We address each major comment below and have made partial revisions to strengthen the discussion of limitations.

read point-by-point responses

Referee: [Simulation setup and results sections] The central claim that differences in explosion energy, kicks, neutrino energies, PNS convection, and GW signals are driven by EOS stiffness and effective nucleon mass requires that the two runs differ only in the EOS table. However, only one 3D realization per EOS is presented with no resolution study, grid-convergence test, or ensemble of initial perturbations reported. In 3D CCSN models, turbulent convection and neutrino-driven heating are known to be sensitive to spatial/angular resolution and small perturbations, so the observed differences could reflect numerical details rather than EOS properties.

Authors: We acknowledge that a single realization per EOS leaves room for stochastic variations in 3D turbulence to influence quantitative outcomes such as explosion energy and kick velocity. The PNS structural differences (larger radius and lower central density for DD2) are, however, a direct and systematic consequence of the EOS stiffness and effective mass, which in turn produce lower mean neutrino energies; these EOS-driven changes in the neutrino field are expected to affect the heating and convection in a consistent manner. We have added explicit language in the revised manuscript (Sections 3.2, 4, and the Discussion) underscoring the preliminary character of the results and the desirability of future ensemble runs. No additional simulations or resolution studies were feasible within the computational budget of this work. revision: partial
Referee: [Nucleosynthesis and yields discussion] The nucleosynthesis comparison (slightly more neutron-rich ejecta and weak r-process for the faster SFHo model) is based on this single-progenitor, single-run setup. Without multi-progenitor explorations or resolution checks, it is unclear whether these yield differences are robust or generalizable.

Authors: We concur that the nucleosynthetic differences are indicative rather than definitive, given the limited setup. The slightly faster explosion in the SFHo case produces modestly more neutron-rich ejecta, resulting in the reported yield variations. We have revised the nucleosynthesis section and the concluding discussion to state clearly that these results apply to the present 9 M⊙ progenitor and single realizations, and that multi-progenitor, multi-realization studies will be required to assess generality. revision: partial

standing simulated objections not resolved

We cannot supply additional realizations, resolution studies, or multi-progenitor runs in the present work; computational cost precludes a definitive statistical separation of EOS effects from stochastic variations.

Circularity Check

0 steps flagged

No circularity: direct numerical outputs from independent pre-existing EOS tables

full rationale

The paper reports outcomes from 3D hydrodynamical simulations of a single 9 solar-mass progenitor using two established nuclear EOS tables (SFHo and DD2) as fixed inputs. Differences in PNS extent, central density, neutrino mean energies, explosion energy, recoil kick, convection, GW signals, and nucleosynthesis are presented as direct simulation results without any fitted parameters, self-referential definitions, or derivations that reduce the target observables to the inputs by construction. No load-bearing self-citations, uniqueness theorems, or ansatzes are invoked to justify the central comparison; the work is explicitly labeled preliminary and calls for future multi-progenitor ensembles. This matches the default non-circular case of simulation-based exploration.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the 3D hydrodynamics and neutrino-transport code together with the two standard EOS tables taken from prior literature; no new entities are postulated.

axioms (1)

domain assumption Standard assumptions of neutrino transport and hydrodynamics in core-collapse supernova simulations hold for the chosen resolution and physics modules
Invoked implicitly when interpreting differences as due to EOS alone.

pith-pipeline@v0.9.0 · 5594 in / 1305 out tokens · 36068 ms · 2026-05-16T05:14:21.664300+00:00 · methodology

discussion (0)

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