Strongly interacting matter with criticality induced by modified excluded volume in core-collapse supernova simulations

Abstract: This article reviews critically the core-collapse supernova explosion mechanism associated with a sufficiently strong first-order phase transition from normal nuclear, in general hadronic matter to deconfined quark matter, which commonly assumes Gibbs conditions for the coexistence of phases and a phase transition construction accordingly. To this end, a novel class of multi-purpose equation of state (EOS) is developed, based on the modified excluded volume (MEV) approach employing a medium-dependent excluded-volume functional within the relativistic mean field framework with density-dependent meson-nucleon couplings. The chosen MEV parametrisation features the change in the number of degrees of freedom, mimicking the EOS softening in excess of nuclear saturation density, featuring a first-order phase transition with van der Waals like behaviour and the presence of a critical point at high temperatures. Simulations of core-collapse supernovae are performed, based on general relativistic neutrino radiation hydrodynamics in spherical symmetry, in order to explore the previously reported supernova explosion scenario within this class of phenomenological modified microscopic hadronic EOS. A burst-like neutrino signature is released, substantially longer than previously reported based on common hadron-quark hybrid model EOS with two-phase approach and Gibbs phase-transition construction, as observable signal, which is complemented by a gravitational wave mode analysis.

• The paper introduces a modified excluded volume (MEV) approach that continuously transitions hadronic matter to quark matter, highlighting its impact on supernova dynamics.
• It extends the DD2 RMF equation of state with a medium-dependent modification that mimics van der Waals features, influencing phase transitions and protoneutron star contraction.
• The study demonstrates that the resulting changes in neutrino bursts and gravitational wave frequencies offer potential observable signatures to distinguish between competing EOS models.

Modified Excluded Volume Criticality in Supernova Simulations: A Technical Assessment

Introduction

This paper provides a comprehensive analysis of the impact of critical phenomena in strongly interacting matter, modeled via a medium-dependent modified excluded volume (MEV) mechanism, on the dynamics of core-collapse supernovae (CCSN). The study critically evaluates both the equation of state (EOS) properties and the resulting hydrodynamic and neutrino signatures arising from first-order phase transitions to deconfined quark matter, going beyond classical Gibbs constructions by implementing a continuous, van der Waals inspired softening of the EOS at supranuclear densities. Both practical and theoretical implications for the nature of supernova explosions, their observable signatures, and the constraints on QCD matter at high densities are addressed.

Equation of State Formulation and Phase Structure

The EOS is constructed by extending the standard DD2 relativistic mean field (RMF) EOS with a temperature- and density-dependent MEV mechanism. This introduces a medium-dependent modification of the available volume for nucleon degrees of freedom, enabling a continuous transition from hadronic to quark matter characterized by van der Waals-like features, including an instability region and a critical endpoint at high temperatures.

Unlike conventional two-phase models—which realize phase coexistence via Gibbs conditions, enforced between distinct hadronic and quark-matter branches—the MEV approach modifies the nucleonic degeneracy factors, producing a continuous variation in the effective number of degrees of freedom. This realization allows for the mimicking of both the softening and subsequent stiffening of the EOS at high density, with the following consequences:

• Phase Diagram Richness: The MEV model allows a nontrivial binodal and spinodal structure with a critical endpoint. The region of negative pressure slope corresponds to a nontrivial mechanical instability, a hallmark of van der Waals-like transitions.
• Contrasts to Two-Phase Models: The density discontinuity across the coexistence region in MEV (Gibbs) is significantly smaller than conventional RDF hybrid EOS, leading to distinct hydrodynamics in CCSN scenarios.

Core-Collapse Supernova Simulations

Simulations are carried out with the AGILE-BOLTZTRAN code (general relativistic, Boltzmann neutrino transport in spherical symmetry) for a $40\,M_\odot$ progenitor, using both DD2-MEV and DD2-MEV (Gibbs) parameterizations. The comparison is extended to the established RDF class of hybrid EOS.

Main Findings

• No Explosion with DD2-MEV (Gibbs): The small density jump in phase coexistence produces only mild PNS contraction post-transition, no secondary strong shock, and ultimately collapse to a black hole. The neutrino burst associated with a dynamical phase transition is not observed.
• Explosion with van der Waals MEV: The direct implementation of van der Waals behavior (without explicit Gibbs construction) allows a rapid—sometimes supersonic—PNS contraction, generating a strong secondary shock that can drive an explosion. The associated neutrino burst (millisecond-duration, all flavors) is broader (5–10 ms) and energetically distinct from previous RDF/bag-motivated models, with much larger initial explosion energy that decays over hundreds of milliseconds due to fallback.
• Nonstandard Thermal Trajectories: With MEV, the post-transition central temperature rises rapidly, contrasting with the temperature dip seen in standard bag and RDF models for comparable entropy, altering the thermodynamics of the post-bounce evolution.

Neutrino and Gravitational Wave Signatures

Neutrino Signal

The simulation demonstrates that a strong, prompt neutrino burst is absent in the DD2-MEV (Gibbs) case and only appears for the van der Waals-type criticality, but its duration, flavor structure, and energy evolution are markedly different from earlier models. The total neutrino burst is significantly broader and persists for longer time, possibly providing a discriminating observable if detected.

Gravitational Wave Mode Analysis

A full GR astroseismology analysis is performed, beyond the Cowling approximation, focusing on the evolution of the f- and lowest-order g-modes ($n=1,\,\ell=2$). Main results:

• Mode Evolution: The f-mode frequency correlates with mean PNS density before the phase transition, but undergoes nontrivial changes during and after the phase transition in MEV-based runs.
• Breakdown of Universal Relations: Standard parameterizations of f- and g-mode frequencies in terms of mean density and compactness fail post phase transition, reflecting the change in EOS degrees of freedom.
• Diagnostic Potential: The altered behavior of PNS oscillation modes in the presence of quark matter and criticality could provide a mechanism to differentiate hadronic and hybrid EOS in observed gravitational wave signals, contingent on future multi-dimensional simulations.

Implications and Perspectives

Theoretical Implications

This work highlights critical dependence of CCSN dynamics on EOS microphysics, particularly the realization of criticality and phase transitions at high density. The MEV approach provides an alternative to two-phase hybrid models, with the capacity to interpolate between soft and stiff behavior intrinsic to QCD-motivated EOS. However, the lack of a large density jump in the critical region suppresses the energetic phase-transition-induced explosion in spherical symmetry, in stark contrast with previous results using bag/RDF hybrid EOS.

Practical and Observational Consequences

The neutrino burst is an observable sensitive to the EOS treatment at the hadron-quark interface. The delayed, broadened neutrino burst and the altered gravitational wave mode structure are robust discriminants between MEV-type and conventional two-phase constructions. These findings suggest that future high-cadence multi-messenger observations could constrain the nature of the EOS and the presence of QCD criticality in the CCSN environment.

Future Directions

• EOS Parameter Exploration: Systematic studies of MEV parameters (e.g., width and depth of the critical region) could further delineate the boundaries for successful explosions and characteristic observables.
• Multi-Dimensional Simulations: Extending this analysis beyond spherical symmetry is essential, especially given the potential for hydrodynamical instabilities in regions of negative sound speed.
• Microphysical Consistency: Further development towards EOS formulations satisfying QCD constraints (causality, asymptotic freedom, confinement) and momentum-dependent interactions remains an important theoretical objective.

Conclusion

The study rigorously establishes that the phenomenology of CCSN and the associated multi-messenger signals are highly sensitive to the treatment of the high-density QCD phase transition, especially the characterization of criticality and the nature of the hadron-quark interface. The MEV framework provides a continuous transition model that exposes nontrivial effects on PNS dynamics and observable signatures, highlighting the necessity for a precise EOS characterization in understanding and interpreting astrophysical transients involving dense QCD matter. This work motivates both further theoretical development of EOS models and their systematic confrontation with future high-precision CCSN observations.

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Reference:

"Strongly interacting matter with criticality induced by modified excluded volume in core-collapse supernova simulations" (2607.10396)