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arxiv: 1907.06597 · v1 · pith:F2BJN5QSnew · submitted 2019-07-05 · ⚛️ nucl-th · astro-ph.HE· hep-ph· physics.space-ph

Hot quark matter and (proto-) neutron stars

G. Malfatti , M. Orsaria , G. A. Contrera , F. Weber , I. F. Ranea-Sandoval This is my paper

Pith reviewed 2026-05-25 01:43 UTC · model grok-4.3

classification ⚛️ nucl-th astro-ph.HEhep-phphysics.space-ph
keywords proto-neutron starsneutron starsquark matterhyperonsdelta isobarsPNJL modelQCD phase diagramneutron star mergers
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0 comments X

The pith

Hot proto-neutron star models contain hyperons and Δ-isobars but no deconfined quarks, which appear only in cold neutron stars.

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

The paper applies a non-local three-flavor Polyakov-Nambu-Jona-Lasinio model that incorporates flavor mixing, momentum-dependent masses, and vector interactions to locate a spinodal region and critical end point in the QCD phase diagram. It then computes the particle content of baryonic matter at zero and finite temperature using entropies and lepton fractions typical of proto-neutron stars. The resulting hot stellar configurations include large fractions of hyperons and Δ-isobars yet remain free of deconfined quarks. These compositions are used to follow the mass evolution from proto-neutron star to cold neutron star. The results bear directly on the interpretation of signals from neutron-star merger events such as GW170817.

Core claim

Using a non-local extension of the 3-flavor PNJL model that includes flavor-mixing, momentum-dependent quark masses, and vector interactions, the authors determine the composition of baryonic matter at finite temperature. They find that proto-neutron stars with entropies and lepton fractions typical of their early evolution contain substantial amounts of hyperons and Δ-isobars but no deconfined quarks. Deconfined quarks appear only in the cold neutron star stage.

What carries the argument

The non-local three-flavor Polyakov-Nambu-Jona-Lasinio (PNJL) model with vector interactions and momentum-dependent masses, used to fix the quark-hadron composition and locate the critical end point in the QCD phase diagram.

If this is right

  • Proto-neutron stars evolve into neutron stars without encountering a deconfined quark phase.
  • Hyperons and Δ-isobars reach significant fractions in the hot phase while quarks remain confined.
  • The baryon-mass versus gravitational-mass diagram traces a specific cooling path set by these compositions.
  • A spinodal region and critical end point exist in the QCD phase diagram at temperatures and chemical potentials reachable in the model.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Gravitational-wave signals from the early hot phase of a merger remnant may lack features associated with quark deconfinement.
  • Cooling curves or neutrino emission from young neutron stars could be compared against the predicted absence of quarks to test the composition sequence.
  • Adding rotation or magnetic fields to the same model framework might shift the temperature at which quarks first appear.

Load-bearing premise

The chosen non-local extension of the 3-flavor PNJL model with its vector interactions and momentum-dependent masses correctly captures the QCD phase structure and baryon composition at the temperatures and densities inside proto-neutron stars.

What would settle it

An independent model calculation that produces deconfined quarks inside proto-neutron star matter at the same entropies and lepton fractions would falsify the claim that quarks exist only after cooling.

Figures

Figures reproduced from arXiv: 1907.06597 by F. Weber, G. A. Contrera, G. Malfatti, I. F. Ranea-Sandoval, M. Orsaria.

Figure 1
Figure 1. Figure 1: FIG. 1: (Color online) Dependence of the dynamical masses of light ( [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: is for quark matter only. This figure, therefore, should not be confused with the full QCD phase diagram. A recent discussion of the QCD phase diagram based on a hadronic model and a chiral quark model (which is simpler than the 3nPNJL model of this work) can be found in Ref. [50]. In order to show the effects of vector interaction we have chosen the values ζv = 0.0 and ζv = 0.5, the latter being the stand… view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: (Color online) Temperature, [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: (Color online) (a) Quark number density, [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: (Color online) Isotherms of the square of the speed of sound, [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: (Color online) Panel (a) shows the construction of the EoS (at [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: (Color online) Panel (a) shows the construction of the EoS (at [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: (Color online) Dynamical masses, [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: (Color online) Comparison of the zero-temperature quark-hybrid EoSs of this work (GM1L, DD2) with models (HLPS, [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: (Color online) Particle population of stellar quark-hybrid matter at zero temperature as a function of baryonic number [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: (Color online)(a) Gravitational mass as a function of central energy density, and (b) gravitational mass as a function [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: (Color online). Energy density as a function of radius for the maximum-mass neutron stars shown in Fig. 11. The [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: (Color online) Gravitational mass, [PITH_FULL_IMAGE:figures/full_fig_p019_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: (Color online) Particle populations of proto-neutron star matter for the GM1L parametrization. The compositions [PITH_FULL_IMAGE:figures/full_fig_p020_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: (Color online) Same as Fig. 14, but for the DD2 parametrization. [PITH_FULL_IMAGE:figures/full_fig_p021_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16: (Color online) Gravitational mass versus baryonic mass of selected stages (characterized by entropy and lepton number) [PITH_FULL_IMAGE:figures/full_fig_p022_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17: (Color online) Tidal deformability versus gravitational mass of pure hadronic stars (solid lines). Hybrid branches are [PITH_FULL_IMAGE:figures/full_fig_p023_17.png] view at source ↗
read the original abstract

In part one of this paper, we use a non-local extension of the 3-flavor Polyakov-Nambu-Jona-Lasinio model, which takes into account flavor-mixing, momentum dependent quark masses, and vector interactions among quarks, to investigate the possible existence of a spinodal region (determined by the vanishing of the speed of sound) in the QCD phase diagram and determine the temperature and chemical potential of the critical end point. In part two of the paper, we investigate the quark-hadron composition of baryonic matter at zero as well as non-zero temperature. This is of great topical interest for the analysis and interpretation of neutron star merger events such as GW170817. With this in mind, we determine the composition of proto-neutron star matter for entropies and lepton fractions that are typical of such matter. These compositions are used to delineate the evolution of proto-neutron stars to neutron stars in the baryon-mass versus gravitational-mass diagram. The hot stellar models turn out to contain significant fractions of hyperons and $\Delta$-isobars but no deconfined quarks. The latter, are found to exist only in cold neutron stars.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript employs a non-local three-flavor PNJL model that incorporates flavor mixing, momentum-dependent quark masses, and vector interactions to locate the critical endpoint and spinodal region in the QCD phase diagram. It then determines the baryon composition of matter at zero and finite temperature for entropies and lepton fractions typical of proto-neutron stars, using these to trace evolutionary tracks in the baryon-mass versus gravitational-mass plane. The central result is that hot models contain significant fractions of hyperons and Δ-isobars but no deconfined quarks, while deconfined quarks appear only in cold neutron stars.

Significance. If the model results hold, the work would contribute to the interpretation of neutron-star merger signals by providing explicit predictions for the hyperon and Δ content of hot matter and the distinction between hot and cold compositions. The use of a single effective model to connect the phase diagram to stellar sequences is a concrete step, though its predictive power depends on the robustness of the chosen parameters.

major comments (2)
  1. [Part two (stellar composition and evolution)] The central claim that deconfined quarks are absent from hot proto-neutron-star matter (S ≈ 1–2, Y_L ≈ 0.3–0.4) but present in cold neutron stars is controlled by the fixed vector coupling G_v and the non-local form factor. The manuscript determines the CEP and spinodal once with these parameters but does not recompute the stellar compositions or evolutionary tracks under modest variations of G_v or the regulator; such variations can shift the deconfinement line at finite temperature and density, directly affecting the reported absence of quarks.
  2. [Abstract and phase-diagram section] No quantitative error estimates, tables of parameter values, or direct comparisons to lattice QCD or alternative models (e.g., other NJL variants or chiral effective theories) are supplied for the high-density, finite-temperature regime. This leaves the composition results (hyperon and Δ fractions, quark absence) without demonstrated uncertainty ranges or cross-validation.
minor comments (2)
  1. The abstract would be clearer if it stated the specific numerical values adopted for the vector coupling and non-local regulator.
  2. Notation for entropy per baryon and lepton fraction should be defined explicitly when first used in the stellar-model discussion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We respond to each major comment below, indicating where we agree and what revisions we will incorporate.

read point-by-point responses

  1. Referee: [Part two (stellar composition and evolution)] The central claim that deconfined quarks are absent from hot proto-neutron-star matter (S ≈ 1–2, Y_L ≈ 0.3–0.4) but present in cold neutron stars is controlled by the fixed vector coupling G_v and the non-local form factor. The manuscript determines the CEP and spinodal once with these parameters but does not recompute the stellar compositions or evolutionary tracks under modest variations of G_v or the regulator; such variations can shift the deconfinement line at finite temperature and density, directly affecting the reported absence of quarks.

    Authors: We agree that the results for the absence of deconfined quarks in hot matter depend on the specific choice of G_v and the non-local form factor. These were fixed by reproducing vacuum meson properties and nuclear saturation density as described in Section II of the manuscript. A full recomputation of all evolutionary tracks under parameter variations would be a substantial extension. In the revised version we will add a dedicated paragraph discussing the sensitivity of the deconfinement line to modest changes in G_v (drawing on existing PNJL literature) and note that the qualitative conclusion remains stable within the range of G_v values consistent with our calibration. We therefore mark this as a partial revision. revision: partial

  2. Referee: [Abstract and phase-diagram section] No quantitative error estimates, tables of parameter values, or direct comparisons to lattice QCD or alternative models (e.g., other NJL variants or chiral effective theories) are supplied for the high-density, finite-temperature regime. This leaves the composition results (hyperon and Δ fractions, quark absence) without demonstrated uncertainty ranges or cross-validation.

    Authors: The model parameters (including G_v and the regulator) are listed in Table I together with the fitting procedure to meson observables and nuclear matter. Direct lattice QCD data at the relevant high chemical potentials are unavailable owing to the sign problem; we will therefore add explicit references to other effective-model studies of the CEP and high-density composition in the revised text. Quantitative uncertainty bands on the stellar composition fractions would require a dedicated Bayesian analysis that lies beyond the present scope. We will expand the discussion of model limitations and cross-model comparisons but cannot supply numerical error estimates without new methodological work. revision: partial

Circularity Check

0 steps flagged

No circularity; stellar composition is direct model output

full rationale

The derivation applies the non-local 3-flavor PNJL model (with fixed vector coupling, non-local regulator, and momentum-dependent masses) to compute the EOS, locate the CEP via vanishing speed of sound, and then solve the Tolman-Oppenheimer-Volkoff equation plus beta-equilibrium conditions at finite entropy and lepton fraction. The reported absence of deconfined quarks in hot matter is an output of those equations at the chosen parameter values, not a re-expression of the inputs. No self-citation is invoked to justify uniqueness, no fitted subset is relabeled as a prediction of the target quantity, and no ansatz is smuggled via prior work. The calculation is self-contained once the model Lagrangian and parameter set are stated.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

All quantitative results rest on the validity of one effective quark model whose parameters are fitted to lower-density data and then extrapolated; no independent first-principles derivation or external benchmark is cited in the abstract.

free parameters (1)
  • PNJL coupling constants and non-local form factors
    The model requires several adjustable parameters for quark interactions, vector repulsion, and momentum dependence that are fixed by fitting to known hadron properties or lattice data.
axioms (1)
  • domain assumption The non-local 3-flavor PNJL model with flavor mixing and vector interactions provides a reliable effective description of QCD thermodynamics at finite temperature and baryon density.
    This assumption underpins both the location of the critical end point and the stellar composition calculations.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Dark Matter Heating in Evolving Proto-Neutron Stars: A Two-Fluid Approach

    astro-ph.HE 2025-11 unverdicted novelty 5.0

    Dark matter cores heat baryonic matter in evolving proto-neutron stars by deepening the gravitational potential while halos cool it, providing a diagnostic distinct from hyperons.

Reference graph

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