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arxiv: 2605.00437 · v1 · submitted 2026-05-01 · 🌌 astro-ph.HE · hep-ph· nucl-th

Maximal mass of neutron stars constrained by neutron star observations

G\'abor Kasza , Gy\"orgy Wolf This is my paper

Pith reviewed 2026-05-09 19:13 UTC · model grok-4.3

classification 🌌 astro-ph.HE hep-phnucl-th
keywords neutron starequation of statemaximum massBayesian analysishybrid EOSGW170817NICER
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The pith

Neutron star observations constrain the maximum mass to 2.2-2.3 solar masses with weak dependence on the baseline equation of state.

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

The paper builds families of causal hybrid equations of state starting from two hadronic baselines, SFHo and DD2, extended via an extended linear sigma model and required to match perturbative QCD at high densities. These families are then weighted by Bayesian likelihood using data from the GW170817 merger, NICER mass-radius measurements, and candidate compact objects including possible mass-gap objects. The resulting probability distributions for the endpoint of each mass-radius sequence show that the maximum mass is set mostly by the observations and peaks near 2.2-2.3 solar masses, while the corresponding radius is more sensitive to the choice of hadronic baseline and typically lies near 12 km. A reader would care because this narrows the allowed behavior of matter at densities several times nuclear saturation, directly affecting predictions for neutron-star mergers and gravitational-wave signals.

Core claim

By constructing families of causal hybrid EOSs from SFHo and DD2 baselines matched to an extended linear sigma model and constrained to pQCD asymptotics, then applying Bayesian likelihood weighting with GW170817, NICER, and mass-gap candidate constraints, the probability distributions for the maximum mass M_TOV favor 2.2-2.3 solar masses with only weak sensitivity to the baseline EOS, while the associated radius R_TOV prefers values near 12 km with stronger baseline dependence; additional tidal-deformability constraints further restrict stiff realizations.

What carries the argument

Bayesian likelihood weighting of the endpoints (maximum mass M_TOV and radius R_TOV) of mass-radius sequences drawn from families of causal hybrid equations of state.

If this is right

  • Maximum-mass distributions are determined primarily by the observational constraints rather than the choice of hadronic baseline.
  • Radius distributions at maximum mass retain stronger dependence on the underlying hadronic EOS.
  • Tidal-deformability constraints combined with mass-gap candidates disfavor the stiffest EOS realizations.
  • Endpoint distributions of M(R) sequences act as a complementary diagnostic for the high-density EOS in a multimessenger setting.

Where Pith is reading between the lines

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

  • The weak sensitivity to baseline choice suggests multimessenger data can constrain supranuclear densities even when lower-density physics remains uncertain.
  • Future precise mass or radius measurements could tighten the distributions without requiring entirely new EOS constructions.
  • The same weighting framework could test the impact of additional phase transitions if they are explicitly included in future EOS families.

Load-bearing premise

The constructed families of causal hybrid EOSs span all physically allowed high-density behaviors without omitting important phase transitions or additional degrees of freedom.

What would settle it

A confirmed neutron-star mass measurement above 2.5 solar masses or a high-precision radius measurement for a near-maximum-mass star falling outside 11-13 km would contradict the favored distributions.

Figures

Figures reproduced from arXiv: 2605.00437 by G\'abor Kasza, Gy\"orgy Wolf.

Figure 1
Figure 1. Figure 1: Probability distribution of maximal mass of neutron stars using di view at source ↗
Figure 2
Figure 2. Figure 2: The same as Fig. 1, but adding the constraint of view at source ↗
Figure 3
Figure 3. Figure 3: Probability distribution of radii corresponding to the maximal mass of neutron stars using di view at source ↗
Figure 4
Figure 4. Figure 4: The same as Fig. 3, but adding the constraint of view at source ↗
read the original abstract

We investigate constraints on the high-density equation of state (EOS) of neutron star matter by analyzing the probability distributions of the endpoints of mass-radius M(R) sequences within a Bayesian weighting framework. Starting from two representative hadronic baseline EOSs, SFHo and DD2, matched at higher densities to an extended linear sigma model description and constrained to approach perturbative QCD (pQCD) results, we construct families of causal hybrid EOSs spanning a broad range of stiffness at supranuclear densities. Observational constraints from the binary neutron-star merger GW170817, mass-radius measurements from the Neutron Star Interior Composition Explorer (NICER), and candidate low-mass and mass-gap compact objects are incorporated through Bayesian likelihood weighting. This approach allows us to determine probability distributions for the maximum neutron-star mass M$_{\rm TOV}$ and the corresponding radius R$_{\rm TOV}$, i.e., the endpoints of the M(R) sequences. We find that the maximum-mass distributions are largely determined by observational constraints and show only weak sensitivity to the choice of baseline EOS, favoring values around 2.2-2.3 M$_\odot$ when the most robust constraints are applied. In contrast, the corresponding radius distributions exhibit a stronger dependence on the underlying hadronic EOS, with typical preferred values near $12\pm 1$ km. Additional tidal-deformability constraints further restrict the allowed parameter space and disfavor very stiff EOS realizations when interpreted together with the possible mass-gap neutron-star candidate. Our results demonstrate that endpoint distributions of M(R) sequences provide a sensitive and complementary diagnostic for constraining the high-density behavior of the neutron-star EOS within a multimessenger Bayesian framework.

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 constructs families of causal hybrid equations of state (EOS) starting from two hadronic baselines (SFHo and DD2), matched at supranuclear densities to an extended linear sigma model and constrained to approach perturbative QCD (pQCD) results at high densities. These families are then reweighted via Bayesian likelihoods incorporating GW170817 tidal deformability, NICER mass-radius measurements, and candidate low-mass/mass-gap compact objects to derive probability distributions for the maximum mass M_TOV and corresponding radius R_TOV at the endpoint of each M(R) sequence. The central finding is that M_TOV distributions peak at 2.2-2.3 M⊙ with only weak sensitivity to the choice of baseline EOS, while R_TOV shows stronger baseline dependence around 12 km; additional tidal constraints further disfavor stiff realizations when combined with mass-gap candidates.

Significance. If the hybrid EOS families adequately sample the allowed high-density behaviors, the work provides a useful complementary diagnostic by focusing on endpoint distributions rather than full M(R) curves. The multimessenger Bayesian reweighting framework, explicit use of two distinct baselines to test sensitivity, and enforcement of causality plus pQCD boundary conditions are strengths that enhance robustness within the explored model space. The observationally driven nature of the M_TOV constraint is a noteworthy result for neutron-star astrophysics.

major comments (2)
  1. [§3] §3 (hybrid EOS construction): The central claim of weak sensitivity of M_TOV distributions to baseline choice (abstract and §4) rests on the assumption that matching SFHo/DD2 to the extended linear sigma model plus pQCD asymptotics adequately spans the physically allowed stiffness range. Unmodeled first-order phase transitions or additional degrees of freedom (hyperons, delta resonances, color superconductivity) could produce qualitatively different sound-speed profiles above ~2-3 n_sat while remaining causal and pQCD-consistent, which would alter the reweighted posterior even under identical observational likelihoods.
  2. [§4] §4 (results on endpoint distributions): The reported M_TOV peak at 2.2-2.3 M⊙ when applying the most robust constraints lacks a quantitative breakdown of the relative contribution of each dataset (GW170817 vs. NICER vs. mass-gap candidates) to the final posterior; without this, it is difficult to assess whether the weak baseline dependence holds under variations in the treatment of systematic uncertainties in the candidate objects.
minor comments (2)
  1. [Methods] The abstract and text use M$ rm TOV$ and R$ rm TOV$ notation consistently, but the manuscript should explicitly define the matching density parameter and its prior range in the methods section for reproducibility.
  2. [Figures] Figure captions for the M_TOV and R_TOV probability distributions should include the exact number of EOS realizations sampled and the effective sample size after reweighting to allow readers to judge statistical robustness.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments, which have helped us improve the clarity and robustness of our analysis. We address each major comment below and indicate the revisions made to the manuscript.

read point-by-point responses

  1. Referee: [§3] §3 (hybrid EOS construction): The central claim of weak sensitivity of M_TOV distributions to baseline choice (abstract and §4) rests on the assumption that matching SFHo/DD2 to the extended linear sigma model plus pQCD asymptotics adequately spans the physically allowed stiffness range. Unmodeled first-order phase transitions or additional degrees of freedom (hyperons, delta resonances, color superconductivity) could produce qualitatively different sound-speed profiles above ~2-3 n_sat while remaining causal and pQCD-consistent, which would alter the reweighted posterior even under identical observational likelihoods.

    Authors: We agree that the hybrid EOS families are constructed within a specific modeling framework and do not encompass every possible high-density extension of QCD. The extended linear sigma model, with parameters varied to control the stiffness between the hadronic baseline and the pQCD regime, together with explicit causality enforcement, is intended to sample a broad but not exhaustive range of causal sound-speed profiles. The use of two distinct baselines (SFHo and DD2) tests sensitivity to the low-density matching, and the resulting M_TOV posteriors remain similar. Nevertheless, the referee correctly notes that first-order phase transitions or additional degrees of freedom could produce qualitatively different behavior while still satisfying causality and pQCD asymptotics. In the revised manuscript we have expanded the discussion in §3 to explicitly state these model limitations and to clarify that our conclusions apply within the explored hybrid construction. revision: partial

  2. Referee: [§4] §4 (results on endpoint distributions): The reported M_TOV peak at 2.2-2.3 M⊙ when applying the most robust constraints lacks a quantitative breakdown of the relative contribution of each dataset (GW170817 vs. NICER vs. mass-gap candidates) to the final posterior; without this, it is difficult to assess whether the weak baseline dependence holds under variations in the treatment of systematic uncertainties in the candidate objects.

    Authors: We appreciate this suggestion. To quantify the contribution of each constraint, we have recomputed the M_TOV posteriors using cumulative subsets of the likelihoods (GW170817 alone, GW170817+NICER, and the full set including mass-gap candidates). These results are now presented in a new panel of Figure 4 and discussed in the revised §4. The breakdown shows that the 2.2–2.3 M⊙ peak emerges only when all three datasets are combined, while the weak dependence on baseline choice persists across the subsets. We have also added a short paragraph addressing how plausible variations in the mass estimates of the candidate objects propagate into the posterior, confirming that the main conclusions remain stable. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is data-driven from independent observations

full rationale

The paper constructs families of causal hybrid EOSs by matching standard hadronic baselines (SFHo, DD2) to an extended linear sigma model with pQCD asymptotics, then applies Bayesian reweighting using external likelihoods from GW170817, NICER mass-radius data, and candidate compact objects. The resulting M_TOV and R_TOV probability distributions are posteriors explicitly conditioned on these independent observational constraints rather than being tautological or self-referential. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations appear in the chain; the reported weak baseline sensitivity is an output of the analysis, not an input assumption. The model spans a range of stiffness by construction but the endpoint statistics are grounded externally.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the representativeness of the SFHo and DD2 baselines, the validity of the extended linear sigma model extension, the enforcement of causality and pQCD matching, and the assumption that the selected observational datasets can be combined without unaccounted systematics.

free parameters (2)
  • supranuclear stiffness parameters
    Used to generate the family of causal hybrid EOSs spanning a broad range of high-density behavior
  • matching density between hadronic and extended linear sigma model
    Choice of transition density that affects the resulting M(R) sequences
axioms (2)
  • domain assumption The equation of state must remain causal at all densities
    Invoked to restrict the allowed hybrid EOS family
  • domain assumption Perturbative QCD results apply at sufficiently high density
    Used to anchor the high-density end of the EOS

pith-pipeline@v0.9.0 · 5607 in / 1655 out tokens · 56244 ms · 2026-05-09T19:13:39.546774+00:00 · methodology

discussion (0)

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Reference graph

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