Robust adjudication between the neutron-star and self-bound quark-star scenarios for compact stars

Are the compact stars observed in pulsars and gravitational-wave events gravitationally bound neutron stars, or can some or all of them be self-bound strange quark stars? Cao and Chen performed Bayesian inference of the dense-matter equation of state for both hypotheses: in their 2023 model-agnostic analysis (arXiv:2308.16783v1) the neutron-star scenario was favored over the quark-star scenario with a Bayes factor of 11.5, a preference driven mainly by one NICER mass-radius posterior (PSR J0030+0451) and sensitive to the perturbative-QCD constraints that shape the inferred sound-speed peak; in the updated accepted version (v2, 2026) the same authors, using a Gaussian-process physics-agnostic equation of state and updated multimessenger data, instead find the most favored case to be a two-family scenario in which neutron stars and strange quark stars coexist, with PSR J0740+6620 favored as a strange quark star — potential astrophysical support for the Witten hypothesis. The open problem is to determine which scenario the current data support and whether the Bayesian verdict on it is robust to improved perturbative-QCD calculations, updated and independent mass-radius measurements, changes of equation-of-state parametrization and priors, and the microphysical consistency questions raised by the negative trace anomaly inferred for quark-star matter in the 2023 version. As of 2026 the question is open and actively contested: the verdict has flipped direction between two versions of the same paper, later analyses reach opposing conclusions in both directions, and no published study has established the stability of any verdict under systematic variations.

Background

A neutron star (NS) is a gravitationally bound compact star: its equation of state (EOS, the relation $p(\epsilon)$ between pressure and energy density) must rise steeply enough with density to support the observed $\sim 2M_{\odot}$ pulsars against collapse, while its surface pressure vanishes and its density tapers to that of ordinary matter. A quark star (QS) is a hypothetical alternative: if three-flavor deconfined quark matter were absolutely stable at zero pressure — the Bodmer-Witten hypothesis (Bodmer 1971; Witten 1984) — compact stars could be self-bound objects made entirely of strange quark matter, with energy per baryon below that of iron-class nuclei and a sharp surface at nearly normal nuclear density. The two hypotheses imply different EOS families over all densities, not just in the core, so observations can in principle discriminate between them.

The inference machinery combines several inputs. Gravitational-wave measurements of binary mergers such as GW170817 constrain the tidal deformability (the induced quadrupole deformation of a star in an external tidal field, which measures its radius for a given mass). NICER (Neutron Star Interior Composition ExploreR, an X-ray telescope) constrains masses and radii of millisecond pulsars by modeling their X-ray pulse profiles. At low density, chiral effective field theory (ChEFT, the low-energy effective theory of QCD in terms of nucleons and pions) constrains the EOS near nuclear saturation density $n_0\approx0.16\ \mathrm{fm}^{-3}$. At asymptotically high density, perturbative QCD (pQCD, the weak-coupling expansion of QCD) constrains pressure and must be matched through thermodynamic stability and causality; the key result (Komoltsev and Kurkela 2022) is that pQCD imposes a pressure bound at neutron-star-relevant densities. In the 2023 version of the analysis, a model-agnostic EOS is built by sampling the squared speed of sound $c_s^2=\mathrm{d}p/\mathrm{d}\epsilon$ at discrete stitching points connected by linear interpolation; the updated version instead uses nonparametric Gaussian process regression. A scale-invariant, conformally symmetric theory has $c_s^2=c^2/3$ and vanishing trace anomaly $\Delta=1/3-p/\epsilon$; the approach of dense matter to this conformal limit, and a conjecture by Fujimoto et al. (2022) that the trace anomaly of dense matter should remain positive, have become standard diagnostics of deconfinement.

Within this framework, Cao and Chen (2023 version, arXiv:2308.16783v1) sampled NS EOSs (ChEFT at low density, $N=6$ sound-speed stitching points with $c_{s,i}^2$ uniform on $[0,1]$, matched to pQCD) and QS EOSs (sampled surface parameters with zero-pressure matching), and constrained both with GW170817, GW190425, and the pulsars PSR J0030+0451, J0740+6620, J1614-2230, J0348+0432. They found a Bayes factor (the ratio of Bayesian evidences, i.e. likelihoods integrated over each model's parameter space) of $\mathcal{B}^{\rm NS}_{\rm QS}=11.5$, conventionally 'strong' evidence for the NS hypothesis. Their own diagnostics showed how contingent this number is: removing the PSR J0030+0451 posterior alone drops it to 1.3 (inconclusive); removing the pQCD constraint raises it to 16.1 but also erases the NS sound-speed peak $c_s^2\sim0.5c^2$ near $3.5n_0$; and the QS branch is inferred to violate trace-anomaly positivity, with $\Delta<0$ above $\sim5n_0$, whose microphysical meaning is unclear. In the updated accepted version (v2, 2026) of the same paper, the authors replaced the stitching-point construction with a physics-agnostic EOS built by nonparametric Gaussian process regression and updated the data to GW170817 together with PSR J0740+6620, J0030+0451, J0437-4715, and J0614-3329 plus the pQCD and ChEFT inputs. There, systematic Bayesian model selection among three competing scenarios — all compact stars are neutron stars, all are up-down quark stars, or a two-family scenario in which neutron stars and strange quark stars coexist — favors the two-family scenario with a Bayes factor of 6.1 relative to the up-down quark-star case, with PSR J0740+6620 favored as a strange quark star; in that favored case the inferred sound speed in both NS and QS matter increases monotonically and saturates at high densities, whereas a pronounced peak structure appears only in the all-neutron-star scenario. Which verdict is correct — and which ingredient decides it — is therefore unresolved.

Problem Statement

Determine which scenario the current data support — whether the compact stars observed in pulsars and gravitational-wave events are gravitationally bound neutron stars or include self-bound strange quark stars — and assess separately whether the Bayesian verdict on this question, which currently points in different directions in different analyses and in the two versions of the same study, is robust; a categorical physical determination is not required, and the expected deliverable is a documented sensitivity of the Bayes factor to the systematic variations below. The assessment is a single deliverable comprising four required facets, all of which must be reported: whether the verdict survives updated and independent mass-radius measurements (including the post-2024 NICER posteriors of PSR J0030+0451, PSR J0437-4715, and PSR J0614-3329) and current gravitational-wave constraints, and how the evidence is distributed among individual sources; how it depends on the pQCD input and its uncertainties and on the $\sim2M_{\odot}$ heavy-pulsar constraints that shape the inferred dense-matter structure (the sound-speed behavior near $3.5n_0$, the approach to the conformal limit $c_s^2=c^2/3$ and $\Delta\to0$, and the inferred quark-star trace anomaly); how it depends on the equation-of-state parametrization and priors — stitching-point versus Gaussian-process constructions, the priors on $c_{s,i}^2$ and on the quark-star surface parameters, and alternative low-density treatments of self-bound matter; and what the microphysical status of the self-bound branch is, i.e. whether the negative trace anomaly inferred for quark-star matter and the violation of trace-anomaly positivity are compatible with stable, microphysically consistent quark matter, or rule out classes of self-bound constructions. The answer must state the verdict of the current data and identify the ingredient(s) that decide it.

References

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