Phase transition and nuclear symmetry energy from neutron star observations: Constraints in light of PSR J0614--3329

TL;DR

This paper addresses whether neutron-star interiors host a first-order phase transition to deconfined matter by employing a nonparametric Gaussian-process EOS that explicitly allows a Maxwell-type FOPT, informed by NICER radii (including PSR J0614--3329), GW170817, and high-density pQCD constraints. The authors perform Bayesian inference on the phase-transition onset n_PT, density jump Δn, and symmetry-energy parameter L, finding only weak evidence for FOPT (Bayes factor ~2.3) with n_PT favored near 4–5 n_s (or, less likely, below 2 n_s) and Δn up to several n_s; L is constrained to about 40 MeV and correlates with the radius difference between 1.4 and 2.0 solar-mass stars. The maximum-mass radius is robustly around 11.6 km with M_TOV ~ 2.25 M_sun, while PSR J0614--3329 nudges radii to smaller values by ~0.3 km; the results also show a negative ΔR and a Λ_1.4 near 300. The study concludes that direct confirmation of a FOPT from current NS observations is difficult, but multi-messenger data and joint nuclear-astro constraints could reveal high-density phase structure in the future.

Abstract

The possible occurrence of a first-order hadron-quark phase transition (FOPT) in neutron-star interiors remains an open question. Whether such a transition can be directly tested with improved observations is a key challenge. Here, we incorporate the latest constraints, especially a new NICER radius measurement for PSR J0614--3329, into a nonparametric Gaussian Process (GP) EOS framework that explicitly includes a first-order transition. We find a Bayes factor of $B\approx2.3$ when comparing models with and without an explicit phase transition, marginally favoring its presence. At $68\%$ credibility, the transition onset density $n_{\rm PT}$ is either below $2\,n_s$ (corresponding to masses $\lesssim1\,M_\odot$, with density jump $Δn\sim0.5\,n_s$) or, more prominently, above $4\,n_s$ (near the central density of the heaviest NS, with $Δn\sim3\,n_s$), where $n_s$ represents the nuclear saturation density. In addition, by using symmetry-energy expansion at low densities ($<1.1\,n_s$), we infer a slope parameter $L=40.2^{+19.3}_{-14.3}$ MeV, in good agreement with nuclear-experiment values. Intriguingly, $L$ correlates positively with the radius difference between $1.4\,M_\odot$ and $2.0\,M_\odot$ stars.

Figures (9)

• Figure 1: Prior (gray) and posterior (blue) joint distributions of the phase transition onset density $n_{\rm PT}$ and the density jump $\Delta n$.
• Figure 2: Mass-radius distributions for NSs whose central densities correspond to the low (orange) and high (blue) modes of the phase‐transition onset density in Fig. \ref{['fig:npt-dn']}. The black dashed curve shows the observed Galactic NS mass distribution, and the vertical dot-dash line marks the lowest reliably measured mass, that of the companion to PSR J0453+1559.
• Figure 3: Prior (gray) and posterior (blue) joint distributions of $n_{\rm PT}$ and the radius of the maximum-mass NS ($R_{\rm TOV}$).
• Figure 4: Prior (gray) and posterior (blue) joint distributions of the symmetry energy slope $L$ and the radius difference $R_{1.4} - R_{2.0}$.
• Figure 5: $68.3\%$ credible ranges for the pressure (as a function of $n$; top) and the squared sound speed $c_s^2$ (bottom), with (blue) and without (gray) the inclusion of PSR J0614--3329. The orange lines show results from EOS models without an explicit FOPT.