Are NICER and GW170817 constraints suggesting a compactified scenario for Neutron stars?

Astrophysical observations from NICER and gravitational wave data constrain the properties of matter at the cores of neutron stars, enabling us to probe high-density matter with greater accuracy. To understand its implications for neutron stars, three distinct class-agnostic equation-of-state ensembles are constructed using the speed-of-sound parametrisation, which can describe matter in neutron-star cores. Bayesian analysis is employed to constrain the parameters, namely, the squared speed of sound and chemical potential, using the observational data. The Bayesian inference shows that the observations effectively constrain the low-density region of the equation of state. The astrophysical bound favours a softer, low-density equation of state in which the phase transition occurs at intermediate densities, thereby reducing the upper mass bounds for neutron stars. For the equation of state with density discontinuity, the discontinuities are preferably small. The equation of state with maximum mass configuration shows considerable stiffening from very low density, providing pressure support to generate maximum mass. In contrast, the equation of state with the maximum compact stellar configuration has a softer low-density equation of state, followed by pronounced stiffening, yielding the maximum compact configuration. The observationally favoured EoS shares the same qualitative structure as the maximum-compactness EoS: relative softness at intermediate densities transitioning to stiffness at high densities, a configuration gravity naturally favours.

💡 Research Summary

The paper investigates how recent NICER X‑ray measurements and the gravitational‑wave signal from the binary neutron‑star merger GW170817 constrain the dense‑matter equation of state (EoS) inside neutron stars, using a model‑independent approach based on the speed‑of‑sound parametrisation. The low‑density regime (up to about 1.1 n₀) is anchored to the BPS crust EoS and a polytropic extension that matches chiral effective‑field‑theory (χEFT) calculations. Above this density, the squared speed of sound c_s² is expressed as a piecewise‑linear function of the baryon chemical potential µ over four segments, giving ten free parameters (five c_s² values and five µ values) plus an optional density jump Δn for discontinuous EoS.

Three broad classes of EoS are constructed: (i) monotonic, where c_s² decreases monotonically from the centre outward (typical hadronic behaviour); (ii) non‑monotonic, where c_s² peaks away from the centre, representing a smooth phase transition; and (iii) discontinuous, where a strong first‑order transition produces a finite density jump. For each generated EoS the Tolman‑Oppenheimer‑Volkoff equations are solved to obtain the maximum‑mass configuration (M_TOV) and the configuration of maximum compactness (largest M/R).

A Bayesian inference framework is employed with the UltraNest nested‑sampling algorithm. Approximately two million likelihood evaluations are performed for each class, yielding about 5 × 10³ posterior samples. The likelihood combines four NICER pulsar measurements (PSR J0030+0451, PSR J0740+6620, PSR J0437‑4715, and the newly reported PSR J0614‑3329) and the GW170817 tidal‑deformability posterior, treated as statistically independent. The NICER likelihood marginalises over the stellar mass, while the GW likelihood integrates over component masses using a kernel‑density estimate of the joint mass–tidal‑deformability distribution. A Gaussian prior enforces χEFT pressure constraints in the low‑density region.

Key results:

1. The first segment of the speed‑of‑sound (c_s²₁) is tightly constrained to ≈0.04 ± 0.01 across all data combinations, reflecting the robustness of χEFT at densities just above nuclear saturation.
2. When both NICER and GW170817 data are included, the intermediate‑density segments (c_s²₂, c_s²₃) shift to lower values (≈0.4–0.5), indicating a relatively soft EoS at 1–2 n₀. The highest‑density segment (c_s²₄) then rises sharply to ≈0.6–0.7, providing the necessary stiffness at >3 n₀. This soft‑to‑stiff pattern mirrors the EoS that yields the maximum compactness rather than the one that yields the maximum mass.
3. For the discontinuous class, the density jump Δn is constrained to be small (≤0.8 fm⁻³); large jumps are incompatible with the combined astrophysical constraints.
4. The “maximum‑mass” EoS typically exhibits early stiffening (higher c_s²₂) to support ≳2.2 M⊙ stars, whereas the posterior‑favoured EoS remains soft at intermediate densities and only stiffens at the highest densities. Consequently, current observations preferentially select EoS that produce more compact stars rather than the most massive ones.

The authors interpret these findings as evidence that gravity, through the observationally accessible mass–radius–tidal‑deformability space, is effectively “compactifying” neutron stars: the data favour configurations where the star’s interior is soft enough to allow a small radius, yet stiff enough at extreme densities to avoid collapse. This suggests a universal structural pattern for dense matter—soft at intermediate densities, stiff at high densities—independent of the detailed microphysics (e.g., specific quark‑matter models). While the analysis does not directly identify a particular phase transition, it demonstrates that the present NICER + GW170817 dataset is already powerful enough to discriminate between EoS families based on their compactness properties, opening a pathway for future multimessenger observations to further probe the high‑density QCD regime.