Inferring the neutron star equation of state with nuclear-physics informed semiparametric models

TL;DR

This work develops a semiparametric neutron-star EoS framework that combines a nuclear-physics informed meta-model at low density with Gaussian Process extensions at high density, stitched at the nuclear-saturation density. The approach enforces causality and leverages chiEFT and experimental constraints to tightly bound sub-saturation pressures while allowing broad, model-agnostic variability at higher densities; Bayesian inference with radio, gravitational-wave, and NICER data yields a posterior median $P(2 ho_{ m nuc}) = 1.98^{+2.13}_{-1.08}\times10^{34}$ dyn/cm$^{2}$, $R_{1.4}=11.4^{+0.98}_{-0.60}$ km, and $M_{ m max}=2.31_{-0.23}^{+0.35}\,M_\odot$. The GP extension permits larger maximum masses and explores a wider range of $c_s^2$ between $2\rho_{ m nuc}$ and $6\rho_{ m nuc}$ than piecewise polytropes, while NICER updates pull radii toward smaller values. Overall, the semiparametric model provides a robust, physically informed prior for NS inference and delivers publicly available EoS samples to facilitate future analyses.

Abstract

Over the past decade, an abundance of information from neutron-star observations, nuclear experiments and theory has transformed our efforts to elucidate the properties of dense matter. However, at high densities relevant to the cores of neutron stars, substantial uncertainty about the dense matter equation of state (EoS) remains. In this work, we present a semiparametric EoS framework aimed at better integrating knowledge across these domains in astrophysical inference. We use a Meta-model at low densities, and Gaussian Process extensions at high densities. Comparisons between our semiparametric framework to fully nonparametric EoS representations show that imposing nuclear theoretical and experimental constraints through the Meta-model up to nuclear saturation density results in constraints on the pressure up to twice nuclear saturation density. We show that our Gaussian Process trained on EoS models with nucleonic, hyperonic, and quark compositions extends the range of EoS explored at high density compared to a piecewise polytropic extension schema, under the requirements of causality of matter and of supporting the existence of heavy pulsars. We find that maximum TOV masses above $3.2 M_{\odot}$ can be supported by causal EoS compatible with nuclear constraints at low densities. We then combine information from existing observations of heavy pulsar masses, gravitational waves from binary neutron star mergers, and X-ray pulse profile modeling of millisecond pulsars within a Bayesian inference scheme using our semiparametric EoS prior. With current astrophysical observations, we find a favored pressure at two times nuclear saturation density of $P(2ρ_{\rm nuc}) = 1.98^{+2.13}_{-1.08}\times10^{34}$ dyn/cm$^{2}$, a radius of a $1.4 M_{\odot}$ neutron star value of $R_{1.4} = 11.4^{+0.98}_{-0.60}$\;km, and $M_{\rm max} = 2.31_{-0.23}^{+0.35} M_{\odot}$ at the 90\% credible level.

Figures (7)

• Figure 1: Semiparametric models trained on different types of core compositions and their rate of change of their sound speeds, with respect to logarithmic energy density. All training EoS are shown in the top panel. Specific composition informed draws, and draws from the overarching distribution are shown in the bottom panel.
• Figure 2: Pressure-density relation of multiple EoS distributions at 90% C.L limits adhering to causality and measurements of heavy pulsars. The semiparametric EoS distribution in blue and a set of meta-model EoS with piecewise polytropic extensions in dark red, both stitched at $\rho_{\rm tr}$, are shown. Additionally, we display the Legred et al. model-agnostic nonparametric EoS in gold.
• Figure 3: Comparison of the 90% C.L of $R_{1.4}$ and $M_{\rm max}$ as supported by both the semiparametric EoS model (blue), and the fully nonparametric EoS model (gold). Both EoS distributions are constrained with heavy pulsar mass measurements from observations PSR J0740$+$6620 and PSR J0348$+$0432.
• Figure 4: Stacking constraints from astrophysical observations of massive pulsars (blue), gravitational waves (orange), and X-ray emissions from millisecond pulsars (green and purple), with bounds on pressure as a function of density (left) and on radius as a function of mass (right). 1-D symmetric bounds of the semiparametric EoS model are shown at 90% credible levels for each density and each pressure. Green lines represent our semiparametric EoS posterior with the NICER constraints of J0030+0451 and J0740+6620 Miller_2019Dittmann_2024. Purple contour lines denote our semiparametric EoS posterior with NICER measurements including J0437-4715 and J0614-3329 Vinciguerra_2024Salmi_2024Choudhury_2024Mauviard_2025.
• Figure 5: Posterior distributions of the semiparametric EoS compared with the astrophysically constrained nonparametric EoS posterior of Legred et al., which includes earlier NICER results for J0030+0451 and J0740+6620 only. Pink lines correspond to that previous nonparametric posterior. Green lines represent our semiparametric EoS posterior with the NICER constraints of J0030+0451 and J0740+6620 Miller_2019Dittmann_2024. Purple contour lines denote our semiparametric EoS posterior with all public NICER measurements including J0437-4715 and J0614-3329 Vinciguerra_2024Salmi_2024Choudhury_2024Mauviard_2025. The 2D contours show the 90% C.L.