Nuclear parameter inference with semi-agnostic priors

TL;DR

The paper addresses how to extract nuclear empirical parameters from neutron-star observations using semi-agnostic equation-of-state priors that combine a low-density meta-model with a high-density polytropic extension. It analyzes four prior sets and tests their ability to recover NEPs by simulating high-precision mass, radius, and tidal deformability data for both low- and high-mass neutron stars, across three injection EoSs. The results show that astrophysical data constrain the $eta$-equilibrated pressure mainly in the density range $n_0$ to about $2n_0$, with strong degeneracies among NEPs at higher densities; $ ext{M}$-only data push to higher pressures, while $M$-$R$ and $M$-$\Lambda$ detections are more informative for moderate densities. The findings highlight that not all NEPs are equally constrained by NS observations and that semi-agnostic priors can outperform fully nucleonic models in some regimes, but degeneracies and sampling challenges require methodological improvements for robust NEP inference in the dense-core regime.

Abstract

Radio pulsar timing, X-ray pulse profile modeling or gravitational-wave detections of binary mergers involving at least one neutron star offer the opportunity to elucidate the properties of dense and neutron rich matter in thermodynamic regimes inaccessible to nuclear laboratories. Such inference relies on building appropriate equation-of-state priors, such as the recently introduced semi-agnostic constructions that incorporate nuclear theory and experimental information available in low to intermediate density regimes, while offering the necessary flexibility at high density. In this paper, we assess how detections of mass, radius, and tidal deformability for low-mass ($\sim 1$M$_{\odot}$) or high-mass ($\sim 1.9$M$_{\odot}$) neutron stars would contribute to constraining nuclear empirical parameters in an inference based on semi-agnostic equation-of-state priors. We first assessed the correlation factors between nuclear empirical parameters and the zero-temperature and $β$-equilibrated pressure in different regimes of density. We then simulate observations for three nucleonic equations of state to test the recovery of the corresponding nuclear empirical parameters. We show that not all nuclear empirical parameters significantly correlate with the pressure and find a competition between them in the high-density regime that challenges their inference. We also find that using semi-agnostic constructions instead of assuming a nucleonic content up to the highest densities in the neutron-star core can help recover more accurately the true nuclear empirical parameters. Parameterizing the high-density regime of the equation of state with the nucleonic meta-model can pollute the inference of nuclear empirical parameters; semi-agnostic constructions are a solution to that. However, many nuclear matter empirical parameters contribute in a similar way to the building of baryonic pressure.

Figures (6)

• Figure 1: Pressure $P$ as a function of the baryon density $n$ (90 % contours) for the EoS sets discussed in this paper.
• Figure 2: Radius $R$ and tidal deformability $\Lambda$ as a function of the mass $M$ (90 % contours) for the EoS sets discussed in this paper; the $M(R)$ and $M(\Lambda)$ sequence for EoSs RG(SLY2), PCP(BSK24) and GPPVA(NL3$\omega\rho$) (used as injection EoSs) are also presented in green, blue and magenta, respectively.
• Figure 3: Pearson correlation factors between the $\beta$-equilibrated pressure $P_{\rm pc}$ and the nuclear empirical parameters as a function of the baryon density $n$, for the sets SA-Exp-n$_0$ and MM-$\chi$ . For SA-Exp-n$_0$ , the matching density to polytropes is represented as a vertical dashed line.
• Figure 4: Pressure $P$ as a function of the baryon density $n$ (90 % contours) for the prior SA-Exp-2n$_0$ (orange) and the posterior informed by the simulated detection of 10 NSs at 1% relative error of $M$ (green), $(M, \Lambda)$ (red) and $(M,R)$ (purple). The injection EoSs (RG(SLY2), PCP(BSK24), and GPPVA(NL3$\omega\rho$)) are presented in black.
• Figure 5: $M-\Lambda$ informed posterior distribution for $E_{\rm sym}$ , $L_{\rm sym}$ , $K_{\rm sym}$ and $Q_{\rm sym}$ for small-mass NSs simulated with an uncorrelated bivariate Gaussian distibution with $\delta E=0.01$. Results are presented for SA-Exp-n$_0$ in orange, SA-Exp-2n$_0$ in blue and MM-$\chi$ in red. For comparison, the prior distributions are shown with a plain line. The injection values of the NEPs for EoSs RG(SLY2), PCP(BSK24) and GPPVA(NL3$\omega\rho$) are represented as a vertical black dashed line.