Bayesian inferences on covariant density functionals from multimessenger astrophysical data: The influences of parametrizations of density dependent couplings

TL;DR

The paper investigates how different density-dependent parametrizations in covariant density functionals (CDFs)—specifically whether couplings depend on vector or scalar densities and whether rational or exponential forms are used—affect the equation of state of dense hadronic matter and neutron-star properties. Using a Bayesian framework constrained by multimessenger astrophysical data (mass, tidal deformability, NICER radii) and microscopic theory (χEFT), the authors compare several models (e.g., VRE, MRE, MRE2, VRR, VRR2) and quantify the impact on nuclear saturation coefficients ($E_{ m sat}$, $K_{ m sat}$, $J_{ m sym}$, $L_{ m sym}$) and high-density coefficients ($K_{ m sym}$, $Q_{ m sym}$, $Z_{ m sat}$). They find that isoscalar parametrizations mainly influence high-density EOS and radii, with $Q_{ m sat}$ correlating strongly with maximum mass and radii, while isovector parametrizations have a more modest effect on bulk CS properties but significantly affect the symmetry-energy density dependence and proton fraction; extending the isovector freedom (e.g., to VRR2) allows larger $F_p$ and potentially direct Urca in some stars. The results support using flexible isoscalar saturation properties and, notably, a rational-function parametrization for the isovector channel to robustly explore high-density isospin effects, highlighting the need for complementary constraints (e.g., neutron-star cooling) to pin down high-density symmetry energy.

Abstract

Covariant density functionals have been successfully applied to the description of finite nuclei and dense nuclear matter. These functionals are often constructed by introducing density dependence into the nucleon-meson couplings, typically through functions that depend only on the vector, i.e., proper baryon density. In this work, we employ a Bayesian framework to investigate how different parametrizations, characterized by distinct functional forms and by their dependencies on vector and scalar densities, affect the properties of dense matter and compact stars. Our analysis demonstrates that although all considered parametrizations yield broadly comparable inferences, the differences in the equation of state and the symmetry energy remain significant at suprasaturation densities, reflecting the sensitivity to the chosen functional form of the density dependence. We find that allowing the nuclear saturation properties in the isoscalar channel, including the skewness coefficient $Q_{sat}$, to be freely adjusted provides adequate flexibility for the current modeling of nuclear and neutron star matter. In contrast, the isovector channel requires further refinement, with freedom extended at least up to the curvature coefficient $K_{sym}$ to capture variations in the symmetry energy and particle composition at high densities. This work advances prior studies by implementing a rational-function parametrization of the density dependence, informed and constrained by multimessenger astrophysical observations.

Figures (5)

• Figure 1: The posterior confidence regions (95.4% CI) for meson-nucleon couplings $g_\sigma$, $g_\omega$ and $g_\rho$ obtained using CDFs with different parametrizations for the density dependence. The vertical bands correspond to the saturation density.
• Figure 2: Mass–radius diagram for CSs, with elliptical contours indicating the 95.4% CI regions of mass–radius estimates for four pulsars from NICER observations. Panel (a) shows the posterior 95.4% CI regions obtained using CDFs with different isoscalar coupling parametrizations, while panel (b) presents the results for variations in the isovector coupling.
• Figure 3: The influences of parametrizations of density-dependent couplings on the $\beta$-equilibrium EOS and its particle composition characterized by proton fraction $F_p$. Left panels (a and c) show the posterior confidence regions (95.4% CI) obtained using CDFs with different parametrizations of isoscalar couplings, while the right panels (b and d) show the corresponding results for variations in the isovector coupling. In the upper panels, the insets magnify the low-density regime. In the lower panels, the contours show the corresponding distributions of the respective 1.4 and 2.0 $M_{\odot}$ stars, and the horizontal bands labeled $F_{\rm DU}$ indicate the admissible proton fraction thresholds for the onset of nuclear direct Urca (DU) cooling process.
• Figure 4: The influences of parametrizations of density-dependent couplings on the energy per particle $E_{\rm SNM}$ of symmetric nuclear matter and symmetry energy $E_{\rm sym}$. Left panels (a and c) show the posterior confidence regions (95.4% CI) obtained using CDFs with different parametrizations of isoscalar couplings, while the right panels (b and d) show the results for variations in the isovector coupling. In the upper panels, the insets magnify the low-density regime.
• Figure 5: The posterior distributions for the nuclear matter characteristic coefficients at saturation density, where shaded regions correspond to the 95.4% CI. Left panel (a) shows the posteriors obtained using CDFs with different parametrizations of isoscalar couplings; while the right panel (b) shows the results for variations in the isovector coupling.