Sensitivity of neutron star observables to microscopic nuclear parameters of realistic equations of state

Abstract

The equation of state of matter at supranuclear densities governs the astrophysical observables of neutron stars. A realistic, though complex, description is provided by the Chiral-Mean-Field model, which depends on many microscopic nuclear-physics parameters. We present a Fisher-information-inspired analysis of the sensitivity of neutron-star observables to the parameters of the Chiral-Mean-Field model at $β$-equilibrium using SLy as a crust. We then compute neutron-star sequences and extract masses, radii, compactnesses, and tidal deformabilities. From the logarithmic derivatives of these observables with respect to each nuclear parameter, we construct a dimensionless, Fisher-inspired sensitivity matrix and perform a principal-component analysis to identify the effective combinations of nuclear parameters that most strongly affect neutron-star observables. Although the ranking depends mildly on the observable, the three most important nuclear parameters are the vacuum value of the dilaton field $χ_0$ (which sets the overall scale of the scalar potential and trace-anomaly contribution), the scalar singlet strength $g_{1}^X$ (which controls the overall scalar attraction through the baryon effective masses), and the $k_0$ quadratic scalar term (which governs the curvature of the scalar potential). This framework provides a reproducible, data-driven approach to quantify parameter sensitivities in dense-matter models and to guide future Bayesian inference of nuclear information from multi-messenger astrophysical observations.

Figures (14)

• Figure 1: Diagnostics for the determination of $n_{\rm sat}$ (a) $p$ vs. $n_B$ and $E_B$ (b) $\varepsilon$ vs. $n_B$ for symmetric matter ($\mu_Q=\mu_S=0$). The saturation point is indicated by the square markers.
• Figure 2: Raw parameter ranges (left) and parameter ranges rescaled by their fiducial values $(\lambda/\lambda^\ast)$ (right). These intervals are obtained from a bisection search that enforces the saturation conditions $n_{\mathrm{sat}}\!\in\![0.10,0.20]~\mathrm{fm}^{-3}$ and $E_B\!\in\![-20,-10]~\mathrm{MeV}$. The diamond symbols represent the fiducial values. Blue segments (“closed”) indicate parameters for which the saturation constraints determine both the lower and upper ends of the allowed interval. Orange (“open upper”) indicates that the constraints determine only the lower bound, with no upper violation found. Magenta (“open lower”) indicates that only the upper bound is set by the constraints. Gray, dotted segments (“open both”) correspond to parameters that satisfy the saturation constraints throughout the entire explored domain, with neither end constrained. The coupling $g_{N\phi}$ is omitted in the right panel because its fiducial value is zero.
• Figure 3: Diagnostic panels of the crust to core connection. (a) Energy density versus normalized baryon density for the SLy (crust) and CMF$\to$Lepton (core) barotropes. (b) Pressure versus normalized baryon density for the same EoSs. (c) Squared speed of sound versus normalized baryon density, comparing the direct hyperbolic-tangent merge (black) to the derivative of the merged EoS obtained from integration of the merged speed of sound (green triangles). (d) Pressure versus energy density for the merged EoS. Insets in panels highlight the detailed behavior between $1$ and $2\,n_{\rm sat}$.
• Figure 4: Variations of the CMF parameter $\chi_0$ on (a) the EoS, pressure as a function of energy density, (b) the squared speed of sound as a function of baryon density, (c) the mass--radius curves, and (d) the tidal deformability as a function of compactness. The fiducial model, corresponding to $\chi_0^* = 401.934$, is shown in black, while colored curves represent variations of $\chi_0$. Colors encode the signed fractional stepsize $h$, with blue (red) tones indicating increasing (decreasing) $\chi_0$. Vertical dashed lines in panels (a) and (b) denote the eleven central energy densities $\varepsilon_{c,k}$ associated with stellar configurations uniformly sampled between $1$ and $2\,M_\odot$ (white markers). In panel (c), dashed trajectories trace the evolution of these fixed $\varepsilon_{c,k}$ configurations under parameter variations. Panel (d) shows the corresponding universal tidal deformability compactness relation; the inset magnifies the local ordering near the fiducial sequence.
• Figure 5: Relative responses for stellar mass, radius, tidal deformability, and compactness as functions of the relative parameter variation $\lambda_k/\lambda_k^*$ (wide view). Each color bundle corresponds to variations of a single CMF parameter $\lambda_k$, while individual curves within each bundle represent different central energy densities $\varepsilon_c$, sampled consistently between $1$ and $2\,M_\odot$. Lighter (darker) shades denote lower (higher) $\varepsilon_c$. The domain of each color might be different as each parameter has its own global bounds (see \ref{['fig:param_bounds']}). The legend is ordered by the average absolute slope of the mass response. The coupling $g_{N\phi}$ is excluded because its fiducial value is zero.