Extracting the Central Sound Speed of Neutron Stars through Intrinsic Stellar Structure Scaling with Reduced Equation-of-State Model Dependence

Abstract

Inferring neutron star (NS) core properties remains sensitive to the assumed equation of state (EOS). Using a nonlinear Walecka model with generalized $\omega$-meson self-interactions, we construct six EOS families, each containing $10^3$ samples subject to identical nuclear and astrophysical constraints. Despite satisfying these constraints, the families predict markedly different high-density behavior and core properties; higher-order $\omega$ interactions can also generate interior sound-speed peaks within purely nucleonic matter. To reduce this model dependence, we use the intrinsic and perturbative analysis of the dimensionless Tolman--Oppenheimer--Volkoff equations (IPAD-TOV) to derive an EOS-independent estimator $\Theta (\mathrm{X},\mathrm{\Psi })$ of the central squared sound speed $s_{\mathrm{c}}^2$, where $\mathrm{X}={\mathrm{P}}_{\mathrm{c}}/{\epsilon }_{\mathrm{c}}$ is the central EOS-parameter and $\Psi$ characterizes the stellar-mass response to central energy density. For canonical $1.4M_{\odot }$ NSs, $\Theta$ correlates linearly with $s_{\mathrm{c}}^2$ across the families ($R^2\approx 0.94$-$0.99$). The family-dependent relations converge toward a common optimum: minimizing their dispersion yields $s_{\mathrm{c}}^2\approx 0.523\pm 0.044$ and $\mathrm{X}\approx 0.173_{-0.018}^{+0.020}$ for all six families, or $s_{\mathrm{c}}^2\approx 0.496\pm 0.092$ and $\mathrm{X}\approx 0.167_{-0.029}^{+0.030}$ when the family without $\omega$ self-interaction is excluded. The corresponding radii are $11.73_{-0.92}^{+1.08}$ and $11.92_{-1.28}^{+1.76}\mathrm{km}$, respectively, with $95\%$ confidence intervals. A unified scaling fitted to all EOS samples supports both extractions. These results show how common stellar-structure relations can constrain NS core properties with reduced EOS-model dependence, even when existing observations cannot distinguish among the underlying EOS descriptions.

Comments: 28 pages, 13 figures