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

Inferring neutron star (NS) core properties remains sensitive to the assumed equation of state (EOS). Using a nonlinear Walecka model with generalized ω-meson self-interactions, we construct six EOS families, each containing 10 cubed 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 ω 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 Θ(,Ψ) of the central squared sound speed s c squared, where =P c/epsilon c is the central EOS-parameter and Ψ characterizes the stellar-mass response to central energy density. For canonical 1.4,M NSs, Θ correlates linearly with s c squared across the families (R 2 about0.94 - 0.99). The family-dependent relations converge toward a common optimum: minimizing their dispersion yields s c 2 about 0.523 plus or minus0.044 and about 0.173+0.020-0.018 for all six families, or s c 2 about 0.496 plus or minus0.092 and about 0.167+0.030-0.029 when the family without ω self-interaction is excluded. The corresponding radii are 11.73+1.08-0.92 and 11.92+1.76-1.28, 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.