While the equation of state (EOS) $P(ϵ)$ of neutron star (NS) matter has been extensively studied, the EOS-parameter $\varphi =P/ϵ$ or equivalently the dimensionless trace anomaly $\mathrm{\Delta }=1/3-\varphi$, which quantifies the balance between pressure $P$ and energy density $ϵ$, remains far less explored, especially in NS cores. Its bounds and density profile carry crucial information about the nature of superdense matter. Physically, the EOS-parameter $\varphi$ represents the mean stiffness of matter accumulated from the stellar surface up to a given density. Based on the intrinsic structure of the Tolman-Oppenheimer-Volkoff equations, we show that $\varphi$ decreases monotonically outward from the NS center, independent of any specific input NS EOS model. Furthermore, observational evidence of a peak in the SSS density profile near the center effectively rules out a valley and a subsequent peak in the radial profile of $\varphi$ at similar densities, reinforcing its monotonic decrease. These model-independent relations impose strong constraints on the near-center behavior of the EOS-parameter $\varphi$, particularly demonstrating that the mean stiffness (or equivalently $\mathrm{\Delta }$) reaches a local maximum (minimum) at the center.

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• Nuclear astrophysics
• Nuclear matter in neutron stars