Is The Trace Anomaly at its Minimum Value at Neutron Star Centers?

TL;DR

This paper investigates the behavior of the EOS-parameter and trace anomaly in neutron star cores, revealing that the mean stiffness decreases outward and is maximized at the center, with implications for understanding superdense matter.

Contribution

It establishes model-independent relations showing the monotonic decrease of the EOS-parameter and constrains its behavior at neutron star centers, based on the structure of TOV equations and observational data.

Findings

The EOS-parameter decreases monotonically outward from the NS center.

Observational evidence rules out a valley and peak in the radial profile of the EOS-parameter.

The mean stiffness reaches a maximum at the neutron star center.

Abstract

While the equation of state (EOS) $P(\varepsilon)$ of neutron star (NS) matter has been extensively studied, the EOS-parameter $\phi = P/\varepsilon$ or equivalently the dimensionless trace anomaly $\Delta = 1/3 - \phi$, which quantifies the balance between pressure $P$ and energy density $\varepsilon$, 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 $\phi$ 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 $\phi$ decreases monotonically outward from the NS center, independent of any specific input NS EOS model. Furthermore, observational evidence of a peak in the speed-of-sound squared (SSS) density-profile near the center effectively rules out a valley and a subsequent peak in the radial profile of $\phi$ at similar densities, reinforcing its monotonic decrease. These model-independent relations impose strong constraints on the near-center behavior of the EOS-parameter $\phi$, particularly demonstrating that the mean stiffness (or equivalently $\Delta$) reaches a local maximum (minimum) at the center.