New Insights into Supradense Matter from Dissecting Scaled Stellar Structure Equations

TL;DR

This paper derives model-independent constraints on the equation of state of neutron star matter by analyzing the scaled TOV equations in strong gravity, revealing bounds on pressure-to-energy density ratio and linking observable properties to the central EOS.

Contribution

It introduces a novel, EOS-model independent method to constrain supradense matter properties using scaled stellar structure equations in strong gravity regimes.

Findings

Bound on pressure-to-energy density ratio: 0.374

EOS-model independent constraints on density profiles and trace anomaly

Scaling relations linking neutron star observables to central EOS properties

Abstract

The strong-field gravity in General Relativity (GR) realized in neutron stars (NSs) renders the Equation of State (EOS) $P(\varepsilon)$ of supradense neutron star (NS) matter to be essentially nonlinear and refines the upper bound for $\phi\equiv P/\varepsilon$ to be much smaller than the Special Relativity (SR) requirement with linear EOSs, where $P$ and $\varepsilon$ are respectively the pressure and energy density of the system considered. Specifically, a tight bound $\phi\lesssim0.374$ is obtained by anatomizing perturbatively the intrinsic structures of the scaled Tolman--Oppenheimer--Volkoff (TOV) equations without using any input nuclear EOS. New insights gained from this novel analysis provide EOS-model independent constraints on properties (e.g., density profiles of the sound speed squared $s^2=\d P/\d\varepsilon$ and trace anomaly $\Delta=1/3-\phi$) of cold supradense matter in NS cores. Using the gravity-matter duality in theories describing NSs, we investigate the impact of gravity on supradense matter EOS in NSs. In particular, we show that the NS mass $M_{\rm{NS}}$, radius $R$ and its compactness $\xi\equiv M_{\rm{NS}}/R$ scale with certain combinations of its central pressure and energy density (encapsulating its central EOS). Thus, observational data on these properties of NSs can straightforwardly constrain NS central EOSs without relying on any specific nuclear EOS-model.