New insights into supradense matter from dissecting scaled stellar structure equations

Abstract

The strong-field gravity in general relativity (GR) realized in neutron stars (NSs) renders the equation of state (EOS) P(ε) of supradense neutron star matter to be essentially nonlinear and refines the upper bound for ϕ≡P/ε to be much smaller than the special relativity (SR) requirement with linear EOSs, where P and ε are respectively the pressure and energy density of the system considered. Specifically, a tight bound ϕ≲0.374 is obtained by perturbatively anatomizing 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 the properties (e.g., density profiles of the sound speed squared s2=dP/dε and trace anomaly Δ=1/3−ϕ) 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 MNS, radius R, and compactness ξ≡MNS/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.