Unraveling Trace Anomaly of Supradense Matter via Neutron Star Compactness Scaling

The trace anomaly Δ≡ 1/3-P/ε quantifies the possibly broken conformal symmetry in supradense matter under pressure P at energy density ε. Perturbative QCD (pQCD) predicts a vanishing Δ at extremely high energy or baryon densities when the conformal symmetry is realized but its behavior at intermediate densities reachable in neutron stars (NSs) are still very uncertain. The extraction of Δ from NS observations strongly depends on the employed model for nuclear Equation of State (EOS). Based on the analytical results from perturbatively analyzing the dimensionless Tolman-Oppenheimer-Volkoff (TOV) equations that are further verified numerically by using 10⁵ EOSs generated randomly with a meta-model in a very broad EOS parameter space constrained by terrestrial nuclear experiments and astrophysical observations, here we first show that the compactness ξ≡ MNS/R of a NS with mass MNS and radius R scales very accurately with Πc/(1+3X²+4X) where X≡ Pc/εc is the ratio of pressure over energy density at NS centers. The scaling of NS compactness thus enables one to readily read off the central trace anomaly Δc=1/3-X directly from the observational data of either the mass-radius or red-shift measurements. We then demonstrate indeed that the available NS data themselves from recent X-ray and gravitational wave observations can determine model-independently the trace anomaly as a function of energy density in NS cores, providing a stringent test of existing NS models and a clear guidance in a new direction for further understanding the nature and EOS of supradense matter.