The trace anomaly $\mathrm{\Delta }\equiv 1/3-P/ϵ=1/3-\varphi$ quantifies the possibly broken conformal symmetry in supradense matter under pressure $P$ at energy density $ϵ$. Perturbative QCD (pQCD) predicts a vanishing $\mathrm{\Delta }$ at extremely high energy or baryon densities when the conformal symmetry is realized but its behavior at intermediate densities reachable in neutron stars (NSs) is still very uncertain. The extraction of $\mathrm{\Delta }$ from NS observations strongly depends on the employed model for nuclear equation of state (EOS). Using the IPAD-TOV method based on an intrinsic and perturbative analysis of the dimensionless (IPAD) Tolman-Oppenheimer-Volkoff (TOV) equations that are further verified numerically by using ${10}^5$ EOSs generated randomly with a metamodel in a very broad EOS parameter space constrained by terrestrial nuclear experiments and astrophysical observations, here we first show that the compactness $\xi \equiv G{M}_{\mathrm{NS}}/R{c}^2\equiv M_{\mathrm{NS}}/R$ of a NS with mass $M_{\mathrm{NS}}$ and radius $R$ scales very accurately with ${\overline{\mathrm{\Pi }}}_{\mathrm{c}}\equiv {\mathrm{\Pi }}_{\mathrm{c}}·(1+18\mathrm{X}/25)\equiv \mathrm{X}/(1+3{\mathrm{X}}^2+4\mathrm{X})·(1+18\mathrm{X}/25)$ where $\mathrm{X}\equiv {\varphi }_{\mathrm{c}}=P_{\mathrm{c}}/{ϵ}_{\mathrm{c}}$ 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 ${\mathrm{\Delta }}_{\mathrm{c}}=1/3-\mathrm{X}$ 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 insensitively 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.

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• Nuclear astrophysics
• Nuclear matter in neutron stars