paper

Unraveling Trace Anomaly of Supradense Matter via Neutron Star Compactness Scaling

arXiv:2406.05025 · doi:10.1103/3p2p-p3d4

Abstract

The trace anomaly quantifies the possibly broken conformal symmetry in supradense matter under pressure at energy density . Perturbative QCD (pQCD) predicts a vanishing 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 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 Perturbatively Analysis of the Dimensionless (IPAD) Tolman-Oppenheimer-Volkoff (TOV) equations that are further verified numerically by using 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 of a NS with mass and radius scales very accurately with $\overlineΠ_{\rm{c}}\equivΠ_{\rm{c}}\cdot(1+18\x/25)\equiv\x/(1+3\x^2+4\x)\cdot(1+18\rm{X}/25)$ where $\x\equivϕ_{\rm{c}}= P_{\rm{c}}/\varepsilon_{\rm{c}}$ 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 $Δ_{\rm{c}}=1/3-\x$ 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-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.

arXiv commentAdded new materials and discussions. Phys. Rev. D in press

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