Tracing the Trace Anomaly of Dense Matter inside Neutron Stars

TL;DR

The paper defines the trace anomaly $\Delta = (\rho - 3P)/(3\rho)$ and uses the proxy $X = P/\rho = 1/3 - Δ$ to study the neutron-star interior. It derives quasi-universal relations linking $X(u, ξ)$ to global observables $C$, $\ln\bar{I}$, and $\ln Λ$ by fitting an eighth-order polynomial over an ensemble of 45 EOS models, enabling reconstruction of the $Δ(z)$ profile from measurements. The authors validate the approach on unseen EOSs, show EOS-insensitive central values within about 10%, and apply the framework to NICER, PSR J0737−3039A, and multimessenger $\Lambda$ constraints to produce central $Δ_c$ estimates with quantified uncertainties. The work provides a practical, EOS-robust pathway to constrain dense-matter conformality inside neutron stars using current and future electromagnetic and gravitational-wave observations.

Abstract

The trace anomaly $Δ$ is an important quantity that measures the broken conformal symmetry in neutron star matter. In this work, we present quasi-universal relations that connect the stellar profile of $Δ$ to the compactness, moment of inertia, and tidal deformability of neutron stars. We apply the quasi-universal relations to determine the trace anomaly profiles for PSR J0030+0451 and PSR J0740+6620 based on their mass-radius measurements. We also analyze PSR J0737-3039A according to its moment of inertia inferred from Bayesian modeling of nuclear equation of state. A recent multimessenger constraint on the tidal deformability is also studied, resulting in an estimate value of the trace anomaly $Δ_c = 0.1770^{+0.0365}_{-0.0432}$ at the center of a $1.4M_\odot$ canonical neutron star. It is expected that more precise observations from both electromagnetic and gravitational-wave channels in the future will provide tighter constraints on the behavior of $Δ$ inside neutron stars.

Figures (9)

• Figure 1: Mass-radius relations of the EOS models employed in this work (see Appendix \ref{['sec:EOS_models']}). The rectangular boxes represent the observational estimates for PSR J0740+6620 Riley_2021 and PSR J0030+0451 Riley_2019.
• Figure 2: First row: $X=P/\rho$ as a function of $r/R$ and $C$ (left panel), $\ln {\bar{I}}$ (middle panel), and $\ln {\Lambda}$ (right panel). Second row: The central value $X_c$ is plotted against $C$, $\ln {\bar{I}}$, and $\ln \Lambda$. The blue line in each panel represents the fit Eq. (\ref{['eq:fit']}) evaluated at the center $r=0$. Third row: The relative differences between the numerical data and the blue lines in the second row.
• Figure 3: Upper panel: Profiles of $\Delta$ for five EOS models, four of which were not used in fitting Eq. (\ref{['eq:fit']}). Two values of compactness, $C=0.2$ (solid lines) and $0.26$ (dashed lines), are considered. The predictions of Eq. (\ref{['eq:fit']}) are represented by the black solid and dashed lines. Lower panel: The errors $\Delta X/X_c$ between the EOS data and the predictions of Eq. (\ref{['eq:fit']}).
• Figure 4: Similar to Fig. \ref{['fig:XC_pred']}, but for two values of normalized tidal deformability $\ln \Lambda = 2.7$ (solid lines) and 5 (dashed lines).
• Figure 5: The trace anomaly profile predicted by Eq. (\ref{['eq:fit']}) according to the allowed range of compactness for PSR J0030+0451 inferred from the mass-radius measurements. The red dashed line represents the profile for the best estimate value $C=0.156$, while the profiles inferred from the upper and lower bounds are represented by the other two dashed lines. The colored band around each line represents an estimated level of $\pm 10\%$ uncertainty of Eq. (\ref{['eq:fit']}) due to EOS sensitivity.