Universal Dense-Matter Trace Anomaly Inferred from Collective Flow in Heavy-Ion Collisions and Global Properties of Neutron Stars

Abstract

The trace anomaly of dense matter, $Δ\equiv 1/3 - P/\varepsilon$, defined in terms of the ratio of pressure $P$ to energy density $\varepsilon$, quantifies deviations from conformal symmetry and plays a central role in both the hydrodynamic response and gravitational equilibrium. While $Δ(\varepsilon)$ has recently been inferred from neutron star observations, we report the first Bayesian extraction of the trace anomaly from collective flow observables in intermediate-energy heavy-ion collisions. By employing transport-model simulations that explicitly decouple the cold-matter mean-field potential from thermal effects, we directly constrain the cold dense-matter equation of state (EOS). Remarkably, the trace anomaly inferred from laboratory flow data agrees quantitatively, within $68\%$ credible intervals, with independent astrophysical posterior bands. This nontrivial agreement demonstrates that heavy-ion collisions and neutron star observations probe the same universal macroscopic properties of dense matter, establishing the trace anomaly as a composition-insensitive descriptor of dense matter across widely different physical environments.

Figures (4)

• Figure 1: Trace anomaly $\Delta(\varepsilon)$ as a function of reduced energy density. Values are shown as inferred from Bayesian analyses of neutron star observational data by (1) Gorda et al.Gorda23, (2) Al-Mamun et al.Mam2021, and (3) Fujimoto et al.Fuji22. Also plotted are the central $\Delta(\varepsilon)$ values CL25-b for the binary neutron stars GW170817 LIGO, PSR J0030+0451 Miller19Riley19, and PSR J0740+6620 Salmi22. These astrophysical constraints are compared with Bayesian-inferred $\Delta(\varepsilon)$ values (green squares) obtained from proton collective flow data measured by the FOPI and HADES Collaborations at GSI FOPIHa2. For historical context, we also include $\Delta(\varepsilon)$ values obtained by converting the continuous pressure bands previously extracted through forward-modeling of kaon production Fuchs05lynch09 and collective flow at BEVALAC and AGS energies Pawel02. The pQCD and GR limits, as well as $\Delta(\rho_0)=1/3$ are indicated by the horizontal lines.
• Figure 2: The averaged speed of sound squared $<c^2_s(\rho)>=P/\varepsilon=\phi$ as a function of reduced baryon density with a Skyrme-like EOS with varying incompressibility parameter $K$ (upper panel) and nuclear symmetry energy (lower panel), respectively.
• Figure 3: Time evolution of central baryon density in mid-central Au+Au reactions with beam energies from 150 to 1200 MeV/nucleon with parameters listed in Table \ref{['mean']}.
• Figure 4: Speed of sound squared derived from the trace anomaly shown in Fig. \ref{['DT1']} using Eq.\ref{['ss_decom']} in comparison with the best-fit curve inferred from neutron star observations using machine learning techniques Fuji22.