[Paper Review] Structure in the speed of sound: from neutron stars to heavy-ion collisions

N. Yao, Agnieszka Sorensen+2 more|arXiv (Cornell University)|Nov 30, 2023

Pulsars and Gravitational Waves Research4 citations

TL;DR

This paper investigates whether equations of state (EOS) featuring a sharp rise in the speed of sound—consistent with observations of massive neutron stars—can also describe low-energy heavy-ion collision data. Using symmetry energy expansion to generate dense nuclear matter EOSs from neutron star-compatible models, and simulating collective flow with the SMASH transport code, the study finds that speed of sound peaks near 2–3 times nuclear saturation density are compatible with experimental flow data, supporting stiff EOSs for both neutron stars and heavy-ion systems.

ABSTRACT

From the observation of both heavy neutron stars and light ones with small radii, one anticipates a steep rise in the speed of sound of nuclear matter as a function of baryon density up to values close to the causal limit. A question follows whether such behavior of the speed of sound in neutron-rich matter is compatible with the equation of state extracted from low-energy heavy-ion collisions. In this work, we consider a family of neutron star equations of state characterized by a steep rise in the speed of sound, and use the symmetry energy expansion to obtain equations of state applicable to the almost-symmetric nuclear matter created in heavy-ion collisions. We then compare collective flow data from low-energy heavy-ion experiments with results of simulations obtained using the hadronic transport code SMASH with the mean-field potential reproducing the density-dependence of the speed of sound. We show that equations of state featuring a peak in the speed of sound squared occurring at densities between 2-3 times the saturation density of normal nuclear matter, producing neutron stars of nearly M_max~2.5 M_Sun, are consistent with heavy-ion collision data.

Motivation & Objective

• To assess the compatibility of neutron star equations of state with a steep rise in the speed of sound and low-energy heavy-ion collision data.
• To bridge the gap between high-density neutron star constraints and dense nuclear matter behavior in heavy-ion collisions.
• To test whether stiff EOSs, required to support massive neutron stars (~2.5 M☉), can also describe collective flow in heavy-ion experiments.
• To develop a framework for translating neutron star–constrained EOSs into forms applicable to symmetric nuclear matter in heavy-ion collisions.
• To evaluate the robustness of results against missing momentum-dependent potentials in transport simulations.

Proposed method

• Construct a family of neutron star EOSs with a peak in the speed of sound squared at 2–3 times nuclear saturation density, consistent with massive neutron stars.
• Apply the symmetry energy expansion to extrapolate these neutron star EOSs into the regime of almost-symmetric nuclear matter relevant for heavy-ion collisions.
• Implement the resulting density-dependent mean-field potentials in the SMASH hadronic transport code to simulate collective flow in low-energy heavy-ion collisions.
• Compare simulated directed and elliptic flow with experimental data from HADES, STAR, and other fixed-target experiments at √sNN ≈ 2.4–4.7 GeV.
• Use Bayesian constraints from neutron star observations (e.g., Mmax ≈ 2.5 M☉) to select high-likelihood EOSs as input for the symmetry energy expansion.
• Assess the sensitivity of results to the absence of momentum-dependent potentials by estimating their expected impact on flow observables.

Experimental results

Research questions

• RQ1 Can equations of state with a high-speed-of-sound peak at 2–3× saturation density, required to support massive neutron stars, be consistent with low-energy heavy-ion collision data?
• RQ2 How does the symmetry energy expansion enable the transfer of constraints from neutron star observations to dense symmetric nuclear matter in heavy-ion collisions?
• RQ3 To what extent do SMASH simulations with mean-field potentials derived from stiff neutron star EOSs reproduce collective flow data from experiments like HADES and STAR?
• RQ4 How do the missing momentum-dependent terms in the mean-field potential affect the validity of the simulation results and flow observables?
• RQ5 Can a unified framework be established to constrain the nuclear EOS simultaneously from neutron star and heavy-ion collision data?

Key findings

• Equations of state featuring a peak in the speed of sound squared at 2–3 times nuclear saturation density, consistent with neutron stars of mass up to ~2.5 M☉, are compatible with collective flow data from low-energy heavy-ion collisions.
• The SMASH simulations with mean-field potentials derived from neutron star–constrained EOSs successfully reproduce experimental directed and elliptic flow data across multiple beam energies.
• The absence of momentum-dependent potentials in the simulations likely leads to an underestimation of repulsion, resulting in a steeper directed flow and less negative elliptic flow, though the overall agreement remains robust.
• The expected corrections from momentum-dependent potentials do not favor alternative EOSs over the 'eos2 min' model, suggesting the core findings are stable under such modifications.
• The framework enables the generation of ~10² EOSs from a single high-likelihood neutron star EOS via symmetry energy expansion, making it feasible to test with transport simulations.
• The study identifies a critical numerical challenge: combining neutron star and heavy-ion constraints via MCMC would require testing ~10⁹ EOSs, currently infeasible with current computational resources.