Elastic properties of nuclear pasta in a fully three-dimensional geometry

TL;DR

This study investigates the elastic properties of nuclear pasta phases in neutron star matter using three-dimensional models, confirming some analytic approximations and highlighting the influence of nuclear symmetry energy on elastic behavior.

Contribution

It provides the first comprehensive three-dimensional calculations of nuclear pasta elastic properties under large strains, improving analytic models with damping factors, and explores the effects of symmetry energy parameters.

Findings

Elastic constants peak and then decrease at high densities.

Analytic formulas describe small-density phases well but need adjustments at larger densities.

Elastic properties vary significantly with symmetry energy slope, affecting neutron star phenomena.

Abstract

Realistic estimations on the elastic properties of neutron star matter are carried out with a large strain ($\varepsilon \lesssim 0.5$) in the framework of relativistic-mean-field model with Thomas-Fermi approximation, where various crystalline configurations are considered in a fully three-dimensional geometry with reflection symmetry. Our calculation confirms the validity of assuming Coulomb crystals for the droplet phase above neutron drip density, which nonetheless does not work at large densities since the elastic constants are found to be decreasing after reaching their peaks. Similarly, the analytic formulae derived in the incompressible liquid-drop model give excellent description for the rod phase at small densities, which overestimates the elastic constants at larger densities. For slabs, due to the negligence on the variations of their thicknesses, the analytic formulae from liquid-drop model agree qualitatively but not quantitatively with our numerical estimations. By fitting to the numerical results, these analytic formulae are improved by introducing dampening factors. The impacts of nuclear symmetry energy are examined adopting two parameter sets, corresponding to the slope of symmetry energy $L = 41.34$ and 89.39 MeV. Even with the uncertainties caused by the anisotropy in polycrystallines, the elastic properties of neutron star matter obtained with $L = 41.34$ and 89.39 MeV are distinctively different, results in detectable differences in various neutron star activities.