Nuclear pasta in hot and dense matter and its influence on the equation of state for astrophysical simulations

TL;DR

This paper investigates nuclear pasta phases in supernova matter at finite temperature, analyzing their impact on the equation of state and phase transitions relevant for astrophysical simulations.

Contribution

It introduces a detailed study of pasta phases using the compressible liquid-drop model, highlighting the effects of finite-size contributions and symmetry energy on phase behavior.

Findings

Pasta phases delay the transition to uniform matter.

Inclusion of pasta enlarges the nonuniform matter region.

The phase diagram is highly sensitive to symmetry energy slope L.

Abstract

We explore the properties of nuclear pasta appearing in supernova matter, i.e., matter at finite temperature with a fixed proton fraction. The pasta phases with a series of geometric shapes are studied using the compressible liquid-drop (CLD) model, where nuclear matter separates into a dense liquid phase of nucleons and a dilute gas phase of nucleons and $\alpha$ particles. The equilibrium conditions for two coexisting phases are derived by minimization of the total free energy including the surface and Coulomb contributions, which are clearly different from the Gibbs conditions for phase equilibrium due to the finite-size effects. Compared to the results considering only spherical nuclei, the inclusion of pasta phases can delay the transition to uniform matter and enlarge the region of nonuniform matter in the phase diagram. The thermodynamic quantities obtained in the present calculation with the CLD model are consistent with those in the realistic equation of state table for astrophysical simulations using the Thomas--Fermi approximation. It is found that the density ranges of various pasta shapes depend on both the temperature $T$ and the proton fraction $Y_p$. Furthermore, the nuclear symmetry energy and its density dependence may play crucial roles in determining the properties of pasta phases. Our results suggest that the pasta phase diagram is most sensitively dependent on the symmetry energy slope $L$ especially in the low-$Y_p$ and high-$T$ region.