Effects of finite size and symmetry energy on the phase transition of stellar matter at subnuclear densities

Abstract

We study the liquid-gas phase transition of stellar matter with the inclusion of the finite-size effect from surface and Coulomb energies. The equilibrium conditions for two coexisting phases are determined by minimizing the total free energy including the surface and Coulomb contributions, which are different from the Gibbs conditions used in the bulk calculations. The finite-size effect can significantly reduce the region of the liquid-gas mixed phase. The influence of the symmetry energy on the liquid-gas phase transition is investigated with the inclusion of finite-size effects. It is found that the slope of the symmetry energy plays an important role in determining the boundary and properties of the mixed phase.

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

“…From the Lagrangian density (1), we derive in the standard way the equations of motion for the nucleon and meson fields, which are coupled with each other and can be solved self-consistently. It is straightforward to obtain the expressions for the free energy density and pressure in uniform nuclear matter at finite temperature [73].…”

“…To describe the pasta phases in hot and dense matter, we employ the CLD model [31,44,73], where the Wigner-Seitz approximation is adopted for simplifying the calculation of the free energy. The nuclear matter inside the Wigner-Seitz cell is assumed to separate into a dense liquid (L) phase and a dilute gas (G) phase by a sharp interface, while the background electron gas is approximated to be uniform with the density determined by the charge neutrality condition.…”

“…The proton and neutron densities in the liquid (gas) phase are denoted by n L p (n G p ) and n L n (n G n ), respectively. The free energy contributed from nucleons in phase i (i = L, G) can be calculated in the RMF models [4,73]. Note that contributions from electrons are not included in Eq.…”

Finite-Size Effects on Equation of State for Supernovae and Neutron Stars

“…The detailed expressions for the surface and Coulomb terms (f surf and f Coul ) can be found in Ref. [25]. By minimizing the free energy density, we obtain the equilibrium conditions between liquid and gas phases,…”

“…The failure of the CP method at low densities may be due to the improper treatment of the surface and Coulomb energies. Another method for taking into account finite-size effects is based on a compressible liquid-drop (CLD) model, where the equilibrium state is determined by minimization of the total energy density including the surface and Coulomb energies [1,22,25]. It was reported in Ref.…”