On the validity of the Wigner-Seitz approximation in neutron star crust

Abstract

The inner crust of neutron stars formed of nuclear clusters immersed in a neutron sea has been widely studied in the framework of the Wigner-Seitz approximation since the seminal work of Negele and Vautherin. In this article, the validity of this approximation is discussed in the framework of the band theory of solids. For a typical cell of ${}^{200}$Zr, present in the external layers of the inner crust, it is shown that the ground state properties of the neutron gas are rather well reproduced by the Wigner-Seitz approximation, while its dynamical properties depend on the energy scale of the process of interest or on the temperature. It is concluded that the Wigner-Seitz approximation is well suited for describing the inner crust of young neutron stars and the collapsing core of massive stars during supernovae explosions. However the band theory is required for low temperature fluid dynamics.

7 pages, with figures - PTH, version 2

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• Superfluidity and Superconductivity in Neutron Stars
• Low-energy collective excitations in the neutron star inner crust
• Nuclear Equation of state for Compact Stars and Supernovae
• The Neutron Star Crust: Nuclear Physics Input
• Neutron drip transition in accreting and nonaccreting neutron star crusts
• Nuclear matter in the crust of neutron stars derived from realistic NN interactions
• Unified equations of state for cold non-accreting neutron stars with Brussels-Montreal functionals. II. Pasta phases in semi-classical approximation
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• Crustal heating in accreting neutron stars from the nuclear energy-density functional theory. I. Proton shell effects and neutron-matter constraint
• Symmetry energy: nuclear masses and neutron stars
• Crystallization of the inner crust of a neutron star and the influence of shell effects
• Constraining the neutron-matter equation of state with gravitational waves
• Entrainment in Superfluid Neutron Star Crusts: Hydrodynamic Description and Microscopic Origin
• Unified description of neutron superfluidity in the neutron-star crust with analogy to anisotropic multi-band BCS superconductors
• On the superfluid properties of the inner crust of neutron stars
• Time-dependent density functional theory with twist-averaged boundary conditions
• Structure and composition of inner crust of neutron stars from Gogny interactions
• Suppression, persistence and reentrance of superfluidity in overflowing nuclear systems
• Time-dependent extension of the self-consistent band theory for neutron star matter: Anti-entrainment effects in the slab phase
• Self-consistent band calculation of slab phase in neutron-star crust
• Analytical determination of the structure and nuclear abundances of the outer crust of a cold nonaccreted neutron star
• A new statistical method for the structure of the inner crust of neutron stars
• Role of the symmetry energy on the neutron-drip transition in accreting and nonaccreting neutron stars
• Wigner-Seitz cells in neutron star crust with finite range interactions
• Comparison between the Thomas-Fermi and Hartree-Fock-Bogoliubov Methods in the Inner Crust of a Neutron Star: The Role of Pairing Correlations
• Nuclei embedded in an electron gas
• Neutron specific heat in the crust of neutron stars from the nuclear band theory
• Superfluid properties of the inner crust of neutron stars. II. Wigner-Seitz cells at finite temperature
• Collective, glitch-like vortex motion in a neutron star with an annular pinning barrier
• Unified equations of state for cold nonaccreting neutron stars with Brussels-Montreal functionals. V. Improved parametrization of the nucleon density distributions
• Superfluid extension of the self-consistent time-dependent band theory for neutron star matter: Anti-entrainment versus superfluid effects in the slab phase
• Finite-size effects and collective vibrations in the inner crust of neutron stars
• The proto-neutron star inner crust in the liquid phase
• Pairing properties and specific heat of the inner crust of a neutron star
• Temperature-dependent nuclear partition functions and abundances in stellar interior
• Superfluid fraction in the crystalline crust of a neutron star: role of BCS pairing
• Upper edge of the neutron star crust : the drip point and around
• Mass fractions in stellar interior during presupernova evolution
• Boundary conditions for star matter and other periodic fermionic systems
• Role of neutron pairing with density-gradient dependence in the semi-microscopic treatment of the inner crust of neutron stars
• Pairing correlations of cold fermionic gases at overflow from a narrow to a wide harmonic trap
• Neutron Star Inner Crust at Finite Temperatures: A Comparison Between Compressible Liquid Drop and Extended Thomas-Fermi Approaches
• How accurately can the Extended Thomas-Fermi method describe the inner crust of a neutron star?
• Pairing properties of the inner crust of neutron stars at finite temperature
• Pressure and chemical potentials in the inner crust of a cold neutron star within Hartree-Fock and extended Thomas-Fermi methods
• On variational trial functions in the extended Thomas-Fermi method
• Nuclear structure calculations for neutron-star crusts
• Fermi Operator Expansion for the Hartree-Fock-Bogoliubov Theory
• Superfluid fraction in the crystalline crust of a neutron star: role of quantum zero-point motion of ions