Effects of pairing gap and band gap on superfluid density in the inner crust of neutron stars

Abstract

Calculations of the superfluid density in the inner crust of neutron stars by different approaches are in strong disagreement, which causes a debate on the accountability of pulsar glitches based on superfluidity. Taking a simple unified model, we study the dependence on approximation of the superfluid density in a periodic potential. In comparison with the Hartree-Fock-Bogoliubov (HF-Bogoliubov) theory which treats the effects of the band gap and the pairing gap on equal footing, we examine the HF-BCS-type approximation in which the former is incorporated in priority, and another approximation in which the latter is incorporated in priority. We find that, when the pairing gap and the band gap are comparable as in the inner crust of neutron stars, they need to be treated on equal footing, and the HF-BCS approximation can considerably underestimate the superfluid density even if the pairing gap is much smaller than the Fermi energy. Our result suggests that the validity of the HF-BCS approximation for evaluating the superfluid density in neutron star crusts is questionable.

9 pages, 4 figures. accepted version in Physical Review Research

References in corpus (6)

• Models of Pulsar Glitches
• Neutron conduction in the inner crust of a neutron star in the framework of the band theory of solids
• A superfluid perspective on neutron star dynamics
• Equation of state and effective mass of the unitary Fermi gas in a 1D periodic potential
• Time-dependent extension of the self-consistent band theory for neutron star matter: Anti-entrainment effects in the slab phase
• Superfluid density in disordered pasta phases in neutron star crusts

Cited by in corpus (9)

• Superfluid extension of the self-consistent time-dependent band theory for neutron star matter: Anti-entrainment versus superfluid effects in the slab phase
• Superfluid density in linear response theory : pulsar glitches from the inner crust of neutron stars
• Superfluid fraction in the slab phase of the inner crust of neutron stars
• Superfluid fraction in the crystalline crust of a neutron star: role of BCS pairing
• Superfluid fraction in the rod phase of the inner crust of neutron stars
• Phase transitions in the inner crust of neutron stars within the superfluid band theory: Competition between ${}^1{\text{S}}_0$ pairing and spin polarization under finite temperature and magnetic field
• Weighted Hartree-Fock-Bogoliubov method for interacting fermions: An application to ultracold Fermi superfluids
• Superfluid fraction in the crystalline crust of a neutron star: role of quantum zero-point motion of ions
• Fermi Operator Expansion for the Hartree-Fock-Bogoliubov Theory