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 using different approaches are in strong disagreement, which causes a debate on the accountability of pulsar glitches based on superfluidity. Using 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 theory, which treats the effects of the band gap and the pairing gap on equal footing, we examine a Hartree-Fock-BCS-type (HF-BCS-type) approximation in which the former is preferentially incorporated and another approximation in which the latter is preferentially incorporated. 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.