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

TL;DR

This study investigates how the pairing gap and band gap influence superfluid density calculations in neutron star crusts, revealing that simplified approximations may significantly underestimate superfluidity when these gaps are comparable.

Contribution

The paper compares different theoretical approaches to calculating superfluid density, highlighting the importance of treating pairing and band gaps on equal footing in neutron star crust models.

Findings

HF-BCS approximation underestimates superfluid density when gaps are comparable.

Treating pairing and band gaps on equal footing is crucial for accurate superfluidity estimates.

Validity of simplified approximations in neutron star superfluid models is questionable.

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.