Unified description of neutron superfluidity in the neutron-star crust with analogy to anisotropic multi-band BCS superconductors

TL;DR

This paper introduces a unified approach to modeling neutron superfluidity in neutron-star crusts by drawing analogies with multi-band superconductors, solving anisotropic BCS equations with boundary conditions, and providing insights into superfluidity and thermal properties.

Contribution

It presents a novel, comprehensive method for neutron superfluidity in neutron-star crusts, improving upon previous approximations by incorporating inhomogeneities and anisotropic effects.

Findings

Inhomogeneities reduce neutron pairing gaps less than previously predicted.

Superfluidity persists at higher temperatures than earlier models suggested.

Calculated neutron specific heat informs neutron star thermal evolution.

Abstract

The neutron superfluidity in the inner crust of a neutron star has been traditionally studied considering either homogeneous neutron matter or only a small number of nucleons confined inside the spherical Wigner-Seitz cell. Drawing analogies with the recently discovered multi-band superconductors, we have solved the anisotropic multi-band BCS gap equations with Bloch boundary conditions, thus providing a unified description taking consistently into account both the free neutrons and the nuclear clusters. Calculations have been carried out using the effective interaction underlying our recent Hartree-Fock-Bogoliubov nuclear mass model HFB-16. We have found that even though the presence of inhomogeneities lowers the neutron pairing gaps, the reduction is much less than that predicted by previous calculations using the Wigner-Seitz approximation. We have studied the disappearance of superfluidity with increasing temperature. As an application we have calculated the neutron specific heat, which is an important ingredient for modeling the thermal evolution of newly-born neutron stars. This work provides a new scheme for realistic calculations of superfluidity in neutron-star crusts.