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

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.

Low-energy collective excitations in the neutron star inner crust

“…This neutron contribution is enormous and will always dominate in the layers where neutrons are normal. Once superfluidity sets in, however, C n V is strongly suppresssed and becomes negligible when the temperature is much lower than the critical temperature T n c [23,24]. Given the density dependence of the neutron 1 S 0 gap there are only two regions, just above the neutron drip point and possibly in the deepest part of the crust, where C n V is relevant (see, e.g., Ref.…”

“…While the existence of two weakly damped longitudinal modes is unique to the superfluid phase, entrainment is fairly insensitive to superfluidity provided the pairing gap ∆ ≪ µ n [21], which is the case in most of the inner crust [22][23][24].…”

Superfluid properties of the inner crust of neutron stars. II. Wigner-Seitz cells at finite temperature

“…Including such correlations the sequence of Wigner-Seitz (WS) cells is remarkably modified compared to the original one proposed by Negele and Vautherin [14]. Several authors have done calculations in this system using nonrelativistic functionals and with zero-range pairing interactions [6][7][8][9][10] or finite range pairing interactions [11,12], but without performing a systematic comparison among the two.…”

Superfluid properties of the inner crust of neutron stars

“…A comparison with the full band theory [22,23] has shown that the WS approximation can reproduce well ground-state properties of the outermost regions of the inner crust. Its validity in the regions closer to the star core, where the clusters nearly touch each other, is still under debate.…”