Unified description of superconductivity in neutron stars

TL;DR

This paper investigates the location and symmetry of superconducting protons in neutron stars, combining TOV equations, EoS models, and tunneling calculations to characterize the superconducting regions and their symmetries.

Contribution

It provides a detailed analysis of the extent and symmetry of superconducting regions in neutron stars using unified EoS models and tunneling rate calculations, highlighting the discreet nature of the pasta phase.

Findings

Superconducting protons occupy about 500m of the core and 100-150m of the core-crust interface.

The maximum coexistence pressure is approximately 0.5 MeV fm^{-3}.

Proton tunneling between slabs in the pasta phase is negligible, indicating discreet symmetry layers.

Abstract

In this paper, I study the location and symmetry of superconducting protons. Solving the Tolman-Oppenheimer-Volkoff (TOV) equations based on the unified Barcelona-Catania-Paris-Madrid equation of state (BCPM EoS) and on the pairing gap calculations by Lim and Holt [1], I find that roughly 500 meters of the liquid core (with isotropic and continuous symmetry) and roughly 100-150 meters of the core-crust interface (with anisotropic symmetry) are superconducting, while the rest of the star is normal. To specify whether the superconducting symmetry is discreet in the pasta phase, I study the coexistence of the saturated nuclear and the pure neutron matter using EoS based on the chiral effective field theory (ChEFT). I find that the maximum pressure at coexistence is $P_{*}\simeq0.5\;{\rm MeV\,fm^{-3}}$. To verify the precision of the coexistence calculations I evaluate the surface and the Coulomb corrections using the compressible liquid drop model. I calculate the proton tunneling rate in the perfectly ordered slab region of the pasta phase and conclude that for the chosen EoS, the proton supercurrent tunneling between the adjacent slabs is negligible and the slab region should be described as a discreet symmetry system of quasi two-dimensional layers.