Poloidal Magnetic Fields In Superconducting Neutron Stars

TL;DR

This paper develops a formalism to compute magnetic fields in superconducting neutron stars, focusing on poloidal fields, and finds surface field strengths and star distortions based on nuclear matter equations of state.

Contribution

It introduces a new formalism for modeling magnetic fields in superconducting neutron stars considering hydrostatic equilibrium and barotropic equations of state.

Findings

Surface magnetic field strength ~3×10^{12} G

Quadrupolar star distortion ~10^{-9}

Field strength depends on nuclear matter equation of state

Abstract

We develop the formalism for computing the magnetic field within an axisymmetric neutron star with a strong Type II superconductor core surrounded by a normal conductor. The formalism takes full account of the constraints imposed by hydrostatic equilibrium with a barotropic equation of state. We specialize to purely poloidal magnetic fields and develop the "most dipolar case" for which we find that the surface field strength is $\simeq H_b\epsilon_b/3\simeq 3\times 10^{12}$ G, where $H_b$ is the magnetic field at the outer edge of the core and $\epsilon_b R$ is the thickness of the normal shell. This value only depends on the equation of state of nuclear matter. We also find that the quadrupolar distortion of the star is $\sim 10^{-9}$.