Poloidal Magnetic Fields In Superconducting Neutron Stars

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 $\sim 10^{-9}$.