Superconductivity and Magnetism at Nuclear-Matter Densities:. AN Astronomical Challenge

We report on a study of the evolution of magnetic fields of neutron stars, driven by the expulsion of magnetic flux out of the proton superconducting core of the star. The rate of expulsion, or equivalently the velocity of outward motion of fluxcarrying proton-vortices is determined from a solution of their equation of motion. A determination of the effective forces on the fluxoids is however confronted with many ambiguities about the properties of this special case of superconductivity in the nature. Also, the behaviour of the fluxoids at the core boundary, and the subsequent evolution of the expelled flux within the highly conductive surrounding crust, are other related issues that have not been so far explored in any great details.