Superconducting Phases in Neutron Star Cores

Using a phenomenological Ginzburg–Landau model that includes entrainment, we identify the possible ground states for the neutron and proton condensates in the core of a neutron star, as a function of magnetic field strength. Combining analytical and numerical techniques, we find that much of the outer core is likely to be a “type-1.5” superconductor (instead of a type-II superconductor as often assumed), in which magnetic flux is distributed inhomogeneously, with bundles of magnetic fluxtubes separated by flux-free Meissner regions. We provide an approximate criterion to determine the transition between this type-1.5 phase and the type-I region in the inner core. We also show that bundles of fluxtubes can coexist with non-superconducting regions, but only in a small part of the parameter space.