Neutron star vortex dynamics and magnetic field decay: Implications for high density nuclear matter

We investigate the effect of the density-dependent proton and neutron gaps on vortex dynamics in neutron stars. We argue that the persistence of neutron star magnetic fields on timescales of 109 y suggests a superconducting gap curve with local maximum at intermediate density. We discuss the implications for exotic core phenomena such as pion/kaon condensation or a transition to quark matter.