Topological Aspects in an Interacting Mixture of a Charged and a Neutral Superfluid in Neutron Stars

By making use of the decomposition of U(1) gauge potential theory and the Φ-mapping method we discuss a mixture of interacting neutral and charged Bose condensates, which is supposed to be realized in the interior of neutron stars in the form of a coexistent neutron superfluid and protonic superconductor. We propose that this system possesses vortex line knotted solitons and the topological charges of vortex lines are characterized by the winding numbers of the Φ-mapping. Furthermore the spatial bifurcation of vortices is also discussed.