Dynamics of Superfluid-Superconducting Magnetars: Magnetic Field Evolution and Gravitational Waves

Magnetars, highly magnetized neutron stars, host superconducting and superfluid phases. We develop a minimal model that captures the interplay between neutron superfluidity, proton superconductivity, and electromagnetic fields using the Gross-Pitaevskii-Poisson, Ginzburg-Landau, and Maxwell equations. Our numerical simulations show that strong rotation enhances the net magnetic field inside the magnetar, suppresses superconductivity there, and amplifies the field near the surface. We explain this by a theory that makes testable predictions, including gravitational-wave signatures.