Fluxtube Bouquets and Type-1.5 Clustering in Superfluid Neutron Star Cores

We study mesoscopic configurations of a neutron superfluid coupled to a proton superconductor in the outer core of a neutron star. The condensates are described by a two-component Ginzburg-Landau free energy with local couplings, neglecting genuine phase-gradient entrainment. In two spatial dimensions, we minimize the free energy using quasi-periodic boundary conditions and constrained phase-imprinting calculations to study vortex-fluxtube and fluxtube-fluxtube interactions. We find that, for locally attractive couplings in the free energy, vortex-fluxtube overlap is energetically favoured and several pre-existing proton fluxtubes can bind around a neutron vortex, forming finite vortex-centred aggregates that we call fluxtube bouquets. These bouquet configurations may become so dense that a vortex can effectively accommodate several quanta of magnetic flux. We also confirm the possible presence of a type-1.5-like regime and find that it survives in the zero-entrainment regime considered here. In this type-1.5 regime, the fluxtube-fluxtube interaction is repulsive at short distances and attractive at intermediate distances, leading to self-assembled clusters while the individual fluxtubes remain topologically distinct. Possible implications for dissipative coupling and transport in neutron stars are discussed.