Force on proton vortices in superfluid neutron stars

Force on proton vortices in superfluid and superconducting matter of neutron stars is calculated at vanishing stellar temperature. Both longitudinal (dissipative) and transverse (Lorentz-type) components of the force are derived in a coherent way and compared in detail with the corresponding expressions available in the literature. This allows us to resolve a controversy about the form of the Lorentz-type force component acting on proton vortices. The calculated force is a key ingredient in magnetohydrodynamics of superconducting neutron stars and is important for modeling the evolution of stellar magnetic field.