Vortex buoyancy in superfluid and superconducting neutron stars

Buoyancy of proton vortices is considered as one of the important mechanisms of magnetic field expulsion from the superconducting interiors of neutron stars. Here, we show that the generally accepted expression for the buoyancy force is not correct and should be modified. The correct expression is derived for both neutron and proton vortices. It is argued that this force is already contained in the coarse-grained hydrodynamics of Bekarevich & Khalatnikov and its various multifluid extensions, but is absent in the hydrodynamics of Hall. Some potentially interesting buoyancy-related effects are briefly discussed.