Unconventional rotational responses of hadronic superfluids in a neutron star caused by strong entrainment and a ${\mathrm{\Sigma }}^{-}$ hyperon gap

I show that the usual model of the rotational response of a neutron star, which predicts rotation-induced neutronic vortices and no rotation-induced protonic vortices, does not hold (i) beyond a certain threshold of entrainment interaction strength nor (ii) in case of nonzero ${\mathrm{\Sigma }}^{-}$ hyperon gap. I demonstrate that in both these cases the rotational response involves creation of phase windings in electrically charged condensate. Lattices of bound states of vortices which are caused these effects can (for a range of parameters) strongly reduce the interaction between rotation-induced vortices with magnetic-field carrying superconducting components.