Neutron superfluid spin-down and magnetic field decay in pulsars

Abstract

The problem of magnetic flux expulsion from the superconducting interior of a neutron star is re-examined under the assumption that superfluid neutron vortices interact strongly with the two-dimensional lattice of proton vortices. We find the response of the proton-electron system to a Magnus force acting on the neutron vortices. An approximate upper limit is obtained for the Magnus force which would move a neutron vortex through the proton vortex lattice. Magnetic flux is expelled from the interior at a rate determined principally by the transport of field in the normally conducting solid crust rather than by the rotation spin-down time. It is shown that a large fraction of the original magnetic flux could remain in the superconducting interior of a binary neutron star, for example, Her X-1, after its initial rapid spin-down and would then be trapped by the inward radial movement of neutron vortices which follows. Both the strong surface fields of high-mass X-ray binaries and the field decay inferred from radio pulsar population surveys are consistent with the qualitative properties of the interior magnetic flux distribution expected for a standard form of neutron star internal structure.