Flux expulsion and field evolution in neutron stars

Models for the evolution of magnetic fields of neutron stars are constructed, assuming the held is embedded in the proton superconducting core of the star. The rate of expulsion of the magnetic flux out of the core or, equivalently, the velocity of outward motion of flux-carrying proton vortices is determined from a solution of the Magnus equation of motion for these vortices. A force due to the pinning interaction between the proton vortices and the neutron-superfluid vortices, in addition to the other more conventional forces acting on the proton vortices, is also taken into account. Alternative models for the held evolution are considered based on the different possibilities discussed for the effective values of the various forces. The coupled spin and magnetic evolution of single pulsars as well as those processed in low-mass binary systems are computed for each of the models. The predicted lifetimes of active pulsars, the field strengths of the very old neutron stars, and the distribution of the magnetic fields versus orbital periods in low-mass binary pulsars are used to test the adopted field decay models. Contrary to the earlier claims, buoyancy is argued to be the dominant driving cause of flux expulsion for single as well as binary neutron stars. However, the pinning is also found to play a crucial role that is necessary to account for the observed low field binary and millisecond pulsars.