Flux Expulsion and Field Evolution in Neutron Stars

Abstract

Models for the evolution of magnetic fields ofneutron stars are constructed, assuming the field is embedded in theproton superconducting core of the star. The rate of expulsion ofthe magnetic flux out of the core or, equivalently, the velocity ofoutward motion of flux-carrying proton vortices is determined from asolution of the Magnus equation of motion for these vortices. A forcedue to the pinning interaction between the proton vortices and theneutron-superfluid vortices, in addition to the other more conventional forcesacting on the proton vortices, is also taken into account. Alternativemodels for the field evolution are considered based on the differentpossibilities discussed for the effective values of the various forces. Thecoupled spin and magnetic evolution of single pulsars as well asthose processed in low-mass binary systems are computed for each ofthe models. The predicted lifetimes of active pulsars, the fieldstrengths of the very old neutron stars, and the distribution of themagnetic fields versus orbital periods in low-mass binary pulsars areused to test the adopted field decay models. Contrary to the earlierclaims, buoyancy is argued to be the dominant driving cause of fluxexpulsion for single as well as binary neutron stars. However, thepinning is also found to play a crucial role that is necessary toaccount for the observed low field binary and millisecond pulsars.