Magnetic evolution of neutron stars in wide low-mass binary systems

Abstract

The low magnetic field strengths $(\sim 10^8 G)$ of millisecond pulsars could be due either to their progenitor neutron stars being born with such low fields or to a decay of their field strength in the course of evolution. One of the mechanisms envisaged for a decrease in field strength is a slow-down-induced field decay. In this scenario, the interpinning of magnetic fluxoids in the proton superconductor with the angular-momentum-carrying vortex lines in the neutron superfluid in the stellar core results in the expulsion of the magnetic flux out to the crust when neutron vortices are forced to migrate outwards due to the spinning-down of the neutron star. Once deposited in the crust, the field may then decay due to ohmic dissipation. If this is indeed true, then the millisecond pulsars, commonly believed to have been recycled in low-mass X-ray binaries, must have had their spin periods increased to very large values $(\geq 1000 s)$ before being spun-up to millisecond periods. To verify the link between the magnetic field evolution and the rotational history of a neutron star, we examine the evolution of a neutron star in a low-mass binary, due to the interaction of its magnetosphere with the stellar wind of the companion. Models for a range of orbital periods, donor masses and mass-loss rates, and certain assumed ohmic decay time-scales in the crust are constructed, and the final surface magnetic field strengths obtained in these cases are presented in this paper. It is concluded that the low magnetic fields of millisecond pulsars may be well accounted for by this mechanism under fairly reasonable circumstances. The models seem to indicate further that an asymptotic value of $\sim 10^8$ G is the lowest possible value for the field obtainable by this mechanism.