  In this paper we investigate the evolution of binary neutron stars, namely,
their magnetic field, spin, and orbital evolution. The core of a neutron star
is considered to be a superfluid, superconductor type II. Flux expulsion of the
magnetic field out of the core of a single neutron star has been discussed by
previous authors. However, the evolution of the core magnetic field is
substantially different for a binary neutron star. While for a single neutron
star the fluxoids of the proton superconductor always move outward through the
core, in a binary neutron star in the accretion phase fluxoids move back into
the core. The subsequent increase of the core magnetic field results in the
increase of the surface magnetic field. We ask weather within the framework of
this model the formation of millisecond pulsars (MSPs) is possible. We show
that despite the increase of the core magnetic field, MSPs are formed in this
model. The evolution of the neutron star with various orbital periods, magnetic
fields, spin periods, and other parameters are numerically investigated. The
equation of state of the neutron star, initial orbital period of the binary,
and other parameters of the binary have substantial effects on the evolution of
period vs. magnetic field.
