LONG-TERM EVOLUTION OF CRUSTAL NEUTRON-STAR MAGNETIC-FIELDS

We have derived an analytic solution to the asymptotic behavior of dip olar magnetic fields that are generated in the crusts of neutron stars . We show that if the conductivity is due to impurity scattering, as e xpected for late stages of evolution, that the surface field strength at the magnetic pole declines with the power law B(p) approximately (t /t0)-2/3. The results are shown to be qualitatively consistent with de tailed numerical calculations. These latter results are consistent wit h some recent analyses of pulsar statistics and the magnetic fields of several binary pulsars with white dwarf companions whose ages have be en determined. The dependence of the surface magnetic field on spin pe riod of the pulsar is derived.