Long-term evolution of crustal neutron star magnetic fields

We have derived an analytic solution to the asymptotic behavior of dipolar magnetic fields that are generated in the crusts of neutron stars. We show that if the conductivity is due to impurity scattering, as expected for late stages of evolution, the surface field strength at the magnetic pole declines with the power law B(sub p) approximately = (t/t(sub 0))(exp -2/3). The results are shown to be qualitatively consistent with detailed numerical calculations. These latter results are consistent with some recent analyses of pulsar statistics and the magnetic fields of several binary pulsars with white dwarf companions whose ages have been determined. The dependence of the surface magnetic field on spin period of the pulsar is derived.