Evidence for heating of neutron stars by magnetic-field decay.

We show the existence of a strong trend between neutron star (NS) surface temperature and the dipolar component of the magnetic field extending through three orders of field magnitude, a range that includes magnetars, radio-quiet isolated neutron stars, and many ordinary radio pulsars. We suggest that this trend can be explained by the decay of currents in the crust over a time scale of approximately 10(6) yr. We estimate the minimum temperature that a NS with a given magnetic field can reach in this interpretation.