Joule Heating and the Thermal Evolution of Old Neutron Stars

We consider Joule heating caused by dissipation of the magnetic field in the neutron star crust. This mechanism may be efficient in maintaining a relatively high surface temperature in very old neutron stars. Calculations of the thermal evolution show that, at the late evolutionary stage ( t ≥ 10 Myr), the luminosity of the neutron star is approximately equal to the energy released due to the field dissipation and is practically independent of the atmosphere models. At this stage, the surface temperature can be of the order of 3 × 10 4 -10 5 K. Joule heating can maintain this high temperature for an extremely long time (≥100 Myr), comparable with the decay time of the magnetic field.