Joule heating in high magnetic field pulsars

Aims. We study the efficiency of Joule heating in the crustal layers of young neutron stars. Methods. The induction equation is solved numerically for a realistic crust model with a conductivity that depends on the density and temperature. Results. We show that dissipation of the magnetic field is highly inhomogeneous in the crust with much faster dissipation in relatively low density layers. In young neutron stars, the rate of Joule heating in the crust can exceed the standard luminosity of non-magnetic stars and can even be comparable to the luminosity of magnetars. Conclusions. The results of calculations are compared with the available observational data. We argued that the crustal field model can well account for the data on the surface temperature and magnetic field of young neutron stars.