2008A&A...486..255A

Many thermally emitting, isolated neutron stars have magnetic fields that are larger than 10¹³G. A realistic cooling model that includes the presence of high magnetic fields should be reconsidered. We investigate the effects of an anisotropic temperature distribution and Joule heating on the cooling of magnetized neutron stars. The 2D heat transfer equation with anisotropic thermal conductivity tensor and including all relevant neutrino emission processes is solved for realistic models of the neutron star interior and crust. The presence of the magnetic field affects significantly the thermal surface distribution and the cooling history during both, the early neutrino cooling era and the late photon cooling era. There is a large effect of Joule heating on the thermal evolution of strongly magnetized neutron stars. Both magnetic fields and Joule heating play an important role in keeping magnetars warm for a long time. Moreover, this effect is important for intermediate field neutron stars and should be considered in radio-quiet isolated neutron stars or high magnetic field radio-pulsars.