The thermal emission from isolated neutron stars is not well understood. The
X-ray spectrum is very close to a blackbody but there is a systematic optical
excess flux with respect to the extrapolation to low energy of the best
blackbody fit. This fact, in combination with the observed pulsations in the
X-ray flux, can be explained by anisotropies in the surface temperature
distribution.We study the thermal emission from neutron stars with strong
magnetic fields in order to explain the origin of the anisotropy. We find
(numerically) stationary solutions in axial symmetry of the heat
transportequations in the neutron star crust and the condensed envelope. The
anisotropy in the conductivity tensor is included consistently. The presence of
magnetic fields of the expected strength leads to anisotropy in the surface
temperature. Models with toroidal components similar to or larger than the
poloidal field reproduce qualitatively the observed spectral properties and
variability of isolated neutron stars. Our models also predict spectral
features at energies between 0.2 and 0.6 keV.Comment: 18 pages, 19 figures, version accepted for publication in A&
