The magnetic structure of neutron stars and their surface-to-core temperature relation

We study the relation between the mean effective surface temperature $\overline{T}_\mathrm{s}$ and the internal temperature $T_\mathrm{b}$ for magnetic neutron stars, assuming that the magnetic field near the surface has a small-scale structure. The heavy-element (iron) and light-element (accreted) heat-blanketing envelopes are considered, and the results are compared with the case of a dipole magnetic field. We argue that the difference in the $T_\mathrm{b}(\overline{T}_\mathrm{s})$-relation for different magnetic configurations is always much smaller than the possible difference caused by variations of the chemical composition in the envelope