Crustal magnetic field decay and neutron star cooling

The ohmic decay of the magnetic field initially confined to the surface layers of the neutron star crust is considered. It is shown that the neutron star cooling can effectively increase the conductivity σ and the characteristic ohmic decay time τ_B. The scenario of the crustal field evolution is as follows. At the initial stage the field decays comparatively rapidly: it can decrease by a factor of 10–100 during the first $$\sim 10^6-10^7$$ yr depending on initial field location. At this stage the conductivity is determined by electron–phonon scattering. After about $$10^6-10^7$$ yr, σ in the crust begins to be determined by the scattering on impurities and may be sufficiently high in pure crystals. At late stages the decay time τ_B is large due to the higher conductivity, and it can increase during the evolution because of magnetic field diffusion into the deep layers of the crust. Our calculations show that the crustal field decays rather slowly even in the case when the field is initially confined to the outer regions of the crust. For instance, if the electric currents were initially concentrated within the layer with $$\rho \le(2-4)\times10^{11} \enspace \text g \enspace \text {cm}^{-3}$$, then the surface field weakens by a factor of $$\sim 10^2-10^3$$ after $$\sim 10^{10}$$ yr.