Correlating Surface Magnetic Field Decay with Internal Field Depth of Isolated Neutron Stars
The long-term evolution of neutron star crustal magnetic fields through Ohmic decay is governed by the transport properties of the crust. In this work, we demonstrate that the depth at which the magnetic flux is anchored plays a significant role in the dissipation timescale. We study the evolution of the magnetic field at the surface of the neutron star due to the crustal field evolution, under the assumption of Ohmic diffusion in a curved spacetime. We employ a cumulative distribution function to parameterise the initial current distribution and explore the effects of varying the equation of state and crustal impurity. We compare results across three neutron star models representing varying degrees of compactness. We find that magnetic fields anchored deeper within the inner crust experience negligible decay over timescales up to $10^{10}$ years. Significant field evolution, necessary to explain the deficit of high-field pulsars at advanced ages, is possible if the magnetic currents are confined to the shallow outer crust. This result holds true regardless of the impurity concentration or the specific geometric thickness of the crust determined by the equation of state.