Magnetic Field Evolution in Neutron Star Crusts Due to the Hall Effect and Ohmic Decay

We present calculations of magnetic field evolution by the Hall effect and Ohmic decay in neutron star crusts. We first discuss when and for which neutron stars the Hall effect is important relative to Ohmic decay. We compute the evolution of an initial field distribution by Ohmic decay, and give approximate analytic formulas for both the surface and interior fields as a function of time. We then discuss the subsequent evolution by the Hall effect, giving several examples which illustrate how the field configuration evolves. Hall wave eigenfunctions are computed, including the effect of the large density change across the crust. We estimate the response of the crust to the magnetic stresses induced by Hall waves, and give a detailed discussion of the boundary conditions at the solid-liquid interface. Finally, we discuss the implications for the Hall cascade proposed by Goldreich & Reisenegger.