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 andOhmic decay in neutron star crusts. We first discuss when and for which neutronstars the Hall effect is important relative to Ohmic decay. We compute theevolution of an initial field distribution by Ohmic decay, and give approximateanalytic formulas for both the surface and interior fields as a function oftime. We then discuss the subsequent evolution by the Hall effect, givingseveral examples which illustrate how the field configuration evolves. Hallwave eigenfunctions are computed, including the effect of the large densitychange across the crust. We estimate the response of the crust to the magneticstresses induced by Hall waves, and give a detailed discussion of the boundaryconditions at the solid-liquid interface. Finally, we discuss the implicationsfor the Hall cascade proposed by Goldreich & Reisenegger.Comment: Submitted to ApJ (18 pages, 13 figures