The eect of Hall drift on the Evolution of Magnetic Fields in the Crusts of Neutron Stars

We consider the eect of Hall-drift on the evolution of magnetic elds in neutron star crusts using a nite dierence code. Previously, most studies have focused on the situation where the ohmic term dominates the evolution. Here, we investigate the case where the ohmic term is small compared to the Hall term. We show that the eect on the magnetic eld energy decay rate is a up to 30 % dierent compared to pure ohmic decay, depending on the initial conditions. In some cases the torroidal eld act as an energy \reservoir " and cause a slower decay rate than the ohmic case. We also investigate the importance of high-order vacuum multipoles and nd that for situations where the Hall term is a couple of orders of magnitude stronger than the ohmic term, hexapoles and up are a signicant part of the magnetic eld at the surface of the neutron star. 1