Hall drift in the stratified crusts of neutron stars

Abstract

We extend our previous numerical model of Hall drift in neutron stars (Hollerbach & Rüdiger 2002) to include variations in density across the depth of the crust. For purely toroidal fields, the results are in perfect agreement with the analytic model of Vainshtein, Chitre & Olinto (2000), who showed that the field would develop very fine structures, which would cause it to decay on the Hall time-scale rather than the much longer ohmic time-scale. However, if we include poloidal fields (which were not considered by Vainshtein et al.), the behaviour is rather different. The field still develops fine structures, but not as fine as before, scaling roughly as R B-1/2 rather than the RB-1 scaling obtained for purely toroidal fields (where the Hall parameter RB measures the ratio of the ohmic time-scale to the Hall time-scale). As a result, the field still decays considerably faster than if ohmic decay alone were acting, but ultimately still on the ohmic time-scale. This is true even if the initial poloidal field is much weaker than the initial toroidal field (with the sign of the toroidal field also playing an important role). Finally, we consider the possible implications for the magnetic fields of real neutron stars.