Hall drift in the crust of neutron stars - necessary for radio pulsar activity?

Abstract

The radio pulsar models based on the existence of an inner accelerating gap located above the polar cap rely on the existence of a small scale, strong surface magnetic field $B_s$. This field exceeds the dipolar field $B_d$, responsible for the braking of the pulsar rotation, by at least one order of magnitude. Neither magnetospheric currents nor small scale field components generated during neutron star's birth can provide such field structures in old pulsars. While the former are too weak to create $B_s \gtrsim 5\times 10^{13}$G$\;\gg B_d$, the ohmic decay time of the latter is much shorter than $10^6$ years. We suggest that a large amount of magnetic energy is stored in a toroidal field component that is confined in deeper layers of the crust, where the ohmic decay time exceeds $10^7$ years. This toroidal field may be created by various processes acting early in a neutron star's life. The Hall drift is a non-linear mechanism that, due to the coupling between different components and scales, may be able to create the demanded strong, small scale, magnetic spots. Taking into account both realistic crustal microphysics and a minimal cooling scenario, we show that, in axial symmetry, these field structures are created on a Hall time scale of $10^3$-$10^4$ years. These magnetic spots can be long-lived, thereby fulfilling the pre-conditions for the appearance of the radio pulsar activity. Such magnetic structures created by the Hall drift are not static, and dynamical variations on the Hall time scale are expected in the polar cap region.