Hall drift and the braking indices of young pulsars

Abstract

Braking index measurements of young radio pulsars are all smaller than the value expected for spin down by magnetic dipole braking. We investigate magnetic field evolution in the neutron star crust due to Hall drift as an explanation for observed braking indices. Using numerical simulations and a semi-analytic model, we show that a $\approx 10^{14}\ {\rm G}$ quadrupolar toroidal field in the neutron star crust at birth leads to growth of the dipole moment at a rate large enough to agree with measured braking indices. A key factor is the density at which the crust yields to magnetic stresses that build up during the evolution, which sets a characteristic minimum Hall timescale. The observed braking indices of pulsars with inferred dipole fields of $\lesssim 10^{13}\ {\rm G}$ can be explained in this picture, although with a significant octupole component needed in some cases. For the stronger field pulsars, those with $B_d\gtrsim 10^{13}\ {\rm G}$, we find that the magnetic stresses in the crust exceed the maximum shear stress before the pulsar reaches its current age, likely quenching the Hall effect. This may have implications for the magnetar activity seen in the high magnetic field radio pulsar PSR~J1846-0258. Observations of braking indices may therefore be a new piece of evidence that neutron stars contain subsurface toroidal fields that are significantly stronger than the dipole field, and may indicate that the Hall effect is important in a wider range of neutron stars than previously thought.