Dissipation of magnetic fields in neutron star crusts due to development of a tearing mode

Dissipation of magnetic fields in Hall plasma of neutron star crusts may power persistent high energy emission of a class of strongly magnetized neutrons stars, magnetars. We consider development of a dissipative tearing mode in Hall plasma (electron MHD) and find that its growth rate increases with the wave number of perturbations, reaching a maximum value intermediate between resistive ${\tau }_r$ and Hall times ${\tau }_H$, $\Gamma\sim 1 / \sqrt{\tau_r \tau_H}$. We argue that the tearing mode may be the principal mechanism by which strong magnetic fields are dissipated in magnetars on times scale of $\sim {10}^4-{10}^5$ yrs powering the persistent X-ray emisison.