MAGNETIC-FIELD EVOLUTION IN NEUTRON-STARS - COUPLING BETWEEN POLOIDAL AND TOROIDAL COMPONENTS IN THE CRUST

We calculate the decay of the magnetic field in a neutron star crust, with allowance for the Hall effect. The magnetic field is represented by the large-scale (dipole and quadrupole) poloidal modes initially confined to the outer crust, as well as the toroidal component wound around the core of the neutron star. We perform our calculations using rapid and relatively slow cooling histories, both implying the possibility of a direct Urca process in the core. At the late stages, after approximately 10(8) yr, the poloidal modes become strongly coupled (due to the Hall term in the conductivity tensor) to each other via the toroidal component. We show that this coupling may strongly affect the subsequent evolution of poloidal modes. In particular, we demonstrate that the presence of an initially very weak quadrupole mode substantially modifies the evolution of the dipole mode. Also, we have found that at t greater than or similar 10(9) yr sign reversal of the poloidal modes may occur.