MAGNETIC-FIELD EVOLUTION IN NEUTRON-STARS - COUPLING BETWEEN POLOIDALAND 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 co nfined to the outer crust, as well as the toroidal component wound aro und the core of the neutron star. We perform our calculations using ra pid and relatively slow cooling histories, both implying the possibili ty of a direct Urca process in the core. At the late stages, after app roximately 10(8) yr, the poloidal modes become strongly coupled (due t o the Hall term in the conductivity tensor) to each other via the toro idal component. We show that this coupling may strongly affect the sub sequent evolution of poloidal modes. In particular, we demonstrate tha t the presence of an initially very weak quadrupole mode substantially modifies the evolution of the dipole mode. Also, we have found that a t t greater than or similar 10(9) yr sign reversal of the poloidal mod es may occur.