MAGNETIC FIELD EVOLUTION IN WHITE-DWARFS - THE HALL-EFFECT AND COMPLEXITY OF THE FIELD

We calculate the evolution of the magnetic fields in white dwarfs, taking into account the Hall effect. Because this effect depends nonlinearly upon the magnetic field strength B, the time dependences of the various multipole field components are coupled. The evolution of the field is thus significantly more complicated than has been indicated by previous investigations. Our calculations employ recent white dwarf evolutionary sequences computed for stars with masses 0.4, 0.6, 0.8, and 1.0 M.. We show that in the presence of a strong (up to similar to 10(9) G) internal toroidal magnetic field, the evolution of even the lowest order poloidal modes can be substantially changed by the Hall effect. As an example, we compute the evolution of an initially weak quadrupole component, which we take arbitrarily to be similar to 0.1%-1% of the strength of a dominant dipole field. We find that the coupling provided by the Hall effect can produce growth of the ratio of the quadrupole to the dipole component of the surface value of the magnetic field strength by more than a factor of 10 over the 10(9)-10(10) year cooling lifetime of the white dwarf. Some consequences of these results for the process of magnetic-field evolution in white dwarfs are briefly discussed.