Modelling surface magnetic field evolution on AB Doradûs due to diffusion and surface differential rotation

From Zeeman-Doppler images of the young, rapidly-rotating KO dwarf AB Doradus, we have created a potential approximation to the observed radial magnetic field and have evolved it over 30 d subject to the observed surface differential rotation, meridional flow and various diffusion rates. Assuming that the dark polar cap seen in Doppler images of this star is caused by the presence of a unipolar field, we have shown that the observed differential rotation will shear this field to produce the observed high-latitude band of unidirectional azimuthal field. By cross-correlating the evolved fields with the initial field each day we have followed the decay with time of the cross-correlation function. Over 30 d it decays by only 10 per cent. This contrasts with the results of Barnes et al., who show that on this time-scale the spot distribution of He699 is uncorrelated. We propose that this is due to the effects of flux emergence changing the spot distributions.