Azimuthally averaged rotation rates from the PFSS models shown in Fig. 3. Averaging is peformed on the open field regions, grey regions indicate closed field at all longitudes (hence no value returned). The limited number of open magnetic field lines over the north pole during the ‘Activity Maximum’ model, lead to some oddity in the north-most latitude bin that should be disregarded. The lower panels show the latitudinal profiles coloured by radial distance from the surface (yellow being the furthest). The rising and declining phases show a clear north-south asymmetry which is also observed in the systematic differences in ⟨θ⟩ between the two hemispheres in Fig. 4.