SO χ² plots for R Dor, W Hya, IK Tau and R Cas. The contours show the confidence intervals and the shading represents the value for the corresponding model, with the colour-bar indicating multiples of the minimum value. The white cross indicates our best-fit model (see Table 6). For IK Tau, the slice for which R_w = 1.8R_p is shown. For R Cas, the slice for which R_w = 1.0R_p is shown.