Same as Fig. 8, showing p-values for magnifications equal to or greater than ten in the smooth CDM model and after adding subhaloes. In this case, the subhalo mass varies between realisations, as colour-coded in the legend, while its position is fixed at half the radius of the radial critical curve from the centre of the main halo. The halo and axion masses correspond to model 22 in Table 1, with M_h = 7 × 10¹¹ M_⊙ and m_ψ = 10⁻²² eV.