p-values for magnification values equal or greater than ten in the smooth CDM model (purple) and adding a subhalo of 10⁷ M_⊙ at different positions relative to the centre of the main halo. As in Figs. 4 and 7, the p-value is the probability of obtaining an image with magnification equal to or greater than ten given the models. The significance values are indicated by the dashed horizontal lines. The halo and axion masses correspond to model 22 in Table 1, with M_h = 7 × 10¹¹ M_⊙ and m_ψ = 10⁻²² eV.