Example of an ambiguous detection of a high S/N duplet ℓ = 2,0 from the PSD of KIC 9139163. The solid line shows the resulting best-fit as computed by Diamonds, while the dashed line represents the mean background model as obtained in Sect. 6.2, according to Eq. (30). Upper panel: case of model ℳ_B where only ℓ = 0 is fitted. Lower panel: case of model ℳ_C where both ℓ = 2,0 are fitted. The resulting lnℬ_CB = 16.5 ± 0.1 strongly favors model ℳ_C, hence the presence of two peaks in the observed structure.