LS periodograms for simulated stars. Top panel: LS periodogram of the dτ_obsm-stretched PSD for a simulated magnetized RG observed pole-on. Middle panel: dπ₀-LS periodogram for the simulated magnetized RG, using ΔΠ₁ = 75.2 s and δν_mag(ν_max) = 0.40 μHz. Bottom panel: LS periodogram of the dπ₀-stretched PSD for the simulated magnetized RG by using ΔΠ₁ = 75.13 s and δν_mag(ν_max) = 0.38 μHz (as calculated in Sect. 4.5). In each panel, the black line indicates the true value of ΔΠ₁, and the dot-dashed blue line indicates the period associated with the maximum amplitude in the LS periodogram. Dashed grey curves are the mirrored central peak around the period associated with the maximum amplitude in the LS periodogram. Curves are thicker within the central peak for better visualization. Hatched areas indicate the typical uncertainty δ(ΔΠ₁)_res = 0.6 s on the measurement of ΔΠ₁ from LS-based methods according to the study of Vrard et al. (2016), centered around ΔΠ₁ = 75.2 s. The skewness of the dominant peak calculated with Eq. (C.1) is indicated in the top left corner of each panel.