Shell decomposition of HD 10700 spectra. Left: representation of the different shells basis components and the time series of the coefficients α_j(t) in fronteach of those shell basis components when modelling the RVs of HD 10700 (see Eq. (4)). All the components are orthogonal to the Doppler shell basis component (DS) displayed at the bottom (similar to Fig. 2) thanks to a Gram–Schimdt algorithm. The pixel grid in the shell space on which the PCA was trained (dots) is shown, as well as a smooth function interpolated on the full shell space using a cubic interpolation algorithm. Middle: generalised Lomb–Scargle periodogram of the α_j (t) shell component coefficients. The 0.1% false alarm probability (FAP) level for each periodogram is indicated by an horizontal dotted-dashed line. From top to bottom, we can see the five first principal shell basis components and the DS. The Pearsoncorrelation coefficient between the α_j(t) and the CCF RV time series is indicated on the right side of each subplot. The lowest periodogram represents the RV time series linearly decorrelated from the α_j coefficients (similar to Eq. (5)). The power at the planetary injected periods (vertical red lines) is never the dominant power for any shell. This is particularly true for the 37-day signal less significant than the 0.1% FAP level. Some power is observed around 122 days for PS₁ and PS₄ due to an alias of a one-year systematics (see main text). Right: explained variance curve of the PCA components. Our cross-validation algorithm (see Appendix A) provides four significant components (> 95%). The components compatible with a single outlier explanation (<80%) are shown in red.