Synthetic data and their analysis. (a) Synthetic data contain all three periods, P₁, P₂, P_long. (b) Residuals (observed minus computed). (c) Histogram of the residuals. (d) GLS periodogram of the residuals, showing a featureless spectrum, demonstrating that the residuals contain only noise. (e) In the full periodogram, the peak at P_long, present in the observational data, is reproduced by the synthetic data. (f) Zoom onto the orbital frequency range. The peaks at the two periods, P₁ and P₂, are present for both observational and synthetic data. For both datasets, there is also a significant feature at the position of P₃, as indicated by the vertical dotted line.