RVs, MLP periodogram, and best-fit model of GJ 581. Top panel: precise Doppler measurements of GJ 581 from HIRES (purple circles), HARPS (orange diamonds), and CARMENES (pink triangles) modeled with a three-planet self-consistent N-body model simultaneously constructed with a GP component that fits the stellar activity periodicity in the RVs. The middle subpanel shows the residuals of the N-body model, where are effectively fit with the rotational kernel GP model. The bottom subpanel shows the data residuals to the total N-body+GP model. Middle panels: phase folded data and N-body model for the three planetary signals as indicated in the subplots. Bottom panel: MLP periodogram of the RV model and GP residuals. No significant periodicity remains after the model is subtracted.