Fig. 6

Panel a: available Doppler measurements for GJ 1148 obtained with HIRES (green diamonds) and CARMENES (red circles) fitted with a two-planet N-body model. Panel b: zoom of the CARMENES time series together with the same model. Panel c: no significant signal is left in the residuals of the two-planet dynamical model. A peak at 62.9 d presents an interesting possibility for a third lower-mass planetary companion that might be locked in a 3:2 MMR with GJ 1148 b, but currently this peak is still below the 1% FAP level. Panel d: results from a stability analysis of the GJ 1148 system composed of planets b and c. This two-planet fit is stable for at least 10 Myr, but for illustrative purposes we plot only a 200 000 yr extent of the orbital evolution of the planetary semi-major axes and eccentricities for the best two-planet dynamical fit. In this configuration the two planets exhibit large secular oscillations of eb and ec with a secular period of ~80 000 years.
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