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Fig. 4

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Radial-velocity and CaII S-index measurements of Kepler-93. Left panel: HIRES (red circles) and HARPS-N (blue circles) radial velocities. The black line shows the best-fit model with a long-term linear slope caused by a non-planetary companion, a Keplerian orbit for the transiting planet Kepler-93b (P = 4.73 d), and Gaussian process regression with a squared exponential kernel to account for long-term stellar activity variations. Right panel: residuals of the HARPS-N radial velocities after subtracting the linear long-term trend and the signal of Kepler-93b (top), and measurements of the stellar activity S index (bottom). The increase in both the RVs and the S index from ~ 7000 to ~ 8300 BJDTDB – 2 450 000 indicates that the small-amplitude long-term variations superposed to the linear slope seen in the left panel are likely due to stellar magnetic activity.

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