Top panel: first row: periodogram of the residuals of the GJ 3543 radial velocities after subtracting the 1.1 d Keplerian orbit. The power excess at P = 23 d has a 2.5% FAP. Second row: periodogram of the S-index of GJ 3543. The significance of the 22 d peak is just under 1σ. Third row: periodogram of the Hα index of GJ 3543. The false-alarm probability of the 19 d peak is 14%. Middle panel: the Hα index phased to the 19 d period. Bottom panel: RVs against the Hα-index, the colors represent phase for the 9.2 d period, as represented in Fig. 11 (bottom), T₀ from Table 6.