MLP power spectrum of RV data. Top panels: HIRES, HARPS, and CARMENES. Bottom panels: CARMENES only. Horizontal dashed lines indicate FAP levels of 10%, 1%, and 0.1%, as defined by Zechmeister & Kürster (2009). The cyan, green, magenta, and blue vertical lines indicate the orbital periods of GJ 581 e, GJ 581 b, GJ 581 c, and of the conjectural GJ 581 [d], respectively. The red vertical line represents the rotational period of GI 581 (P_rot = 132.5 ± 6.3 days), with shaded regions indicating the associated uncertainty range (see Table 1).