GLS periodograms for GJ 720 A RV data (blue solid lines), photospheric stellar activity (red solid lines), and spectroscopic stellar activity (green solid lines) in the frequency range 0.001–0.1 d⁻¹ (1000–10 days in time range). In all the panels the horizontal dashed lines indicate FAP levels of 10% (blue), 1% (orange), and 0.1% (green). The shadowed areas indicate the region where the RV highest peaks are found. Panels a and b: spectral window (yellow line) and HARPS-N RVs (blue line), respectively. Panel c: SuperWASP binned photometric data. Panels d and e: MEarth binned photometric data and the residuals after removing the highest peak found at ~ 100 days (black vertical dashed line). Panel f: EXORAP B filter. Panel g: APACHE V filter binned photometric data. Panels h–l: HARPS-N NaD1, NaD2, Ca II H & K (S-index), and Hα HARPS-N spectroscopic activity indicators with a linear trend removed. Panel m: HARPS-N RV residuals after removing the 42.1 days signal, indicated as a black vertical dashed line. Panel n: HARPS-N RV residuals after removing the planet candidate signal at 19.5 days. Panel o: HARPS-N RV residuals after removing the 19.5 and 42.1 days signals. All the activity indicators and the RV data show a significant broad peak between 35 and 45 days. This is likely associated with the rotation period of GJ 720 A.