Stellar-activity analysis of the nearby M dwarf GJ 526

M dwarfs are the most abundant stars in the Galaxy, and their low masses make them natural favourites for exoplanet radial-velocity (RV) searches. Nevertheless, these stars often demonstrate strong stellar activity that is yet to be fully understood. We used high-precision ESPRESSO, HIRES, and HARPS spectroscopy to perform a stellar-activity analysis on the nearby early M dwarf GJ 526 (d = 5.4 pc). We carried out a joint modelling of (i) the stellar rotation in RV, full width at half maximum (FWHM), and Mount Wilson S-index through Gaussian processes; (ii) long-term trends in these three physical quantities; and (iii) RV planetary signals. We constrained the stellar-rotation period to Prot = 48.7 ± 0.3 d, and discovered a weak sinusoidal signature in RV, FWHM, and S-index of period Pcyc = 1680−40+50d. We propose phase-space trajectories between RV and activity indicators as a novel means to visualise and interpret stellar activity. Current evidence does not support planetary companions of GJ 526.