Aims. We aim to evaluate how well the variation of small-scale magnetic fields on the stellar surface can be monitored with time-series observations. Further, we aim to establish to what extent the measured total unsigned magnetic field traces other activity indicators. Methods. We measured the total unsigned magnetic field on four young, Sun-like, stars using the Zeeman splitting of magnetically sensitive Ti I and Fe I lines from high-resolution time series spectra obtained with the spectropolarimeters ESPaDOnS at Canada France Hawaii Telescope and NARVAL at Bernard Lyot Telescope. We then characterised the magnetic field variations using both sinusoidal variation and Lomb-Scargle periodograms. We evaluated how the rotational variation of the total unsigned magnetic field strength correlates with the activity indicators S-index, Hα-index, Ca IRT-index, and the large-scale magnetic field obtained from Zeeman Doppler imaging maps obtained in earlier studies. Results. We find clear signals of rotational modulation of the total magnetic field on HIP 76768 and tentative detection on Mel 25-5. This is supported both by the sinusoidal fitting as well as the periodogram. For the other stars, we find no clear modulation signals of the total magnetic field. We find positive correlations between the total magnetic field and activity indices on all four stars, indicating that indirect magnetic activity indicators trace the underlying magnetic field variability. However, comparing the activity-magnetic field relationship between the stars in our sample shows a significant deviation between activity level and measured magnetic field strength. Conclusions. Small-scale magnetic field variability can evidently be traced using the Zeeman effect on magnetically sensitive lines, provided that the star is sufficiently active. It is also possible to self-consistently recover rotational periods from such measurements. The primary limit for the detection of magnetic field variations on less active stars is the precision of Zeeman broadening and intensification measurements.
Hahlin et al. (2026) studied this question.