A long-term study of the magnetic field and activity in the M giant RZ Ari

Aims. We present a detailed long-term study of the single M6 III giant RZ Ari to obtain direct and simultaneous measurements of the magnetic field, activity indicators, and radial velocity in order to infer the origin of its activity. We study its magnetic activity in the context of stellar evolution, and for this purpose, we also refined its evolutionary status and Li abundance. In general, for the M giants, little is known about the properties of the magnetic activity and its causes. RZ Ari possess the strongest surface magnetic field of the known Zeeman-detected M giants and is bright enough to allow a deep study of its surface magnetic structure. The results are expected to shed light on the activity mechanism in these stars.Methods. We used the spectropolarimeter Narval at the T & eacute;lescope Bernard Lyot (Observatoire du Pic du Midi, France) to obtain a series of Stokes I and Stokes V profiles for RZ Ari. Using the least-squares deconvolution technique, we were able to detect the Zeeman signature of the magnetic field. We measured its longitudinal component by means of the averaged Stokes V and Stokes I profiles. In addition, we also applied Zeeman-Doppler imaging (ZDI) to search for the rotation period of the star, and we constructed a tentative magnetic map. It is the first magnetic map for a star that evolved at the tip of red giant branch (RGB) or even on the asymptotic giant branch (AGB). The spectra also allowed us to monitor chromospheric emission lines, which are well-known indicators of stellar magnetic activity. From the observations obtained between September 2010 and August 2019, we studied the variability of the magnetic field of RZ Ari. We also redetermined the initial mass and evolutionary status of this star based on current stellar evolutionary tracks and on the angular diameter measured from CHARA interferometry.Results. Our results point to an initial mass of 1.5 M-circle dot so that this giant is more likely an early-AGB star, but a lotaction at the tip of the RGB is not completely excluded. With a v sin i of 6.0 +/- 0.5 km s(-1), the upper limit for the rotation period is found to be 909 days. On the basis of our dataset and AAVSO photometric data, we determined periods longer than 1100 days for the magnetic field and photometric variability, and 704 days for the spectral line activity indicators. The rotation period determined on the basis of the Stokes V profiles variability is 530 days. A similar period of 544 days is also found for the photometric data. When we take this rotation period and the convective turnover time into account, an effective action of an alpha-omega-type dynamo seems to be unlikely, but other types of dynamo could be operating there. The star appears to lie outside the two magnetic strips on the giant branches, where the alpha-omega-type dynamo is expected to operate effectively, and it also has a much higher lithium content than the evolutionary model predicts. These facts suggest that a planet engulfment could speed up its rotation and trigger dynamo-driven magnetic activity. On the other hand, the period of more than 1100 days cannot be explained by rotational modulation and could be explained by the lifetime of large convective structures. The absence of linear polarization at the time the magnetic field was detected, however, suggests that a local dynamo probably does not contribute significantly to the magnetic field, at least for that time interval.