Abstract
This Thesis presents a study of five magnetically active cool evolved stars of different spectral types and different evolutionary status. All the stars are studied using long-term monitoring in high resolution spectropolarimetry obtained with the instrument Narval and its successor, NeoNarval, installed on the Télescope Bernard Lyot at the Observatoire du Pic du Midi, France. The studied stars are three M giants (RZ Ari, β Peg, EK Boo), located on the tip-RGB and early-AGB, one post-AGB pulsating variable (R Sct) and one red supergiant (α Ori, a.k.a. Betelgeuse). To extract the mean polarization features from the stellar spectra, the Least Square Deconvolution (LSD) method is used.For the M giant stars, the surface magnetic field is detected and its longitudinal component (Bl) is directly measured from circular polarization observations (Stokes V). The temporal variability of the surface magnetic field is compared to that of spectral lines - indicators of magnetic activity: Ca H&K, Hα and the Ca infrared triplet lines. Based on the variability of Bl and the spectral activity indicators, the characteristics of the respective magnetic fields are inferred in the three M giants. An original improvement of the classical method for the determination of stellar parameters, including the projected rotational velocity vsini and the macroturbulent velocity vmac, is developed. This new method which combines spectrum synthesis and multi-line tools (LSD) is then used in order to determine the parameters vsini and vmac for the M giant RZ Ari. A more precise vsini will help for a better understanding of the origin of its surface magnetic field. For RZ Ari, a planet engulfment event is suspected to have triggered its magnetic activity. Another possible explanation for the magnetic field in M giants could be a local dynamo due to large convective cells, if such cells exist there. For β Peg and EK Boo, a possible explanation for the origin of the magnetic field is the α-Ω dynamo.For the post-AGB pulsating variable star R Sct, Stokes V signatures are detected from circular polarization observations collected along the longest high resolution spectropolarimetric monitoring ever done on this target. Their stellar origin is confirmed and attributed to a weak surface magnetic field which manifests itself through the Zeeman effect. The timescale of variation of this surface magnetic field is shown to be of a few months, similar to the timescale of the stellar pulsation. The differences between the dynamics in the lower, near-photospheric and the upper layers of the extended atmosphere of R Sct are illustrated by analysing the high resolution spectra of the star. A refined approach is presented for the application of the LSD method in order to better probe the surface magnetic field in the case of such pulsating stars with a very extended atmosphere. This approach is then used on R Sct to estimate the longitudinal component of the magnetic field (Bl), and the presented study shows that shockwaves propagating throughout its atmosphere might amplify the magnetic field strength of this cool evolved star.In order to study the convective motions at the level of the photosphere of the red supergiant Betelgeuse, a new method is developed for building three-dimensional (3D) images of the surface of this star using high resolution observations in linear polarization (Stokes Q & U). This method is used to create the first such 3D images for Betelgeuse. From their investigation, the presence of at least one force which counteracts gravity at this level of the atmosphere of Betelgeuse is suggested. This force (or forces) allows for convective velocities close to the escape velocity of Betelgeuse and could, at least partially, explain the mass-loss observed for this target and also for other red supergiant stars.