Magnetic fields are present throughout the universe and are very important for many astrophysical processes. Magnetic field influences a star throughout its life and affects nearby objects such as planets. Stellar magnetic field can be detected by measuring the Zeeman splitting of spectral lines in the intensity spectra (Stokes I) if the field is strong, or by analyzing polarization spectra if the field is weak. Magnetic fields in stars similar to the Sun are ubiquitous but, in general, relatively weak. Until recently these fields were detected through circular polarization (Stokes V) only since linear polarization (Stokes QU) is significantly weaker. The information embedded in different Stokes spectra is used for reconstruction of the surface magnetic field topology with Zeeman Doppler imaging (ZDI) technique. However, cool stars often have complex field geometries and this, combined with a low field strength, partial Stokes parameter observations and the presence of cool spots, makes accurate magnetic mapping difficult. We have performed numerical tests of ZDI to investigate some of the problems of magnetic inversions and ways to overcome them. The most reliable results were found when magnetic field and temperature inhomogeneities were modelled simultaneously and all four Stokes parameters were included in the reconstruction process. We carried out observations of active cool stars in all four Stokes parameters trying to find an object with linear polarization signatures suitable for ZDI. The RS CVn star II Peg was identified as a promising target, showing exceptionally strong linear polarization signatures. We reconstructed the magnetic field in II Peg using full Stokes vector observations for the first time in a cool star. Compared to the magnetic maps recovered from the Stokes IV spectra, the four Stokes parameter results reveal a significantly stronger and more complex surface magnetic field and a more compact stellar magnetosphere. Spectropolarimetric observations and magnetic inversions can also be used to investigate magnetic activity of the young Sun and its implications for the solar system past. To this end, we studied a sample of six stars with parameters very similar to the present Sun, but with ages of only 100-650 Myr. Magnetic field maps of these young solar analogues suggest a significant decrease of the field strength in the age interval 100-250 Myr and a possible change in the magnetic field topology for stars older than about 600 Myr.

We report the direct imaging detection of a low-mass companion to a young, moderately active star V450. And, that was previously identified with the radial velocity (RV) method. The companion was found in high-contrast images obtained with the Subaru Telescope equipped with the HiCIAO camera and AO188 adaptive optics system. From the public ELODIE and SOPHIE archives we extracted available high-resolution spectra and RV measurements, along with RVs from the Lick planet search program. We combined our multi-epoch astrometry with these archival, partially unpublished RVs, and found that the companion is a low-mass star, not a brown dwarf, as previously suggested. We found the best-fitting dynamical masses to be m(1) = 1.141(-0.091)(+0.037)and m(2) = 0.279(-0.020)(+0.023) M-circle dot. We also performed spectral analysis of the SOPHIE spectra with the iSpec code. Hipparcos time-series photometry shows a periodicity of P = 5.743 day, which is also seen in the SOPHIE spectra as an RV modulation of the star A. We interpret it as being caused by spots on the stellar surface, and the star to be rotating with the given period. From the rotation and level of activity, we found that the system is 380(-100)(+220) Myr old, consistent with an isochrone analysis (220(-90)(+2120) Myr). This work may serve as a test case for future studies of low-mass stars, brown dwarfs, and exoplanets by combination of RV and direct imaging data.

Cette thèse a pour objectif de comprendre les différents aspects de l'évolution des amas d’étoiles massives NGC3603 et R136 qui possèdent les étoiles les plus massives connues de l'univers local. L'analyse photométrique des noyaux de R136 et NGC3603 utilisant l’imagerie infrarouge de l’instrument SPHERE sur VLT et son système d’optique adaptative extrême de SPHERE, m’a permis de détecter pour la 1ière fois un grand nombre d’étoiles de faibles masse et luminosité au coeur de ces amas et pour la plupart au voisinage des étoiles les plus lumineuses et massives. La comparaison des données de SPHERE de NGC3603 à celles du HST montre l’absence de ségrégation de masse dans le noyau de cet amas. De plus la pente de la fonction de masse de cette région est la même que celle de la région suivante et similaire aux valeurs de la MF correspondant aux régions extérieures de l’amas connues jusqu’ici. L’amas R136 est partiellement résolu par SPHERE/IRDIS dans l’IR. La majorité de ses étoiles massives ont des compagnons visuels. En prenant compte des mesures spectroscopiques et photométriques et leurs erreurs sur l'extinction et l'âge des membres de l’amas, j’ai estimé une gamme de masse pour chaque étoile identifiée. La MF a été calculée pour différents âges ainsi que les erreurs sur les masses stellaires. J’ai simulé des séries d'images de R136 grâce au code Nbody6, et les ai comparées aux observations du HST/WFPC2. Ces simulations permettent de vérifier l'effet de la binarité initiale des étoiles de l’amas, la ségrégation de masse et l'évolution des étoiles sur l'évolution dynamique propre à R136. / This thesis aims at studying 2 massive clusters NGC3603 and R136, and the mechanisms that govern their physics, These clusters host the most massive stars known in the local universe so far and are important clues to understand the formation and fate of very massive star clusters. The manuscript outlines the photometric analysis of the core of R136 and NGC3603 on the basis of HST data in the visible and the VLT high dynamic imaging that I obtained in the infrared thanks to the SPHERE focal instrument operated since 2015 and its extreme Adaptive Optics, In an extensive photometric study of these data I discovered a significantly larger number of faint low-mass stars in the core of both these clusters compared to previous works. These stars are often detected in the vicinity of known massive bright objects. By comparing HST and SPHERE measures, NGC3603 does not show any signature of mass segregation in its core since the MF slope of the very core and the next radial bin are similarly flat and agree well with the MF found in previous works of the outer regions. On the other hand R136 is partially resolved using the SPHERE/IRDIS mode with most of the massive stars having visual companions. Considering the spectroscopic and photometric errors on the extinction and the age of cluster members, I estimate a mass range for each detected star. The MF is plotted at different ages with given errors on stellar masses. Finally I demonstrate that we need more resolution to go further on studying R136 which is 7-8 times further than NGC3603.