Galaxies in dense environments are subject to interactions and mechanisms which directly affect their evolution by lowering their gas fractions and reducing their star-forming capacity earlier than their isolated counterparts. The aim of our project is to get new insights about the role of environment on the stellar and baryonic content of galaxies using a kinematic approach, through the study of the Tully-Fisher relation (TFR). We study a sample of galaxies in 8 groups spanning a redshift range of $0.5<z<0.8$ and located in 10 pointings of the MAGIC MUSE Guaranteed Time Observations program. We perform a morpho-kinematics analysis of this sample and set up a selection based on galaxy size, [OII] emission line doublet signal-to-noise ratio, bulge-to-disk ratio and nuclear activity to construct a robust kinematic sample of 67 star-forming galaxies. This selection considerably reduces the number of outliers in the TFR, which are predominantly dispersion-dominated galaxies. Our results suggest a significant offset of the TFR zero-point between galaxies in low- and high-density environments, whatever kinematics estimator is used. This can be interpreted as a decrease of either stellar mass by $sim 0.05 - 0.3$ dex or an increase of rotation velocity by $sim 0.02 - 0.06$ dex for galaxies in groups, depending on the samples used for comparison. We also studied the stellar and baryon mass fractions within stellar disks and found they both increase with stellar mass, the trend being more pronounced for the stellar component alone. These fractions do not exceed 50%. We show that this evolution of the TFR is consistent either with a decrease of star formation or with a contraction of the mass distribution due to the environment. These two effects probably act together with their relative contribution depending on the mass regime.
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