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This is the first of a series of papers presenting the results from our survey of 25 Galactic globular clusters with the MUSE integral-field spectrograph. In combination with our dedicated algorithm for source deblending, MUSE provides unique multiplex capabilities in crowded stellar fields and allows us to acquire samples of up to 20 000 stars within the half-light radius of each cluster. The present paper focuses on the analysis of the internal dynamics of 22 out of the 25 clusters, using about 500 000 spectra of 200 000 individual stars. Thanks to the large stellar samples per cluster, we are able to perform a detailed analysis of the central rotation and dispersion fields using both radial profiles and two-dimensional maps. The velocity dispersion profiles we derive show a good general agreement with existing radial velocity studies but typically reach closer to the cluster centres. By comparison with proper motion data, we derive or update the dynamical distance estimates to 14 clusters. Compared to previous dynamical distance estimates for 47 Tuc, our value is in much better agreement with other methods. We further find significant (>3 sigma) rotation in the majority (13/22) of our clusters. Our analysis seems to confirm earlier findings of a link between rotation and the ellipticities of globular clusters. In addition, we find a correlation between the strengths of internal rotation and the relaxation times of the clusters, suggesting that the central rotation fields are relics of the cluster formation that are gradually dissipated via two-body relaxation.
We utilise multi-epoch MUSE spectroscopy to study binary stars in the core of the Galactic globular cluster NGC 3201. Our sample consists of 3553 stars with 54 883 spectra in total comprising 3200 main-sequence stars up to 4 magnitudes below the turn-off. Each star in our sample has between 3 and 63 (with a median of 14) reliable radial velocity measurements within five years of observations. We introduce a statistical method to determine the probability of a star showing radial velocity variations based on the whole inhomogeneous radial velocity sample. Using HST photometry and an advanced dynamical MOCCA simulation of this specific cluster we overcome observational biases that previous spectroscopic studies had to deal with. This allows us to infer a binary frequency in the MUSE field of view and enables us to deduce the underlying true binary frequency of (6.75 +/- 0.72)% in NGC 3201. The comparison of the MUSE observations with the MOCCA simulation suggests a large portion of primordial binaries. We can also confirm a radial increase in the binary fraction towards the cluster centre due to mass segregation. We discovered that in the core of NGC 3201 at least (57.5 +/- 7.9)% of blue straggler stars are in a binary system. For the first time in a study of globular clusters, we were able to fit Keplerian orbits to a significant sample of 95 binaries. We present the binary system properties of eleven blue straggler stars and the connection to SX Phoenicis-type stars. We show evidence that two blue straggler formation scenarios, the mass transfer in binary (or triple) star systems and the coalescence due to binary-binary interactions, are present in our data. We also describe the binary and spectroscopic properties of four sub-subgiant (or red straggler) stars. Furthermore, we discovered two new black hole candidates with minimum masses (M sin i) of (7.68 +/- 0.50)M-circle dot, (4.4 +/- 2.8)M-circle dot, and refine the minimum mass estimate on the already published black hole to (4.53 +/- 0.21)M-circle dot, These black holes are consistent with an extensive black hole subsystem hosted by NGC 3201.