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This is the first of a series of papers presenting the results from oursurvey of 25 Galactic globular clusters with the MUSE integral-fieldspectrograph. In combination with our dedicated algorithm for sourcedeblending, MUSE provides unique multiplex capabilities in crowded stellarfields and allows us to acquire samples of up to 20 000 stars within thehalf-light radius of each cluster. The present paper focuses on the analysis ofthe internal dynamics of 22 out of the 25 clusters, using about 500 000 spectraof 200 000 individual stars. Thanks to the large stellar samples per cluster,we are able to perform a detailed analysis of the central rotation anddispersion fields using both radial profiles and two-dimensional maps. Thevelocity dispersion profiles we derive show a good general agreement withexisting radial velocity studies but typically reach closer to the clustercentres. By comparison with proper motion data we derive or update thedynamical distance estimates to 14 clusters. Compared to previous dynamicaldistance estimates for 47 Tuc, our value is in much better agreement with othermethods. We further find significant (>3sigma) rotation in the majority (13/22)of our clusters. Our analysis seems to confirm earlier findings of a linkbetween rotation and the ellipticities of globular clusters. In addition, wefind a correlation between the strengths of internal rotation and therelaxation times of the clusters, suggesting that the central rotation fieldsare relics of the cluster formation that are gradually dissipated via two-bodyrelaxation.

A stellar census in globular clusters with MUSE: The contribution of rotation to cluster dynamics studied with 200 000 stars