Hubble Space Telescope proper motions of Large Magellanic Cloud star clusters. I. Catalogues and results for NGC1850

We present proper motion (PM) measurements for a sample of 23 massive star clusters within the Large Magellanic Cloud using multi-epoch data from the Hubble $. To demonstrate the potential and limitations of our PM data set, we analysed the cluster NGC 1850 and showcase a selection of different science applications. The precision of the PM measurements allows us to disentangle the kinematics of the various stellar populations that are present in the HST field. The cluster has a centre-of-mass motion that is different from the surrounding old field stars and also differs from the mean motion of a close-by group of very young stars. We determined the velocity dispersion of field stars to be $0.128 $ (corresponding to $30.3 $). The velocity dispersion of the cluster inferred from the PM data set most probably overestimates the true value, suggesting that the precision of the measurements at this stage is not sufficient for a reliable analysis of the internal kinematics of extra-galactic star clusters. Finally, we exploit the PM-cleaned catalogue of likely cluster members to determine any radial segregation between fast and slowly-rotating stars, finding that the former are more centrally concentrated. With this paper, we also release the astro-photometric catalogues for each cluster.