tokens: The PM diagrams of Fig. 1 present spike features for high velocity stars. 2 These spikes reflect low-quality astrometric measurements, specifically due to a dishomogeneous scanning pattern of Gaia , and can be identified through the astrometric quality parameter variability_periods_used (see e.g. Lindegren et al. 2018 ). The details of the effects on kinematics of these features are described in a follow up paper (Bianchini et al. in preparation). In this work, we verify that the rotation detections reported in the next sections do not depend on these features: kinematics subsamples that include a cut in the variability_periods_used give results fully consistent with the one obtained in the following sections. 3.2 Global rotation measurements To measure the rotation on the plane of the sky, we convert the stellar positions into cartesian coordinates centred on each cluster (centres from the Harris Catalogue; Harris 1996 ), with the positive x -axis pointing towards West and the positive y -axis pointing towards North, using equation ( 1 ) from van de Ven et al. ( 2006 ). The PMs in the RA and Dec. components are converted accordingly into a cartesian coordinate system using the orthographic projection reported in equation ( 2 ) of Gaia Collaboration et al. ( 2018a ), with positive μ x in the direction of West. 3 Finally, we transform the PMs in radial and tangential components (μ r , μ t ) in polar coordinates, with positive μ r indicating velocities away from the cluster centre and positive μ t indicating counterclockwise movements. In the rest of this paper we will focus on the analysis of the tangential component of the PMs and analyse the radial component in Section 4.2 . We compute the global rotation along the tangential component within 3 R h using equation ( 2 ), as described in Section 2 . The results are reported in Table 1 and plotted in Fig. 2 . Out of the 51 GCs analysed, 11 display an average value of μ t significantly different than zero at a confidence level >3σ. These clusters are indicated as red symbols in Fig. 2 . We confirm the detection of rotation in NGC 104, NGC 5139, NGC 5272, NGC 5904, NGC 6656, NGC 6752, NGC 6809, and NGC 7078 reported by Gaia Collaboration et al. ( 2018a ), and additionally we detect rotation in NGC 4372, NGC 6273, and NGC 7089. Figure 2. Mean PM along the tangential component measured in a three half-light radii field of view around the cluster centres. The absolute value of μ t ( 3 R h ) is plotted as a function of the distance of the clusters. Red stars indicate clusters for which rotation is detected at least with a 3σ confidence level. Dotted lines indicate PM values in km s −1 for a given distance (, with μ measured in mas yr −1 , v measured in km s −1 , and d in kpc). Gaia Collaboration et al. ( 2018a ) and Lindegren et al. ( 2018 ) reported that systematics errors are present in Gaia DR2, in particular a ∼1° small-scale component, related to the Gaia scan pattern. Following the procedure
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