Abstract
We use stellar proper motions (PM) from Gaia Data Release 2 for studying the internal kinematics of Milky Way globular clusters. In addition to statistical measurement errors, there are significant spatially correlated systematic errors, which cannot be ignored when studying the internal kinematics. We develop a mathematically consistent procedure for incorporating the spatial correlations in any model-fitting approach, and use it to determine rotation and velocity dispersion profiles of a few dozen clusters. We confirm detection of rotation in the sky plane for similar to 10 clusters reported in previous studies, and discover a few more clusters with rotation amplitudes exceeding similar to 0.05 mas yr(-1). However, in more than half of these cases the significance of this rotation signature is rather low when taking into account the systematic errors. We find that the PM dispersion is not sensitive to systematic errors in PM, however, it is quite sensitive to the selection criteria on the input sample, most importantly, in crowded central regions. When using the cleanest possible samples, PM dispersion can be reliably measured down to 0.1 mas yr(-1) for similar to 60 clusters.