Centauri: a MUSE discovery of a counter-rotating core

omega Centauri is considered the most massive globular cluster of the Milky Way and likely the former nuclear star cluster of a Galaxy accreted by the Milky Way. It is speculated to contain an intermediate-mass black hole (IMBH) from several dynamical models. However, uncertainties regarding the location of the cluster centre or the retention of stellar remnants limit the robustness of the IMBH detections reported so far. In this paper, we derive and study the stellar kinematics from the highest-resolution spectroscopic data yet, using the Multi Unit Spectroscopic Explorer (MUSE) in the narrow field mode and wide field mode. Our exceptional data near the centre reveal for the first time that stars within the inner 20 arcsec (similar to 0.5 pc) counter-rotate relative to the bulk rotation of the cluster. Using this data set, we measure the rotation and line-of-sight velocity dispersion profile out to 120 arcsec with different centres proposed in the literature. We find that the velocity dispersion profiles using different centres match well with those previously published. Based on the counter-rotation, we determine a kinematic centre and look for any signs of an IMBH using the high-velocity stars close to the centre. We do not find any significant outliers >60 km s(-1) within the central 20 arcsec, consistent with no IMBH being present at the centre of omega Centauri. A detailed analysis of Jeans' modelling of the putative IMBH will be presented in the next paper of the series.