We compared high-contrast near-infrared images of the core of R136 taken by VLT/SPHERE, in two epochs separated by 3.06 years. For the first time we monitored the dynamics of the detected sources in the core of R136 from a ground-based telescope with adaptive optics. The aim of these observations was to search for High prOper Motion cAndidates (HOMAs) in the central region of R136 (r<6) where it has been challenging for other instruments. Two bright sources (K<15mag and V<16mag) are located near R136a1 and R136c (massive WR stars) and have been identified as potential HOMAs. These sources have significantly shifted in the images with respect to the mean shift of all reliable detected sources and their neighbours, and six times their own astrometric errors. We calculate their proper motions to be 1.36pm0.22 mas/yr (321pm52 km/s) and 1.15pm0.11 mas/yr (273pm26 km/s). We discuss different possible scenarios to explain the magnitude of such extreme proper motions, and argue for the necessity to conduct future observations to conclude on the nature of HOMAs in the core of R136.
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