Context. Photometric monitoring of the variability of brown dwarfs can provide useful information about the structure of clouds in their cold atmospheres. The brown-dwarf binary system Luhman 16AB is an interesting target for such a study, as its components stand at the L/T transition and show high levels of variability. Luhman 16AB is also the third closest system to the Solar system, allowing precise astrometric investigations with ground-based facilities. Aims. The aim of the work is to estimate the rotation period and study the astrometric motion of both components. Methods. We have monitored Luhman 16AB over a period of two years with the lucky-imaging camera mounted on the Danish 1.54m telescope at La Silla, through a special i+z long-pass filter, which allowed us to clearly resolve the two brown dwarfs into single objects. An intense monitoring of the target was also performed over 16 nights, in which we observed a peak-to-peak variability of 0.20 pm 0.02 mag and 0.34 pm 0.02 mag for Luhman 16A and 16B, respectively. Results. We used the 16-night time-series data to estimate the rotation period of the two components. We found that Luhman 16B rotates with a period of 5.1 pm 0.1 hr, in very good agreement with previous measurements. For Luhman 16A, we report that it rotates slower than its companion and, even though we were not able to get a robust determination, our data indicate a rotation period of roughly 8 hr. This implies that the rotation axes of the two components are well aligned and suggests a scenario in which the two objects underwent the same accretion process. The 2-year complete dataset was used to study the astrometric motion of Luhman 16AB. We predict a motion of the system that is not consistent with a previous estimate based on two months of monitoring, but cannot confirm or refute the presence of additional planetary-mass bodies in the system.
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