Astrometry with the MCAO instrument MAD. An analysis of single-epoch data obtained in the layer-oriented mode

Context. Current instrument developments at the largest telescopes worldwide involve the installation of multi-conjugated adaptive optics (MCAO) modules. The large field of view and more uniform correction provided by these systems is not only highly beneficial for photometric studies but also for astrometric analysis of, e.g., large dense clusters and exoplanet detection and characterization. The Multi-conjugated Adaptive optics Demonstrator (MAD) is the first such instrument and was temporarily installed and tested at the ESO/VLT in 2007. Aims: We analyzed the first available MCAO imaging data in the layer-oriented mode obtained with the MAD instrument in terms of astrometric precision and stability. Methods: We analyzed two globular cluster data sets in terms of achievable astrometric precision. Data were obtained in the layer-oriented correction mode, one in full MCAO correction mode with two layers corrected (NGC 6388) and the other applying ground-layer correction only (47 Tuc). We calculated Strehl maps for each frame in both data sets. Distortion corrections were performed and the astrometric precision was analyzed by calculating mean stellar positions over all frames and by investigating the positional residuals present in each frame after transformation to a master-coordinate frame. Results: The mean positional precision for stars of brightnesses K = 14-18 mag is ≈ 1.2 mas in the full MCAO correction mode data of the cluster NGC 6388. The precision measured in the GLAO data (47 Tuc) reaches ≈1.0 mas for stars corresponding to 2MASS K magnitudes between 9 and 12. The observations were such that stars in these magnitude ranges correspond to the same detector flux range. The jitter movement used to scan a larger field of view introduced additional distortions in the frames, leading to a degradation of the achievable precision.Instrumentatio