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| - Precision multi-epoch astrometry with VLT cameras FORS1/2
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| - Aims. We investigate the astrometric performance of the FORS1 and FORS2 cameras of the VLT at long time scales with emphasis on systematic errors which normally prevent attaining a precision better than 1 mas. Methods. The study is based on multi-epoch time series of observations of a single sky region imaged with a time spacing of 2-6 years at FORS1 and 1-5 months at FORS2. Images were processed with a technique that reduces atmospheric image motion, geometric distortions, and takes into account relative displacement of reference stars in time. Results. We performed a detailed analysis of a random error of positions that was shown to be dominated by the uncertainty of the star photocenter determination. The component of the random error corresponding to image motion was found to be caused primarily by optical aberrations and variations of atmospheric PSF size but not by the effect of atmospheric image motion. Comparison of observed and model annual/monthly epoch average positions yielded estimates of systematic errors for which temporal properties and distribution in the CCD plane are given. At frame center, the systematic component is about 25 μas. Systematic errors are shown to be caused mainly by a combined effect of the image asymmetry and seeing variations which therefore should be strongly limited to avoid generating random and systematic errors. For a series of 30 images, we demonstrated presicion of about 50 μas stable on daily, monthly, and annual time scales. Small systematic errors and a Gaussian distribution of positional residuals at any time scale indicate that the astrometric accuracy of the VLT is comparable to the precision. Relative proper motion and trigonometric parallaxes of stars in the center of the test field were derived with a precision of 20 μas yr -1 and 40 μas for 17-19 mag stars. Therefore, distances at 1 kpc could be determinable at a 4% precision if suitably distant reference objects are in the field. Conclusions. We prove that the VLT with FORS1/2 cameras are not subject to significant systematic errors at time scales from a few hours to a few years providing that observations are obtained in narrow seeing limits. The astrometric performance of the VLT imaging cameras meets requirements necessary for many astrophysical applications, in particular, exoplanet studies and determination of relative trigonometric distances by ensuring a high accuracy of observations, at least 50 μas attained for image series of 0.5 hour.
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