# Precision multi-epoch astrometry with VLT cameras FORS1/2

## TL;DR

This study demonstrates that high-precision multi-epoch astrometry with VLT FORS cameras can achieve around 50 micro-arcseconds accuracy over various time scales by analyzing and mitigating systematic errors caused by optical and atmospheric factors.

## Contribution

The paper provides a detailed analysis of systematic and random errors in VLT FORS astrometry, achieving unprecedented precision levels and characterizing error sources over long time scales.

## Key findings

- Systematic errors are about 25 micro-arcseconds at frame center.
- Precision of about 50 micro-arcseconds is stable over daily, monthly, and yearly scales.
- Proper motions and parallaxes of stars were measured with 20 and 40 micro-arcseconds accuracy.

## Abstract

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 attainning a precision better than 1mas. 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. 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 mu-as. 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 mu-as stable on daily, monthly, and annual time scales. Relative proper motion and trigonometric parallaxes of stars in the center of the test field were derived with a precision of 20 mu-as/yr and 40 mu-as for 17-19 mag stars.