Limits of ultra-high-precision optical astrometry stellar surface structures

Aims. To investigate the astrometric effects of stellar surface structures as a practical limitation to ultra-high-precision astrometry (e.g. in the context of exoplanet searches) and to quantify the expected effects in different regions of the HR-diagram. Methods. Stellar surface structures (spots, plages, granulation, non-radial oscillations) are likely to produce fluctuations in the integrated flux and radial velocity of the star, as well as a variation of the observed photocentre, i.e. astrometric jitter. We use theoretical considerations supported by Monte Carlo simulations (using a starspot model) to derive statistical relations between the corresponding astrometric, photometric, and radial velocity effects. Based on these relations, the more easily observed photometric and radial velocity variations can be used to predict the expected size of the astrometric jitter. Also the third moment of the brightness distribution, interferometrically observable as closure phase, contains information about the astrometric jitter. Results. For most stellar types the astrometric jitter due to stellar surface structures is expected to be of the order of 10 micro-AU or greater. This is more than the astrometric displacement typically caused by an Earth-size exoplanet in the habitable zone, which is about 1-4 micro-AU for long-lived main-sequence stars. Only for stars with extremely low photometric variability (< 0.5 mmag) and low magnetic activity, comparable to that of the Sun, will the astrometric jitter be of the order of 1 micro-AU, sufficient to allow the astrometric detection of an Earth-sized planet in the habitable zone. While stellar surface structure may thus seriously impair the astrometric detection of small exoplanets, it has in general a negligible impact on the detection of large (Jupiter-size) planets and on the determination of stellar parallax and proper motion. From the starspot model we also conclude that the commonly used spot filling factor is not the most relevant parameter for quantifying the spottiness in terms of the resulting astrometric, photometric and radial velocity variations.