Astrometry with ALMA: a giant step from 0.1 arcsecond to 0.1 milliarcsecond in the sub-millimeter

We discuss astrometric capabilities of the future interferometer ALMA that will be located at a high altitude site (5000m) in Northern Chile to operate in the sub-millimeter range. In this paper, we estimate the astrometric precision of ALMA to be ~0.18 milliarcsecond at the optimum observing frequency of 345 GHz from an error budget including the thermal noise and the systematic errors caused by uncertainties in antenna coordinates, reference source coordinates, Earth orientation parameters, dry atmosphere parameter and by phase fluctuations due to moisture above the site. We briefly discuss three applications: first, astrometric search of exoplanets around 446 nearby stars detectable by ALMA; second, proper motions and parallaxes of pre-stellar cores and protostars; third, the rotation rate of the debris disk around ε Eri to test the theory of dust trapping in mean motion resonances with unseen planets.