The Tycho-Gaia Astrometric Solution

Gaia DR1 is based on the first 14 months of Gaia's observations. This is not long enough to reliably disentangle the parallax effect from proper motion. For most sources, therefore, only positions and magnitudes are given. Parallaxes and proper motions were nevertheless obtained for about two million of the brighter stars through the Tycho-Gaia astrometric solution (TGAS), combining the Gaia observations with the much earlier Hipparcos and Tycho-2 positions. In this review I focus on some important characteristics and limitations of TGAS, in particular the reference frame, astrometric uncertainties, correlations, and systematic errors.