Astrometric radial velocities II. Maximum-likelihood estimation of radial velocities in moving clusters

Accurate proper motions and trigonometric parallaxes of stars in nearby ope n clusters or associations permit to determine their space motions relative to the Sun, without using spectroscopy for their radial-velocity component . This assumes that the member stars share the same mean velocity vector, a part from a (small) random velocity dispersion. We present a maximum-likeli hood formulation of this problem and derive an algorithm for estimating the space velocity and internal velocity dispersion of a cluster using astrome tric data only. As a by-product, kinematically improved parallaxes and dist ances are obtained for the individual cluster stars. The accuracy of the me thod, its robustness, and its sensitivity to internal velocity fields, are studied through Monte Carlo simulations, using the Hyades as a test case. F rom Hipparcos data we derive the centroid velocity and internal velocity di spersion of the Hyades cluster. The astrometric radial velocities are obtai ned with a standard error of 0.47 km s(-1) for the cluster centroid, increa sing to about 0.68 km s(-1) for the individual stars due to their peculiar velocities. If known binaries are removed, this improves to 0.60 km s(-1).