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Astrometric radial velocities
II. Maximum-likelihood estimation of radial velocities in moving clusters *
Soren Madsen and
Received 1 September 1999 / Accepted 10 February 2000
Accurate proper motions and trigonometric parallaxes of stars in nearby open 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, apart from a (small) random velocity dispersion. We present a maximum-likelihood formulation of this problem and derive an algorithm for estimating the space velocity and internal velocity dispersion of a cluster using astrometric data only. As a by-product, kinematically improved parallaxes and distances are obtained for the individual cluster stars. The accuracy of the method, its robustness, and its sensitivity to internal velocity fields, are studied through Monte Carlo simulations, using the Hyades as a test case. From Hipparcos data we derive the centroid velocity and internal velocity dispersion of the Hyades cluster. The astrometric radial velocities are obtained with a standard error of 0.47 km s-1 for the cluster centroid, increasing 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.
Key words: methods: data analysis techniques: radial velocities astrometry stars: distances stars: kinematics Galaxy: open clusters and associations: general
Online publication: April 17, 2000