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Astron. Astrophys. 356, 1119-1135 (2000)

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1. Introduction

In a previous paper (Dravins et al. 1999, hereafter Paper I) three methods were described by which stellar radial velocities can be determined astrometrically, i.e. from geometric measurements independent of spectroscopy. Such astrometric radial velocities are of interest as they allow to disentangle the space motions of the stars from other astrophysical phenomena causing spectroscopic line shifts, such as internal motions in stellar atmospheres and gravitational redshift. In normal stars such shifts are typically less than 1 km s-1. A corresponding accuracy is needed in the astrometric radial velocity to permit useful comparison with spectroscopic data. Two of the methods outlined in Paper I use the progressively changing parallax or proper motion of a star to infer its motion relative to the Sun. Reaching [FORMULA] km s-1 accuracy with these methods requires astrometric observations on the microarcsec accuracy level, currently unavailable but likely to be achieved in future space astrometry programmes.

The third method is based on the changing angular extent of a star cluster as it approaches or recedes from the Sun: the relative rate of apparent contraction equals the relative change in distance. Since the distance is known from trigonometric parallaxes, the radial velocities follow. Only this method can provide sub-km s-1 radial velocity estimates from existing astrometric data. In the present paper we develop a maximum-likelihood (ML) algorithm, first described by Dravins et al. (1997), for estimating the space velocity vector and other kinematic parameters of a cluster. These results can then be used to estimate the radial velocities of individual member stars, simply by projecting the cluster velocity vector onto their lines of sight.

An overview of the method is presented in Sect. 2, followed by the precise mathematical formulation in Sect. 3. Details of the practical implementation are given in Appendix A. The validity of the method is studied in Sect. 4 by means of Monte Carlo simulations, and in Sect. 5 we apply the method to the Hyades cluster as observed by Hipparcos. It is concluded that the method can indeed yield accurate results under realistic assumptions, although special procedures are needed to correctly estimate the internal velocity dispersion of the cluster and the accuracies of the estimated parameters. In a subsequent paper (Paper III: Madsen et al., in preparation) the method is systematically applied to Hipparcos observations of nearby open star clusters.

A by-product of the moving-cluster method is that the distance estimates to the individual cluster stars may be significantly improved compared with the original parallax measurements. As discussed in Paper I (Sect. 6.3), these `kinematically improved parallaxes' can be understood as resulting from a combination of trigonometric and kinematic distance information, where kinematic distances follow from the observed proper motions and the derived cluster velocity.

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© European Southern Observatory (ESO) 2000

Online publication: April 17, 2000