Structure and colour-magnitude diagrams of Scorpius OB2 based on kinematic modelling of Hipparcos data

All stars in a 'moving group' share the same space motion. The presence of such a coherent structure in velocity space can be used to derive (improved) estimates of the stellar parallaxes from the observed positions and proper motions. A Lund Observatory group (Dravins et al.) describes an elegant and sophisticated maximum likelihood procedure to do so using Hipparcos data. Their method determines the cluster centroid space motion, the internal velocity dispersion, which is assumed to be isotropic, and the individual model parallaxes for all member stars, implicitly using the assumption of a 'compact' cluster with a 'small' velocity dispersion. We implement the Lund procedure, and test it extensively using Monte Carlo simulations. We discuss the effects on the derived parallaxes of a 'large' velocity dispersion, as measured for physically extended, 'loose' OB associations. We also investigate the influence of an overall expanding motion, which is relevant to such unbound groups. We conclude that the method is robust against all systematic effects that we considered, except for the maximum likelihood estimate of the one-dimensional internal velocity dispersion sigma(v), which is always underestimated. The model parallax accuracies are limited by the internal velocity dispersion for nearby groups (mean distance D less than or similar to 50-150 pc, depending on Galactic longitude). We present an application to the nearby association Scorpius OB2, which consists of the three subgroups Upper Scorpius (mean distance 145 pc), Upper Centaurus Lupus (140 pc), and Lower Centaurus Crux (118 pc). Membership of these groups has recently been established by de Zeeuw et al. using Hipparcos data. The resulting model parallaxes are (1) statistically consistent with and (2) more precise by a factor of similar to 2 than the Hipparcos trigonometric parallaxes; they (3) significantly narrow the locus of stars in the (B-V)(0)-M-V0 colour-absolute magnitude diagram, and (4) define a single-star main sequence which is consistent with Mermilliod's zero-age main-sequence calibration. We find, after bias correction based on Monte Carlo simulations, that sigma(v)less than or similar to 1.0-1.5 km s(-1) for all three subgroups; these values are confirmed by the statistics of the residual (mu(perpendicular to)) proper motion components. Whereas, as a result of their consistency with the Hipparcos values, the model parallaxes do not improve significantly upon the mean association distances derived by de Zeeuw et al. from Hipparcos trigonometric parallaxes, they do resolve the parallax distribution, and thus the spatial structure, for Upper Centaurus Lupus and Lower Centaurus Crux.