The velocity distribution of nearby stars from Hipparcos data I. The significance of the moving groups
We present a three-dimensional reconstruction of the velocity distribution of nearby stars (<~ 100 pc) using a maximum likelihood density estimation technique applied to the two-dimensional tangential velocities of stars. The underlying distribution is modeled as a mixture of Gaussian components. The algorithm reconstructs the error-deconvolved distribution function, even when the individual stars have unique error and missing-data properties. We apply this technique to the tangential velocity measurements from a kinematically unbiased sample of 11,865 main sequence stars observed by the Hipparcos satellite. We explore various methods for validating the complexity of the resulting velocity distribution function, including criteria based on Bayesian model selection and how accurately our reconstruction predicts the radial velocities of a sample of stars from the Geneva-Copenhagen survey (GCS). Using this very conservative external validation test based on the GCS, we find that there is little evidence for structure in the distribution function beyond the moving groups established prior to the Hipparcos mission. This is in sharp contrast with internal tests performed here and in previous analyses, which point consistently to maximal structure in the velocity distribution. We quantify the information content of the radial velocity measurements and find that the mean amount of new information gained from a radial velocity measurement of a single star is significant. This argues for complementary radial velocity surveys to upcoming astrometric surveys.