Modeling Complete Distributions with Incomplete Observations: The Velocity Ellipsoid fromHipparcosData

[abridged] A "missing data" algorithm is developed to model (ie, reconstruct)the three-dimensional velocity distribution function of a sample of stars usingdata (velocity measurements) every one of which has one dimension unmeasured(the radial direction). It also accounts for covariant measurementuncertainties on the tangential velocity components. The algorithm is appliedto tangential velocities measured in a kinematically unbiased sample of 11,865stars taken from the Hipparcos catalog. The local stellar velocity distributionfunction of each of a set of 20 color-selected subsamples is modeled as amixture of two three-dimensional Gaussian ellipsoids of arbitrary relativeresponsibility. In the fitting, one Gaussian (the "halo") is fixed at the knownmean velocity and velocity variance tensor of the Galaxy halo, and the other(the "disk") is allowed to take arbitrary mean and arbitrary variance tensor.The mean and variance tensor (commonly the "velocity ellipsoid") of the diskvelocity distribution are both found to be strong functions of stellar color,with long-lived populations showing larger velocity dispersion, slower meanrotation velocity, and smaller vertex deviation than short-lived populations.The local standard of rest (LSR) is inferred in the usual way and the Sun'smotion relative to the LSR is found to be(U,V,W)_{\odot}=(10.1,4.0,6.7)+/-(0.5,0.8,0.2) km/s. Artificial data sets aremade and analyzed, with the same error properties as the Hipparcos data, todemonstrate that the analysis is unbiased. The results are shown to beinsensitive to the assumption that the velocity distributions are Gaussian.Comment: ApJ accepted for publicatio