An algorithm is developed to model the three-dimensional velocity distribution function of a sample of stars using only measurements of each star ’ s two-dimensional tangential velocity .
The algorithm works with “ missing data ” : it reconstructs the three-dimensional distribution from data ( velocity measurements ) every one of which has one dimension unmeasured ( the radial direction ) .
It also accounts for covariant measurement uncertainties on the tangential velocity components .
The algorithm is applied to tangential velocities measured in a kinematically unbiased sample of 11,865 stars taken from the Hipparcos catalog , chosen to lie on the main sequence and have well-measured parallaxes .
The local stellar velocity distribution function of each of a set of 20 color-selected subsamples is modeled as a mixture of two three-dimensional Gaussian ellipsoids of arbitrary relative responsibility .
In the fitting , one Gaussian ( the “ halo ” ) is fixed at the known mean 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 disk velocity distribution are both found to be strong functions of stellar color , with long-lived populations showing larger velocity dispersion , slower mean rotation velocity , and smaller vertex deviation than short-lived populations .
The local standard of rest ( LSR ) is inferred in the usual way and the Sun ’ s motion relative to the LSR is found to be ( U,V,W ) _ { \odot } = ( 10.1 , 4.0 , 6.7 ) \pm ( 0.5 , 0.8 , 0.2 ) ~ { } \mathrm { km s ^ { -1 } } .
Artificial data sets are made and analyzed , with the same error properties as the Hipparcos data , to demonstrate that the analysis is unbiased .
The results are shown to be insensitive to the assumption that the velocity distributions are Gaussian .