The Parameters of Galactic Kinematics Determined from Total Least Squares

Abstract

Problems of Galactic kinematics have usually been solved by the method of least squares, but this may lead to biased results because least squares assume that error resides only in the observations, not in the equations of condition. The latter, however, generally incorporate error, at least in some of the columns of the data matrix. Total least squares represents the ideal mathematical tool for just this sort of problem. In this paper, the method, or better stated a mixed total-ordinary least squares method, is applied to over 100,000 stars taken from the Hipparcos catalog to calculate twelve parameters of Galactic kinematics: the nine components of the deformation tensor, related to such quantities as the Oort A and B parameters, the K term, Galactic vorticity, and the Solar motion. Reasonable values for all of these is obtained, showing that high quality astrometric data and an adequate reduction method can produce good results for global solutions when in the past this proved difficult or impossible.