Efficient Calculation of Covariances for Astrometric Data in the Gaia Catalogue

Abstract

For users of the Gaia astrometric catalogue it will be essential to have access to the covariance between any pair of astrometric parameters when computing quantities that combine multiple catalogue parameters. The computation and storage of the full covariance matrix for the expected 5 ×10⁹ astrometric parameters (∼10⁸ TeraByte) is, however, expected to be infeasible considering near-future storage and floating-point capabilities. In this paper we describe (without going into the mathematical details) how the covariance of arbitrary functions of the astrometric parameters can be estimated in a computationally efficient way from a reduced amount of data (∼ 2 TeraByte). We also include two examples, explaining how to practically compute the covariance for the average parallax of a star cluster and the acceleration of the solar system barycentre in a cosmological frame.