# 3.5.7 Correlations in the Gaia data

Author(s): Lennart Lindegren

Correlations among the astrometric data exist on several different levels, e.g.:

• within-source correlations (between the different astrometric parameters of the same source);

• between-source correlations (between the same astrometric parameter, e.g. parallax, for different sources);

• general correlations (between arbitrary astrometric parameters of different sources).

Within-source correlations are always provided, when relevant, in the Gaia Archive. They are estimated from the $5\times 5$ normal matrix of the individual sources. Because they are computed by neglecting the between-source correlations, they are only approximations of the actual within-source correlations, but probably sufficiently good for all astrophysical applications. They are principally needed when transforming the five astrometric parameters to other representations (e.g. calculation of galactic coordinates, tangential velocity, or epoch transformation).

Between-source correlations are important when calculating quantities that depend on several sources, such as the mean parallax or internal kinematics of a stellar cluster. In the final Gaia data such correlations are expected to be important mainly on small angular scales (less than a few degrees), but in Gaia DR2 they could exist on much larger angular scales (tens of degrees).

Between-source correlations and general correlations are much harder to estimate than the within-source correlations, principally because their rigorous calculation would involve the inversion of extremely large matrices. Approximate methods to estimate general correlations exist (e.g. Holl and Lindegren 2012; Holl et al. 2012a) but have not been implemented in the Gaia data processing. Empirically, the between-source correlations can be estimated by analysing the spatial correlations of the astrometric residuals, or from statistical analysis of the parallaxes and proper motions for distinct groups of sources, such as in stellar clusters and quasars. For Gaia DR2 the between-source correlations have not been extensively studied but they are believed to be very significant and arising mainly from modelling errors in the attitude or instrument. A limited correlation study of the astrometric residuals in Gaia DR2 is reported in Section 5.4 of Lindegren et al. (2018).