Principles of statistical astrometry

We present a coherent scheme of ‘statistical astrometry’ for high-precision measurements. Statistical astrometry provides methods and tools for treating quantitatively the overall statistical effect of the presence of many individually unresolved or unmodelled astrometric binaries in a stellar ensemble. The non-linear motions of the photo-centers of these binaries give rise to deviations from long-term linear motions. These deviations may be called ‘cosmic errors’, since they represent a source of ‘noise’ (in addition to measuring errors) with respect to the assumed linear motions of the stars. For bright HIPPARCOS stars, the cosmic errors are on average larger than the measuring errors of the ‘instantaneous’ positions and proper motions of these stars. Basic tools of statistical astrometry are correlation functions between the orbital displacements in position and velocity relative to the mean motions of the stars. We present methods for calculating the mean errors of stellar positions predicted on the basis of measured instantaneous data or of mean data, including the cosmic errors. We discuss the comparison of astrometric catalogues, containing either instantaneous data or mean ones, the question of using acceleration terms, the treatment of ‘averaged’ observational data, and some problems connected with the determination and the behaviour of the correlation functions. Our general conclusion is that in high-precision astrometry, the effect of the cosmic errors is often dominant with respect to the measuring errors and should therefore be treated properly.