The combination of ground-based astrometric compilation catalogues with the HIPPARCOS Catalogue II. Long-term predictions and short-term predictions

The combination of ground-based astrometric compilation catalogues, such as the FK5 or the GC, wit]l the results of the ESA Astrometric Satellite HIPPARCOS produces for many thousands of stars proper motions which are significantly more accurate than the proper motions derived from the HIPPARCOS observations alone. In Paper I (Wielen, et al. 1999, A&A, 347, 1046) ive have presented a method of combination for single stars (SI model. The present Paper II derives a combination method which is appropriate for an ensemble of apparently single-stars which contains undetected astrometric binaries. In this case the quasi-instantaneously measured HIPPARCOS proper motions and positions are affected by cosmic errors, caused by the orbital motions of the photo-centers of the undetected binaries with respect to their center-of-mass. In contrast, the ground-based data are mean values obtained from a long period of observation. We derive a linear long-term prediction (LTP mode) for epochs far from the HIPPARCOS epoch TH similar to 1991.25, and a linear short-term prediction (STP mode! for epochs close to TH. The most accurate prediction for a position at an arbitrary epoch is provided by. a smooth, non-linear transition from the STP solution to the LTP solution. We present an example for the application of our method, and we discuss the error budget of our method for the FK6 (a combination of the FK5 with HIPPARCOS) and for the combination catalogue GC+HIP. For the basic fundamental stars, the accuracy of the FK6 proper motions in the LTP mode is better than that of the HIPPARCOS proper motions (taking here the cosmic errors into account) by a factor of more than 4.