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Register a new userThe Combination of HIPPARCOS Data with Ground-Based Astrometric Measurements
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The combination of HIPPARCOS measurements with suitable ground-based astrometric data improves significantly the accuracy of the proper motions of bright stars. The comparison of both types of data allows us also to identify and to eliminate, at least partially, cosmic errors in the quasi-instantaneously measured HIPPARCOS data which are caused by undetected astrometric binaries. We describe a simple averaging method for the combination of two independent compilation catalogues. The combination of the basic FK5 with HIPPARCOS leads to the Sixth Catalogue of Fundamental Stars (FK6). The accuracy of the FK6 proper motions is higher than that of HIPPARCOS by a factor of about 2 in the single-star mode, and by a factor of more than 4 in the long-term prediction mode which takes cosmic errors into account. We present also the error budget for a combination of the Boss General Catalogue (GC) with HIPPARCOS data. We point out problems with known binaries, and identify an ensemble of astrometrically excellent stars.
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The combination of ground-based astrometric compilation catalogues, such as the FK5 or the GC, with 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 the combination of the basic FK5 with the HIPPARCOS Catalogue (i.e., in the FK6), the gain in accuracy is about a factor of two for the proper motions of single stars. The use of the GC still improves the accuracy of the proper motions by a factor of about 1.2. We derive and describe in detail how to combine a ground-based compilation catalogue with HIPPARCOS. Our analytic approach is helpful for understanding the principles of the combination method. In real applications we use a numerical approach which avoids some (minor) approximations made in the analytic approach. We give a numerical example of our combination method and present an overall error budget for the combination of the ground-based data for the basic FK5 stars and for the GC stars with the HIPPARCOS observations. In the present paper we describe the single-star mode of our combination method. This mode is appropriate for truly single stars or for stars which can be treated like single stars. The specific handling of binaries will be discussed in subsequent papers.
The combination of ground-based astrometric compilation catalogues, such as the FK5 or the GC, with 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) we have presented a method of combination for single stars (SI mode). 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 T_H ~ 1991.25, and a linear short-term prediction (STP mode) for epochs close to T_H. 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 catalog 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.
The statistical test described by Wielen et al.(1994) is used to derive new zero-points of ground-based Cepheid period-luminosity (PL) and period-luminosity-colour (PLC) relations. Eleven relations are compared with the Hipparcos data. Our results argue for a typical increase of the adopted distance scale by about 8% +- 8%. Our zero-point for the PL relation of Caldwell & Laney (1991) is in agreement with that of Feast & Catchpole (1997).
Stochastic field distortions caused by atmospheric turbulence are a fundamental limitation to the astrometric accuracy of ground-based imaging. This distortion field is measurable at the locations of stars with accurate positions provided by the Gaia DR2 catalog; we develop the use of Gaussian process regression (GPR) to interpolate the distortion field to arbitrary locations in each exposure. We introduce an extension to standard GPR techniques that exploits the knowledge that the 2-dimensional distortion field is curl-free. Applied to several hundred 90-second exposures from the Dark Energy Survey as a testbed, we find that the GPR correction reduces the variance of the turbulent distortions $approx12times$, on average, with better performance in denser regions of the Gaia catalog. The RMS per-coordinate distortion in the $riz$ bands is typically $approx7$ mas before any correction, and $approx2$ mas after application of the GPR model. The GPR astrometric corrections are validated by the observation that their use reduces, from 10 to 5 mas RMS, the residuals to an orbit fit to $riz$-band observations over 5 years of the $r=18.5$ trans-Neptunian object Eris. We also propose a GPR method, not yet implemented, for simultaneously estimating the turbulence fields and the 5-dimensional stellar solutions in a stack of overlapping exposures, which should yield further turbulence reductions in future deep surveys.
A comparison was made between $Gaia$ magnitudes and magnitudes obtained from ground-based observations for astrometric radio sources . The comparison showed that these magnitudes often not agree well. There may be several reasons for this disagreement. Nevertheless, such an analysis can serve as an additional filter for verification of the object cross-identification. On the other hand, it can help to detect possible errors in optical magnitudes of astrometric radio sources coming from unreliable or inconsistent data sources.
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