4. The linking to extragalactic reference frame
The optical astrometry results described above overlap partially with the VLBI observations. In order to get the link angles of Hipparcos we use only the last part of our solution, in the interval 1980.0-1992.0. This part is based on 1 350 807 observations of 2 907 different stars. The distribution of these stars on the celestial sphere is shown in Fig. 2
- one can see that the distribution in right ascension is rather good but there is a big asymmetry in declination, due to the geographic distribution of the observatories participating in the project. The magnitude distribution of the observed stars is displayed in Fig. 3.
The VLBI results obtained at different analysis centers and combined by the IERS are used; namely we use the solution IERS C04 that is referred to the prepared ICRS (Arias et al. 1995 ). According to Gambis (1995 ), who made the solution available, the series consists of the observed values after 1984.0 while the data before that date represent a backward extrapolation using the model of Souchay et al. (1995 ). Nevertheless, we made sure that the extrapolated data of C04 series fit well to rather sporadic and less precise VLBI observations made before 1984.0. The solution is given at daily intervals and is slightly smoothed so that it enables a simple linear interpolation to the irregular 5-day epochs of optical astrometry.
The differences between our new optical astrometry solution and IERS C04 (877 values) are then used to calculate the link angles at different epochs using Eqs. (2). Their time evolution is displayed in Fig. 4.
It can be seen from the figure that the third component, , is determined less accurately than the first two, and . It is caused partially by the geographic distribution of the observatories (time is determined with the same accuracy as latitude only by instruments located near the equator), partly by larger systematic errors in measured universal time. The trends in two of the three components are obvious. The trend is especially large in the third component; it is improbably high and, in addition, it differs substantially from the results of other groups working on the same problem by different methods. This leads us to the inevitable conclusion that the value is not constant, in contrast to our original expectations. This can be caused, e.g., by a secular change of the directions of local verticals at some of the observatories with respect to VLBI baselines. Systematic instrumental errors are also not ruled out. Thus we can determine, by this indirect method, only four of the six parameters needed, i.e., , (for an epoch ) and .
The individual values of (corresponding to epochs ) are not determined quite independently, being the result of a preceding least-squares estimation. The inspection of the full variance-covariance matrix shows that the only significant correlations exist between and for (i.e., for the values referred to the same epoch) while all the other correlations (like and or and for ) are quite negligible. In agreement with our previous expectations (Vondrák et al. 1992 ), these correlations vary with semi-annual period, typically within the range , only exceptionally reaching as much as 0.25. We take namely these correlations into account when calculating full (i.e., not diagonal) weight matrix, used for the subsequent least-squares estimation. Linear regression is used to estimate the values of orientation angles at an epoch and their rates , using the weights of individual points and correlations coming from the optical astrometry solution.
An analysis of the results shows that the most accurately determined values of are achieved for the mean epoch of common observations of optical astrometry with VLBI, i.e., (). In this case, the angles and rotations are practically de-correlated, the rotations being independent of the choice of the epoch . Nevertheless, the requirements imposed by the Hipparcos Science Team lead us to use the mean epoch of Hipparcos, . The results, referred to the final combined link of Kovalevsky et al. (1996 ) are shown in Table 2 ; we do not display the orientation of H37C since it is only one of the several intermediary catalogs used in the process of producing the final Hipparcos catalog and it is not available to general astronomical community. Their standard errors and correlation matrix are also shown.
Table 2. Results of linking (in mas and mas per year), and their correlation matrix. The basic epoch is that of Hipparcos (), the results are referred to the final orientation of Hipparcos catalog
Unfortunately, there is a lack of optical astrometry observations after 1991, what leads to rather large difference between the mean epoch of Hipparcos and that of common observations of VLBI with optical astrometry. Relatively high correlations between () and () and big values of standard errors in are due namely to this difference.
© European Southern Observatory (ESO) 1997
Online publication: July 3, 1998