## 3. Comparison## 3.1. MethodWe compare the proper motions in the different catalogues by examining the normalized proper-motion difference in Right Ascension (RA) and Declination (Dec) for each pair of catalogues. We define the normalized proper motion difference as where and
are the proper motions in either RA
or Dec in catalogues because (the real proper motion of the same star). For the standard deviation of we find which should equal unity when the quoted errors
and
in the catalogues reflect the real
errors and
, respectively. However, when the
proper-motion errors in catalogue The normalized proper-motion difference distribution should in principle be a normal distribution with zero mean and unit variance. Any deviations from this distribution are indicative of systematic errors in the catalogues or systematic differences between catalogues. To obtain the mean and standard deviation of the observed distribution we determine the best fitting Gaussian using a maximum likelihood scheme. Stars deviating more than five times the width (from the 16th to the 84th percentile) of the were rejected before the fit. For each pair of catalogues we calculate
for all stars in common between the
two catalogues (), and for all stars
in common between the two catalogues which are also contained in the
HIP Catalogue (). To construct
we use the formal errors of the
individual stars as quoted in the Catalogues. The comparison is done
for each Astrographic Catalogue Declination zone to detect any zonal
dependence of the results. Furthermore, to investigate if any
magnitude effect is present in , we
also divide the sample into four magnitude intervals: (1) all
magnitudes, (2) bright stars ( mag),
(3) intermediate stars ( mag), and
(4) faint stars ().
is one of the broad-band filters of
the Tycho experiment, and is similar to the Johnson ## 3.2. ResultsFig. 1 and Fig. 2 show the mean and standard deviation of resulting from the Gaussian fits. We first discuss the zone-independent results and then report on some peculiar zones.
## 3.2.1. Underestimation of ACT proper-motion errorsThe third panel of Fig. 2 shows that the standard deviation of
is larger than unity for all zones
but one. Using
mas yr
Since the binaries have been treated differently in the ACT than in
TRC construction we investigate wether the large standard deviations
might be caused by binary contamination. We remove all HIP and TYC
entries with the slightest indication of
duplicity The standard deviations of the distribution are mostly consistent with unity, except for declinations between and . Nine of the 20 zones of the distribution have standard deviations larger than unity while for the distribution this is the case for 19 of the 20 zones. ## 3.2.2. Faint Tycho starsThe and standard deviations show a very dramatic trend with magnitude (see Fig. 2). This trend is similar for all zones. Fig. 2 shows that the samples of faint stars, and therefore also the complete samples, have standard deviations on the order of 1.6 whereas the bright and intermediate samples have standard deviations close to unity. The typical errors in the Tycho Catalogue are an order of magnitude larger than those in the TRC and ACT, and therefore dominate the normalized proper-motion difference distribution. This means that the faint stars in the TYC Catalogue have underestimated proper-motion errors up to 40% (Eq. (4)). We do not see these large standard deviations in the faint sample of the and distributions. The standard errors of the proper motions given in the Tycho catalogue are known to be underestimates for the faint stars (see ESA 1997: Vol. 1 p. xv and p. 142 and Vol. 4 Sect. 18.5). ## 3.2.3. Systematic differences between TRC and ACTThe mean values of the
distribution show a large scatter around zero (see Fig. 1). For
13 of the 20 zones the mean of in
either RA or Dec differs by more than 0.1 from zero (see also
Fig. 3 for an example). Assuming typical errors of
3 mas yr ## 3.2.4. TRC and ACT correlatedThe standard deviations for and are systematically smaller than unity, with only a few exceptions. This is indicative of a correlation between the proper motions in the catalogues. This comes as no surprise as both catalogues originate from the same material, the Astrographic Catalogue and the Tycho Catalogue, and have been constructed in a similar manner. and are independent of magnitude except for the Cape zone (see Sect. 3.2.5). ## 3.2.5. Peculiar zonesOnly two of the 20 zones show some peculiarities. These are the Cape and Vatican zones. The Cape zone is peculiar in that the standard deviations of its distributions show a magnitude dependence which is not present in any of the other zones. The trend with magnitude is similar to that found for the and distributions. The normalized proper-motion difference distributions for other catalogue pairs in the Cape zone do not show any peculiarities. The Vatican zone is special in the sense that it has large standard deviations. While most of the zones have standard deviations close to unity, the standard deviation of the Vatican zone is as large as 1.5. The Vatican zone also has one of the largest standard deviations. The other catalogue comparisons for the Vatican zone do not show any deviating characteristics. We do not know what caused these peculiarities in these two zones. The median epochs are 1903 for the Cape zone and 1909 or the Vatican zone. The peculiarities can thus not be due to a small epoch difference for these two zones. © European Southern Observatory (ESO) 2000 Online publication: July 27, 2000 |