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Astron. Astrophys. 335, L65-L68 (1998)

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3. Verification and quality assessment

The positions of TRC are practically identical to the TYC positions at epoch 1991.25 as already discussed in Sect. 1. The TRC proper motions need, however, an assessment of their quality with respect to random and systematic errors. Presently only three catalogues are suited for this purpose: HIP, TYC and ACT none of which being strictly external to TRC. Based on the quality of the Astrographic Catalogue and the epoch difference to TYC of some 85 years, one cannot hope for a better precision than about 2.5 mas/yr.

3.1. Comparison with the Hipparcos Catalogue

The Hipparcos Catalogue was the primary reference catalogue for TRC and a strong correlation between TRC and HIP proper motions must be expected. Fig. 1 shows the precision and systematic differences of TRC relative to HIP as function of the Tycho blue magnitude, [FORMULA]. Robust estimates have been used. The errors in Fig. 1a were obtained as one half the difference between the 84th and the 16th percentiles in the distribution function corrected for the contribution from HIP, and the systematic differences in Figs. 1b are obtained as median values. The precision of about 2.2 mas/yr which follows from Fig. 1 cannot be expected to represent a valid estimate for the non-Hipparcos stars.

[FIGURE] Fig. 1. Precision and systematic differences of TRC proper motions relative to HIP for [FORMULA] common stars as functions of the Tycho blue magnitude, [FORMULA]. a  Precision; b  Systematic differences. Abbreviation: [FORMULA].

3.2. Comparison with the Tycho Catalogue

The Tycho proper motions were not used in the construction of TRC and constitute the best source for estimating the systematic errors of the TRC proper motions. Such a comparison will be dominated by the rather low precision of the TYC proper motions of about 40 mas/yr, but this is partly compensated by their large number and very small systematic errors with respect to HIP (cf. Fig. 18.3 of Vol. 4 of ESA 1997). Fig. 2 shows the systematic differences, TRC-TYC, of [FORMULA] as a function of declination for stars common to TRC and ACT. Each point represents the trimmed mean value for 5000 stars. The figure confirms that systematic errors, as function of declination or magnitude, are generally below 1 mas/yr, at least for [FORMULA]. A minor part of the small trends as function of declination common for Figs. 2b and 2c (of the order 0.5 mas/yr) may be due to errors in the Tycho proper motion system, but AC is probably the main contributor. The corresponding diagrams (not shown) for [FORMULA] look similar. We conclude that the systematic errors of TRC proper motions are less than about 1.0 mas/yr. For the faintest stars, however, we cannot rule out larger systematic errors, up to 2.5 mas/yr. This is indicated by the differences between Figs. 2b and 2c because a magnitude effect is more likely in AC than in TYC.

[FIGURE] Fig. 2. Systematic differences of the proper motion [FORMULA] in TRC, as function of declination. a  TRC-HIP for [FORMULA] mostly bright stars; b  TRC-TYC for the [FORMULA] stars with [FORMULA] mag; c  TRC-TYC for the remaining fainter [FORMULA] stars.

3.3. Comparison with the ACT catalogue

The TRC and the ACT catalogues have the same aim and are based on the very same observational material, but different strategies were adopted for the reduction of the AC material, the cross identification between TYC and AC and also the initial selection of TYC stars. A comparison between ACT and TRC is of interest because it can tell about errors introduced by the adopted plate models and also errors in the cross identifications.

Although TRC and ACT both contain about [FORMULA] stars, they have only [FORMULA] stars in common. The ACT contains [FORMULA] stars not in TRC and TRC contains [FORMULA] stars not in ACT. These latter are flagged in TRC.

The distribution of differences between TRC and ACT proper motion components is shown in Fig. 3a and the standard deviation in Fig. 3b. The standard deviation, of about 2.65 mas/yr, exceeds the internal standard errors of either catalogue and demonstrates, without the least mercy, the immense importance of the reduction model used. More than [FORMULA] stars (2 per cent) differ more than 10 mas/yr in either [FORMULA] or [FORMULA] (flagged in TRC) and a few differ even by more than 400 mas/yr. This clearly demonstrates the difficulties involved in spanning up to 100 years in a cross identification, which could have been ameliorated by including observations from more epochs.

[FIGURE] Fig. 3. Comparison between TRC and ACT proper motions. a  distribution of differences (note logarithmic scale!); b  standard deviation of the differences.

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© European Southern Observatory (ESO) 1998

Online publication: June 26, 1998