6 Proper motions quality assessment

  To derive truly external error estimates of the final TRC proper motions would require an independent set of proper motions of comparable (or better) quality. The only catalogue satisfying the quality requirement - the Hipparcos Catalogue - was used for the AC reduction. It is therefore unsuitable for the purpose, due to the correlation with TRC. Under such circumstances, the only reasonable approach is to estimate the external errors as a combination of the internal standard errors and estimated residual systematic errors.

The internal error estimates (cf. Sect. 5.1) assess the random errors of the proper motions, plus a portion of the residual plate-scale systematic errors. The rms value of the internal estimates is 2.3 mas/yr per proper motion component.

  

Figure 9: Systematic differences between the final TRC proper motions and the proper motions in the Hipparcos and Tycho Catalogues, in units of mas/yr, as functions of declination. Top row: proper motion differences TRC-Hipparcos for 93078 stars of median magnitude $B_{\mathrm{T}}=9.35$ mag; each point represents the mean of 1000 differences. Middle row: TRC-Tycho for 458601 stars brighter than $B_{\mathrm{T}}=11.25$ mag; each point represents the mean of 5000 differences. Bottom row: TRC-Tycho for 491636 stars fainter than $B_{\mathrm{T}}=11.25$ mag

The comparison of the final TRC proper motions with Hipparcos (Fig. 9, top row) suggests that for bright (median $B_{\mathrm{T}}=9.35$ mag) stars the residual systematic errors do not exceed 0.2 mas/yr. But, of course, this estimate will be too optimistic due to the correlation between TRC and Hipparcos.

Another resource for the estimation of the residual TRC systematic errors, especially for faint stars, is the Tycho Catalogue. Tycho proper motions, though of poor precision, are in the nature of the case tied to the Hipparcos system and should be virtually free from magnitude equation. Unfortunately, the Tycho proper motions have been shown to possess systematic errors depending on ecliptic latitude, with values reaching 1 mas/yr for some latitudes (Høg et al. 1998a). This fact, which actually prevented a direct application of the Tycho proper motions to the correction of the zonal magnitude equation, should be taken into account in the following comparison.

The comparison of the TRC and Tycho proper motions for stars brighter than $B_{\mathrm{T}}=11.25$ mag (Fig. 9, middle row) shows that the systematic errors of TRC at this magnitude are less than 0.5 mas/yr rms. For fainter stars (Fig. 9, bottom row) the comparison suggests that a considerable magnitude equation is still present in the TRC proper motions. Based on the comparison, the residual systematic errors of the TRC proper motions for stars fainter than $B_{\mathrm{T}}=11.25$ mag may be estimated as 1 mas/yr rms.

Summing up, we estimate the external errors of the final TRC proper motions as 2.4 mas/yr per component, by a combination of the internal error estimates (2.3 mas/yr rms) and estimated residual systematic errors (0.5 mas/yr rms at $B_{\mathrm{T}}=11.25$ mag). Nonetheless, we should note the possibility of larger residual systematic errors (up to 2 mas/yr) for the faintest TRC stars in some declination zones.