3 Data analysis

Although the internal accuracy of the measurements is not affected, to first order, by the number of reference stars, the orientation of the obtained local frame would be. This was shown by the experimental solutions based on Hipparcos stars only. To obtain a sufficient number of those, it would be required to extend the observation too long, risking to be trapped by anomalous refraction. Therefore, the reductions were made relatively to the three densest, precise catalogues, ACT, Tycho and TAC. We point that due to the inhomogeneity of TAC, one field (of the star UX Com) could not be reduced, because there were only a few (3) reference stars on it.

Figure 2 compares the observed minus catalogue offsets. All distributions display a normal characteristic. The ACT histogram (dashed line) shows the largest degree of peakness, while the Tycho histogram (solid line) shows the most pronounced side tails. The kurtosis follows the degree of proper motion precision. The TAC histogram (dotted line) confirms the inherent precision of the catalogue data and the good quality of its supplement of proper motions.

  

Figure 2: Right ascension and declination observed minus catalogue distribution. The reference stars with more than two used observations contribute to the plot as in Fig. 1. ACT solution ($\sigma_{\alpha}$ = 0$\hbox{$.\!\!^{\prime\prime}$}$09; $\sigma_{\delta}$ = 0$\hbox{$.\!\!^{\prime\prime}$}$11) is displayed by the dashed line, Tycho solution ($\sigma_{\alpha}$ = 0$\hbox{$.\!\!^{\prime\prime}$}$29; $\sigma_{\delta}$ = 0$\hbox{$.\!\!^{\prime\prime}$}$26) by the solid line and TAC solution ($\sigma_{\alpha}$ = 0$\hbox{$.\!\!^{\prime\prime}$}$13; $\sigma_{\delta}$ = 0$\hbox{$.\!\!^{\prime\prime}$}$16) by the dotted line, with $\sigma$ being the standard-deviation

In Fig. 3 the distributions of the standard error on the final position of the program radio stars are presented, according to magnitude, number of field reference stars and number of observations. The distributions are only presented relatively to the ACT reductions, since the results for the other catalogues are similar (as shown by Fig. 1).

Within the instrumental optimal range of magnitude there is no apparent variation of precision. The noticeable exception is HBC652, in the outskirts of the optimal range. We must however, point that for HBC652 there were also a small number of reference stars and observed nights. There appears to be no loss of precision when the number of reference stars is larger than a tens or so. The largest errors in the plot pertain to HBC652, discussed above. Finally, it seems that usually 5 observations are sufficient to attain good internal precision, without the need of a numerous series.

  

Figure 3: Error distribution. Open circles refer to right ascension and filled circles to declination

As also apparent in Figs. 1 and 2, right ascensions are, in general, slightly better determined than declinations.