7 Final proper motions

  The data from the 27 individual photographic plates and the CCD pseudo-plate were introduced into the ICOA (Sect. 4) in order to determine relative proper motions. Since magnitude effects had been previously removed (Sect. 6), the plate-to-plate transformations included only the geometrical part of the plate models shown in Eqs. (4) and (5) (Q_x=Q_y=0).

7.1 Weighting system

  The heterogeneity of our astrometric material requires a careful weighting system, in order to combine all the data in the same process. We devised a somewhat sophisticated weighting system, to take into account the different plate scales, the possible different astrometric quality of plates obtained with the same telescope but with different emulsions (i.e., grain sizes) or in different seeing and guiding conditions, and to distinguish the intrinsically different accuracy of measurements of stars very different in brightness on the same plate.

As described in Sect. 6.2, for the determination and correction of inter-plate magnitude equations, plates were averaged in groups of equal epoch. Three modern Schmidt plates were transformed into the master plate magnitude equation system and averaged with it (Sect. 6.2.1). When computing the relative magnitude equation from each of these source plates to the master one, the dispersion around the magnitude equation was evaluated as a function of magnitude. The functions describing these dispersions, transformed to the master plate scale, were used for assigning magnitude-dependent weights to the stars in each modern epoch source plate. The master plate was individually compared to the CCD pseudo-plate, and the dispersion around this transformation was used for weighting purposes. For the CCD pseudo-plate, weights were assigned considering the dispersion of the positions in the zones overlapped among different CCD fields, in the master plate scale, as a function of magnitude.

Old epoch plates were averaged in groups before transforming them into the average modern plate for computing their magnitude equation (Sect. 6.2.3). The dispersion of the transformation inside each old epoch group, transformed to the master plate scale, was used for assigning magnitude-dependent weights to the star positions from these plates.

7.2 Some details about the calculation

Five iterations of the ICOA (Sect. 4) were enough for stabilizing the final proper motions. The transformation-crossing loop (Sect. 4.1) was, by far, the most time-consuming step of the whole procedure. Only two internal iterations of the transformation-crossing loop (three at most, in some cases) were needed for all plates in all the ICOA iterations.

  

Table 5: Stars detected in each plate, and number of rejections in the calculation of proper motions in the last ICOA iteration

When performing the fits of Eqs. (6) and (7) for computing the proper motions, some star positions were rejected by the 3$\sigma$ clipping criterion. The different quality of the plates lead to clear tendencies in this rejection. Table 5 displays the statistics of detected and rejected points for each astrometric plate in this calculation step for the last ICOA iteration. As can be seen, the Heidelberg and several of the Astrographic Catalog plates are the less accurate from the astrometric point of view.