8.4.2 Quality control of Astrometry

The different filters used in the astrometric reduction and that filter out complete transits, with a code for further referencing, are listed in Table 8.7. Filters that did not reject a single transit are omitted from this list.

All these filters will remove complete transits with all their positions. They are listed in the sequence in which they are encountered in the pipeline. Transits thus filtered out leave no trace in the catalogue.

Table 8.8 lists, per filter and per magnitude bin, how many transits were filtered out in the astrometric reduction. A magnitude bin $n$ is to be understood as the range from $n-0.00005$ to $n+0.99995$. The first line lists the number of transits at input for each magnitude bin; the last line lists the number of transits at output. The last column gives the total for all magnitude bins.

Table 8.9 lists, per filter and per magnitude bin, which percentage of the remaining (after all previous filters were applied) transits were filtered out in the astrometric reduction. The last line combines the numbers for all filters together. The last column gives the total for all magnitude bins.

We see that filters at transit level reject only a small number of transits, if we take into account that filter T-13 is in fact the result of filtering at CCD level, see Subsection 8.4.2. At input, 3 496 067 transits were received for the astrometric reduction and, at output, there were 3 218 410 transit left, which means a rejection rate of 7.9 %.

The different filters used in the astrometric reduction and that filter out individual positions, with a code for further referencing, are listed in Table 8.10. Again, filters that did not reject a single position are omitted from this list. Note that filters that act on complete transits, in fact also filter out all the positions from those transits. Therefore, in the tables with the effect of filtering at CCD level, also the filters acting on complete transits are listed.

These filters are listed in the sequence in which they are encountered in the pipeline, with a common numbering for transit-based filters and CCD-based filters. Individual positions thus filtered out are no longer present in the catalogue. However, if the corresponding transit is still present, astrometric_outcome_ccd gives a code for all CCDs of the transit, also those that have been rejected, so that the user can check why a particular position has been rejected.

Table 8.11 lists, per filter and per magnitude bin, how many positions were filtered out in the astrometric reduction. Again, a magnitude bin $n$ is to be understood as the range from $n-0.00005$ to $n+0.99995$. The first line lists the number of positions at input for each magnitude bin, the last line the number of positions at output. The last column gives the total for all magnitude bins. Transit-based filters are also mentioned, since they effectively remove all the remaining positions of the transit. Filters are listed in the sequence they are encountered in the software. Note that SM positions had already been discarded right from the start and are not taken into consideration in these numbers.

Table 8.12 lists, per filter and per magnitude bin, which percentage of the remaining (after all previous filters were applied) positions were filtered out in the astrometric reduction. The last line combines the numbers for all filters together. The last column gives the total for all magnitude bins.

We see that most filters tend to reject more brighter objects than fainter objects. The big exception is filter C-08, which filters more faint objects. We also see that filter T-13, which seemed to filter out a lot of transits, in fact, removes only few positions. This is because transits removed by filter T-13 had only 0 or 1 position left. At input, the astrometric reduction module received 30 958 007 positions in the focal plane, including those without derived centroid. This comprises 9 AF positions for rows 1–3 and 5–7, and 8 AF positions for row 4. At output, the astrometric reduction module produced 23 368 616 positions in the sky, which corresponds to a rejection rate of 24.5 %. Rejected positions are mainly those for which the SSO had left the transmitted window or where the object was too close to the window border to produce a reliable position.

In the case of 2D windows, we have also the full positional information in the AC direction. All objects brighter than magnitude 13 will, in principle, have 2D windows (note that this concerns only a small proportion of all transits), but also a limited number of faint objects will have 2D windows. One can also wonder whether, for faint objects, the behaviour in AL is the same for those with 1D or 2D windows.

Table 8.13 gives, for each magnitude bin, the number of 2D positions at input of the astrometric reduction. Note the small numbers in the magnitude range 13–18, so that statistics in this magnitude range will not tell us a lot.

Figure 8.27 and Figure 8.28 give the random-type and systematic-type residuals divided by their computed dispersion, restricted to 2D windows. Comparison with Figure 8.18 and Figure 8.22 gives immediately that AL residuals behave the same for 1D and 2D windows.

Figure 8.29 and Figure 8.30 give the RAND residuals in AC for 2D windows and the same residuals divided by their computed uncertainty. We see a behaviour very similar to the RAND residuals in AL. However, looking at the scale we see immediately that residuals in AC are a lot larger than residuals in AL for comparable magnitude. This has of course to do with the larger pixel size in AC.

Figure 8.31 and Figure 8.32 give the SYST residuals in AC for 2D windows and the same residuals divided by their computed uncertainty. Here we notice some unexplained features: for faint objects, the residuals are substantially larger than expected (this is the reverse of AL), whereas we see also an asymmetry in the residuals, which is more pronounced for faint objects than for bright objects.

Table 8.14 lists the performance of the different filters for 2D windows in the same way as Table 8.12 for the complete population. Comparison of the two tables shows that the global picture is the same for 1D and 2D windows with the exceptions that, for faint objects, filter C-08 hardly filters out any 2D windows, whereas the reverse is true for filter C-10.

In Gaia DR2, truncated windows (see Section 1.1.3) were rejected as having unreliable positions. However, in Gaia DR3, the truncated windows are less of a problem than initially thought. To check this, the residuals of truncated windows were analysed.

After looking at the epochs, it turned out that three different lists could be set up of transits labelled with the truncated windows code:

• •

  List 1 composed of all transits with epochs in the range 2015 May 08.33926–12.47973, 13 293 transits in total;

• •

  List 2 composed of all transits of row 5 with epochs in the range 2015 Apr 11.37156–12.40084, 484 transits in total;

• •

  List 3 composed of all other transits with the bits for truncation set, 1759 transits in total.

Lists 1 and 2 probably do not contain really truncated windows but were the result of VPU parameter adjustments (see Section 1.1.3). List 3 is probably the only list of transits with really truncated windows and contains less than 0.1 % of all transits. It is not the intention to give all the pictures for all the residuals for each of these lists. We just give as an example Figure 8.33, showing the SYST residuals in AL divided by their expected value for truncated windows of List 3. Note that the expected value of the residual does not depend on the fact whether the window is truncated or not. Since all truncated windows are fainter than magnitude 14, corresponding for a vast majority to 1D windows, AC residuals will not tell us anything interesting.

In List 3, the SYST residuals in AL are a bit larger than in the complete sample. But, apart from that, we see no significant difference between the AL residuals of the truncated windows and those of the complete list. Especially, in List 1, the RAND residuals follow rigourously the same distribution.

Table 8.15 gives, per magnitude bin, the performance of each position-based filter. Comparison with Table 8.12 shows that most filters behave in the same way for the truncated windows as for the non-truncated windows, with, however, one major exception, filter C-09. It shows a clear correlation between the presence of transits marked as having truncated windows and poor attitude.

The conclusion from this analysis is that there is no good reason to reject truncated windows.

Another way to assess the quality of the positions is to compare the motions of the SSOs as derived from the fit of a linear motion to the positions of single transits to those from a priori ephemerides. These ephemerides are derived from observations spread over many years, and hence motions from ephemerides will be much more accurate than motions derived from a single transit spanning only about 40 s, even if these positions are individually of much higher accuracy than those used for the ephemerides. In what follows, we assume that there is no error in the motions from the ephemerides, and that all differences between the motions from the ephemerides and those from the Gaia observations reflect the errors and the uncertainties of the Gaia observations.

From the uncertainties on the individual positions, one can derive a theoretical uncertainty in the motions. These uncertainties are computed as follows. Let $t_i$ be the epoch of position $i$ of the transit, ${𝒙}_i$ the corresponding position as a vector with two components, AL and AC, ${𝐖}_i$ the weight matrix of the position, i.e., the inverse of the covariance matrix of the random uncertainty (systematic errors do not influence the derived motion of an object), $v$ the square of the inverse of the uncertainty on the timing, which is supposed to be the same for all timings, ${\sum }_i$ the summation over all positions of the transit that have not been removed by any of the filters, and let Tr be the trace of the matrix. Compute as follows:

Then, $𝒃$ is the motion of the SSO derived from the fit of a linear motion to the positions, and ${\sigma }^2\{𝒃\}$ is its covariance matrix. In an (AL, AC) coordinate system, there is no correlation between the AL and AC motions, so that we can take the square root of its diagonal elements to get the uncertainties.

Figure 8.34 and Figure 8.35 show the difference between the motion derived in the astrometric reduction and the motion from the ephemerides as a function of magnitude. The motion is in milliarcseconds per second (mas s${}^{-1}$) . Note that typical values for the motion of an SSO observed by Gaia are of the order of 0–10 mas s${}^{-1}$. Quite expected, we find a minimum around magnitude 14 with differences of the order of 0.01 mas s${}^{-1}$. There is no more systematic offset, except that for very faint objects there is a systematic offset of only $-$0.008 mas s${}^{-1}$, which is really small.

Figure 8.36 shows the same difference in motion in AL divided by its computed uncertainty as given by Equation 8.38. We see that the behaviour of the difference is close to the expected behaviour, where for faint objects the difference is a bit smaller than expected and for bright objects a bit larger, but overall there is a rather good agreement with the expectations, and the asymmetry that was present in previous studies, has disappeared. It is thought that this is thanks to the application of the correct geometric calibration, as explained in Subsection 8.3.3.

The same exercise can be done in AC, but only for 2D windows. This is given in Figure 8.37 for the absolute difference and in Figure 8.38 for the relative difference. The figures are restricted to the magnitude range 8–13, because outside this range there are not enough transits with 2D windows to do the statistics. Results are comparable to those in AL.