6 Error estimation

In order to measure the internal errors of the catalogue, data can be used from the overlap regions and repeat observations. The results of such an analysis are given in Table 2. However, it must be understood that since correlations exist between the data and unaccounted for systematic errors, these measurements will tend to underestimate the true, external, errors of the data.

 

 

Table 2: The median internal and external errors for the CMT. The units for the RA and declination are milliarcsec and those for the magnitudes are millimagnitudes.

Internal
$r'_{\rm CMT}$	RA	Dec	Mag
<13	21	21	16
14	31	26	30
15	55	42	58
16	112	91	124

        

External
$r'_{\rm CMT}$	RA	Dec	Mag
<13	36	37	25
14	45	40	35
15	68	55	70
16	113	90	170

Figure 7: The internal and external positional errors as a function of magnitude. The solid line gives the median external errors and the dashed line shows the equivalent internal errors. RA is shown in red and declination in green.

The measurement of external errors can be problematical since it requires a comparison with another catalogue where the errors are either much smaller, and the residuals yield the external errors directly, or where the errors are very well determined, and can thus be accounted for in the residuals. In the former case, not many such catalogues exist and even in those cases the data is quite sparse, and in the latter, the estimation is dependant on the external errors of the comparison catalogue being reliable.

A comparison of the CMT data has been carried out with respect to Tycho 2, but this did not yield very useful results since it was limited to the brighter end ( $r~^\prime_{\rm CMT}<12$) of the CMT catalogue. Also, the average error of a faint Tycho 2 star, which is in common with the CMT data, is slightly larger than the average CMT error. In combination with the low number of stars in these comparisons, this makes a CMT error calculation difficult to estimate using just Tycho 2 data. Although the results are quite noisy, it is possible to produce an approximate external error for the CMT catalogue of 40 mas.

Another technique available involves the use of 2 or more deep comparison catalogues, where it is then possible to measure the external errors directly of all the catalogues involved without having to assume any external error measurements. As with a comparison with a single catalogue, allowance must be made for proper motions and, if the epoch difference between the catalogues is large, the errors in the proper motions.

The basis of the technique is the assumption that the residuals between any two catalogues result from the quadrature sum of the external errors. If three catalogues exist, it is possible to derive these external errors from the three sets of residuals by simple substitution. If an appreciable epoch difference exists, an allowance must be made for the errors in the proper motions used in the comparison. This acts as an additional term in the quadrature sum and has to be removed using the quoted proper motion error values.

Comparisons with the FASTT and UCAC catalogues (Stone et al. 1999; Zacharias et al. 2000) using this technique showed that the astrometric accuracy of the CMT catalogues, before secondary calibrations (atmospheric fluctuations and CTE correction) are carried out is 50-80 milliarcsec (mas) at the bright end. After such calibrations are applied, the accuracy improves to 25-45 mas. The dependency of these accuracies as a function of magnitude is given in Table 2. Although only one value is quoted per magnitude bin in these tables, there exists a range of accuracies, as quoted earlier, which is caused by the varying density of Tycho 2 standards across the sky. For a region of the sky which has more standards in it, the accuracy of the catalogue at that point will be better.

Figure 7 shows these results in graphical form. For bright stars ( $r~^\prime_{\rm CMT}<13$), the accuracy of the astrometry is about 35 mas for both RA and declination, but as you go fainter the accuracy in RA becomes gradually worse than that for declination. The most probable explanation is that this is caused by further effects resulting from the CTE problem which the calibration has not yet accounted for. This would only affect RA.

For photometry, the external accuracy estimates are more uncertain since the comparison catalogues are not primarily photometric ones. Additionally, there are probably some differences in the passbands used, which would result in unaccounted colour terms. Assuming the quoted errors from Stone et al. (1999), a comparison with the FASTT data yields rough estimates for the external errors and are given in the external part of Table 2. The internal photometric errors were calculated from the overlaps in the same way as that for the astrometry and are also given in this table.