next previous
Up: photoelectric photometric

2. The critical evalutation

The first step of the evaluation of the data is the same as that used in the past, i.e. a search for common stars with a master list, and the computation of mean differences and standard errors. On this basis, each publication receives a weight. As the system is used by more and more persons, its homogeneity diminishes and systematic errors appear as well as more or less discrepant data. Due to the size of the catalogue, it is neither possible to trace back every problem nor feasible to explain each difference. Therefore, the procedure adopted here keeps the publication weights, but gives a low weight to discrepant data. We have adopted for this new version the precepts developed for computing mean values for the UBV system (Mermilliod & Mermilliod 1994), which are explained below.

A two-step iterative procedure has been adopted: the first step consists of a simple weighted mean, the weight being the number of measurements to the 2/3 power and the publication weight. The exponent used gives slightly less weight to observations with a number of measurements much larger than usually found. This is also the unique step for stars with only two sources of measurements.


displaymath705
where X represents V, (b-y), m1, or c1. n is the number of measurements and tex2html_wrap_inline731 is the weight (in a scale 0 to 4) of each publication. The second step uses the differences tex2html_wrap_inline733 of the individual values (Xi) to the mean (tex2html_wrap_inline737) to compute new weighted mean values. The weight (pi) has the form:


displaymath706
where
displaymath707
is a normalisation factor, so that the sum of the weights is close to the sum of sources when the error (Ei) is close to the mode of the errors (tex2html_wrap_inline743). The weighted mean values are simply computed with the formula:


displaymath708

The values of tex2html_wrap_inline743 have been estimated from the distribution of the differences for stars with two sources. The adopted values for tex2html_wrap_inline747, tex2html_wrap_inline749, tex2html_wrap_inline751, tex2html_wrap_inline753, and tex2html_wrap_inline755are equal to 0.005, 0.003, 0.004, 0.005, and 0.005 respectively. This means that the expression


displaymath709

for values of Ei close to tex2html_wrap_inline743 and pi is close to unity for the majority of the stars. The dispersion is computed in the usual way:


displaymath710

As desired, this procedure gives a lower weight to discrepant values, and the computed mean value is closer to that defined by the majority of the sources.

Mean values of variable stars have been computed in the same manner. Due to the procedure used to include them in the catalogue (only the brightest value of the published light curve or list of observations has been taken) the final dispersion may be artificially small and not representative of the real amplitude of variation. For a number of stars with large deviant data which could affect too much the computation of mean values, the number of measurements has been set "manually" to 0. Thus the reference is kept but the values are not taken into account in the computation of the mean value.


next previous
Up: photoelectric photometric

Copyright by the European Southern Observatory (ESO)