5. Application of the de-censoring software to the photometric standard stars
5.1. The mean magnitudes
The mean and magnitudes of the photometric standards are derived from the transits collected during all the Tycho mission, using the de-censoring procedure. The differences between the derived magnitudes and the on-ground measurements are plotted on Fig. 3. The large bias affecting the actual measurements has vanished, although a close examination still reveals that the de-censored magnitudes are about 0.06 mag too faint when mag. In the channel, a bias of 0.05 mag appears also when mag. Simple functions are used to fit the biases, and the de-censored magnitudes and then corrected. The corrected de-censored magnitudes are called the "Tycho magnitudes" hereafter.
5.2. The uncertainties
As long as the measurements are considered individually, the uncertainties of the Tycho are rather large; for instance, it comes from the equations above that the error of a measurement of mag is 0.21 mag, when mag and when a moderate background counts is assumed. Fortunately, a lot of measurement are used to derive the mean magnitudes: for the photometric standard stars, the median number of photometric transits is 109. Therefore, the error of the mean magnitude mag is only 0.023 mag when 100 measurements as the one considered in the example above are taken into account. The errors of the mean magnitudes of the photometric standard stars are plotted in Fig. 4. They are around 0.013 mag when mag, but they increase dramatically for stars fainter than 10.5 mag, when the number of detections is falling off (for stars with mag, about 20 % of transits are censored).
For checking the validity of the errors, they are compared to the differences between the Tycho magnitudes and the on-ground magnitudes. The sizes of the error intervals are calculated as the quadratic sums of the errors of the de-censored magnitudes and of the on-ground magnitudes. The proportion of stars outside the error interval is plotted for in Fig. 5. It appears from this figure that the proportion is smaller than 16 % when mag, suggesting that the errors are overestimated. However, the Tycho error is usually smaller than the error of the on-ground magnitude when mag, and the overestimation is obviously due to the former. For the faint magnitudes, the proportion is a little larger than 16 %, but it remains on average less than 20 %.
A similar statistic is given in Fig. 6 for the Tycho colour index . Only the stars fainter than mag are taken into account in this plot, since the de-censoring is not very frequent for the bright stars. The large deviations at the extremities are not statistically significant, but are due to the small numbers of blue and red standard stars.
In conclusion, the de-censoring software provides the mean magnitudes of faint stars with small biases that are easily corrected. Moreover, the estimated errors look fairly reliable. In the Tycho catalogue, the mean magnitudes were derived from the median magnitudes for 30 000 stars brighter than mag and mag, but the de-censored magnitudes were prefered for the 1 018 000 other stars.
© European Southern Observatory (ESO) 1997
Online publication: May 5, 1998