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Astron. Astrophys. 325, 360-366 (1997)

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5. Application of the de-censoring software to the photometric standard stars

5.1. The mean magnitudes

The mean [FORMULA] and [FORMULA] 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 [FORMULA] 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 [FORMULA] mag. In the [FORMULA] channel, a bias of 0.05 mag appears also when [FORMULA] 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.

[FIGURE] Fig. 3. Same as Fig. 1, but with the de-censored [FORMULA] magnitudes in place of the medians of the measurements.

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 [FORMULA] mag is 0.21 mag, when [FORMULA] mag and when a moderate background [FORMULA] 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 [FORMULA] 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 [FORMULA] magnitudes of the photometric standard stars are plotted in Fig. 4. They are around 0.013 mag when [FORMULA] mag, but they increase dramatically for stars fainter than 10.5 mag, when the number of detections is falling off (for stars with [FORMULA] mag, about 20 % of transits are censored).

[FIGURE] Fig. 4. The errors of the [FORMULA] magnitudes of the photometric standard stars, computed with the de-censoring software.

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 [FORMULA] in Fig. 5. It appears from this figure that the proportion is smaller than 16 % when [FORMULA] mag, suggesting that the errors are overestimated. However, the Tycho error is usually smaller than the error of the on-ground magnitude when [FORMULA] 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 %.

[FIGURE] Fig. 5. The proportions of stars outside the error intervals for [FORMULA]. The upper line is the proportion of photometric standard stars with Tycho magnitudes too faint at the [FORMULA] level when compared to the on-ground magnitudes. The thick line is the excess of stars with Tycho magnitudes fainter than the on-ground magnitudes (it is zero when the median of the Tycho magnitudes is exactly equal to the on-ground magnitude). The lower line is the proportion of photometric standard stars with Tycho magnitudes too bright at the [FORMULA] level; Note that the figure contains the faint stars at the top.

A similar statistic is given in Fig. 6 for the Tycho colour index [FORMULA]. Only the stars fainter than [FORMULA] 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.

[FIGURE] Fig. 6. Same as Fig. 5, but for [FORMULA]. The upper line refers to the stars with Tycho colour indexes too large, and the lower to the stars with Tycho colour indexes too small when compared to the uncertainty intervals. Only the standard stars with [FORMULA] mag are taken into account.

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 [FORMULA] mag and [FORMULA] mag, but the de-censored magnitudes were prefered for the 1 018 000 other stars.

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© European Southern Observatory (ESO) 1997

Online publication: May 5, 1998