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

1. Introduction

Tycho is a project using the star mapper from the ESA Hipparcos satellite for deriving the positions, magnitudes and color indices of about stars. The photometric passbands, called and , are close to the B and V passbands of the Johnson photometry. The scientific mission of the satellite began in November 1989, and ended in March 1993. The reduction of the Tycho data was completed in mid-1996, and the Tycho Catalogue (ESA 1997) will be published in June 1997. The instrument and the general organisation of the data analysis have been described in Hog et al. (1992a); the most important steps of the data reduction were the preparation of the Tycho Input Catalogue (Egret et al. 1992), the prediction of transits (performed at Astronomisches Rechen-Institut in Heidelberg), the detection of transits (Bässgen et al. 1992), the background determination (Wicenec and Bässgen 1992), the revision of the input catalogue (Halbwachs et al. 1992, Halbwachs et al. 1994), the astrometric reduction (Hog et al. 1992b, Hog et al. 1995), and the photometric reduction (Scales et al. 1992, Großmann et al. 1995). The main points related to the Tycho photometry are summarized hereafter:

• The star mapper consists of two groups of slits in the focal plane of the telescope. One of them is called the "vertical" slit system, and the other one is the "inclined" slit system. When a star was crossing a slit, its light was simultaneously recorded by two photometers, one for each colour. The raw Tycho data are the photon counts that were constantly recorded with a sampling rate of 600 Hz.
• The data analysis is based on predictions of crossings of the slits systems by the stars of an input catalogue. A detection algorithm is used to search star signals in the photon counts of the and of the channels, considered together (the sum of the and channels is called the T channel hereafter). This search is performed within small intervals centered on the predicted epochs of the transits. A detection is recorded when its signal-to-noise ratio is larger than 1.5. The amplitudes of the signals are then estimated in the and in the channels. In a few cases however, the estimation algorithm fails to produce a signal amplitude.
• The Tycho photometry is calibrated on the basis of a set of photometric standard stars from the Geneva database (Großmann et al. 1995). and magnitudes are derived every times the signal amplitudes were obtained.
• The final selection of stars is performed after the final astrometric reduction. Among other criteria, one condition is that each star must have received at least 30 transit detections considered as acceptable for astrometry. Since the selection of detections was more restrictive for photometry than for astrometry, the Tycho catalogue contains a few stars with even less than 30 photometric measurements, although the mean number of transits per star is more than 100. As a consequence, the vast majority of the stars are too faint for being measured every time they were crossing a slit system.

The next step of the data reduction in photometry is the derivation of the mean magnitudes of the stars. The treatment of bright stars is presented in Großmann et al.; it consists in taking the median of the measurements obtained for each channel. This method cannot be applied to the faint stars, however: only a part of their transits were detected, and the faintest measurements coming from the statistical variations of the photon counts were censored. The median of the measurements is then biased toward bright magnitudes. This effect was already pointed out by Großmann et al., and it is shown again in Fig. 1: the difference between the observed Tycho magnitudes and the actual magnitudes of the photometric standards is increasing almost linearly for stars fainter than =11 mag, so that the median of the measurements is always around =10.5. It is then impossible to evaluate the bias for about 50 % of the Tycho catalogue when only the detections are taken into account.

Fig. 1. The distribution of the differences between the median magnitudes of the photometric standard, and the magnitudes coming from on-ground measurements.

It was contemplated to derive the median magnitudes by considering the missing measurements as faint measurements. Unfortunately, the validity range of this simple method is severely limited: for the bright stars, the median of the actual measurements is better than the median of all transits, since some missing measurements are "spurious non-detections", as explained in Sect. 3.2. On the other side, the faintest magnitudes that could be derived from the median of all transits depend on the maximum value permitted for the background; as a consequence, it comes from the model presented in this paper that the magnitudes of stars with would have been properly computed only until mag. Therefore, since another method was necessary anyway, the median of all transits was ignored.

The method used to derive the magnitudes of the faint stars is explained hereafter. It is based on the "de-censoring" of the transits that did not lead to measurements. The principles of de-censoring are presented in Sect. 2. The model describing the data acquisition is in Sect. 3, and the complete procedure is described in Sect. 4. The results are presented in Sect. 5.

© European Southern Observatory (ESO) 1997

Online publication: May 5, 1998

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