3. Sample of stars
For simplicity, a single, double or multiple `system' is here identified with an `entry' in the Hipparcos Catalogue (i.e. having a unique HIP number). With few exceptions, this means that resolved components within 10 arcsec of the primary are considered as a system, while more separated components are regarded as separate systems. Although this convention deviates from normal practice in double-star work, it should not bias the analysis as long as the same convention is used for the synthetic (model) catalogues as for the observed catalogue.
To avoid selection effects originating from the construction of the Hipparcos Input Catalogue (Turon et al. 1992), only stars well within the original survey limits were used for this study. The limits used for constructing the survey part of the Input Catalogue depended both on galactic latitude (b) and the spectral type or colour index of the stars, and had to be based on the partially inaccurate and incomplete data available at the time. As a result these limits are somewhat diffuse and difficult to model. We have chosen to adopt a stricter (brighter) limit based on post-Hipparcos photometry, at the expense of the number of stars included. The `survey' criterion used here is
where is the total magnitude of components within 10 arcsec of the primary. This selection gave 25 710 catalogue entries. Furthermore, only main-sequence stars were considered in order to have a well-defined mass-luminosity relation. The discrimination against giants was made by means of the parallax,
where corresponds to the same dividing line in the observational HR diagram as used by Dehnen & Binney (1998, their Fig. 1). This gave a final selection of 13 092 entries satisfying both the `survey' and `main sequence' criteria.
Some statistical characteristics of the resulting sample are shown in Table 1. Divided according to spectral type, 22% are O and B stars, 36% A, 33% F, 8% G and 1% K and M stars. The typical representative of the sample is an A5V star with a mass of , located 100 pc from the Sun.
Table 1. Statistical characterisation of the investigated sample of Hipparcos Catalogue entries. For each quantity, the 5th, 50th and 95th percentiles are given. The absolute magnitude is computed from V and without taking into account extinction and statistical bias effects.
Dividing the sample into the different solution categories (Sect. 2) gave 1930 entries of type C (including 37 triple and 1 quadruple star), 572 of type G (including 144 with cubic terms), 112 of type O, 9 of type V, and 126 of type X. Counting the resolved triple and quadruple stars as 2 and 3 companions, respectively, and disregarding the VIM solutions gives the following statistics:
Here N is the total sample size and , are the number of quadratic and cubic G solutions.
These counts should be corrected for optical doubles stars and false detections before comparing with our model. We have used the Tycho-2 Catalogue (Hog et al. 2000) to estimate the number of optical doubles among the C solutions, and find that only 5 chance stars with magnitude difference are expected within a radius of 10 arcsec from the sample stars. Only the G solutions can be statistically corrected for false detections. The detection criteria (Eqs. [2.3.3]-[2.3.4] in Vol. 1 of the Hipparcos Catalogue) are such that the risk of false detection is 0.27%. Thus, among the entries not classified as C, O, V or X, some 30 false G solutions are expected. We assume that these are distributed proportionally among the quadratic and cubic solutions. The corrected counts are therefore:
A sample of delta-mu binaries (Sect. 2.6) was identified by comparing the proper motions in the Hipparcos Catalogue with FK5 (Fricke et al. 1988). Regional systematic errors in FK5 were first eliminated by spline smoothing as function of right ascension and declination. Among the 1535 FK5 stars, satisfied the main-sequence criterion, Eq. (2). Of these, the following numbers were found with exceeding 5, 10 and 20 mas yr-1:
Many of them are classified as G, O or X solutions in the Hipparcos Catalogue, so this sample is not independent of the ones in Eq. (4).
© European Southern Observatory (ESO) 2000
Online publication: October 2, 2000