The frequency of stellar multiplicity and the distributions of key parameters such as mass ratio () and semi-major axis (a) are important for several astrophysical problems, not least as tracers of conditions in star-forming environments (Zinnecker 1984; Duquennoy & Mayor 1992; Brandner & Köhler 1998, and references theirein). Unfortunately, binary statistics are often severely affected by selection effects and uncertainties due to small-number statistics. Only for the very nearby ( pc) late-type main-sequence stars has it been possible to establish the distribution functions with some completeness and reliability (Duquennoy & Mayor 1991; Fischer & Marcy 1992). This has been the result of big efforts to obtain complete, volume-limited samples and to close the classical gap between spectroscopic and visual binaries (Blaauw 1981) through high-precision radial-velocity surveys and speckle observations.
Duquennoy & Mayor (1991, hereafter DM) studied multiplicity among solar-type stars in the Galactic field of the solar neighbourhood. Key results include: (1) a broad, approximately log-normal distribution of orbital periods with median value yr; (2) a mass-ratio distribution continuously increasing towards small values of q; and (3) a total multiplicity of 57% (i.e., 0.57 companions per primary star, where a single star is counted as a primary). The DM results serve as a template for comparison with other stellar samples, e.g. pre-main-sequence stars (Mathieu 1994; Köhler & Leinert 1998), clusters of various ages (Bouvier et al. 1997; Abt & Willmarth 1999; Duchêne et al. 1999) and Population II stars (Köhler et al. 1999). Many of the samples (e.g. in star-forming regions) are by necessity much more distant ( pc) than the DM sample, resulting in very incomplete statistics. For example, the gap referred to above, between spectroscopic and visual binaries (at 1-10 AU or 1-30 yr), is again evident e.g. in the Pleiades data (Bouvier et al. 1997) and a survey of O-type systems (Mason et al. 1998). In view of the probable non-uniqueness of the distribution in a (Brandner & Köhler 1998) one cannot confidently extrapolate from observations covering only a small range of separations.
There are thus good reasons to try to improve the coverage in semi-major axis for distances up to at least a few hundred parsecs, where sufficient numbers can be found of objects representing different conditions of star formation. It is the purpose of this paper to explore some of the possibilities offered by current and future space astrometry, using the Hipparcos Catalogue (ESA 1997) as a test case. Historically, astrometry has contributed to binary statistics mainly through the detection of common proper motion pairs and astrometric binaries, pertaining respectively to very long periods and very nearby stars. With Hipparcos, deviations from a linear proper motion by a few milliarcsec (mas) could be detected from observations covering just a few years. This opens new possibilities to study binaries in the separation range 1-10 AU, corresponding to 10-100 mas at 100 pc, and periods up to a few decades.
The Hipparcos satellite was designed primarily for observing single stars (i.e., unresolved point sources), but certain provisions were made to allow more complex objects to be profitably observed (Mignard et al. 1992; ESA 1997; Quist & Lindegren 1999). Any information to be gained on double and multiple stars had to be extracted from the same type of data as obtained for the single stars. Several different object models were used in the data reductions to represent various situations. Of the entries in the Hipparcos Catalogue, about 17 000 received some kind of double-star treatment, which are called C, G, O, V and X solutions in the catalogue (Sect. 2). Their numbers reflect both the actual distribution of binary properties and the observation and data reduction techniques. One goal of this paper is to test if these numbers can be reproduced by a simple and reasonable model.
The general technique used in this paper is to calculate the expected numbers in the different categories under given assumptions, and to compare these numbers with the actual numbers found in the Hipparcos Catalogue. To this end, we combine a synthetic model of the Galaxy (Sect. 4.1) with models of binary distributions (Sect. 4.2), the Hipparcos observations (Sect. 4.3) and the binary detection scheme within the Hipparcos data reductions (Sect. 4.4). The comparison with observed numbers is discussed in Sect. 5. To the extent that the observation and detection processes are correctly modelled, it is also possible to derive some information about the binary distributions by inversion. This is considered in Sect. 5.3.
The capability of the Hipparcos satellite to discover many new binaries and even new types of binaries was realised very early during the mission definition (Lindegren 1979). The statistical implications were analysed in some detail by Söderhjelm (1985). In a sense this present paper provides the corresponding a posteriori analysis, and a projection of the conclusions to future missions.
© European Southern Observatory (ESO) 2000
Online publication: October 2, 2000